Proceedings of the 4th International Workshop on Induced Polarization, IP2016, Aarhus (Denmark), June 6-8, 2016

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Proceedings of the 4th International Workshop on Induced Polarization, IP2016, Aarhus (Denmark), June 6-8, 2016

Table of contents :
IP2016 Abstracts from Session A
A01 Weller.pdf
A02 Philippe
A03 Kelter
A04 Kang
A05 Martin
A06 Abdulsamad
A07 Halisch
A08 Orozco
A09 Fiandaca
A10 Viezzoli
IP2016 Abstracts Poster Session A.pdf
PA01 Titov
PA02 Volkmann
PA03 Boerner
PA04 Ingham
PA05 Hoerdt
PA06 Pilawski
PA07 Halisch1
PA08 Martin1
PA09 Maloteau
PA10 Radic
PA11 Guenther
PA12 Seidel
PA13 Gallistl
PA14 Langenbach
PA15 Auken
PA16 Moeller
PA17 Brethes
IP2016 Abstract from Session B.pdf
B01 Robinson
B02 Shefer
B03 Olsson
B04 Madsen
B05 Stebner
B06 Maurya
B07 Gao
B08 Zimmermann
B09 Lajaunie
B10 Oldenburg
B11 Hoerdt
IP2016 Abstracts from Poster Session B.pdf
PB01 Hallbauer
PB02 Hallbauer1
PB03 Weigand
PB04 Bairlein
PB05 Wu
PB06 Kaouane
PB07 Maury
PB08 Jouen
PB09 Shalem
PB10 Razavirad
PB11 Ghorbani
PB12 Tsourlos
PB13 Tarasov
PB14 Johansson
PB15 Wemegah
PB16 Bording
PB17 Peruzzo
PB18 Jirku
PB19 Kulikov
IP2016 Abstracts from Session C.pdf
C01 Zhang
C02 Adrian
C03 Dahlin
C04 Klitzsch
C05 Mellage
C06 Lysdahl
C07 Berube

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06_Abstracts_from_Session_A

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07_Abstracts_from_Poster_Session_A

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08_Abstracts_from_Session_B

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09_Abstracts_from_Poster_Session_B

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10_Abstracts_from_Session_C

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4th International Workshop on Induced Polarization IP2016 Aarhus (Denmark), June 6-8, 2016

The 4th International Workshop on Induced Polarization (IP) will take place on June 6-8, 2016 in Aarhus, Denmark, hosted by the Hydrogeophysics Group, Aarhus University. On June 4-5, a short course for professionals and students will be arranged. Here we will introduce the method, the equipment, the processing and inversion software, and examples of applications. Three previous workshops on IP in Near-Surface Geophysics have already taken place in Bonn (Germany, 2009), in Golden (Colorado, USA, 2011) and in Ile d'Oléron (France, 2014). The aim of the first workshop was to present the latest developments and applications of the method for near surface hydrogeological and environmental investigations. The goal of the second workshop was to focus on the understanding of the mechanisms generating IP signals in the earth. The third workshop focused on discussing the developments of the method within the geophysicist community and with other scientific communities that use the same physical processes even if with other names. Today, the IP method has developed significantly within theoretical understanding, laboratory characterization, and field methodologies. However, there is a growing need for a better understanding of the links between these levels and the aim of this fourth workshop is to narrow the gap between theory, laboratory findings in controlled environments, and field experiments on real geologies. The most important findings will be presented in the areas of: • Petrophysics of IP • Laboratory and field scale measurements and observations • Advances in data acquisition, processing and inversion We are looking forward to seeing you in Aarhus. Gianluca Fiandaca and Esben Auken [email protected]

Detailed Program Sunday 5 June 17:00 – 18:30

Ice Breaker Dept. of Chemistry Auditorium I Aarhus University Langelandsgade 140 DK-8000 Aarhus C

Monday 6 June 9:00 – 9:25

Welcome Session A – Morning Chairs: Esben Auken & Christian Camerlynck

9:25 – 9:50

A01 Induced polarization and pore radius – a discussion Andreas Weller (Institut für Geophysik, TU Clausthal), Zeyu Zhang (Southwest Petroleum University), Lee Slater (Rutgers University), Sabine Kruschwitz (Bundesanstalt für Materialforschung und –prüfung), Matthias Halisch (Leibniz-Institut für Angewandte Geophysik) Permeability estimation from spectral induced polarization (SIP) measurements is based on a fundamental premise that the characteristic relaxation time () is related to the effective hydraulic radius (reff) controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We examine the link between and reff for an extensive database of sandstone samples where mercury porosimetry data confirm that reff is reliably determined from a modification of the Hagen- Poiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of 1 or 2 distinct representative diffusion coefficients but instead demonstrates strong evidence for 6 orders of magnitude of variation in an apparent diffusion coefficient that is well correlated with both reff and the specific surface area per unit pore volume (Spor). Two scenarios can explain our findings: (1) the length-scale defined by t is not equal to reff and is likely much longer due to the control of pore surface roughness; (2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g. silica, clays) making up the rock. In either case, the estimation of reff (and hence permeability) is inherently uncertain from SIP relaxation time.

9:50 – 10:15

A02 Modeling the evolution of spectral induced polarization during calcite precipitation on glass beads Leroy Philippe (BRGM), Li Shuai (Imperial College), Jougnot Damien (CNRS), Revil André (CNRS), Wu Yuxin, (LBNL) When pH and alkalinity increase, calcite frequently precipitates and hence modifies the petrophysical properties of porous media. The complex conductivity method can be used to directly monitor calcite precipitation in porous media because it is very sensitive to the evolution of the pore structure and its connectivity. We have developed a mechanistic grain polarization model considering the electrochemical polarization of the Stern layer surrounding calcite particles. This model depends on the surface charge density and mobility of the counter-ions in the Stern layer. Our induced polarization model predicts the evolution of the size of calcite particles, of the pore structure and connectivity during spectral induced polarization experiments of calcite precipitation on glass beads pack. Model predictions are in very good agreement with the complex conductivity measurements. During the first phase of calcite precipitation experiment, calcite crystals growth, and the inverted particle size distribution moves towards larger calcite particles. When calcite continues to precipitate and during pore clogging, inverted particle size distribution moves towards smaller particles because large particles do not polarize sufficiently. The pore clogging is also responsible for the decrease of the connectivity of the pores, which is observed through the increasing electrical formation factor of the porous medium.

10:15 – 10:30

Break

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10:30 – 10:55

A03 Field evaluation of wideband EIT measurements M. Kelter (Institute of Bio- and Geosciences, Agrosphere), J. A. Huisman (Institute of Bio- and Geosciences, Agrosphere), E. Zimmermann (Central Institute for Engineering), H. Vereecken (Institute of Bio- and Geosciences, Agrosphere) Field applications of wideband electrical impedance tomography (EIT) remain challenging, despite recent advances to obtain images of the complex electrical conductivity with sufficient accuracy for a broad range of frequencies (mHz – kHz). The aim of this study is to evaluate to what extent recent improvements in the inversion and processing of wideband field EIT measurements have improved the accuracy and spectral consistency of images of the real and imaginary part of the electrical conductivity. In a first case study, timelapse surface EIT measurements were performed during an infiltration experiment to investigate the spectral complex electrical conductivity as a function of water content. State-of-the-art data processing and inversion approaches were used to obtain images of the complex electrical conductivity in a frequency range of 100 mHz to 1 kHz, and integral parameters were obtained using Debye decomposition. Results showed consistent spectral and spatial variation of the phase of the complex electrical conductivity in a broad frequency range, and a complex dependence on water saturation. In a second case study, borehole EIT measurements were made in a wellcharacterized gravel aquifer. These measurements were inverted to obtain broadband images of the complex conductivity after correction of inductive coupling effects using a recently developed procedure relying on a combination of calibration measurements and modelbased corrections. The inversion results were spatially and spectrally consistent in a broad frequency range up to 1 kHz only after removal of inductive coupling effects.

10:55 – 11:20

A04 3D TEM-IP inversion workflow for galvanic source TEM data Seogi Kang and Douglas W. Oldenburg ( University of British Columbia) Electrical induced polarization (EIP) surveys have been used to detect chargeable materials in the earth. For interpretation of the time domain EIP data, the DC-IP inversion method, which first invert DC data (on-time) to recover conductivity, then inverts IP data (off-time) to recover chargeability, has been successfully used especially for mining applications finding porphyry deposits. It is assumed that the off-time data are free of EM induction effects. When this is not the case, an EM-decoupling technique, which removes EM induction in the observation, needs to be implemented. Usually responses from a half-space or a layered earth are subtracted. Recent capability in 3D TEM forward modelling and inversion allows us to revisit this procedure. Here we apply a 3D TEM-IP inversion workflow to the galvanic source example. This includes three steps: a) invert DC and early time channel TEM data to recover the 3D conductivity, b) use that conductivity to compute the TEM response at later time channels. Subtract this fundamental response from the observations to generate the IP response, and c) invert the IP responses to recover a 3D chargeability. This workflow effectively removes EM induction effects in the observations and produces better chargeability and conductivity models compared to conventional approaches.

11:20 – 12:00

Poster Presentations – session A Presentations of all the posters of session A (two minutes for each presentation). The list of posters can be found at the end of the day’s program.

12:00 – 13:00

Lunch & Poster session A

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Session A – Afternoon Chairs: Estella Atekwana & Andreas Weller 13:00 – 13:25

A05 SIP investigation at historical mining slag heaps Tina Martin (Federal Institute for Geosciences and Natural Resources (BGR), Thomas Günther (Leibniz Institute for Applied Geophysics (LIAG) Geophysical investigations at historical slag heaps are increasingly in focus due to economic, environmental or archaeological reasons. We present in this study the investigation of a historical slag heap in the Harz Mountains, Germany, where laboratory and field measurements were conducted. Previous detailed laboratory measurements of different synthetic mineral-sand mixtures have shown that there is a relationship between chargeability and mineral concentration as well as between relaxation time and mineral grain size. With the development of a new approach for the simultaneous fitting of the whole spectral field data set to different models we are now able to interpret the field measurements further. We started to show that the relationships found in laboratory can be in principle transferred to the field data. However, in situ samples also show that the SIP response can be very different between samples from the same heap. So a general statement of the mineral content/grain size of a slag heap only from some field profiles is not possible. With the help of additional mineralogical, chemical and optical methods we try to characterize the different SIP response with the aim of rough classification of slag heap areas.

13:25 – 13:50

A06 Spectral induced polarization in a sandy medium containing semiconductor materials: study of the polarization mechanism Feras Abdulsamad (Sorbonne Université UPMC-CNRS), Nicolas Florsch (Sorbonne Université, UPMC-IRD), Christian Camerlynck (Sorbonne Université, UPMC-CNRS) Induced polarization (IP) is useful for mineral exploration. In the presence of sulphides (more generally speaking: semi-conductors), the charge carriers inside particles are electrons and electron gaps. The inner diffusivity and the charge concentration are very high with respect to the background solution ones. Mechanisms of induced polarization are still under questioning in those cases. In order to improve our knowledge about the mechanisms controlling IP in such mediums, we propose new lab experiments on unconsolidated mineralized medium and begin numerical modelling by using the Poisson-Nernst-Planck (PNP) equation set as well. Four different types of semi-conductors (graphite, pyrite, chalcopyrite and galena) are involved in the experiments. The polarization effect of grain size, mineral concentration as well as electrolyte salinity and type are investigated at the lab scale. We find that the total chargeability of the medium is a function of the mineral volume but is independent of the electrolyte salinity and electrolyte type. However, the time constant (τ) is highly dependent on the grain size and the electrolyte salinity, and is slightly dependent on the mineral type. These results appear to be in agreement with the classical Wong’s theory, but we assume here that no significant redox phenomenon does happen at the grain surface. The observed dependence of the chargeability and the time constant on the salinity could be explained by considering the mineral grain as a dipole impacting the potential and consequently charge distribution in its vicinity. This dipole is generated inside the particle to compensate the primary electrical field and the whole particle is –as a first approximation- a spherical boundary (and volume) with a constant potential on (and in) it. The distribution of the charged particles in the area around the dipole electric will respond accordingly to this boundary condition and is driven by the potential. Since the equations are coupled, the potential depends on return on the resulting ions distribution. Although the finiteelement numerical approach used here is still preliminary, it opens wide perspectives in the understanding of IP in more complex media.

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13:50 – 14:15

A07 Quantification of Rock Structures with High Resolution X-Ray μ-CT for Laboratory SIP Measurements Matthias Halisch (Leibniz- Institut für Angewandte Geophysik (LIAG), Sabine Kruschwitz (Bundesanstalt für Materialforschung und –prüfung (BAM), Mayka Schmitt (Federal University of Santa Catarina), Andreas Weller (Institut für Geophysik, Technische Universität Clausthal) Spectral Induced Polarization (SIP) measurements are used in many different ways to characterize natural rocks and soils. Main foci of interest are the enhanced characterization of the causes of IP-effects in clastic rocks (especially sandstones), the interactions between the matrix-fluid-system and within the electrical double layers as well as the correlation with “classical” petrophysical parameters, such as specific surface area, permeability, mercury intrusion capillary pressure (MICP) and others. Nevertheless, for all of these investigations, knowledge of the inner structure of the sample material is essential in order to create reliable and validated models as well as to interpret and to assess the data most completely. Unfortunately, many of the methods used, to get access to the inner structure of rocks are destructive (e.g. MICP, thin sectioning, etc.) and the valuable sample is lost. In addition, data is either of volume integrated nature or only available for the 2D case and the usage of sister cores does not necessarily lead to reliable results. In this paper, the authors showcase the possibilities of non-destructive and three dimensional X-ray computed tomography and of enhanced image analysis capabilities for the quantification of rock structures at the pore scale.

14:15 – 15:15

Break & Poster session A

15:15 – 15:40

A08 Decay-Curve Analysis for the Quantification of Data Error in Time-Domain Induced Polarization Imaging Adrián Flores Orozco (TU-Wien), Jakob Gallistl (TU-Wien),, Matthias Bücker (TU-Wien), Kenneth H. Williams (Lawrence Berkeley National Lab) Recent studies have demonstrated the advantages of a careful processing of induced polarization (IP) imaging datasets. In particular, inversion results based on an adequate quantification of data error provide IP images with enhanced contrasts and a better correlation with subsurface structures and processes. The analysis of the discrepancy between normal and reciprocal readings is a widely accepted measure to assess quality of imaging datasets and parametrize error models. However, the collection of reciprocal measurements increases acquisition time and is not always feasible. Therefore, we propose an alternative methodology to quantify data error of time-domain IP (TDIP) imaging measurements based on the analysis of the recorded IP decay curve. Our approach provides detailed information about data error as required for the identification of outliers and the quantification of error parameters without the need of reciprocal measurements. Comparison of the error parameters and imaging results following our proposed decay-curve analysis (DCA) and the conventional normal-reciprocal analysis revealed consistent results, demonstrating the accuracy of our approach. We illustrate the practical applicability of our approach with the inversion results for an extensive field data set collected at the floodplain scale aiming at the localization of so-called “biogeochemical hotspots”, which are areas characterized by high rates of microbial activity and the accumulation of iron sulphides.

15:40 – 16:05

A09 Advances in spectral inversion of time-domain induced polarization Gianluca Fiandaca, Esben Auken, and Anders Vest Christiansen (Department of Geoscience, Aarhus University) The extraction of spectral information in the inversion process of time-domain (TD) induced polarization (IP) data is changing the use of the TDIP method. Data interpretation is evolving from a qualitative description of the subsurface, able only to discriminate the presence of contrasts in chargeability parameters, towards a quantitative analysis of the investigated media, which allows for detailed soil- and rock-type characterization. In this work a review of the recent advances in spectral inversion of TDIP data is presented, in terms of: supported IP parameterizations; modelling of transmitter waveform; support for buried electrodes; model regularization; computation of the depth of investigation.

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16:05 – 16:30

A10 Viezzoli Andrea (Aarhus Geophysics ApS), Vlad Kaminski (Aarhus Geophysics ApS), Gianluca Fiandaca (Department of Geoscience, Aarhus University) There have been multiple evidences in the literature in the past several years of what has been referred to as IP effect in the Time Domain Airborne EM data (TDEM). This phenomenon is known to be responsible for incorrect inversion modelling of electrical resistivity, lower interpreted depth of investigation and lost information about chargeability of the subsurface as well as about other valuable parameters. Historically there have been many suggestions to account for the IP effect using the Cole-Cole model. In current paper we are showing the possibility to extract IP information from airborne TDEM data including inverse modelling of chargeability from airborne TDEM, both synthetic and actual VTEM data with a field example from Russia (Amakinskaya kimberlite pipe). The synthetic examples illustrate how it is possible to recover deep chargeable targets (depths to over 130 m) in association with both high electrical conductivity and in resistive environments. Furthermore, modelling of IP effects allows corrected resistivity models. The Amakinskaya kimberlite pipe results highlight the relevance of chargeability for kimberlite exploration.

16:30 -18:00

Field/software demo & Poster session A

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Poster Session A Chair: Gianluca Fiandaca PA01 Effect of mineralogy on Spectral Induced Polarization of sediments: A conceptual model of membrane polarization Konstantin Titov and Daniil Chuprinko, St. Petersburg State University

We discuss a membrane polarization effect produced by the difference in mineral composition of walls of two sequential pores, which can occur, for example when the first pore is encased in calcite and the second – in alumosilicate. We assume that the zeta potential values of these minerals differ from each other. This leads to a difference in the cation and anion transference numbers (even if the above two pores are of the same radius) and, therefore, to a membrane polarization when an electrical field is applied. We model this effect for two pores filled with water of low salinity (1 and 10 Mol.m3), and for three pore radius values (10-6, 10-7 and 10-8 m). We assume that one pore is “passive,” i.e., the interface potential is zero, and the other pore is “active”, with zeta potential of 75 mV. We calculate the maximum values of phase shift and the corresponding values of peak frequency as a function of lengths of the active and passive pores. We show that the maximum phase shift corresponds to a case where the pores have the same length. The shift values are between 13 and 210 mrad depending on the ion concentration in free water and on the pore radius. The peak frequency distributions for all modeled cases are very similar and, therefore, depend mostly on the pore length. We assume that the ratio of the pore length to its diameter can achieve values between 10 and 50. With this assumption, for the pore radius of 10-8, 10-7, and 10-6 m, the membrane polarization effect can be detected in the frequency range from 1.6 kHz to 1MHz, from 20 Hz to 1 MHz, and from 0.20 Hz to 1 MHz, respectively. Our modeling shows that the effect of mineral composition can appear superimposed on the polarization effect of the Stern layer, which coats the mineral grains.

PA02 Evaluation of low frequency polarization models using well characterized sintered porous glass samples Jan Volkmann and Norbert Klitzsch, Applied Geophysics and Geothermal Energy, E.ON Energy Research Center

We assess the results of published theoretical and experimental findings regarding low frequency rock polarization for a reference system, consisting of sintered porous glass samples. Thereby, we benefit from well characterized samples, which allow for direct tests of theoretical predictions and empirical relations. We find that: (1) The correlation σ″~Sm is stronger than σ″~Spor for a wide range of fluid conductivities and frequencies above 1 Hz. (2) Correlation coefficients for the imaginary conductivity to inner surface area relations are strongly frequency dependent. (3) Normalized chargeability, obtained by fitting a Cole–Cole model to the spectral data, provides a fair alternative to single frequency information. (4) Salinity dependence of proportionality factors a1=Sm/σ″ and a2=Spor/σ″ due to a salinity dependent partition coefficient is confirmed qualitatively. Quantitative theoretic predictions of a1 or a2 fail due to the assumption of non-reduced Stern layer mobility for clay free silica. (5) Earliest grain size related models provide the best quantitative estimate of relaxation time. (6) Results agree well with published data for sands and sandstones with respect to (i) quantitative estimates of a1 or a2 and (ii) influences of rock structural parameters on relaxation time.

PA03 SIP of the three-phase system CO2-brine-sand under reservoir conditions Jana H. Börner, Volker Herdgen, Jens-Uwe Repke, Klaus Spitzer, TU Bergakademie Freiberg

We present laboratory measurements of the spectral complex electrical conductivity of water-bearing sand samples during exposure to and flow-through by carbon dioxide. Pressures up to 300 bar and temperatures up to 80°C were applied. Steady-state experiments serve for investigating the physicochemical equilibrium of the fluid phases. Dynamic experiments aim at analysing the impact of partial saturation and chemical interaction on complex conductivity. The steady-state dissolution experiments show that be-sides the conductivity-increasing dissociation a second opposing process may be observed, which results in a significant reduction of conductivity at high salinities despite the added CO2. We explain our observations with a semi-analytical formulation for the electrical conductiv-ity taking into account the interactions of ion and neutral species. A significant reduction of saturation is observed during CO2 flow and drainage. The spectral complex conductivi-ty maps both changes in saturation and chemical interac-tion. Including the semi-analytical correction for pore-water conductivity allows for a good reconstruction of saturation from SIP-measurements. Additionally we get access to an indicator for changes of the inner surface area, which is related to mineral dissolution or precipitation processes.

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PA04 Predictive relationships for the permeability of unconsolidated sands based on SIP and pore surface fractal dimensions Malcolm Ingham and Sheen Joseph, Victoria University of Wellington We present calculations of specific internal surface (Spor) and pore surface fractal dimension (D) based on

measurements on unconsolidated sand samples. It is found that for these samples, for which the effective hydraulic radius is greater than 10 m, D 2 and the generalized PaRiS model of Weller et al. (2015) gives a good prediction of permeability both for the unconsolidated samples and for the sandstone samples reported by Zhang and Weller (2014). We use fitted relationships to Spor for both the SIP time constant () and the measured imaginary part of the conductivity at a frequency of 1 Hz () to deduce predictive relationships for permeability based on and , on the assumption that D = 2. These relationships both overestimate permeability but improved predictions are obtained by using a slightly lower value of D commensurate with the average of the calculated values.

PA05 Induced polarization of seafloor massive sulfides Andreas Hördt, Katharina Bairlein (TU Braunschweig), G. Spagnoli (Bauer Maschinen GmbH), M. Jegen, M. Hannington, S. Petersen, T. Laurila (GEOMAR Helmholtz Centre for Ocean Research)We investigate under which conditions membrane

polarization might be relevant for realistic pore space geometries. We review some basic properties of the theoretical model and illustrate general constraints by modelling studies. We focus on geometrical parameters of the model, e.g. radii r and lengths L of two cylindrical pores. In principle, a wide range of spectra can be generated, covering orders of magnitude in both maximum phase shift and characteristic time scales. One ingredient to obtain large phase shift is a small radius of the narrow pore in the range of tens of nm. Time scales are mainly controlled by pore lengths. Generating large time scales and phase shifts at the same time in principle requires large ratios between pore lengths and radii. However, within the four-dimensional parameter space, which exhibits regimes of different behaviour, examples can be found where moderate L/r ratios (10:1) can produce time scales in the range of seconds with phase shifts of a few mrad. The results encourage further attempts to combine impedances of 2pore systems to approach the simulation of real rock systems.

PA06 On the α-polarization of bacterial suspensions: SIP measurements on E. coli K12 and Rhodococcus erythropolis T902.1 Tamara Pilawski (University of Liège), Wolfgang Tappe (Forschungszentrum Jülich GmbH), Egon Zimmermann (Forschungszentrum Jülich GmbH), Johan Alexander Huisman (Forschungszentrum Jülich GmbH), Frank Delvigne (University of Liège), Frederic Nguyen (University of Liège)

The influence of bacteria on the electrical properties of porous media has been explained by different mechanisms. A few studies have also reported direct bacterial polarization using measurements on bacterial suspensions at frequencies below 10 kHz, so-called α-polarization. These measurements were performed by dielectric spectroscopy techniques relying on two electrodes and models to correct for electrode polarization at low frequencies. We performed complex conductivity measurements on bacterial suspensions from 0.01 to 45,000 Hz with an impedance spectrometer (phase accuracy better than 0.1 mrad below 1 kHz for a measurement on water) that used four-point measurements and thus does not require large corrections for electrode polarization). Two strains were studied: Escherichia coli (Gram-negative bacterium) and Rhodococcus erythropolis (Gram-positive bacterium). The imaginary parts of the complex conductivity of suspensions of both strains were very similar to the one of water. These preliminary results suggest that microbial alterations of the complex electrical conductivity measurements of porous media observed in previous studies are more likely related to other mechanisms than αpolarization of the bacteria, such as bioclogging, biomineralization, and growth and attachment of microbial cells to the sediment grains. We are planning to test additional strains to verify these results.

PA07 www.sip-archiv.de – an internet based, interactive archive and database for SIP data Matthias Halisch, Jens Gramenz, Lothar Gorling, Klaus Krause, Iakov Bolotovski, Leibniz Institute for Applied Geophysics (LIAG)

Long-term storage of scientific data has become a topic of utmost importance for the scientific community. Due to European and national (here: German) initiatives, new guidelines and laws have been validated to ensure a reliable storage and documentation of scientific primary data. As a result of a workshop and discussion round of the working committee induced polarization (AK-IP) of the German Geophysical Society (DGG), the Leibniz Institute for Applied Geophysics (LIAG) accepted the challenge to develop and create a safe, free and easy to use, internet based database and archive for SIP measurements.

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PA08 Methods for measuring the complex resistivity spectra of rock samples in the context of mineral exploration Tina Martin (Federal Institute for Geosciences and Natural Resources (BGR) Stephan Costabel Federal Institute for Geosciences and Natural Resources (BGR), Thomas Günther (Leibniz Institute for Applied Geophysics (LIAG)

For the geophysical exploration of mineral resources knowledge about petrophysical parameters of the expected investigation material is essential. If it is not possible to measure samples in a common geometry, new approaches have to be developed. In this preliminary study three approaches for adequate and proper measurements of spectral induced polarization at rock samples are introduced. First results show that additionally to the measurement in a common 4-point measuring cell, also measurements with stuck electrodes connected to rock samples with irregular geometry seem to be promising. Furthermore the detection of a buried antimonite sample in a sand-box could be demonstrated by the strong phase anomaly it produced. Nevertheless further investigations are necessary, such as considering possible anisotropy effects and verification of the methods for a broader range of samples with irregular geometry. Also the electrode material for the measurements in the sandbox should be modified to avoid unwanted polarization effects. In addition, alternative materials for coupling the electrodes directly to the rock surface will be tested in the future.

PA09 Influence of plant roots on induced polarization of cultivated soil columns Sophie Maloteau (UR TERRA, Gembloux Agro-Bio Tech, ULg), Guillaume Blanchy (Gembloux Agro-Bio Tech, ULg), Frédéric Nguyen ( Bât. B52/3 Géophysique appliquée), Sarah Garré (UR TERRA, Gembloux Agro-Bio Tech, ULg)

Here the influence of plant roots on geophysical measurements is tested. For this purpose, electrical resistivity (ER) and induced polarization (IP) measurements are conducted on cultivated soil columns with one plant of Brachypodium.The preliminary results in known media show that acceptable values are obtained from the IP measurements. Even though, we are still testing the specific impact of the electrodes and the column layout on the IP measurements, the decay curves display the expected form and behaviour. The results from this experiment will give us a first idea of the ability of IP to serve as a proxy for the presence of roots in a column. This, combined with ERT and TDR measurements, should lead us to a better understanding of the electrical signature of bulk soil with roots at different soil moisture levels.

PA10 Concept of our New Multi-Channel SIP Instrument: SIP256D Tino Radić (www.radic-research.de)

The quality of SIP measurements is largely determined by the hardware concept of the measuring instrument. High frequency impedance measurements are only possible with the shortest possible current and potential cables. For this, the transmitter should always be located at the electrodes. The current and potential measurement should also be carried out directly at the corresponding electrodes. Our newly developed instrument SIP256D satisfies all these requirements.

PA11 Spectral Inversion of SIP field data using pyGIMLi/BERT Thomas Günther, Leibniz Institute for Applied Geophysics (LIAG), Tina Martin (Federal Institute for Geosciences and Natural Resources (BGR), Carsten Rücker (Berlin Institute of Technology

With the developing SIP instruments there are increasing applications of spectral induced polarization in the field. The spectral content of the electric parameters has the potential of characterizing the subsurface and must therefore be retrieved from inversion. Up to now there is no open available inversion package for researchers. We present the open-source library pyBERT, a C++-Python library for inversion of field resistivity data. It is able to analyse the measured spectra with a variety of different approaches. A Python manager class allows nonprogrammers to access and visualize in different ways and includes pre-processing of the data as well as postprocessing of results, e.g. fitting Cole-Cole models. We give an impression on how to use these codes and present results based on a synthetic model demonstrating that spectral parameters can be reliably retrieved.

PA12 On the Effectiveness of 1D Inversions of TEM Data affected by Induced Polarization Marc Seidel and Bülent Tezkan (Institute of Geophysics and Meteorology, University of Cologne)

In case of a polarizable subsurface, effects of inductively induced polarization (IP) can have an impact on timedomain electromagnetic measurements (TEM) and may lead to nonmonotonous voltage responses or even sign reversals in the recorded transients. For this reason, we developed a new 1D inversion algorithm for the centralloop and the separate-loop TEM configurations using the Cole-Cole relaxation model. 1D forward calculations for a polarizable homogeneous half-space were conducted with the aim of analyzing the impacts of varying Cole-Cole parameters on TEM transients with respect to possible sign reversals.Additionally, we considered the variation of geometrical parameters like the transmitter size and the receiver offset. For the inversion of TEM data, one consequence of these modelings is the large number of equivalences that arise from the additional ColeCole parameters. Subsequently, 1D inversions of synthetic data were performed to study the potentials and

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limitations of the new inversion algorithm regarding the resolution of the Cole-Cole parameters. The obtained findings were eventually adopted on the inversion of real TEM field data that contained considerable IP signatures such as sign reversals. One field dataset was recorded at the Nakyn kimberlite field in Western Yakutiya, Russia in the central-loop configuration. The second field dataset originates from a waste site in Cologne, Germany, and was measured utilizing the separate-loop configuration

PA13 Characterization of Abandoned Mine Tailings by means of Time- and Frequency-Domain Induced Polarization Imaging Jakob Gallistl, Adrian Flores Orozco, Matthias Bücker (TU-Wien)

Induced Polarization (IP) imaging datasets were collected in both time domain (TDIP) and frequency domain (FDIP) for the characterization of abandoned mine-tailings and in order to assess possible down-gradient transport of sulphide minerals. The study area is characterized by measurable iron and copper concentrations of fine-grained minerals (gain size < 1 mm), which are expected to cause a distinct IP response. This study aims at the evaluation of the applicability of TDIP and FDIP at the field scale, its capability to quantify metallic volumetric content and to discriminate between different metallic minerals. Furthermore, the analyses of water samples down gradient from the tailings have revealed significant concentrations of heavy metals, such as arsenic and mercury. Hence, imaging results of an extensive mapping campaign were used to delineate preferential flow paths of sulphides and the extensions of the contaminated volume.

PA14 2D Cole-Cole Inversion of Time-Domain IP Data Measured in Krauthausen, Germany Hannah Langenbach, Bülent Tezkan (Institute of Geophysics and Meteorology)

In October 2012 and 2013 overall 14 time domain IP profiles were measured in Krauthausen, Germany using the Terrameter LS. A gradient array with an electrode distance of 2.5 m was used. The data quality conforms to the high requirements of the inversion algorithm. Time series were measured at every profile for at least 200 electrode combinations. Every time series consists of 7-11 transients. For inversion of our IP time series we use the time dependence of the resistivity and evaluate the Cole-Cole models in time domain. Using an approximate solution the forward model for every time point is solved directly in time domain and independently from each other. For each cell a composed transient is inverted into a homogeneous Cole-Cole model independently of each other. We were able to achieve a satisfying Cole-Cole model for the survey area. A two layer resistivity model is estimated. The second more resistive layer is also more chargeable. Model areas with high chargeability are correlated with areas with higher frequency exponents and higher relaxations times.

PA15 Mapping the lithotypes using the in-situ measurement of time domain induced polarization: Ellog Esben Auken, Gianluca Fiandaca, Anders V Christiansen, Pradip Kumar Maurya, Helle Holm(Department of Geoscience, Aarhus University)

This study presents a novel application of the El-log-drilling technique for measurement while drilling of the DC, time domain IP and gamma log. In addition pore water samples can be taken at arbitrary levels. The technique itself is developed in Denmark and has been widely used in the field of ground water and environmental studies. The Ellog drilling method yields detailed information on small changes in lithology, sediment chemistry and water quality and with data comparable to what can be obtained in the laboratory. We collected the data at a landfill site located near Grindsted in the southern part of Denmark. The purpose of the study was 1) to obtain a direct correlation between the undisturbed geophysical logs and surface measurements, 2) correlation of IP parameters to lithology and grain size distribution and 3) to investigate any correlation with effluent and IP parameters. We inverted the recorded resistivity and IP decays using full decay modelling with the Cole –Cole model and found that the chargeability correlates very well the clay content in the sandy aquifer.

PA16 Is the IP response related to geology or contaminants in a leachate plume at the Grindsted Landfill, Denmark? Ingelise Møller (GEUS), Pradip K. Maurya (Department of Geoscience, Aarhus University), Nicola Balbarini (Technical University of Denmark), Gianluca Fiandaca (Department of Geoscience, Aarhus University), Anders V. Christiansen (Department of Geoscience, Aarhus University), Helle Holm (Department of Geoscience, Aarhus University),, Vinni K. Rønde (Technical University of Denmark), Knud E.S. Klint (GEUS), Esben Auken (Department of Geoscience, Aarhus University), Poul L. Bjerg (Technical University of Denmark)

Contaminants in leachate plumes from landfills and other contaminated sites are a threat to the environment. Efficient site characterization methods are needed. The perspectives of the IP method are investigated in combination with geological sampling and chemical analyses of water samples. Along a leachate plume from a landfill hosting both household and chemical waste, borehole IP data, geological samples, grain size, and contaminant concentrations in water samples are examined for correlations related to geology and concentrations of contaminants. Results relating the Cole-Cole parameters with sediment types and pore water resistivity representing the concentrations of the contaminants show that the formation resistivity primarily is controlled by

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the contaminant concentrations while the IP parameters primarily are related to the clay content and grain size distribution of sandy sediments at the site.

PA17 Mapping and characterization of Induced Polarization in airborne TEM data from central East Greenland – application of a Self-Organizing Map procedure Anaïs Brethes (GEUS), Thorkild M. Rasmussen (Luleå University of Technology), Pierpaolo Guarnieri (GEUS), Tobias Bauer (Luleå University of Technology),

Induced Polarization (IP) effects were observed in airborne Time Domain EM (TEM) data acquired in central East Greenland in the context of exploration for disseminated sulphides in a sedimentary basin. Some of the IP anomalies were targeted by drilling which revealed the absence of mineralization. In order to understand the possible causes of the IP effects we first identified them in the TEM data. IP indicators were extracted from the shape of the transient curves at every measurement location and were analysed by using a Self-Organizing Map (SOM) procedure. Results from K-mean clustering of the SOM are visualized on a geographical map showing the transient curves’ characteristics. Some of the clusters are clearly correlated with the geology whereas others merely reflect recordings below the noise level. In order to interpret the cause of the IP anomalies the airborne TEM data were inverted for the Cole-Cole parameters.

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Tuesday 7 June Session B – Morning Chairs: Adrian Flores-Orozco & Yuxin Wu 9:00 – 9:25

B01 SIP time constant based petrophysical relations for two sandstone formations: the role of pore volume normalized surface area Judy Robinson (Rutgers University-Newark), Lee Slater (Rutgers University-Newark), Kristina Keating (Rutgers University-Newark), Beth Parker (University of Guelph, CA), Carla Rose (University of Guelph, CA), Tonian Robinson (Rutgers University-Newark) Recent models propose the prediction of permeability for spectral induced polarization (SIP) data using estimates of formation factor and a hydraulic length scale related to fluid flow based on either a dominant relaxation time () or a representative imaginary conductivity (). We acquired SIP and supporting petrophysical data on two sandstone fractured rock sites in the United States. The time constant based model describes the permeability reasonably well from one site that is characterized by relatively low values of pore volume normalized surface area (Spor). However, the fitting is poor for the samples from the second site that are characterized by higher values of Spor and a wider variation in Spor. We find that imaginary conductivity is related to Spor and that our samples are consistent with a previously defined empirical relation determined for a wide range of samples spanning multiple datasets. We also find that imaginary conductivity of our samples is correlated with permeability, supporting the application of models based on the formation factor (F) and . However, such models involve F raised to a large exponent, meaning that highly accurate estimates of the formation factor are needed for reliable permeability prediction.

9:25 – 9:50

B02 Identifying pollutants in soils using spectral induced polarization Idit Shefer (Technion), Nimrod Schwartz (Catholic university of Louvain), Alex Furman (Technion) The main objective of this study is to examine SIP as a tool for identifying and quantifying the presence of organic and inorganic pollutants in the soil. Several experiments were performed in this study. First the influence of a free-phase organic liquid on the SIP signature was examined on an unsaturated sandy loam soil. The added non-aqueous phase liquid (NAPL; decane) caused a decrease of the imaginary part of the soil's complex conductivity as well as the relaxation frequency. We suggest that membrane polarization is the main polarization mechanism responsible for these results. Altering the characteristic pore throat length, due to the interaction between water and decane, controls the SIP response when a free-phase compound is added to the system. Further, we used Loess soil (calcium rich) to investigate the SIP effect of several different organic pollutants and their mixtures, in order to examine the ability to distinguish them by the SIP method. The same trend of decreasing polarization was observed. However, the real part of the conductivity had a clear decrease when decane was added. The calcium rich environment had apparently contributed to the formation of different surface interactions of the polar organic compounds in the presence of decane. Furthermore, we present an artificial neural network classification with preliminary satisfying ability to indicate the existence of a specific contaminant. Third, the soil solution and adsorbed phase inorganic composition influence on the SIP signature was examined. A clear influence on the soil's electrical signature was observed. Coherent changes exist in the relaxation time and chargeability when the chemical composition of the soil was changed. Addition of divalent cation to the porous media causes an instantaneous shift in the relaxation frequency, while the polarization magnitude is affected in a more gradual way. Three types of data driven models to potentially predict inorganic species are introduced. Dominant species were fairly well predicted.

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9:50 – 10:15

B03 Doubling the spectrum of time-domain induced polarization: removal of non-linear self-potential drift, harmonic noise and spikes, tapered gating, and uncertainty estimation Per-Ivar Olsson (Engineering Geology, Lund University), Gianluca Fiandaca (Department of Geoscience, Aarhus University), Jakob Juul Larsen (Engineering, Aarhus University) Torleif Dahlin (Engineering Geology, Lund University), Esben Auken (Department of Geoscience, Aarhus University) This paper presents an advanced signal processing scheme for time-domain induced polarization full waveform data. The scheme includes several steps with an improved induced polarization (IP) response gating design using convolution with tapered windows to suppress high frequency noise, a logarithmic gate width distribution for optimizing IP data quality and an estimate of gating uncertainty. Additional steps include modelling and cancelling of non-linear background drift and harmonic noise and a technique for efficiently identifying and removing spikes. The cancelling of non-linear background drift is based on a ColeCole model which effectively handles current induced electrode polarization drift. The modelbased cancelling of harmonic noise reconstructs the harmonic noise as a sum of harmonic signals with a common fundamental frequency. After segmentation of the signal and determining of noise model parameters for each segment, a full harmonic noise model is subtracted. Furthermore, the uncertainty of the background drift removal is estimated which together with the gating uncertainty estimate and a uniform uncertainty gives a total, data-driven, error estimate for each IP gate. The processing steps is successfully applied on full field profile data sets. With the model-based cancelling of harmonic noise, the first usable IP gate is moved one decade closer to time zero. Furthermore, with a Cole-Cole background drift model the shape of the response at late times is accurately retrieved. In total, this processing scheme achieves almost four decades in time and thus doubles the available spectral information content of the IP responses compared to the traditional processing.

10:15 – 10:30

Break

10:30 – 10:55

B04 An analysis of Cole-Cole parameters for IP data using Markov chain Monte Carlo L. M. Madsen, C. Kirkegaard, G. Fiandaca, A. V. Christiansen, and E. Auken (Department of Geoscience, Aarhus University) The Markov chain Monte Carlo (MCMC) method is used to invert time-domain induced polarization (TDIP) data. A novel random-walk algorithm samples models from a probability distribution based on a realisation of the model covariance matrix, allowing the algorithm to vary step lengths according to parameter uncertainty. The algorithm was found to converge to the posterior distribution over one hundred times faster than a standard Gaussian distributed model proposer. Synthetic TDIP data, simulating homogenous half spaces and three-layer models, are inverted using the MCMC method. The results show bell-shaped posterior distributions for all spectral Cole-Cole parameters with clear correlations between the parameters. Small values of the frequency exponent (C) are found to decrease the resolution of the model parameters. A comparative analysis between the standard deviations of the MCMC posterior distributions and the results of a linearized inversion shows that the linearized approach works well with wellresolved model parameters. We have compared inversion results of different acquisition times and current waveforms. We found that as the time range decreases the parameter correlations become nonlinear and the parameters become poorly resolved or completely unresolved. Combined, the inversion results show that it is possible to extract the spectral Cole-Cole parameters from time-domain IP data and that a linearized approach is justified for a sufficient acquisition range.

10:55 – 11:20

B05 Simulation of membrane polarization for 2D and 3D pore networks Hermann Stebner Andreas Hördt (TU Braunschweig)

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We extend an existing membrane polarization model to 2D and 3D pore combinations networks, which are numerically solved to obtain an overall SIP response. We investigate the behaviour of these networks by varying the distribution function of the pore combinations and the size of the network. Equally distributed pore combinations show a dominance of high phase shifts. For empirically distributed combinations, obtained from measured pore radii distributions, high phase shifts tend to dominate only in big 3D networks. Our simulations show that for networks, which are comparable to real rocks, higher maximum phase shifts than the mean of the original pore combinations are possible. The results suggest that networks may allow a simulation of more realistic pore geometries than the original 2-pore system. 11:20 – 12:00

Poster Presentations – session B Presentations of all the posters of session B (two minutes for each presentation). The list of posters can be found at the end of the day’s program

12:00 – 13:00

Lunch & Poster session B

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Session B – Afternoon Chairs: Jakob Juul Larsen & Lee Slater 13:00 – 13:25

B06 Lithological characterization of a contaminated site using Direct current resistivity and time domain Induced Polarization Pradip Kumar Maurya, Gianluca Fiandaca, Esben Auken and Anders Vest Christiansen (Department of Geoscience, Aarhus University) Characterization tools for contaminated sites have become advanced with the continued development of geophysical methods. Resistivity methods and time-domain induced polarization methods have proven their capability to delineate the subsurface properties by complementing each other. In the present study a large contaminated site in Denmark was investigated using direct current resistivity and time domain induced polarization (DCIP). For this purpose 14 profiles were collected alongside a stream in order to investigate the contamination and delineate the lithological units. 2D inversion using a cole-cole model of two selected profiles are presented. They show that the resistivity model alone cannot depict the geology as inferred in the borehole. However, when including the models of chargeability and mean relaxation time the geological units are clearly defined, which helps in identifying the possible contaminations.

13:25 – 13:50

B07 Spectral induced polarization of sand-biochar mixtures: experiments and modeling Z. Gao, F.-H. Haegel, J.A. Huisman and H. Vereecken (Institute of Bio- and Geosciences, Agrosphere) Biochar attracts increasing research interest due to its potential for agricultural and environmental purposes such as soil amendment and greenhouse gas reduction. To better monitor and investigate biochar in soil, non-invasive measurement approaches that can be applied in the laboratory and at field scale are needed. The goal of this work is to examine the sensitivity of the spectral induced polarization (SIP) method to the presence of disseminated biochar in sand. We investigate the complex electrical conductivity of saturated mixtures of sand and sieved biochar, and use a mechanistic SIP model that accounts for the redox reactions at the surface of the polarized particles to invert the measured data. The magnitude of the measured complex electrical conductivity showed a positive correlation with the mass fraction of biochar, while the peak frequency of the imaginary part showed a negative correlation with the particle size of the biochar. The model provides reasonable fitting results for low mass fraction of biochar in the mixtures.

13:50 – 14:15

B08 Numerical correction of phase errors due to leakage currents in wideband EIT measurements E. Zimmermann (Central Institute for Engineering, Electronics and Analytics, Electronic Systems), J. A. Huisman (Institute of Bio- and Geosciences, Agrosphere), A. Mester and S. van Waasen (Central Institute for Engineering, Electronics and Analytics, Electronic Systems) Advanced model-based data correction methods are needed in order to determine the small phase response of low-polarizable soils and rocks in the higher frequency range up to 10 kHz. Methods have been developed to correct several system-dependent errors, such as amplification errors, signal drift, current measurement errors, potential measurement errors due to high electrode impedances, propagation delay of the signal due to the long cables, and phase errors introduced by inductive coupling between the electrode cables. However, measurements at test sites with high resistivity have shown a new dominating phase error, which was found to be related to capacitive leakage currents between system ground and the soil. In order to correct this error, we enhanced the FEM modelling used for the reconstruction of the electrical conductivity distribution. Using this new formulation of the FEM forward model, this source of error was reduced by a factor of five or more. This enables an electrical conductivity reconstruction for frequencies up to 10 kHz. In future work, it will be investigated whether the capacitive leakage currents can be reduced by optimization of the cable layout. In any case, it is helpful to use the leakage current as a proxy for data error during data filtering, and it can also be used to decide if the enhanced FEM model presented here should be used.

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14:15 - 15:15

Poster session B

15:15 – 15:40

B09 Comparison of Cole-Cole and Constant Phase Angle modeling in timedomain induced polarization Myriam Lajaunie (EOST, Ecole et Observatoire des Sciences de la Terre), Pradip Kumar Maurya and Gianluca Fiandaca (Department of Geoscience, Aarhus University) The Cole-Cole model and the constant phase angle (CPA) model are two prevailing phenomenological descriptions of the induced polarization (IP), used for both frequency domain (FD) and time domain (TD) modeling. The former one is a 4-parameter description, while the latest one involves only two parameters. Choosing between a Cole-Cole description and a CPA one to invert a specific frequency domain data set is easy, since a look at the data is enough to estimate their spectral content. This is, however, not the case with TDIP data. This work aims at understanding how the spectral content is reflected in TDIP data, and therefore, at identifying (1) if and when it is possible to distinguish, in time domain, between a Cole-Cole description and a CPA one, and (2) if features of time domain data exist in order to know, from a simple data inspection, which model will be the most adapted to the data. Synthetic forward responses were computed for homogeneous Cole-Cole models, varying both time range of the modeled IP data and Cole-Cole parameters. Subsequently, CPA inversions were carried out on the Cole-Cole data. The inversion results show that it is generally possible to distinguish CPA and Cole-Cole models in time domain, except when the Cole-Cole frequency exponent is small (below 0.1) or for specific combinations of the Cole-Cole parameters. The distinctness increases with the time range of the IP data, but usually two decades in time are sufficient to distinguish the two models. Furthermore, forward modeling of quadrupolar sequences on 1D and 2D heterogeneous CPA models shows that the CPA decays differ among each other only by a multiplication factor. Consequently, the inspection of field data in log-log plots gives insight on the modeling needed for fitting them: the CPA inversion cannot reproduce the shape variability of the IP decays. Field examples of this latter result are presented.

15:40 – 16:05

B10 Airborne IP for Kimberlite Exploration Douglas W. Oldenburg and Seogi Kang (University of British Columbia) Negative transients in coincident loop airborne time domain electro-magnetic (ATEM) data have often been observed when exploring for kimberlite deposits. It is usually supposed that the negative transients arise from chargeable material such as surficial clays or ice in permafrost. As such, this EM signal is generally regarded as a “problem” in mineral exploration because it distorts the EM signals from the conductive kimberlites, and if not corrected for, results in an incorrect conductivity. However, chargeability could be reflective of the kimberlite, hence the induced polarization (IP) effects can be valuable “signal”. The ATEM surveys at the Tli Kwi Cho (TKC) kimberlite complex have been a testbed for illustrating the existence of negative transients and we focus on that region. The two pipes that constitute TKC have been extensively drilled and the resultant geologic models can be used to validate our inversion results. In addition, the complex impedance of TKC core samples have been measured in the laboratory and the results showed that the kimberlites can be chargeable and that different kimberlite units have different IP characteristics. In this paper, we first address the important issue about depth of resolution of buried chargeable bodies relevant to kimberlite exploration. After showing its potential we remove the EM effects from the IP data and invert them to recover 3D distributions of pseudochargeability at multiple time channels. The recovered pseudo-charge-ability at different times provides meaningful information about the diamondiferous portion of the pipe and distinguishes it from other kimberlitic rocks.

16:05 – 16:30

B11 Geometrical constraints for membrane polarization Andreas Hördt, Katharina Bairlein and Hermann Stebner (TU Braunschweig) We investigate under which conditions membrane polarization might be relevant for realistic pore space geometries. We review some basic properties of the theoretical model and illustrate general constraints by modelling studies. We focus on geometrical parameters of the model, e.g.

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radii r and lengths L of two cylindrical pores. In principle, a wide range of spectra can be generated, covering orders of magnitude in both maximum phase shift and characteristic time scales. One ingredient to obtain large phase shift is a small radius of the narrow pore in the range of tens of nm. Time scales are mainly controlled by pore lengths. Generating large time scales and phase shifts at the same time in principle requires large ratios between pore lengths and radii. However, within the four-dimensional parameter space, which exhibits regimes of different behaviour, examples can be found where moderate L/r ratios (10:1) can produce time scales in the range of seconds with phase shifts of a few mrad. The results encourage further attempts to combine impedances of 2-pore systems to approach the simulation of real rock systems. 16:30 – 18:00 18:30 -

Poster session B Workshop Dinner at: ’Det Glade Vanvid’ Pakkerivej 2b 8000 Aarhus C.

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Poster Session B: Chair: Anders Vest Christiansen PB01 New technology for delineation of resistive and polarizable kimberlite fissures using TEM method in South Africa V. Hallbauer-Zadorozhnaya, Council for Geoscience

TEM sounding have been carried out in the Limpopo province, South Africa. The aim of the research is to delineate a kimberlite fissure in some portion of diamond fields. The edge of kimberlite fissure is located at the depth about 20-25 m. Rocks composed the fissure, are quite resistive, polarizable and have low susceptibility. TEM survey had been performed along 10 profiles, all of then crosses the fissure but delineation of fissure had to be done with very high accuracy (about 2-3 meters in lateral). Using TEM FAST 48 we observed that the fissure should be seen at least twice when both sides of square loop locates above the fissure. Using instrument Tsickl 5 and horisontal magnetic dipole we obtained more stronger signals related to the fissure. This phenomenon relates to the theory of electromagnetic field proporation on ingemoginated media. Mathematical modeling of dipped/vertical S plane overlapped by horizontal S plane (both can be polarizable) for both components dBz/dt and dBy/dt have been calculated. The result shows that the preferable TEM configuration for searching quasi vertical objects is large transmitter loop and horizontal magnetic dipole. We are proud to tell that following drillings of seven boreholes opened the fissure in all proposed points.

PB02 Different kinds of IP effects and laboratory measurements samples V. Hallbauer-Zadorozhnaya (Council for Geoscience ), G Santarato ( University of Ferrara ) L. Maré ((Council for Geoscience )

Several kinds of Induced Polarization (IP) effects occur and will be reviewed in the present paper, namely electrosmosis effect, membrane polarization, Maxwell-Wagner effect and electrolytical polarization. All effects are based on different physical phenomena. The electrosmosis processes occur in all rocks/sediments. However the amount of double electric layer plays the major role. This phenomenon is described by Helmholtz-Smoluhowsky equation and is linear. Decay constant of electrosmosis process is usually in range 10-6-10-2 s and can be mostly observed on Transient Electro-Magnetic (TEM) signals. The membrane polarization is based on constrictivity of pore. When an electrical current flows through rocks containing channels and pores with different sizes, an excess/loss of ions accumulates at the boundaries. The homogeneous diffusion equation, with specified (nonlinear) boundary conditions, has been used for solving this problem. This type of polarization is non-linear, depends on applied current and may depend on current pulse length (in TEM method). Duration of membrane polarization can reach 10 s and more. Maxwell-Wagner model consists of isolated pores. The homogeneous diffusion equation also has been used for solving the problem of ions distribution in the pores. However the boundary conditions are linear. The ions move in the pores with constant velocity and accumulated the neighbour of the pore ends. Duration of process of redistribution is comparable with duration of the electro osmosis process. The pores with unallocated ions may be represented by an equivalent electrical circuit (a capacitor). The Cole-Cole or capacitor discharging formula can be used to describe the effect. Numerous laboratory measurements of different types of rocks and minerals and some field TEM data demonstrate different kinds of IP effects.

PB03 Relationship between Cole-Cole model parameters and spectral decomposition parameters derived from SIP data Maximilian Weigand and Andreas Kemna (Department of Geophysics Steinmann Institute)

Spectral induced polarization (SIP) signatures are ana-lyzed using different phenomenological model descrip-tions. One approach uses the Cole-Cole (CC) model, or variants of it, to describe one or several distinct polariza-tion peaks. The other approach yields a relaxation time distribution (RTD) by using a decomposition procedure which describes SIP data by a superposition of a large number of polarization terms. Based on this RTD, inte-gral spectral parameters similar to CC model parameters can be derived. We here compare chargeability and relax-ation time parameters, obtained with Debye and Warburg decomposition approaches, with the original CC parame-ters used to generate synthetic SIP data. Understanding the relationship between CC decomposition parameters helps to prevent interpretation errors when results from both approaches are combined. We identified potential underestimations of the CC chargeability by up to 80% and deviations of 𝜏𝑚𝑒𝑎𝑛 from the CC relaxation time by up to three orders of magnitude. These results highlight the importance of consistent SIP data analysis procedures.

PB04 Temperature dependence of complex surface conductivity Katharina Bairlein and Andreas Hördt (Institute of Geophysics and extraterrestrial Physics TU Braunschweig)

The complex electrical conductivity of water-saturated rocks, measured with induced polarization (IP), is affected by temperature. The main reason for the temperature dependence of fluid conductivity is that the mobility of the ions in the pore fluid is increased with temperature. In addition to the fluid conductivity, surface conductivity is influenced by temperature, but it is not investigated yet, which parameters of the rock surface and the fluid are the dominating factors.

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We measured the complex electrical conductivity of a sandstone sample at temperatures between 0 and 40 °C and ion concentrations from 1 to 2000 mol/m3. From measurements at high salinities, we are able to separate surface conductivity from the real part of bulk conductivity and to determine its dependence both on temperature and salinity. The experimental results are compared to calculations of a membrane polarization model. We use a Walden exponent as a measure of the strength of the temperature dependence. The Walden exponent of the real part of surface conductivity increases, while the Walden exponent of the imaginary part slightly decreases with increasing salinity. Calculations with the model predict a decrease in both the temperature dependence of the real and imaginary part of conductivity. The measured and calculated surface conductivities show, that temperature dependence in the electrical double layer cannot be attributed to an ion mobility similar to the mobility in the free electrolyte.

PB05 Complex Resistivity for Dynamic Imaging of Plant Root Traits and Root – Soil Interactions Yuxin Wu Susan Hubbard Baptiste Dafflon (Lawrence Berkeley National Lab)

Electrical methods (complex resistivity and ERT) are explored for plant root trait imaging and the study of dynamic root – soil interactions. The links between the moisture dynamics, root architectural and morphological traits and electrical properties of the plant roots and root zone soil are established for a deciduous plant (Acer palmatum) under controlled temperature and soil moisture conditions. Specifically, resistivity – moisture correlation is closely linked with the plant’s seasonal growth cycle and the effects of the roots on soil resistivity are evident. In addition to deploying previously tested configurations under controlled laboratory conditions, we employed novel imaging strategies that utilize root systems as distributed electric transmitters to quantify critical root structural and morphological traits and their responses to variable soil and climatic conditions. The links between root architectural (root distribution, rooting depth) and morphological traits (root mass, effective root area) and root dielectric signals are clearly demonstrated during the different stages of plant growth, indicating the dynamic changes of root activity in response to water and nutrient needs and availability during different stages of plant growth. These results demonstrated the potential of electrical methods for the study of root zone dynamics, which can lead to a new direction in developing much needed, minimally invasive and in-situ root phenotyping tools with broad application in terrestrial carbon cycle, forestry and agricultural studies.

PB06 SIP response of compacted natural and lime-cement-treated loam Carole Kaouane (CEREMA-Normandie Centre), Michel Chouteau (Ecole Polytechnique de Montreal), Philippe Côte (IFSTTAR – Nantes)

We investigate the applicability of Spectral Induced Polarization (SIP) to geotechnical engineering for assessing soil compaction. We make two groups of samples at different compaction levels: group N is made from a silty loam and group T is from the same loam treated with 1% lime and 5 % cement. Groups show distinct complex conductivity spectrums. Debye decomposition is applied to the measured data and we extract the relaxation time distribution (RTD). Group-N samples show an increase of total chargeability M with an increase in saturation and no dependence of the mean frequency on saturation, while group-T samples show a decrease of M and an increase of the mean frequency with an increase in saturation. We suggest that the compacted loam possesses a continuous conductive matrix composed of saturated silt aggregates. We cannot derive firm conclusions on group-T samples because of the possible chemical reactions, which transform the porous matrix of the samples. The observation of the RTD could be a practical tool to monitor those reactions.

PB07 Sodium Persulfate In Situ Chemical Oxidation monitored by geophysical and geochemical methods : laboratory work T. Maury,M. Franceschi, M. Schmutz (ENSEGID, EA 4592 G&E, Bordeaux University)

Hydrocarbon contamination represents the main situation of polluted sites in France (64%). Among the different technics that are developed for remediation, In Situ Chemical Oxydation (ISCO) showed interesting results in laboratory and field contexts. Anyway, the technic is perfectible and there is a need for an easier and cheaper way to monitor the efficiency and the quality of ISCO remediation. By injecting a strong conductive solution, ISCO seems to be a good candidate for geoelectrical monitoring. Thus, the aim of our study is to evaluate the possibility to monitor ISCO remediation by geoelectrical signals thanks to our laboratory work. For the present study, the chosen hydrocarbon is decane and the oxidative solution is sodium persulfate. The electrical signal of this mixture is monitored in a sample holder within three different media (sands, clayish sands and sands with organic matter). A second sample holder where no oxidative solution is added, is used as reference. During the hydrocarbon degradation, resistivity, IP signal and spontaneous potential will be measured as well as various geochemical parameters of the solution (reactants concentrations, pH, alcalinity, temperature,...) or known to influence ISCO efficiency. The first goal of our experiment is to compare electrical signal variations and geochemical variations to understand the links between both. Then, the second goal is to modelize the phenomenon that take place during the ISCO reaction between decane and sodium persulfate and the signal created. We expect to highlight

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possibilities to monitor ISCO reactions by in situ geophysical measurements. Our presentation will deal with the working methodology, flow processing and will present the first results.

PB08 Geoelectrical monitoring during waste biodegradation process Jouen Thomas, Clément Rémi, Mazéas Laurent (National Research Institute of Science and Technology for Environment and Agriculture (IRSTEA), Loisel Simon (SAS Les Champs Jouault), Moreau Sylvain (IRSTEA)

The aim of this experiment is to provide tools that allow characterisation of waste biodegradation state at a laboratory scale. Four geophysical methods, self-potential, electrical resistivity, temporal and spectral induced polarization, will be monitored from the beginning to the end of municipal solid waste biodegradation cycle. For this reason five columns were filled with waste and equipped with measurement electrodes. The measurements were started in February and will continue until the waste has completely degraded.

PB09 The electrical signature of soils contaminated by heavy metals Tamar Shalem (Technion), Renduo Zhang (Sun Yat-sen University), Alex Furman ( Technion)

Soil and groundwater pollution in general, and by heavy metals in particular, is a major threat to human health, and especially in rapidly developing regions. Fast, accurate and low cost measurement of heavy metal contamination is of high desire. Spectral induce polarization (SIP) may be one alternative to the tedious sampling techniques typically used. The high sorption affinity of heavy metals suggests that their electrical signature may be significant, even at relatively low concentrations. The goal of this research is to examine the electrical signature of soil contaminated by heavy metals, in a non-tomographic fashion. This will be achieved by a series of laboratory experiments and development of data-driven screening model. The work-plan includes 'sterile' experiments looking at the SIP response of mono-ionic soil to various contaminants (heavy metals) and different concentrations, moving to complex contamination 'cocktails', ending with measurement of the SIP response of real contaminated soils (at the Pearl river delta, China). The poster will present the research plan in details and preliminary results of the SIP signature of several different heavy metals.

PB10 Permeability estimation of hydrocarbon reservoirs samples using Spectral Induced Polarization (SIP) and Nuclear Magnetic Resonance (NMR): a laboratory investigation F. Razavirad (Yazd University), A. Ghorbani (Yazd University), M. Schmutz (ENSEGID, Bordeaux INP University), S. Galaup (ENSEGID, Bordeaux INP University), A. Binley (Department of Environmental Science, Lancaster University), L. Pigot (ENSEGID, Bordeaux INP University)

There is growing interest for using geophysical methods such as spectral induced polarization (SIP) and nuclear magnetic resonance (NMR). Permeability is a key parameter associated with the subsurface production and injection. The goal of this study is to investigate: 1) a relationship between permeability of sample plugs (obtained from a reservoir) and electrical and hydraulic parameters (quadrature conductivity, porosity, surface area per unit pore volume (Spor) and grain size distribution) and 2) permeability estimation of plugs using a joint model between SIP and NMR measurements. We also compare SIP and NMR porosimetry analysis. 30 plug samples have been provided by Iranian Offshore Oil Company (a subsidiary of National Iranian Oil Company). These relatively unconsolidated sandstone plugs have been cored from Soroush oil field located in Persian Gulf. As fluids, tap water and brine will be used for experiments. First, it is desired to study the effect of brine saturation on NMR and SIP responses. It is planned to saturate plugs with tap water (25, 50,75 and 100%) and perform NMR and SIP tests at each step. Next, brine is introduced to the plugs (the brine conductivity is 200, 400, 600 and 800 microsiemens per centimeter) and NMR and SIP response will be measured. These measurements will be done at different saturations.

PB11 On electromagnetic coupling of half-space from Spectral Induced polarization studies Ahmad Ghorbani (Yazd University) , Myriam Schmutz (EA4592 Bordeaux INP – ENSEGID), K. Malekpour Dehkordi (Yazd University)

Spectral Induced Polarization (SIP) is widely used for environmental and hydrogeophysics, but one major limitation concerns the electromagnetic coupling effect. We investigated inductive coupling properties of a half-space with complex resistivity following the process: Cole-Cole parameters of half-space are used to calculate inductive coupling spectrum using Sunde equation. Then during an inversion process, a Cole-Cole function is superposed to the calculated inductive coupling impedance. At last, Cole-Cole parameters of inversion process (inductive coupling curve properties) are compared with Cole-Cole parameters of half-space. We noticed that the inductive coupling impedance (the integration of P function in Sunde equation) on the half-space with a Cole-Cole model shows a dispersion phenomenon only at higher frequencies while the mutual impedance shows at least two dispersion at both of lower and higher parts of spectrum (1 mHz to 10 kHz) relative to IP and inductive coupling. The results show that Dipole-Dipole parameters (a and n) and DC resistivity of half-space have significant effects on the inductive coupling spectrum. On the contrary, the polarization parameters of half-space (time constant, frequency dependency, and chargeability lower than 0.3) do not have a significant effect on the inductive coupling spectrum. These results show that the mutual impedance of a half-space (known DC resistivity) can be a good estimate of the

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inductive coupling impedance if IP effects are not very large. In other words, IP effects of a half-space Cole- Cole model type can be obtained from subtraction of the mutual impedance of a half-space (SIP measurements) and the mutual impedance of a half-space without IP effects (calculation). The resistivity of half-space can be suggested from DC resistivity measurement or from the lowest frequency of real part of impedance. This process is applied to field data and through 2 field examples, we show the impact of inductive effects on real data.

PB12 Combined ERT and IP modelling for monitoring DNAPLs: preliminary results Panos Tsourlos (Aristotle Univ. of Thessaloniki), Christopher Power ( Cape Breton University), Jason Gerhard (Western University), Torleif Dahlin (University of Lund)

In this work we explore the potential of combined time-lapse ERT and induced polarization (IP) techniques for monitoring the remediation of DNAPL source zones. Recently, we have established a realistic DNAPL-geoelectrical ERT linkage model within the time-lapse monitoring framework and we are now seeking to extend this particular approach by also including IP time-lapse models. In this framework, we propose a modelling approach and present the appropriate tools. Finally, we present preliminary ERT and IP models to investigate the potential of this approach. Preliminary results are encouraging and suggest that the focus needs to be given into a more advanced linkage model between DNAPL flow and the IP response.

BP13 Spectral induced polarization of the ore zone of the gold deposit Sukhoi Log Andrey Tarasov (Saint Petersburg State University), Grigory Gurin VIRG-RUDGEOFIZIKA JSC)

The spectral induced polarization tomography (ERT-SIP) survey carried out on giant gold deposit Sukhoi Log (Russian, East Siberia). SIP was a part of comprehensive geological and geophysical surveys including geochemistry, gravity, ground magnetic, aerogeophysic (aeromagnetic and aero-gamma spectrometry) methods, audiomagnetotelluric sounding (AMTS) and self-potential method. These surveys provided in the 2013-2014s for testing of the modern searching technology of the gold deposits. The ERT-SIP in the time domain included two sets of IP measurements with different duration of the current pulses (1 s and 8 s). The complicated SIP data processing allowed to determine in geophysical term various morphological types sulfide mineralization.

BP14 Superimposed IP relaxations in sand and silty clay deposits measured in the time domain Sara Johansson and Torleif Dahlin (Engineering Geology, Lund University)

While the low frequency response of time domain decays commonly can be fitted with a Cole-Cole model, early time gates corresponding to more than 50-100Hz in the frequency domain have been observed to deviate from this shape. Therefore, the aim of this paper is to evaluate if several relaxations can be distinguished and fitted with superimposed relaxation models. The results show that reasonable values can be extracted from two superimpose Cole-Cole models fitted to raw data measured at sand and silty clay. The high frequency relaxations can have their origin in short polarizable length scales or interfacial polarization mechanisms in the geological media. They could also, fully or partly, origin in coupling effects or the distribution of Cole-Cole parameters in the subsurface.

BP15 Spectral time-domain induced polarization and magnetic surveying – an efficient tool for characterization of solid waste deposits in developing countries David Dotse Wemegah (KNUST University), Gianluca Fiandaca (Department of Geoscience, Aarhus University), Esben Auken (Department of Geoscience, Aarhus University), Aboagye Menyeh (KNUST University), (Sylvester Kojo Danuor (KNUST University)

Time-domain induced polarization (IP) and magnetic data were acquired to map and characterize the decommissioned, un-engineered, municipal solid waste deposit site of the Kwame Nkrumah University of Science and Technology (KNUST), located in the Kumasi Metropolis of Ghana. Thirteen induced polarization profiles 500800 m long and twenty-six magnetic profiles 600-800 m long were acquired, and two drillings were carried out in order to help in the interpretation of the geophysical data. The study was carried out with the aim of determining the risk posed by the waste deposit to the quality of the soil and the groundwater system, which is the main potable water supply for the Secondary School, the University Teaching Hospital and the Veterinary School, situated within the catchment area of the site. Full-decay 2-D time-domain IP inversions in terms of Cole-Cole parameters were used for interpreting the polarization data. The chargeability, resistivity, and the normalized chargeability distributions, together with the magnetic results, aided in a full characterization of the site geology, the waste and the associated pollution plume. In particular, clear contrasts in resistivity and in the polarization parameters were found between the saprolite layer and the granite bedrock, the main lithological units of the area. Furthermore, it was found that the KNUST waste deposit is characterized by a low-chargeability and low-resistivity signature, and that the low-resistivity area spreads out from the waste deposit into the permeable saprolite layer, indicating the presence of a leachate plume. A fracture zone in the granite bedrock, which is at a risk of leachate contamination, was also identified. The research thus provides the information needed for assessing the future impact of the waste on the water quality in the area as well as for designing risk-mitigation actions.

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BP16 Mapping possible flowpaths of contaminants through surface and cross-borehole spectral timedomain induced polarization Thue Bording, Gianluca Fiandaca, Pradip Kumar Maurya,Esben Auken, Anders Vest Christiansen (Department of Geoscience, Aarhus University)

Traditional methods for mapping possible flowpaths of contaminants in sedimentary environments by boreholes may often be insufficient. Additional information may be acquired by geophysical methods. In the present study, cross-borehole and surface measurements were performed using time-domain induced polarization (TDIP). After measurements the entire test site was dug out, and the geology was described. A 2D spectral inversion of the combined dataset is presented, which is in great correspondence with the observed geology.

BP17 Evaluation of copper mobility with SIP and geochemical analysis: First results Luca Peruzzo, Myriam Schmutz, Susan Hubbard, Michel Franseschi (Lawrence Laboratory Berkeley)

The induced polarization (IP) has been shown sensitive to the adsorption of different cations at the laboratory scale. Extending these previous works we present the results of laboratory spectral induced polarization (SIP) measurements investigating the signature of Cu in natural soil samples taken from a vineyard in the Bordeaux area (Fr). The copper concentration is expected to be suitable for our purposes as a consequence of a long-term used of copper fungicides. Our work is supported by the access to the detailed historical register of the products used in the vineyard (treated subarea, day, type and amount of product used). Exploiting this information we will focus on a sloping area. The average slope is about 10% and it decreases towards the bottom. The upper part have been cultivated and treated since a longer time in comparison to the lower part. Thus, our working idea is based on two features: (i) part1 could present a higher copper concentration and (ii) the slope itself could cause a transfer of copper from the top to the bottom whose concentration in this case would increase. Then, both initial explorative ERT and IP field measurements and the consequent collection of the samples will be performed in order to investigate which one of the two previous hypotheses is dominant. Grain size distribution, specific surface area, mineral composition, organic matter content, moisture content, soil pH and Cu concentration are analysed to understand how these parameters affect the SIP response. By changing the Cu concentration and the moisture content we highlight their contributions to the induced polarization response compared to the other parameters which are kept constant. The results will be then combined in an empirical model able to predict the Cu IP signature supporting our investigation on the copper mobility and adsorption on the field.

BP18 Time-domain IP as a tool for observing processes in crystalline rocks? Jaroslav Jirku (Faculty of Science in Prague), Jan Vilhelm (Faculty of Science in Prague), Jaroslav Barta(G IMPULS Praha spol. s r.o.)

Within the purview of our research we use electrical resistivity tomography (ERT) for long-term, non-invasive monitoring of processes occurring in granite mass, in the close vicinity of an underground excavation. Understanding of such processes can be used for deep geological repositories of nuclear waste. In the Czech Republic crystalline rocks are being considered as the host rock – therefore our in situ experiments are carried out in a granite gallery, directly on the rock wall. Apart from time-lapse apparent resistivity measurements we also measure induced polarization in time-domain. We believe that changes in apparent chargeability can provide additional information on processes and mechanisms in the zone around the gallery´s vault. Our in situ data consists of continuous measurements, when, simultaneously with apparent resistivity measurements, four 2D IP cross-sections per day (i.e. every six hours, approximately ¾ year in total) were collected. Our permanently placed layout consists of 48 stainless electrodes, with 20 cm spacing. Together with field data analysis we discuss possible methodology´s modifications, in terms of using time-domain IP in hard-rocks, i.e. mainly problems of stainless (polarizable) electrodes in high grounding resistance environment, limitations connected with the capacitive coupling phenomenon (in case of a single cable for potential and current loop), or electrode polarization´s appearance in the multichannel ERT protocols.

BP19 Application of spectral induced polarization method (SIP) at complex studying of low-contrast magnetic anomaly V. Kulikov and A. Solovieva (Lomonosov Moscow State University)

The purpose of this study is to identify the various geophysical and geological section parameters by integrating electrical and magnetic exploration. The object of research is the Miocene paleovalley filled with deposits of clay, loam and sand. The complex geophysical work presented a detailed ground magnetic prospecting, electric profiling and spectral induced polarization method (SIP), which is based on the IP measurements at several frequencies. SIP method was carried out using a symmetrical four-electrode Schlumberger array with special spacing (AB/2) and step between points. This array allows to view data as a result of electric tomography and to carry out twodimensional inversion. Particular attention was paid to section elements, which are characterized by high values of magnetic susceptibility and chargeability. For all the collected materials complex interpretation was performed, we

22

received two-dimensional model of resistivity and chargeability and held lithological core analysis. The main conclusion of our research is that the anomalies in the magnetic field and the high values of the induced polarization are due to the presence of finely dispersed iron compounds and the iron in amorphous form.

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Wednesday 8 June Session C Chairs: Torleif Dahlin & Andreas Kemna 9:00 – 9:25

C01 Pore radius distribution and fractal dimension derived from spectral induced polarization Zeyu Zhang (Southwest Petroleum University), Andreas Weller (Institut für Geophysik, TU Clausthal) The pore radius distribution provides a suitable description of the pore space geometry that can be used to investigate the fractal nature of the pore space or to determine a fractal dimension. Fractal dimension describes the size of geometric objects as a function of resolution. It can be integrated into models of permeability predicting. We investigated the fractal dimension of the pore space of 24 Eocene sandstone samples from China. We propose an approach to use induced polarization spectra to determine the fractal dimension of the pore space. Debye decomposition was used to determine the relaxation time distribution from the spectra The relaxation time was transferred into a curve showing the cumulative volume intensity as a function of pore radius. The slope of this curve in double logarithmic presentation indicates the fractal dimension. Additionally, the fractal dimension was derived from data of the capillary pressure curves from mercury intrusion and the transversal relaxation time distribution of nuclear magnetic resonance. The results were compared and discussed. For samples with an effective pore radius larger than one micrometer, good agreements exist between the values of fractal dimension derived from the three different methods.

9:25 – 9:50

C03 2D DCR/TDIP Two-step Inversion: Detectability of ore deposits and Depth of Investigation Juliane Adrian and Bülent Tezkan (Institute of Geophysics and Meteorology, University of Cologne) The joint application of the Direct Current Resistivity (DCR) and Time-domain Induced Polarization (TDIP) methods is a helpful tool to investigate ore deposits with sulfidic content. The combined interpretation yields a resistivity and chargeability model of the subsurface which is superior to a pure resistivity model, especially when dealing with disseminated deposits. We present a newly developed smoothness constrained 2D inversion algorithm for DCR and TDIP data applying a two-step approach. It contains a Finite Element forward calculation on an unstructured triangular mesh which amongst others simplifies the incorporation of topography. The new algorithm is tested regarding the quality of the chargeability resolution with respect to the resistivity model. Furthermore, the resolution of the lower boundary of a highly chargeable model block is investigated and compared to the depth of investigation which is determined by the coverage matrix. Finally, 2D inversion results of field data acquired on a sulfidic copper ore deposit in Turkey are shown using the newly developed algorithm and a feasible interpretation is given .

9:50 – 10:15

C04 Large Scale IP Survey at Önneslöv in Southern Sweden Torleif Dahlin, Per-Ivar Olsson, and Matteo Rossi (Engineering Geology, Lund University) A DCIP survey, i.e. a geoelectrical survey with combined measurement of DC resistivity and induced polarization (IP), was conducted in southern Sweden. The purpose was to identify soil depth and bedrock structures and variations in rock quality. Data were acquired data with 100% waveform from which IP of good quality data were extracted. The inverted model sections show a wide variation in the electrical properties of the bedrock that are expected to relate to variation in rock quality. The results, together with results of other geophysical methods, form the basis for a drilling program in order to identify variations in quality rock of importance to the construction of an underground facility.

24

10:15 – 10:30

Break

10:30 – 10:55

C05 An Approach for Microscale Simulation for Induced Polarization Dr. Norbert Klitzsch and Saurabh Singh(E.ON ERC, RWTH Aachen University) In this paper, we discuss an approach for the microscopic simulations for Induced Polarization that describes the dynamics of ion transport with the help of the Nernst-Planck-Poisson (NPP) model. The NPP model is governed by coupled diffusion and migration equations. The equations are solved by means of the Finite Difference Method and Euler schemes. The goal is to develop SIP simulation tool that takes the inner 3D microstructure of the porous media into account. So far we have successfully verified and validated the 1D and 2D NPP models. We also introduced time dependent IP simulations on simple 2D models.

10:55 – 11:20

C06 Non-invasive geophysical monitoring of subsurface biogeochemical processes under redox oscillating conditions Adrian Mellage, Geertje J. Pronk, Tatjana Milojevic, Anthony L. Endres (University of Waterloo, Earth & Env. Sciences), Estella A. Atekwana (Oklahoma State University, School of Geology), Alex Furman (Technion), Fereidoun Rezanezhad and Philippe Van Cappellen (University of Waterloo, Earth & Env. Sciences) In order to determine the effects of water table dynamics on subsurface biogeochemistry, we are currently conducting state-of-the-art automated soil column experiments with fully integrated monitoring of hydro-bio-geophysical variables under both constant and oscillating water table conditions. An artificial, homogeneous mixture consisting of minerals and organic matter is used to provide a well-defined starting material. The artificial soil is packed into 60 cm high, 7.5 cm wide columns. In this experiment, three replicate columns are incubated while keeping the water table constant at mid-depth, while another three columns alternate between drained and saturated conditions. Periodic spectral induced polarization (SIP) measurements are performed, in order to monitor the development of the soil’s geophysical signature and relate this to the observed changes in biogeochemical properties. Thus far, during the initial “wetting and drying” cycle of the experiment, the measured imaginary conductivity (σ'') response in the fluctuating column shows a decrease during the wetting phase, followed by an increase during the drying phase. Also, the magnitude of σ'' increases with decreasing depth, despite the expected lower moisture content closer to the surface. These results are opposite of what would be expected based on the saturation-σ'' relationship and have potential implications as to how σ'' data are interpreted in variably saturated media. Concurrent measurements of pore-water geochemistry and solid phase microbial analyses will allow us to track changes in soil biogeochemistry and relate these back to the observed complex conductivity response, in order to develop a full theoretical understanding of the processes controlling the observed signals. The experiment is ongoing with an expected total duration of 6 months.

11:20 – 11:45

C07 The IP response of black shales in the Oslo graben, Norway Asgeir Kydland Lysdahl, Erik Endre (Norwegian Geotechnical Institute (NGI), Tino Radic (Radic Research), Jürgen Scheibz Norwegian Geotechnical Institute (NGI) This work presents time-domain IP and resistivity field measurements of a black shale lithology in the Oslo graben, as well as a frequency-domain laboratory characterization of the complex impedance of core samples from the same lithology. The time domain inversion models resemble well the known lithology and the black shales stands out with high (40 msec) chargeability. A large phase shift (up to 19 degrees) is recorded in the complex impedance data at low frequencies in two out of three black shale samples. Both results show a significant IP response and suggest the existence.

11:45 – 12:10

C08 Bayesian inference of spectral induced polarization parameters at the Canadian Malartic disseminated gold deposit Charles Lafrenière-Bérubé, Michel Chouteau (École Polytechnique Montréal), Gema R. Olivo (Queen’s University)

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Spectral induced polarization (SIP) parameters can be extracted from field or laboratory complex resistivity measurements, and even airborne or ground frequency domain electromagnetic data. There is a growing interest in application of SIP to environmental problems and mineral exploration. SIP measurements were conducted on 211 rock samples from the Canadian Malartic disseminated gold deposit to study its electric signature that could be detected by geophysical prospecting. Then, the SIP parameters were inferred using Markov-chain Monte Carlo simulation with the Cole-Cole, Dias, Debye decomposition and Shin models. Metasedimentary rocks with a well-defined schistosity and pyrite alteration produce higher chargeability peaks than pyrite-poor or silicified samples. The characteristic relaxation time is also inversely related to the observable quantity of finegrained (1 to 100 microns) pyrite per unit area. Metasedimentary rocks of Canadian Malartic with a pyrite content of 1 to 5% are commonly associated with gold contents above 1 ppm, and they produce a chargeability peak at short relaxation times (0.01 to 0.1 s). Nonmineralized rocks with fewer, larger pyrite grains produce a chargeability peak at longer relaxation times (0.1 to 10 s). Spectral induced polarization may be the key in defining the electric footprint of the Canadian Malartic and similar disseminated gold deposits, where high gold grades are associated with finely disseminated sulphides. 12:10 – 12:30

Goodbye and prizes

12:30 – 13:30

Lunch and individual departures

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Short course Program Saturday 4 June

Day 1 9:00 – 9:15 9:15 – 10:00

Welcome Theory of IP mechanisms Andreas Hördt (TU Braunschweig)

10:00 – 10:45

Acquisition and processing of field data – time domain Gianluca Fiandaca (Aarhus University)

10:45 – 11:00 11:00 – 13:00

Break Acquisition of time domain IP data (in the field) Supervision by: Pradip Kumar Maurya (Aarhus University)

13:00 – 13:45 13:45 – 14:30

Lunch Introduction to Aarhus Workbench for IP processing Pradip Kumar Maurya (Aarhus University)

14:30 – 17:00

Processing of the data acquired during the short course Students working on their own – with supervision

Sunday 5 June

Day 2 9:00 – 9:45

Inversion of IP data Gianluca Fiandaca (Aarhus University)

9:45 – 10:45

Inversion of the data acquired during the short course Students working on their own – with supervision

10:45 – 11:00 11:00 – 13:00

Break Inversion of the data acquired during the short course Students working on their own – with supervision

13:00 – 13:45 13:45 – 14:30

Lunch IP for landfill characterization and environmental problems Torleif Dahlin (Lund University)

14:30 – 15:15

Acquisition and processing of field data – frequency domain Adrián Flores Orozco (TU-Wien)

15:15 – 16:45

IP in hydrogeophysics and lab measurements Andreas Weller (Institut für Geophysik, TU Clausthal)

16:45 – 17:00

End and good bye

Adrian Adrian Alex Anaïs Anastasia Andi Andrea Andreas Andreas Andreas Andrey Arne Asgeir Benoît Björn Bülent Carl‐Axel Carole Catherine Charles Chi Christian David Doug Egon Esben  Estella Fatima Feras Frederic Fredrik

Flores Orozco Mellage Furman Brethes Solovieva Pfaffhuber Viezzoli Hördt Kemna Weller Tarasov Bargheer Lysdahl Texier Heincke Tezkan Triumf Kaouane Truffert Lafreniere‐Berube Zhang Camerlynck Dotse Wemegah Oldenburg Zimmermann Auken Atekwana RazaviRad Abdulsamad Nguyen Nyqvist

IP2016 ‐ List of Participants [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]‐bs.de [email protected]‐bonn.de [email protected]‐clausthal.de [email protected] [email protected] [email protected] [email protected]‐instruments.com [email protected] [email protected]‐koeln.de carl‐[email protected] [email protected] [email protected]‐instruments.com charles.lafreniere‐[email protected] [email protected] [email protected] [email protected] [email protected] [email protected]‐juelich.de [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

TU‐Wien University of Waterloo Technion GEUS Moscow State University NGI Aarhus Geophysics TU Braunschweig University of Bonn TU Clausthal Saint‐Petersburg State University Bargheer Geophysics Norwegian Geotechnical Institute IRIS INSTRUMENTS GEUS University of Cologne Sveriges Geologiska Undersökning CEREMA Normandie Centre IRIS INSTRUMENTS Ecole Polytechnique Montreal The University of Kansas UPMC‐UMR Metis KNUST University U of British Columbia Forschungszentrum Jülich GmbH HGG, Aarhus University Oklahoma State University Yazd university UPMC‐UMR Metis University of Liege Guideline Geo

Gianluca Hamza Hanna Hannah Hasan Helle Hermann Idit Ingelise Ivan J.A. (Sander) Jakob Jakob Jana Jean Jesper Jimmy Jukka‐Pekka Juliane Julien Karen  Katharina Kim Konstantin Kristine  Lee Lichao Line Luca Malcolm Manuel Marc Mats

Fiandaca Abou Rafea Leväniemi Langenbach Aktarakci Holm Stebner Shefer Møller Yelamos Vela Huisman Juul Larsen Gallistl Börner Bernard Bjergsted Pedersen  Adcock Kujasalo Adrian Gance Engell Dalsgaard Bairlein Frankcombe Titov Albers Olsen Slater Liu Meldgaard Madsen Peruzzo Ingham Gabler Seidel Thörnelöf [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]‐koeln.de [email protected]

[email protected] hamza‐[email protected] [email protected] [email protected]‐koeln.de [email protected] [email protected] [email protected]‐bs.de [email protected] [email protected] [email protected] [email protected]‐juelich.de [email protected] [email protected] [email protected]‐freiberg.de [email protected]‐instruments.com [email protected] [email protected] jukka‐[email protected] [email protected]‐koeln.de [email protected]‐instruments.com [email protected] [email protected]‐bs.de [email protected] [email protected] HGG, Aarhus University Wintershall Norge AS Geological Survey of Finland University of Cologne ADVANCED GEOSCIENCES EUROPE SL HGG, Aarhus University Institute for Geophysics and Extraterrestrial Physics Technion GEUS Aarhus University, HGG Forschungszentrum Juelich GmbH HGG, Aarhus University TU Wien TU Bergakademie Freiberg IRIS INSTRUMENTS HGG, Aarhus University Guideline Geo Geological Survey of Finland University of Cologne IRIS INSTRUMENTS HGG, Aarhus University TU Braunschweig, IGEP ExploreGeo St. Petersburg State University Alectia Rutgers University Newark HGG, Aarhus University Department of Geoscience, Aarhus University IDEX France Victoria University of Wellington GuidelineGEO  University of Cologne Geological Survey of Sweden Deler plads

Matteo Matthias Max Maximilian Michael Michel Mike Myriam Myriam Nick Nikolaj Nimrod Norbert Orlando Per‐Ivar Pernille Peter Peter Philippe Pradip Sara Sara Sarah Seogi Shogo Solomon Sophie  Sven Søren Tamar Tamara Theis Raaschou Thorkild

Rossi Halisch Halkjær Weigand Tauchnitz Chouteau Hoversten Lajaunie Schmutz Williams Foged Schwartz Klitzsch Leite Olsson Aabye Marker Kowalczyk Thomsen Leroy Maurya Bazin Johansson Hupfer Kang Komori Ehosioke Maloteau Herlitz Bjørn Shalem Pilawski Andersen Rasmussen

[email protected] [email protected]‐hannover.de [email protected] [email protected]‐bonn.de [email protected]‐geoservices.com [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]‐aachen.de [email protected]‐instruments.com per‐[email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]‐hannover.de [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

Lund University, LTH Leibniz Institute for Applied Geophysics (LIAG) Ramboll University of Bonn Terratec Geophysical Services École Polytechnique Chevron EOST ‐ University of Strasbourg  ADERA ‐ BxINP‐EA4592 High Power Exploration (HPX) Aarhus University, HGG Catholic University of Louvain RWTH Aachen University IRIS INSTRUMENTS Lund University DTU Ocean Floor Geophysics Inc. Rambøll BRGM HGG, Aarhus University NGI Lund University Leibniz Institute for Applied Geophysics University of British Columbia Geological Survey of Japan University of Liege ULg AguaEx ALECTIA Technion University of Liège VIA University College Luleå Univerersity of Technology

Holm

Helle Nikolaj Foged

Chouteau

Frankcombe 

Michel

Kim 

Har kone med til middagen:

Bording  Archer Martin Radic Højbjerg Søltoft Dahlin Jensen Boesen Zhang Gao

Thue  Tim  Tina Tino Toke Torleif Tue Zeyu Zhan

[email protected] [email protected]

[email protected]

[email protected] [email protected]‐geophys.co.uk [email protected] [email protected]‐online.de [email protected] [email protected] [email protected] [email protected] [email protected]‐juelich.de

Départ. Génies CG&M; École Polytechnique ExploreGeo

HGG, Aarhus University

HGG, Aarhus University Reid Geophysics Limited BGR  Radic Research Aarhus GeoSoftware Lund University HGG, Aarhus University Southwest Petroleum University Forschungszentrum Jülich

en med Søren Bjørn, men skal have et navneskilt

Errata: In the abstracts PA08 should be A05, whereas A05 should be PA08.

Abstracts from session A

Induced polarization and pore radius – a discussion Andreas Weller

Zeyu Zhang

Lee Slater

Institut für Geophysik, TU Clausthal Arnold-Sommerfeld-Str.1, 38678 Clausthal-Zellerfeld, Germany [email protected]

Southwest Petroleum University Institute of Earth Science and Technology Chengdu, China [email protected]

Rutgers University Dpt. Earth and Environm. Sci. Newark, New Jersey, USA [email protected]

Sabine Kruschwitz

Matthias Halisch

Bundesanstalt für Materialforschung und –prüfung Unter den Eichen 87, 12205 Berlin, Germany [email protected]

Leibniz-Institut für Angewandte Geophysik Stilleweg 1, 30655 Hannover, Germany [email protected]

SUMMARY Permeability estimation from spectral induced polarization (SIP) measurements is based on a fundamental premise that the characteristic relaxation time (τ) is related to the effective hydraulic radius (reff) controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We examine the link between τ and reff for an extensive database of sandstone samples where mercury porosimetry data confirm that reff is reliably determined from a modification of the HagenPoiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of 1 or 2 distinct representative diffusion coefficients but instead demonstrates strong evidence for 6 orders of magnitude of variation in an apparent diffusion coefficient that is well correlated with both reff and the specific surface area per unit pore volume (Spor). Two scenarios can explain our findings: (1) the length-scale defined by τ is not equal to reff and is likely much longer due to the control of pore surface roughness; (2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g. silica, clays) making up the rock. In either case, the estimation of reff (and hence permeability) is inherently uncertain from SIP relaxation time. Key words: pore radius, mercury intrusion capillary pressure, spectral induced polarization, relaxation time.

another useful method that can be used to estimate the pore size distribution. MICP is a laboratory method. Under favourable conditions, NMR is also applicable in field surveys. Induced Polarization (IP) has been proposed to be another potential method providing access to the pore size distribution. Several authors observed relations between the pore size and different types of relaxation times (e.g. Scott and Barker, 2003; Binley et al., 2005; Kruschwitz et al. 2010). It is difficult to explain all these observations by a uniform physical model. Instead of a pore size distribution, a so-called characteristic pore size is assumed. Most authors prefer to use the dominant pore size determined from MICP that corresponds to the pressure of maximal incremental mercury intrusion. Similarly, a characteristic relaxation time is assumed, which can be determined by different procedures. The resulting time constant from fitting procedures related to models of the Cole-Cole type is a widely used approach. Others use the mean relaxation time resulting from Debye decomposition (Nordsiek and Weller, 2008). In other approaches, if the measured IP spectra show a maximum in the curves of imaginary part of conductivity or the phase angle the frequency of the maximum is simply transformed into a relaxation time (Scott and Barker, 2003; Revil et al., 2015). The latter approach is quite simple because it does not require any fitting procedure. We used this approach for a set of sandstone samples that has been investigated in different labs. All IP spectra show a maximum of imaginary part of conductivity inside the investigated frequency interval between 2 mHz and 100 Hz. The effective hydraulic radius of this set of samples has been determined from permeability and formation factor. We evaluate whether any relation between characteristic relaxation time and effective hydraulic radius exists.

METHOD INTRODUCTION The key parameters for reservoir characterization are porosity and permeability. A variety of field, logging and laboratory methods provide porosity. Permeability can be determined by gas flow measurements in the lab. Permeability prediction in a field or logging survey is based on correlations to other measurable parameters. Beside porosity, the pore size is an important parameter that is closely related to permeability. However, the determination of a reliable value of an effective pore size is a challenging problem. The Mercury Intrusion Capillary Pressure method (MICP) provides the distribution of the pore throat radius. Nuclear Magnetic Resonance (NMR) is IP2016 – 6-8 June, Aarhus, Denmark

1

The simplest model of permeability prediction is based on bundles of uniform capillaries that pervade a solid medium. Based on geometric considerations and considering the Hagen-Poiseuille equation, permeability k can be easily determined by the geometric quantities porosity φ, pore radius r and tortuosity T according to the following equation:

k=

r 2φ . 8T

(1)

The ratio T/φ can be replaced by the formation factor if the electric tortuosity is assumed to equal the hydraulic tortuosity. Equation 1 can be used to determine an effective hydraulic

Induced polarization and pore radius

Weller et al.

radius reff of any sample if permeability and formation factor are known: (2)

A good estimation of reff is a decisive step in permeability prediction because the variation in the formation factor is considerably lower than in reff. A variety of models have recently been proposed to relate a characteristic pore size Λ with a characteristic relaxation time τ0 (Revil et al., 2012; 2015):

τ0 =

Λ2 2 D( + )

(3)

with D(+) being the diffusion coefficient of the ions in the Stern layer. A characteristic relaxation time τpeak can easily be determined from the frequency of the maximum (peak frequency fpeak) of the spectrum of imaginary part of conductivity σ”(f):

τ peak =

1 2πf peak

(4) 10

assuming that a measurable maximum exists inside the investigated frequency range. We equate the effective hydraulic radius reff that is determined from equation 2 to the characteristic pore size Λ. The resulting equation

reff = 2 D( + )τ peak

100

rdom (µm)

reff = 8 Fk .

a fixed diffusion coefficient. The solid red line corresponds to a value of D(+) = 3.8 × 10-12 m²/s that has been proposed by Revil (2013) for clayey material. The dashed line indicates the diffusion coefficient of clean sand with D(+) = 1.3 × 10-9 m²/s (Revil, 2013). Two of our clean sandstone samples (BU12 and F1) fall close to the dashed line. However, the other sample close to the dashed line (ES-14) is an Elbe-sandstone with abundant clay minerals. Some shaly sandstone samples follow the trend of the solid red line. However, a considerable number of samples fall below the solid line. The large scatter in the data points, along with numerous data points falling below the solid red line, does not support the existence of two fixed values of the diffusion coefficient as proposed by Revil (2014).

(5)

1

relates the relaxation time τpeak to the effective hydraulic radius reff. We check the general validity of equation 5 for a set of sandstone samples.

CS samples Bahariya Fm. other sandstones rdom = reff

SAMPLES

RESULTS Most studies regard the dominant pore throat radius (rdom) determined by MICP as a suitable characteristic pore size. The dominant pore throat radius indicates for most samples a slight overestimation of reff (Figure 1). We find for our samples a better agreement between reff and the median pore throat radius r50 determined from MICP. It can be seen from Figure 2 that the deviation from reff becomes less if rdom is replaced by r50. Nevertheless, both r50 and rdom can be regarded as suitable parameters to estimate the effective hydraulic radius reff. The good agreement between r50 and reff enables the evaluation of equation 5 even in the case that no MICP data are available. Figure 3 displays the relation between τpeak and reff in a double logarithmic plot. The red lines indicate the expected curve for

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0.1

1

10

100

reff (µm)

Figure 1. Comparison of reff determined according to equation 2 and the dominant pore throat radius rdom from MICP for a set of sandstone samples. 100

10

r50 (µm)

Our set of sandstone samples originates from several studies including 21 Eocene sandstone samples of the Shahejie formation (CS samples, China, Zhang and Weller, 2014), eight samples of the Cretaceous Bahariya formation (Egypt), and 17 samples from different locations in Germany (Bentheimer, Buntsandstone, Elbe-sandstone, Flechtinger, Green sand, Obernkirchen, Röttbacher, Udelfanger), France (Fontainebleau), Poland (Skala), the UK (Helsby), and Vietnam (Dong Do). All samples are characterized by a measurable maximum in the spectrum of the imaginary part of conductivity. The permeability and the formation factor of all samples are known and the effective hydraulic radius reff has been determined by equation 2. Additionally, MICP measurements and the specific surface area per unit volume (Spor) of most samples are available.

0.1

1 CS samples Bahariya Fm. other sandstones r50 = reff 0.1 0.1

1

10

100

reff (µm)

Figure 2. Comparison of reff determined according to equation 2 and the median pore throat radius r50 from MICP for a set of sandstone samples.

2

Induced polarization and pore radius

Da = 0.782reff1.77 .

CS samples Bahariya other sandstones D(+) = 3.8 µm²/s

1.5

Weller et al.

ES-14

with Da given in µm /s and reff. in µm. Kruschwitz et al. (2010) reported a similar trend for their set of sandstone samples. They determined an apparent diffusion coefficient from the dominant pore throat diameter ddom and the time constant of a generalized Cole-Cole fitting model. The resulting graph indicates the proportionality

BR5 GR-1

D(+) = 1300 µm²/s 1 F1

BH7

Ska GR1

BE

1.68 Da ∝ d dom

Ud

BU12

log(reff in µm)

(7)

2

Roett

0.5

OK

OK-4

0

FL NS2/2R

-0.5

(8)

with a similar exponent. Figure 5 displays the relation between the specific surface area per unit pore volume Spor and the apparent diffusion coefficient Da. An increasing specific internal surface is related to a decrease in Da.

Bu-1

1000 BU3

-1 -2.5

-2

-1.5

-1

-0.5

0

0.5

100

1

Figure 3. Comparison between τpeak and reff in a double logarithmic plot for a set of sandstone samples.

Da (µm2/s)

log(τpeak in s) 10

1

1000 0.1

CS samples Bahariya other sandstones Da = 49.4 (Spor)-1.31

100

Da (µm2/s)

0.01

10

0.1

1

10

100

1000

Spor (1/µm) 1

Figure 5. Relation between specific surface area Spor and apparent diffusion coefficient Da for a set of sandstone samples.

CS samples Bahariya other sandstones Da = 0.782 (reff)1.77

0.1

DISSCUSSION

Da = 3.8 µm²/s

0.01

Da = 1300 µm²/s 0.1

1

10

100

reff (µm)

Figure 4. Relation between effective hydraulic radius reff and apparent diffusion coefficient Da for a set of sandstone samples. Assuming the validity of equation 5, an apparent diffusion coefficient Da can be defined:

Da =

reff2 2τ peak

.

(6)

This apparent diffusion coefficient, which can be determined for each sample, is presented as a function of reff in Figure 4. It varies over a range of nearly six orders of magnitude. A remarkable trend is observed: the increasing effective hydraulic radius is accompanied by an increasing apparent diffusion coefficient. The fitting equation reads

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The wide variation in apparent diffusion coefficient and its dependence on effective hydraulic radius and the specific surface area raises doubt regarding the applicability of equation 5 for estimating pore geometric characteristics of sandstone samples. There are two main concerns: (1) The effective hydraulic radius cannot be the relevant pore size for IP relaxation if a nearly constant diffusion coefficient is assumed for the clayey sandstone samples. The diffusion path would be considerably longer than the pore radius for most samples that are displayed below the solid red line in Figure 3. The increasing pore surface roughness, which is reflected by larger values of Spor, generates a considerable surface tortuosity and longer diffusion paths along the pore surface. It can be assumed that the true length of the diffusion path can be determined by IP relaxation time, but this length is not simply related to the effective hydraulic radius. (2) A decrease in the ion mobility and consequently in the diffusion coefficient caused by increasing clay content and increasing specific surface area offers an alternative explanation of the experimental findings. It can be expected that a stronger binding of ions at the surfaces of clay minerals

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Induced polarization and pore radius

dominates the diffusion in smaller pores. A variation of the diffusion coefficient with the type and amount of clay makes the application of equation 5 for estimating reff difficult. A permeability prediction that assumes the validity of equation 5 and a constant diffusion coefficient will only work for those samples that are indicated close to the red lines in Figure 3. In the specific case of the plotted red lines, the apparent diffusion coefficient is close to the assumed diffusion coefficient for either clayey material (solid line) or clean sandstones (dashed line). The majority of samples indicates a diffusion coefficient different from these two fixed values. Most samples with an apparent diffusion coefficient lower than the value of clayey material (D(+) = 3.8 × 10-12 m²/s) are characterized by an effective pore radius smaller than 2 µm and a permeability smaller than 1 mD. Revil et al. (2015) exclude these samples from their approach of permeability prediction based on IP relaxation time and formation factor. The binary binning into clayey material and clean sands has been recently disputed (Revil, 2014; Weller et al., 2014). Our experimental findings do not support the existence of two fixed values of the diffusion coefficient. Considering the varying clay content in our samples, it would be difficult to define a sharp boundary between the two groups. What concentration of clay minerals would be tolerated in a sandstone for it to be referred to as clean sand? In our opinion, a sandstone should be characterized by an effective diffusion coefficient representing a weighting between the different minerals. The data points falling between the two red lines in Figure 3 indicate the existence of sandstone samples with behaviour between clean sand and clayey material. All approaches of permeability prediction that are based on IP relaxation time remain problematic. Sandstone samples that do not indicate a characteristic relaxation time in the investigated frequency cannot be considered. As shown in our study, the relation between IP relaxation time and pore size is far from unique. Alternative approaches, which are based on quadrature conductivity instead of relaxation time, have proved to be successful in permeability prediction of sandstones and unconsolidated material (e.g. Weller et al., 2015).

CONCLUSIONS Our study presents experimental evidence that the effective hydraulic radius, which is a key parameter in permeability prediction, cannot be determined by the IP relaxation time in a direct way. The apparent diffusion coefficient that relates effective hydraulic radius and IP relaxation time varies over six orders of magnitude. The assumption of a constant diffusion coefficient suggests that the true diffusion path is much larger than the effective hydraulic radius. A strongly varying diffusion coefficient has to be assumed if the effective hydraulic radius is accepted to be related to the diffusion length. The practical use of IP relaxation time is strongly restricted if both effective hydraulic radius and diffusion coefficient are variable parameters in sandstone samples.

ACKNOWLEDGMENTS The authors thank Katrin Breede, Henning Schröder, and Nguyen Trong Vu for providing data of their sandstone samples.

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Weller et al.

REFERENCES Binley, A., Slater, L. D., M. Fukes, M., and Cassiani, G., 2005, Relationship between spectral induced polarization and hydraulic properties of saturated and unsaturated sandstone, Water Resources Research., 41, W12417, doi:10.1029/2005WR004202. Kruschwitz, S. F., Binley, A., Lesmes, D., and A. Elshenawy, A., 2010, Textural controls on low-frequency electrical spectra of porous media: Geophysics, 75, 4, WA113–WA123. Nordsiek, S., and Weller, A., 2008, A new approach to fitting induced-polarization spectra: Geophysics, 73, No. 6, F235F245, doi: 10.1190/1.2987412. Revil, A., 2013, Effective conductivity and permittivity of unsaturated porous materials in the frequency range 1 mHz1GHz, Water Resources Research, 49, 306-327, doi: 10.1029/2012WR012700. Revil, A., 2014, Comment on: “On the relationship between induced polarization and surface conductivity: Implications for petrophysical interpretation of electrical measurements” (A. Weller, L. Slater, and S. Nordsiek, Geophysics, 78, no. 5, D315-D325): Geophysics, 79, no. 2, X1-X5. Revil, A., Binley, A., Mejus, L., and Kessouri, P., 2015, Predicting permeability from characteristic relaxation time and intrinsic formation factor of complex conductivity spectra: Water Resources Research, 51, 6672-6700, doi:10.1002/2015WR017074. Revil, A., Koch, K., and Holliger, K., 2012, Is it the grain size or the characteristic pore size that controls the induced polarization relaxation time of clean sands and sandstones?, Water Resources Research, 48, W05602, doi:10.1029/2011WR011561. Scott, J. B., and Barker, R., 2003, Determining pore-throat size in Permo-Triassic sandstones from low-frequency electrical spectroscopy: Geophysical Research Letters, 30(9), 1450, doi:10.1029/2003GL016951. Weller, A., Slater, L., and Nordsiek, S., 2014, Reply to the discussion by A. Revil, Comment on: “On the relationship between induced polarization and surface conductivity: Implications for petrophysical interpretation of electrical measurements” (A. Weller, L. Slater, and S. Nordsiek, Geophysics, 78, no. 5, D315-D325): Geophysics, 79, no. 2, X6-X10. Weller, A., Slater, L., Binley, A., Nordsiek, S., and Xu, S., 2015, Permeability prediction based on induced polarization: Insights from measurements on sandstone and unconsolidated samples spanning a wide permeability range: Geophysics 80, No. 2, D161-D173. Zhang, Z., and Weller, A., 2014, Fractal dimension of porespace geometry of an Eocene sandstone formation: Geophysics, 79, No. 6, D377-D387. doi: 10.1190/geo20140143.1.

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Modeling the evolution of spectral induced polarization during calcite precipitation on glass beads Leroy Philippe

Li Shuai

BRGM Orléans, France [email protected]

Imperial College London, England [email protected]

Jougnot Damien

Revil André

CNRS, UMR 7619 METIS Paris, France [email protected]

SUMMARY When pH and alkalinity increase, calcite frequently precipitates and hence modifies the petrophysical properties of porous media. The complex conductivity method can be used to directly monitor calcite precipitation in porous media because it is very sensitive to the evolution of the pore structure and its connectivity. We have developed a mechanistic grain polarization model considering the electrochemical polarization of the Stern layer surrounding calcite particles. This model depends on the surface charge density and mobility of the counter-ions in the Stern layer. Our induced polarization model predicts the evolution of the size of calcite particles, of the pore structure and connectivity during spectral induced polarization experiments of calcite precipitation on glass beads pack. Model predictions are in very good agreement with the complex conductivity measurements. During the first phase of calcite precipitation experiment, calcite crystals growth, and the inverted particle size distribution moves towards larger calcite particles. When calcite continues to precipitate and during pore clogging, inverted particle size distribution moves towards smaller particles because large particles do not polarize sufficiently. The pore clogging is also responsible for the decrease of the connectivity of the pores, which is observed through the increasing electrical formation factor of the porous medium.

Wu Yuxin

CNRS, UMR 5275 LBNL Le Bourget du Lac, France Berkeley, USA. [email protected] [email protected]

beads packed column. From their imaginary part of complex conductivity data, the evolution of calcite precipitation in porous media was clearly observed. The empirical Cole-Cole model (Cole and Cole, 1941) was used by Wu et al. (2010) to interpret the complex conductivity signature of calcite precipitation in glass beads. However, the lack of physical processes in the Cole-Cole model to interpret the complex conductivity data restricts the understanding of the effects of calcite precipitation on the evolution of the pore structure and connectivity in glass beads column. The induced polarization of calcite precipitates needs to be further clarified using a mechanistic complex conductivity model accounting for the EDL properties and the particle size distribution. In this study, a mechanistic model for the induced polarization of calcite is proposed, which depends on the surface charge density and ions mobility of the counter-ions in the Stern layer and on the particle size distribution. The predictions of the model are compared to the imaginary conductivity data of Wu et al. (2010), and the evolution of the pore structure during calcite precipitation in glass beads is estimated accordingly.

THEORETICAL BACKGROUND AND COMPARISON WITH EXPERIMENTAL DATA We consider a porous medium containing particles, glass beads grains (of millimetric size) and calcite crystals (of micrometric size), and water (subscript “w”). The complex conductivity model is presented at Figure 1.

Key words: calcite precipitation, complex conductivity, Stern layer, particle size, pore clogging.

INTRODUCTION Calcite is one of the most abundant minerals in the earth crust and frequently precipitates when alkalinity and pH increase (Vancappellen et al., 1993). Calcite precipitation modifies the rock porosity, and can have positive or harmful effects for the mechanical and transport properties of porous media. Calcite precipitation in porous media has broad applications in geotechnical engineering for soil strengthening (DeJong et al., 2006) and in environmental studies for the sequestration of heavy metals (Sturchio et al., 1997), radionuclides (Fujita et al., 2004) and CO2 in geological formations (Pruess et al., 2003). However, calcite precipitation can also have undesirable effects such as the decrease of the efficiency and permeability of reactive barriers for the remediation of aquifers (Wilkin et al., 2003). Wu et al. (2010) performed complex conductivity measurements and modeling of calcite precipitation on glass IP2016 – 6-8 June, Aarhus, Denmark

1

Figure 1. Sketch of thecomplex conductivity model of the porous medium. Maxwell-Wagner polarization occurs at the boundary between the different phases (solid, water) possessing different electrical properties. The differential effective medium (DEM) theory (Sen et al., 1981) is used to compute the electrical conductivity of the porous medium according to the conductivity of the particles and liquid. The complex surface

Modeling spectral induced polarization of calcite precipitation

conductivity of the particles of different sizes is calculated considering the superposition principle and using the particle size distribution (PSD) (Leroy et al., 2008). The complex surface conductivity of the particle is computed using the spectral induced polarization model of Leroy et al. (2008) generalized to the electrochemical polarization of different counter-ions at the mineral/water interface. The specific surface conductivity of the particle is calculated considering the superposition of the AC (Stern layer) and DC current densities (diffuse layer) (Figure 2). The distribution of ions in the Stern and diffuse layer of the calcite/water interface is computed using an electrostatic surface complexation model (Li et al., 2016) (Figure 3).

Leroy, P., Li, S., Jougnot, D., Revil, A., Wu, Y.

solution was introduced into the column from the injection port at the middle section to initiate calcite precipitation. The ionic concentrations were diluted once inside the column due to the equal volume mixing of these two solutions (initial ionic concentrations divided by two). The flow rate of both solutions was kept at 36 L min-1 for the duration of the experiment, which continued for 12 days past injection of Na2CO3. In the complex conductivity experiment of Wu et al. (2010), sodium ion is the dominating cation in solution. The evolution of the modeled imaginary conductivity as a function of frequency and time (in days) is in good agreement with the measurements of Wu et al. (2010) (Figure 4). The model parameters are presented at Table 1. Table 1. Parameters of our complex conductivity model. Parameters Values Ions mobility in the Stern layer (m2 s-1 V-1) 5.7×10-8 Surface charge density in the Stern layer (C m-2) 0.1 Initial cementation exponent of the particles 1.5 Initial glass beads porosity 0.30 Bulk pore water conductivity (S m -1) 0.356

Figure 2. Sketch of the complex conductivity model of Leroy et al. (2008) for particles of different sizes surrounded by discontinuous Stern layers and overlapping diffuse layers in a saline aqueous solution. Figure 4. Imaginary conductivity spectra of calcite precipitation on glass beads pack as a function of time in days before the pore clogging by the calcite precipitates (a.) and during the pore clogging by the calcite precipitates (b.). The predictions of the complex conductivity model are represented by the lines and the symbols represent the imaginary conductivity measurements of Wu et al. (2010). The evolution of the modeled particle size distribution during the precipitation experiment is presented at Figure 5.

Figure 3. The basic Stern model used by Li et al. (2016) to describe the calcite/water interface (calcite (1 0 4) surface) when calcite is in contact with a NaCl and CaCl2 aqueous solution at equilibrium with a pCO2. Wu et al. (2010) monitored calcite precipitation in glass beads pack using spectral induced polarization measurements in the frequency range [0.1 10000 Hz] under controlled laboratory conditions. Their porous medium consisted in smooth glass beads of mean diameter of 3 mm packed in a transparent plexiglass column 8.4 cm long and 2.54 cm wide. The measured porosity was equal to 30%. Wu et al. (2010) mixed two aqueous electrolytes, one containing CaCl2 at a concentration of 26.2 milli mol L-1 (mM) (water electrical conductivity 0.635 S m -1), and the other containing Na2CO3 at a concentration of 29 mM (water electrical conductivity 0.567 S m-1) at a fixed pH value of 9 to favor calcite precipitation in glass beads column. The saline CaCl2 solution was injected through the bottom of the column to establish an equilibrated baseline state. Following this, a second stream of Na 2CO3

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Figure 5. Evolution of the computed calcite particle size distribution during calcite precipitation experiments. The quadrature conductivity measurements of Wu et al. (2010) were inverted using the Matlab code developed by Florsch et al. (2014) to obtain the discretized relaxation time and particle size distribution. Florsch et al. (2014) used generalized relaxation basis functions (such as the generalized Cole–Cole function) and the L-curve approach to optimize the damping parameter required to get smooth and realistic inverse solutions (read Florsch et al., 2014 for further information relative to the inversion procedure). The relaxation time distribution was converted to the particle size distribution using the surface mobility value of the counter-ions in the Stern layer.

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Modeling spectral induced polarization of calcite precipitation

The smallest particles size information is missing due to lack of the complex conductivity measurements at high frequency (> 10 kHz). Before clogging (referred to phase 1 in Wu et al., 2010, at day 9), the modeled particles size increases as experiment continues (also shown in Figure 5). It is consistent with the visual observations from SEM (scanning electron microscopy) images in the experiment (Wu et al., 2010). The calcite particles increase approximately from less than 1 to 20 µm, as reported by Wu et al. (2010). During the first stage of calcite precipitation, the modeled volume of the pore water decreases due to calcite precipitation (Figure 6). As the calcite precipitation experiment continued over 9 days, the clogging occurred in the sample holder. At the second stage, the formation factor of glass beads increases significantly as shown in Figure 6, from 6.08 to 7 (day 10), 11 (day 11) and 12 (day 12). The changes of the formation factor is due to the loss of connectivity of glass beads pores affected by the clogging even though the porosity of the sample (glass beads, porous medium) has a tiny change. The modeled particle size distribution obtained from the inverted imaginary conductivity spectra (quadrature conductivity) moves towards smaller particles as experiment continues (Figure 4b and Figure 5b). This could be explained by that the large calcite particles created during the clogging process do not play an important role in the complex conductivity spectra (they do not polarize sufficiently) and only smaller particles are the effective ones contributed to the complex surface conductivity. Calcite precipitation induces a smaller pore volume fraction, therefore, a slight increase of the formation factor F. The occurrence of pore clogging may explain the increase of the cement exponent from 1.5 to 2 for glass beads materials, which leads the formation factor F increasing from 6.08 to 12 under the same porosity.

Leroy, P., Li, S., Jougnot, D., Revil, A., Wu, Y.

during the precipitation process were inverted from imaginary conductivity data. Model predictions are in very good agreement with the measured imaginary conductivity spectra and the microscopy observations of the evolution of the pore structure and connectivity during calcite precipitation. The tangential mobility of the counter-ions in the Stern layer is found to be similar to their mobility in bulk water. The kinetic of calcite precipitation in glass beads column is described by considering two different stages, one before the pores clogging where modeled particle size distribution moves to larger particles due to the growth of calcite crystals, and another during the pores clogging where only the smaller particles influence the polarization response. During the first stage of calcite precipitation, the electrical formation factor of glass beads remains constant and the modeled pore water volume decreases due to calcite precipitation. During the second stage of calcite precipitation, the electrical formation factor of glass beads increases considerably because of the loss of pores connectivity due to the clogging process and the modeled pore water volume remains constant. These observations can be explained by the aggregation of the calcite precipitates merging at the surface of glass beads, which can significantly alter the connectivity and current paths of the pore space of glass beads even though the total porosity remains nearly unchanged. This study shows that spectral induced polarization can be an efficient and cost effective geophysical method to monitor non-invasively and continuously calcite precipitation in porous media because of its sensitivity to polarization processes occurring at the mineral/water interface. A mechanistic induced polarization model is also necessary to interpret induced polarization experiments in terms of evolution of particle size distribution, pores structure and connectivity during calcite precipitation.

ACKNOWLEDGMENTS

Figure 6. Computed relative volume of the fluid to the volume of the porous medium and relative volume of the bulk water to the volume of the fluid mixture and formation factors F and F’ changes during the calcite precipitation experiment of Wu et al. (2010). The pore clogging happens at day 9, the formation factor of the porous medium (glass beads) changes dramatically.

CONCLUSIONS A mechanistic complex conductivity model was used to interpret spectral induced polarization experiments of calcite precipitation on millimetric glass beads containing CaCl2 and Na2CO3 aqueous electrolytes in equal concentration. The conductivity model considers the electrochemical polarization of the Stern layer surrounding calcite particles and depends on the surface site density and surface mobility of counter-ions in the Stern layer, which were kept constant during the simulation of the precipitation experiment. The particle size distribution, porosity and electrical formation factor evolution

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This work was supported by the BRGM-Carnot Institute and the H2020 CEBAMA project. We are indebted to Dr. Mohamed Azaroual and Francis Claret for their support through the BRGM-Carnot Institute. Dr. Shuai Li postdoctoral grant was supported by the BRGM-Carnot Institute. We thank Dr. Nicolas Devau for fruitful discussions. REFERENCES Cole, K.S. and Cole, R.H., 1941, Dispersion and absorption in dielectrics. I. Alternating current characteristics, The Journal of Chemical Physics, 9, 341-351. DeJong, J.T. et al., 2006, Microbially induced cementation to control sand response to undrained shear, Journal of Geotechnical and Geoenvironmental Engineering, 132, 13811392. Florsch, N. et al., 2014, Inversion of generalized relaxation time distributions with optimized damping parameter, Journal of Applied Geophysics, 109, 119-132. Fujita, Y. et al., 2004, Strontium incorporation into calcite generated by bacterial ureolysis, Geochimica Et Cosmochimica Acta, 68, 3261-3270.

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Modeling spectral induced polarization of calcite precipitation

Hanai, T., 1968, Electrical properties of emulsions. in Emulsions Science, pp. 354-477, ed. Sherman, P. Academic Press, New York. Leroy, P. et al., 2008, Complex conductivity of watersaturated packs of glass beads, Journal of Colloid and Interface Science, 321, 103-117. Li, S. et al., 2016, Influence of surface conductivity on the apparent zeta potential of calcite, Journal of Colloid and Interface Science, 468, 262-275

Leroy, P., Li, S., Jougnot, D., Revil, A., Wu, Y.

reflectivity studies, Geochimica Et Cosmochimica Acta, 61, 251-263. Vancappellen, P. et al., 1993, A Surface Complexation Model of the Carbonate Mineral-Aqueous Solution Interface, Geochimica Et Cosmochimica Acta, 57, 3505-3518. Wilkin, R.T. et al., 2003, Long-term performance of permeable reactive barriers using zero-valent iron: Geochemical and microbiological effects, Ground Water, 41, 493-503.

Pruess, K. et al., 2003, Numerical Modeling of aquifer disposal of CO2, Spe Journal, 8, 49-60.

Wu, Y. et al., 2010, On the complex conductivity signatures of calcite precipitation, Journal of Geophysical ResearchBiogeosciences, 115, 1-10.

Sen, P.N. et al., 1981, A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads, Geophysics, 46, 781-795.

.

Sturchio, N.C. et al., 1997, Lead adsorption at the calcite-water interface: Synchrotron X-ray standing wave and X-ray

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Field evaluation of wideband EIT measurements M. Kelter

J. A. Huisman*

E. Zimmermann

H. Vereecken

Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, Germany [email protected]

Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, Germany [email protected] * Presenting author

Central Institute for Engineering, Electronics and Analytics, Electronic Systems (ZEA-2), Forschungszentrum Jülich GmbH, Germany [email protected]

Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, Germany [email protected]

SUMMARY Field applications of wideband electrical impedance tomography (EIT) remain challenging, despite recent advances to obtain images of the complex electrical conductivity with sufficient accuracy for a broad range of frequencies (mHz – kHz). The aim of this study is to evaluate to what extent recent improvements in the inversion and processing of wideband field EIT measurements have improved the accuracy and spectral consistency of images of the real and imaginary part of the electrical conductivity. In a first case study, timelapse surface EIT measurements were performed during an infiltration experiment to investigate the spectral complex electrical conductivity as a function of water content. State-of-the-art data processing and inversion approaches were used to obtain images of the complex electrical conductivity in a frequency range of 100 mHz to 1 kHz, and integral parameters were obtained using Debye decomposition. Results showed consistent spectral and spatial variation of the phase of the complex electrical conductivity in a broad frequency range, and a complex dependence on water saturation. In a second case study, borehole EIT measurements were made in a well-characterized gravel aquifer. These measurements were inverted to obtain broadband images of the complex conductivity after correction of inductive coupling effects using a recently developed procedure relying on a combination of calibration measurements and modelbased corrections. The inversion results were spatially and spectrally consistent in a broad frequency range up to 1 kHz only after removal of inductive coupling effects. Key words: electrical impedance tomography, inductive coupling, wideband measurements

INTRODUCTION Laboratory measurements of the complex electrical conductivity in a broad frequency range (i.e. mHz to kHz) using spectral induced polarization (SIP) measurements have shown promise to characterize important hydrological properties (e.g. hydraulic conductivity) and biogeochemical processes (Kemna et al. 2012). However, translating these findings to field applications remains challenging, and significant improvements in spectral electrical impedance tomography (EIT) are still required to obtain images of the complex electrical conductivity in a broad frequency range (mHz to kHz) with sufficient accuracy in the field. Many field investigations with EIT are limited to frequencies below 10 Hz (e.g. Flores-Orozco et al., 2011), mostly because the higher frequencies are strongly affected by IP2016 – 6-8 June, Aarhus, Denmark

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electromagnetic coupling, especially inductive coupling, when long multicore cables are used. In order to remove inductive coupling effects from spectral EIT measurements, Zhao et al. (2013, 2015) proposed a combination of calibration measurements and model-based corrections to account for inductive coupling within and between multicore cables. The aim of this study is to evaluate to what extent recent improvements in data correction, inversion, and processing of wideband field EIT measurements have improved the accuracy and spectral consistency of images of the real and imaginary part of the electrical conductivity. For this, we use data from two case studies where spectral EIT measurements were used to i) monitor infiltration and ii) characterize aquifer heterogeneity.

METHODS AND RESULTS We made EIT measurements in the mHz to kHz frequency range using a modified version of the data acquisition system described in Zimmermann et al. (2008) that also allows reciprocal measurements. The system has 40 channels, which can be used for current as well as potential measurements. Potentials are measured simultaneously at all electrodes relative to system ground, which allows the calculation of arbitrary voltage pairs in post-processing. Case study I: infiltration experiment Time-lapse surface EIT measurements were performed during an infiltration experiment to investigate the spectral complex electrical conductivity as a function of water content. We used a transect of 28 non-polarizable Cu/CuSo4 electrodes with an electrode spacing of 25 cm. Wetted sponges were used to obtain a homogeneous contact to the uneven soil surface. A considerable advantage of this type of electrode is their large contact area with the soil surface, which reduces the electrode contact impedance. The electrodes were connected to the EIT system using individual 5 m long twisted-pair cables as used in laboratory EIT experiments. Therefore, inductive coupling between cables was not considered in this first case study. Inversion of the EIT data was done using the 2.5 D inversion code CRTomo developed in Kemna (2000). This code uses log-transformed magnitude and phase as data and iteratively minimizes the error-weighted root mean square error between data and model until convergence criteria have been reached for each frequency independently. EIT measurements were filtered and processed as outlined in Kelter et al. (2015), and the integral spectral parameters (i.e. normalized total chargeability and mean relaxation time) were obtained using Debye decomposition of the complex electrical resistivity spectra for each pixel of the inverted tomograms. Data error was obtained from filtered reciprocal measurements where current and potential electrodes were exchanged.

Field evaluation of wideband EIT measurements

Figure 1 shows a compilation of spectral complex electrical imaging results obtained during and after infiltration. The results clearly show that the electrical conductivity, the normalized total chargeability, as well as the mean relaxation time all increased with increasing soil water content. For all three integral spectral parameters, a clear maximum is obtained for the measurement where stationary flow conditions were assumed (20131003-2), whereas minimum values are obtained for the first measurement in driest conditions. The imaging results also indicate a two layered soil in both the electrical conductivity and normalized total chargeability images. Figure 2 presents inverted phase spectra of complex electrical conductivity for selected pixels. The consistency of the spectra across a broad frequency range is evident, and this confirms the feasibility of wideband spectral EIT for near-surface applications with short cable lengths where inductive coupling can be neglected. Case study II: Aquifer characterization Wideband borehole EIT measurements were made to investigate the well-characterized heterogeneous unconfined aquifer at the Krauthausen test site (Müller et al. 2010). The base of the aquifer is located at a depth of 11 to 13 meter and consists of intermitting layers of clay and silt, whereas the upper part of the aquifer consists of 3 layers with Rur sediments at the top followed by the upper and lower Rhine sediments. In contrast to the first case study, multicore electrode chains as developed in Zhao et al. (2013) were used with an electrode separation of 1 m. EIT measurements were performed using two electrode chains in borehole B75 and B76 using both single well and cross-well electrode configurations. Therefore, calibration measurements and numerical modelling of the cable layout of the electrode chains were used in order to correct for inductive coupling effects. The details of this correction procedure are described in Zhao et al. (2015). Processing and inversion of the measured impedance data was identical to the first case study. Analysis of reciprocal measurements showed that data error was very similar for uncorrected and corrected data. This confirms that errors associated with inductive coupling are of reciprocal nature, as already postulated by Zhao et al. (2015). Figure 3 shows inversion results for the imaginary part of the electrical conductivity at four frequencies for uncorrected and corrected data. In the low frequency range (until 10 Hz), the images of the uncorrected and the corrected data show very similar results, whereas the images of the uncorrected data show increasingly strong artefacts for frequencies higher than 10 Hz. In contrast to the erratic images of the uncorrected data, the corrected data shows the same structures that are present in the lower frequencies and even an increase in the contrast for the high frequencies, indicating the value of spectral information in complex electrical imaging. Spectral electrical images were compared with estimates of clay content and gravel content determined from material extracted during drilling of the wells and showed good agreement.

CONCLUSIONS In this study, we presented wideband EIT measurements obtained in two field studies. The results show that the use of dedicated EIT measurement equipment in combination with calibration measurements and model-based correction methods in addition to appropriate data processing and inversion strategies allow the accurate determination of spectral electrical properties in the mHz to kHz frequency range. In particular, spatially and spectrally consistent IP2016 – 6-8 June, Aarhus, Denmark

Kelter, Huisman, Zimmermann and Vereecken

inversion results were obtained up to a frequency of 1 kHz during an infiltration experiment, which illustrated the ability of spectral EIT to monitor near-surface vadose zone processes using surface electrodes and short cables. In the case of aquifer studies that extend beyond the top few meters of the soil, longer cables are required that may lead to unwanted inductive coupling effects. In this study, it was shown that a previously developed combination of calibration measurements and model-based corrections successfully removed inductive coupling effects and provided spatially and spectrally consistent electrical properties up to 1 kHz. Overall, we conclude that wideband spectral EIT has matured to such an extent that routine applications are becoming feasible.

ACKNOWLEDGMENTS We gratefully acknowledge the SFB/TR32 "Patterns in SoilVegetation-Atmosphere Systems: monitoring, modeling, and data assimilation“, which is funded by the Deutsche Forschungsgemeinschaft (DFG) for financial support. REFERENCES Flores Orozco, A., Williams, K.H., Long, P.E., Hubbard, S.S., and Kemna, A., 2011. Using complex resistivity imaging to infer biogeochemical processes associated with bioremediation of an uranium-contaminated aquifer. Journal of Geophysical Research, 116: G03001. M. Kelter M., Huisman, J.A., Zimmermann, E. Kemna, A. Vereecken, H., 2015, Quantitative imaging of spectral electrical properties of variably saturated soil columns, Journal of Applied Geophysics, 123, 333 - 344. Kemna, A. (2000). Tomographic inversion of complex resistivity – theory and application. Ph.D. thesis, RuhrUniversity of Bochum, Germany. Kemna, A., Binley, A., Cassiani, G., Niederleithinger, E., Revil, A., Slater, L., and Zimmermann, E., 2012. An overview of the spectral induced polarization method for near-surface applications. Near Surface Geophysics, 10(6), 453-468. Müller, K., Vanderborght, J., Englert, A., Kemna, A., Huisman, J. A., Rings, J., & Vereecken, H., 2010. Imaging and characterization of solute transport during two tracer tests in a shallow aquifer using electrical resistivity tomography and multilevel groundwater samplers. Water Resources Research, 46(3), W03502. Zhao, Y., Zimmermann, E., Huisman, J.A., Treichel, A., Wolters, B., van Waasen, S., Kemna, A., 2013. Broadband EIT borehole measurements with high phase accuracy using numerical corrections of electromagnetic coupling effects. Measurement Science Technology, 24 (8), 085005. Zhao, Y., Zimmermann, E., Huisman, J.A., Treichel, A., Wolters, B., van Waasen, S., Kemna, A., 2015. Phase correction of electromagnetic coupling effects in crossborehole EIT measurements. Measurement Science Technology, 26 (1), 015801. Zimmermann, E., Kemna, A., Berwix, J., Glaas, W., Vereecken, H., 2008. EIT measurement system with high phase accuracy for the imaging of spectral induced polarization properties of soils and sediments. Measurement Science Technology, 19, 094010.

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Figure 1. Spectral complex electrical inversion results in terms of DC-conductivity, normalized total chargeability, and mean relaxation time, obtained by pixel-wise debye-decomposition for all spectral electrical measurements during the irrigation experiment. Black dots indicate the positions of the electrodes.

Figure 2. Inverted phase spectra of complex electrical conductivity, obtained for certain pixels at a lateral position of 3 m along the profile and depths of 20 cm (left) and 60 cm (right) for representative measurement dates. Solid lines illustrate the obtained Debye-decomposition fits.

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Figure 3. EIT imaging results for frequencies of 2, 10, 100 and 1000 Hz for uncorrected (top) and corrected (bottom) data in terms of the imaginary part of the complex electrical conductivity.

3D TEM-IP inversion workflow for galvanic source TEM data Seogi Kang

Douglas W. Oldenburg

University of British Columbia University of British Columbia 6339 Stores Rd., Vancouver, Canada 6339 Stores Rd., Vancouver, Canada [email protected] [email protected]

SUMMARY Electrical induced polarization (EIP) surveys have been used to detect chargeable materials in the earth. For interpretation of the time domain EIP data, the DC-IP inversion method, which first invert DC data (on-time) to recover conductivity, then inverts IP data (off-time) to recover chargeability, has been successfully used especially for mining applications finding porphyry deposits. It is assumed that the off-time data are free of EM induction effects. When this is not the case, an EMdecoupling technique, which removes EM induction in the observation, needs to be implemented. Usually responses from a half-space or a layered earth are subtracted. Recent capability in 3D TEM forward modelling and inversion allows us to revisit this procedure. Here we apply a 3D TEM-IP inversion workflow to the galvanic source example. This includes three steps: a) invert DC and early time channel TEM data to recover the 3D conductivity, b) use that conductivity to compute the TEM response at later time channels. Subtract this fundamental response from the observations to generate the IP response, and c) invert the IP responses to recover a 3D chargeability. This workflow effectively removes EM induction effects in the observations and produces better chargeability and conductivity models compared to conventional approaches. Key words: Induced polarization, EM-decoupling, galvanic source, time domain EM, 3D inversion

INTRODUCTION The electrical conductivity of earth materials can be frequency dependent with the effective conductivity decreasing with decreasing frequency due to the buildup of electric charges that occur under the applied electric field. Effectively, the rock is electrically chargeable. Controlled-source electromagnetic (EM) methods excite the earth using either galvanic (a generator attached to two grounded electrodes) or inductive source (arising from currents flowing in a wire loop). A typical EIP survey layout (Siegel, 1959) is shown in Figure 1. Grounded wire

Figure 1. Conceptual diagram of a ground-based galvanic source with half-duty cycle current waveform. It consists of grounded electrodes carrying a current waveform (like the square wave shown) and electrodes to measure IP2016 – 6-8 June, Aarhus, Denmark

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voltage differences. When the ground is chargeable the received voltage looks like that in Figure 2. The decay in the off-time is the IP effect. To interpret observed IP data, a twostage inversion is usually deployed (Oldenburg and Li, 1994). The first step is to invert late on-time data (V0) using a DC inversion to obtain the background conductivity. The second step is to use the obtained conductivity to generate a sensitivity function, and then invert late off-time data (Vs); this is often called DC-IP inversion.

Figure 2. A typical overvoltage effects in EIP data. Although application of this method has been successful, a main concern is the second step. The time decaying fields are assumed to be purely the result of IP phenomena and any EM induction effects in the data are ignored. This assumption can be violated when the earth has a significant conductivity and EM coupling can remain even in the late off-time. Removing the effects of EM induction from the measured data is referred to as EM-decoupling and it has been a focus of attention for many years. Most analyses have used simple earth structures: half-space and layered earth to ameliorate its effects (Wynn and Zonge, 1975). However, with our current capability to handle 3D forward modelling and inversion it is timely to revisit this issue. In a recent work (Kang and Oldenburg, 2016), we developed a workflow for inverting airborne IP data using inductive sources. This involved three main steps: a) inverting early time TEM data to recover a 3D conductivity, b) EM-decoupling (forward modelling the EM response and then subtracting it from the observations), and c) IP inversion to recover pseudochargeability distribution at each time channel. The current problem of inverting IP data using grounded sources follows the same workflow but some aspects are greatly simplified because EIP measures data when electric fields, and charge accumulations, have reached a steady state. This provides another data set from which information about the electrical conductivity can be extracted. A major difference between conventional EIP inversion and our approach is the use made of early time channels in the EIP data. In conventional work these have been considered as “noise” and hence been thrown away. However, we consider these as “signal” to recover conductivity. In this study, we apply a 3D TEM-IP inversion workflow to the synthetic galvanic source example (gradient array). This will include the three steps in the workflow listed above but the first step is

3D TEM-IP inversion workflow

altered so that we invert the DC data, and early time channels of TEM data, to recover the 3D conductivity.

SEPARATION OF EM AND IP RESPONSE Assuming the earth has chargeable material, the observed responses from any TEM survey has both EM and IP responses. To be more specific, we first define the complex conductivity in the frequency domain as (1) is the conductivity at infinite frequency, and  is where angular frequency (rad/s). For the Cole-Cole model from Pelton et al. (1978), , (2) where  is intrinsic chargeability,  is time constant, and c is frequency dependency. Following Smith et al. (1988), the observed datum including both EM and IP effects can be defined as , (3) where dF and dIP are respectively the fundamental and IP responses. Here the fundamental response is , where F[] is a Maxwell’s operator; this takes the conductivity and computes EM responses without IP effects. Note that when =0. A main goal of our 3D TEM-IP inversion workflow is to evaluate the dF and dIP components. To illustrate the challenge, we perform a simple TEM forward modelling using a galvanic source as shown in Figure 1. We inject a half-duty cycle rectangular current through a grounded wire. A chargeable body is embedded in the earth. Figure 3 shows the measured voltage at a pair of potential electrodes on the surface. It is different from the conventional over-voltage diagram shown in Figure 2. At early on- and off-time, we observe significant EM induction effects. It is only at late offtimes that we can identify typical over-voltage effects which are characteristic of the IP responses. The fact that EM dominates the data at early times and IP effects dominate the late-time data suggests it may be possible to separate the EM and IP responses in time. For a clearer demonstration of this, we view only the off-time data, and plot them on a log-log plot as shown in Figure 4. Black, blue, and red lines correspondingly indicate observed, fundamental, and IP responses; solid and dotted lines distinguish negative and positive data. At early times, the fundamental response is much greater than the IP data; this is the region of EM dominance. At later times, the IP signal is much greater than the fundamental; this is the region of IPdominance. Importantly, there is an intermediate time region when both EM and IP are considerable. Our following inversion workflow is based upon this natural separation of EM and IP in time.

3D TEM-IP INVERSION WORKFLOW Our inversion workflow is based upon Kang and Oldenburg (2016) which was built for an inductive source case, but is applicable here. Figure 5 shows the 3D TEM-IP inversion workflow to be applied. The first step is to invert the TEM data to recover the 3D model. As in our inductive source work, we use only early time data that we feel are not IPcontaminated. We note that these early time data have previously been considered as “noise” in conventional IP2016 – 6-8 June, Aarhus, Denmark

Seogi Kang and Douglas W. Oldenburg

analyses and hence have been thrown away. However, here we consider these as “signal” and use them to recover a better conductivity model. Another possibility for obtaining a background conductivity is to use the steady-state fields just prior to switching the current off. These are the potentials that are traditionally used in DC-IP inversion. Inversion of these data yields a conductivity that is but if  is small enough then this will be a reasonable approximation to . The inversion of DC data is analogous to inverting only one frequency in a frequency-domain data set. Hence it might be expected that inverting data at multi-times (equivalent to multi-frequencies) would produce a better result. Our experience verifies this. Nevertheless, the DC fields are valuable and we wish to use them. The options are to invert the DC and TEM data together, or treat them as two separate data sets. For the present we have chosen the latter since we then do not have to contend with the issue that the DC fields are really . The approach implemented here is first to invert the DC data and then use the resulting model as a starting and reference model for the TEM inversion

Figure 3. Observed voltage with EM induction effects. EM effects dominate the early off-time data.

Intermediate

EM Induction

IP

Figure 4. Transients of observed (black line), fundamental (blue crosses) and IP (red line) at the off-time in the log-log plot. Solid and dotted lines distinguish positive and negative datum. The second step of the workflow is EM decoupling. The estimated conductivity model, est, from step 1 is used to generate raw IP data according to , (4) where is the observed data, F [est] is estimated fundamental data. Here, we identify that the predicted fundamental response might be different from true fundamental response, because est is not the same as . Potential errors in raw IP data will be significant especially at early times, but they will decrease as time increases. The effective region for EM-decoupling will be in the intermediate time when both EM and IP are considerable (Figure 4). Note dobs

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Seogi Kang and Douglas W. Oldenburg

that at late time (IP-dominant) EM-decoupling may not be required. The final step in the process is to carry out the IP inversion. We adopt the conventional IP inversion approach (e.g. Oldenburg and Li, 1994), which uses a linear form of IP responses written as ,

(5)

where G is the sensitivity function and is the pseudochargeability. The conductivity model est is required to generate the sensitivity matrix. We invert each time channel of IP data separately, and recover pseudo-chargeability at multiple times. Interpreting this recovered pseudochargeability to extract intrinsic IP information such as , , and c is possible, but we do not treat that in this study.

Figure 5. A 3D TEM-IP inversion workflow for galvanic source TEM data.

GALVANIC SOURCE EXAMPLE

3D DC and TEM inversion , we use the first six channels of the TEM data To recover (1-6 ms), which have minor contamination from IP. In addition, we have DC data which contain IP effects, but have minor EM induction effects. We first invert the DC data, and recover 3D conductivity. By using the recovered DC conductivity as a reference model, we invert the TEM data. The recovered conductivity models from the 3D DC and TEM inversions are shown in Figure 8. The conductive blocks A1 and A3 are much better imaged with the TEM inversion.

A1

A2

A3

A4

As an example, we use a galvanic source and multiple receivers which measures voltages as shown in Figure 3. Four and blocks (A1-A4) presented in Figure 6 have different  values (see Table 1); all blocks have  =0.5 sec and c=1 (Debye model). Only A2 and A3 blocks are chargeable. The length of the transmitter wire is 4.5 km and potential differences between two electrodes along easting lines are measured at 625 locations. The measured time channels are logarithmic-based ranging from 1-600 ms (60 channels). Computed responses at 5, 80, and 350 ms are shown in Figure 7. At 5 ms, EM induction effects are dominant, and all data are negative. At 80 ms, both EM and IP effects are considerable, but still all data are negative. Note that A2 and A3 are chargeable, but A1, which is conductive, is not. Therefore, it is difficult to differentiate chargeability and conductivity anomalies just by looking at observed data at 80 ms. At 350 ms, EM induction effects are significantly decayed, hence IP is dominant. Only A2 and A3 show positive anomalies that originate from chargeability. Depending on the measured time window, and IP parameters of chargeable bodies, we could have data in IP-dominant time or not. Hence, whenever our measured time window is not late enough to be considered as IP-dominant time, EM-decoupling is crucial step. Note that the A1 anomaly at 80 ms could be misinterpreted as a chargeable response, if this is the latest time channel. Table 1. Conductivity at infinite frequency and intrinsic chargeability values for five units: A1-A4 and half-space.

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A2

A3

A4

Figure 6. Plan and section views of the 3D mesh. Black solid lines show the boundaries of four blocks (A1-A4). Only A2 and A3 are chargeable. Arrows indicate a wire path for the galvanic source. 5 ms

Synthetic TEM data

A1

350 ms

80 ms

A1

A2

A1

A2

A1

A2

A3

A4

A3

A4

A3

A4

Figure 7. Plan maps of the observed TEM data at 5 ms (left panel), 80 ms (middle panel), 350 ms (right panel). Dashed and solid contours differentiate negative and positive data.

(a) DC inversion

(b) TEM inversion

A1

A2

A1

A2

A3

A4

A3

A4

A1

A3

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A4

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Figure 8. Recovered conductivity models from (a) DC and (b) TEM inversions. EM-decoupling

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3D TEM-IP inversion workflow

Seogi Kang and Douglas W. Oldenburg

The next step is EM-decoupling. We implement Eq. (4) using est from the TEM inversion (Figure 8b). In Figure 9, we present observed, predicted and raw IP data at 80 ms. At this time, both EM and IP effects are considerable. Our EMdecoupling procedure effectively removes EM effects due to conductivity especially for regions close to A1 (not chargeable) and A3 (chargeable). Removing the conductive anomaly at A1 is crucial, because this could have been misinterpreted as chargeable anomaly.

of positivity on the chargeability (Oldenburg and Li, 1994). Depth weighting, invoked for the airborne case, was not used for this 3D IP inversion. The recovered 3D pseudochargeability model is shown in Figure 11. The two true chargeable bodies, A2 and A3, are well imaged without significant artefacts. It is also noted that the pseudochargeability of A2 is stronger than that for A3. This is compatible with the known amplitude from the true IP data shown in Figure 10.

The crucial aspect of our EM-decoupling procedure is the effect of the background conductivity. To show this we , b) halfconsider two other candidates, namely a) true space conductivity (half). We compare performance of EMdecoupling for all three different conductivity models. Figure 10 shows predicted fundamental response and IP data generated using the three conductivity models. The EM clearly shows two conductive response computed using anomalies. A similar conclusion can be drawn from the results using est. The A1 and A3 conductive anomalies are effectively removed resulting in A1 being stronger anomaly than A3. As shown in the left panel Figure 7, A3 was stronger in the observation. The half-space conductivity however does a poor job at predicting the EM effects and the resultant raw IP data have numerous artifacts, especially at A1 and A3 where there are conductive blocks and where the IP data is overestimated. If these data are input to a 3D IP inversion, they produce strong artefacts from which incorrect conclusions can be drawn.

CONCLUSIONS

dobs

P dIr aw

F [σest ] A1

A2

A3

A4

In this study, we have applied the 3D TEM-IP inversion workflow to a galvanic source TEM example. First, we inverted DC data and recovered a 3D conductivity. Then, by using that as a reference model, we inverted six of the earliest time channels of TEM data, which have minor IPcontamination, and recovered a 3D conductivity. These early TEM data often have been thrown away because they are considered as “noise”. However, by considering them as “signal” and inverting them, we recovered a better conductivity model. Second, the recovered conductivity, est was used in our EM-decoupling procedure to generate raw IP data. The procedure was effective for removing EM induction in the observations, especially for regions close A1 and A3, which had significant conductivity responses. Third, we inverted the IP data set generated from the TEM conductivity model using conventional 3D IP inversion. The recovered pseudo-chargeability successfully imaged two true chargeable anomalies A2 and A3. This demonstrates that our TEM-IP inversion workflow can be effective for recovering a good estimate of electrical conductivity, for removing EM signals from IP data, and for obtaining a 3D distribution of pseudochargeability.

A1

A2

A3

A4

Figure 9. Plan maps of observed (left panel), estimated fundamental (middle panel) and raw IP (right panel) at the 80 ms. EM

σ1

σest

σh al f

A1

A2

A3

A4

Figure 11. Plan and section views of the recovered pseudochargeability.

REFERENCES IP

Flis, M. F., G. A. Newman, and G. W. Hohmann, 1989, Inducedpolarization effects in timedomain electromagnetic measurements: Geophysics, 54, 514–523.

Figure 10. Comparison of EM (top panel) and IP (bottom panel) responses obtained from three different conductivity , b) half, and c) est from TEM models. (a) true inversion. 3D IP inversion To recover 3D pseudo-chargeability, we invert raw IP data sets at 80 ms obtained using the estimated conductivity, est, from the TEM inversion. This conductivity is used to generate the linearized sensitivities as outlined in Kang and Oldenburg (2016). This linear system is inverted with the added constraint

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Kang, S., and D. W. Oldenburg, 2016, On recovering distributed IP information from inductive source time domain electromagnetic data (in revision): Geophysical Journal International. Marchant, D., E. Haber, and D. Oldenburg, 2014, Threedimensional modeling of IP effects in time-domain electromagnetic data: Geophysics, 79, E303–E314. Oldenburg, D., and Y. Li, 1994, Inversion of induced polarization data: Geophysics, 59, 1327–1341. Pelton, W., S. Ward, P. Hallof, W. Sill, and P. Nelson, 1978, Mineral discrimination and removal of inductive coupling with multifrequency IP: Geophysics, 43, 588–609.

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Seigel, H., 1959, Matehmatical formulation and type curves for induced polarization: Geophysics, 24, 547–565.

Weidelt, P., 1982, Response characteristics of coincident loop transient electromagnetic systems: 47, 1325–1330.

Smith, R. S., P. Walker, B. Polzer, and G. F. West, 1988, The time-domain electromagnetic response of polarizable bodies: an approximate convolution algorithm: Geophysical Prospecting, 36, 772–785.

Wynn, J. C., and K. L. Zonge, 1975, EM coupling, its intrinsic value, its removal and the cultural coupling problem: Geophysics, 40, 831–85

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Methods for measuring the complex resistivity spectra of rock samples in the context of mineral exploration Tina Martin

Stephan Costabel

Federal Institute for Geosciences and Natural Resources (BGR) Wilhelmstr. 25-30 D-13593 Berlin/Germany [email protected]

Federal Institute for Geosciences and Natural Resources (BGR) Wilhelmstr. 25-30 D-13593 Berlin/Germany [email protected]

SUMMARY For the geophysical exploration of mineral resources knowledge about petrophysical parameters of the expected investigation material is essential. If it is not possible to measure samples in a common geometry, new approaches have to be developed. In this preliminary study three approaches for adequate and proper measurements of spectral induced polarization at rock samples are introduced. First results show that additionally to the measurement in a common 4-point measuring cell, also measurements with stuck electrodes connected to rock samples with irregular geometry seem to be promising. Furthermore the detection of a buried antimonite sample in a sand-box could be demonstrated by the strong phase anomaly it produced. Nevertheless further investigations are necessary, such as considering possible anisotropy effects and verification of the methods for a broader range of samples with irregular geometry. Also the electrode material for the measurements in the sandbox should be modified to avoid unwanted polarization effects. In addition, alternative materials for coupling the electrodes directly to the rock surface will be tested in the future. Key words: SIP, laboratory measurement, hard rock sample, arbitrary geometry, antimonite

Thomas Günther Leibniz Institute for Applied Geophysics (LIAG) Stilleweg 2, D-30655 Hannover/Germany [email protected]

resistivity and magnetic susceptibility, samples of antimonite and the deposit surrounding material are required. However, at least in Germany, in situ samples cannot be obtained anymore due to closed mining pits. Only existing samples in rock collections are available. The problem is that it is mostly not allowed to destroy or cut these samples so new approaches for measuring of the complex resistivity have to be developed. The following study demonstrate preliminary results of potential strategies to overcome the given limitations.

MATERIAL AND METHODS Most of the samples in geological rock collections have an approximate size of a fist and exhibit arbitrary geometries (Figure 1). It is usually not allowed or even possible to drill cylindrical samples matching a common four-point measuring cell for measuring the complex resistivity, because the samples are too precious, too small or too instable. For a reliable data acquisition, three different approaches are pursued: 1.) If possible, cylindrical core samples are measured in the measuring cell. 2.) Fist-sized samples with irregular geometry are measured using small (nail) electrodes stuck on the rock surface. 3.) Samples with irregular geometry are buried in a sandboxes for measuring exact phase values.

INTRODUCTION Critical raw materials such as Sn, W, In and rare earth metals are very important today for producing electronic equipment. In the past decades the exploration activities in Germany for mineral resources were low and therefore the research in this field. Nowadays efforts are undertaken to develop new technologies and exploration systems (e.g. using helicopter electromagnetics as in the project, where this work is involved in). Along with the geophysical exploration, it becomes important to know about petrology and the genesis of the expected mineral deposits and the knowledge about petrophysical characterization of the rocks involved are essential. This information can then be used for improving (threedimensional) images of the electrical resistivity distribution in the subsurface and can thus provide indications of mineralized deposits and their geological, tectonic, and structural properties. The main focus in the current research project are antimonite deposits. To measure petrophysical parameters such as density, IP2016 – 6-8 June, Aarhus, Denmark

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Figure 1: Picture of an antimonite from the BGR rock collection. For measuring the complex resistivity * we use an SIP (spectral induced polarization) instrument (SIP-ZEL, Zimmermann et al., 2008), which provides magnitude (||) and

SIP at rock samples

phase () of the complex resistivity. These parameters are related to the real (´) and imaginary (´´) parts of resistivity by 1 𝜌∗ = |𝜌|𝑒 𝑖𝜑 = 𝜌′ + 𝜌′′ = ∗ 𝜎 with * being the electrical conductivity. The magnitude (||) and the phase () are associated with: |𝜌| = √𝜌′2 + 𝜌′′2 and 𝜌′′ 𝜑 = arctan [ ′ ]. 𝜌 1.) Cylindrical core samples For the laboratory measurements we use a four-point measuring cell (Figure 2Figure 2 a) with stainless steel current electrodes at the face side of the cell and potential electrodes (Ni-Co alloy) being ring wires placed outside the electrical field in the central part of the cell (more information in Kruschwitz 2008). The core samples were drilled in cylindrical shape with 2 cm in diameter and various lengths (Figure 2Figure 2 b). The cores were extracted from two different directions to consider possibly occurring anisotropy effects and are measured under controlled conditions in a climatic chamber (20°C) at a frequency range between 2 mHz and 45 kHz. As coupling agent we used an Agar-Agar gel.

Martin, Costabel and Günther

each other. To consider the anisotropy of the samples further electrodes on each side are possible.

Figure 3: Picture of a rock sample with stuck electrodes. To digitize the geometry and to calculate the geometry factor the samples are scanned by a 3-D scanner (Matter and Form, 2016). It provides a high resolution and also photographic recording (Figure 4). With the exact geometry and the position of the electrodes the necessary factors are calculated using a tetrahedral Finite-Element mesh that is generated from the surface mesh with the mesh generator TetGen (Rücker et al., 2006).

The complex resistivity * is then calculated by 𝐴 𝜌∗ = 𝑅 𝐿 where R is the measured resistance. The ratio A/L is the geometric factor of the sample holder with the length L between the potential electrodes and the cross-section area A. Figure 4: Results from 3-D scan. a) Photographic, b) 3-D scan points, c) connection between the scanned points.

3.) Measurements in a sandbox

Figure 2: a) 4-point measuring cell. b) Cylindrical core samples from antimonite.

2.) Measurements using stuck electrodes

To measure exact phase values, the fist-sized samples were also buried in a sandbox (44 x 25 x 25 cm) filled with pure fully saturated quartz sand. A principal feasibility study could be shown by Radic (1984). Newer result (for the detection of tree roots) can be found in Zanetti et al. (2011). In our previous studies this sand showed negligible phase effects and resistivities in the range of 45 m (fluid conductivity: 700 µS/cm/14.3 m). Due to the limited size of the sandbox boundary effects may occur and therefore resistivity can be overestimated. We used 12 stainless steel nails as electrodes, which are arranged in line with a distance of 3 cm (Figure 5), so different measurement arrays with varying depth levels and multichannel recording are possible. An inversion of the data can be done with the BERT algorithm (Günther et al, 2006). To account for the geometry of the tank, we use a hybrid 2D/3D approach, i.e. a 3D forward calculation is combined with a 2D inversion (Ronczka et al., 2014).

To measure the complex resistivity at the fist-size samples small holes (< 2 mm) were drilled. Silver wire electrodes were stuck with conductive epoxy or silverpaint (very well conducting glue) at the sample. At least four electrodes are needed for a measurement (Figure 3). In our first tests, the electrodes are placed in line with a distance of about 1 cm to

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when plotted using a log-log scaling, which indicates inductive effects from the measurement system.

Figure 5: Picture of the sandbox with electrode line. Figure 7: First results of a fist-sized sample of antimonite with stuck electrodes (two repetitions).

RESULTS AND DISCUSSION 3.) Measurements in a sandbox 1.) Cylindrical core samples Example spectra of antimonite core samples are shown in Figure 6. All five rock samples were cut from one rock sample but with perpendicular orientation (orientation A: 1 and 2; orientation B: 3, 4 and 5). The resistivity values (left) are clustered: two samples exhibit higher resistivities (10 000 m) and three exhibit lower values (~ 2000 m). Unfortunately this observation cannot be fully related to the orientation. In contrast, the phase values can be related to the orientation: higher phases (10 mrad) are associated with orientation B and lower (5 mrad) values with A. However, in general the phases are relatively small and their behaviour over the entire frequency range is more or less constant, except for high frequencies, which is assumed to be an artefact caused by unavoidable inductive effects of the measurement setup.

Figure 6: First results of an antimonite core samples. Sample 1 and 2 are perpendicular to 3, 4, and 5.

2.) Measurements using stuck electrodes In Figure 7 the preliminary results for an SIP measurement with stuck electrodes at a fist-sized antimonite sample is shown. The coupling resistance between current and potential electrodes was sufficiently small with < 3 kAs a preliminary estimate, the geometry factor was calculated assuming the four-pointelectrode line over a halfspace, which yields at least a rough estimation of the order of magnitude for the resistivity of the rock. In future, the calculation of the geometry factor will be repeated by simulated resistance measurements using the digitized 3-D model. However, the preliminary resistivity estimate of the investigated sample is in principal agreement with the core samples around 2000 m. In contrast to the core samples, we observe no phase effects, only a continuous increase from low to high frequencies that appears to be linear

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Various measurements in the sandbox were carried out. To characterize the filling sand after saturation with water (700 µS/cm), it was measured first in the four-point measuring cell. After filling the sandbox, the water-saturated sand was measured again with two different arrays (Wenner-alpha and dipole-dipole). At least for small electrode distances (first level), the resistivity measurement in the sandbox corresponded to the reference measurement in the cell. For higher levels, the boundary of the sandbox caused an overestimation of the resistivity. On the other hand, the zero-phase in the sandbox was only found for the higher levels, while a peak with a maximum between 2 and 38 mrad at frequencies between 0.1 and 1 Hz in the phase spectrum was found for the first levels. It is contemplated whether this artefact is associated with polarizing effects at the steel electrodes. After the reference measurements using the pure sand, a fistsized native antimonite sample was buried in the centre of the sandbox (just below electrodes 6, 7 and 8) at a depth between 3 and 7 cm. In Figure 8 the results of these measurements using a Wenner-alpha array are shown. At the electrodes 5, 6, 7 and 8 (red open triangle), resistivities of about 45 m and very small phase values were measured corresponding to the pure sand characteristics. One electrode position further (6, 7, 8, 9 orange triangle), a remarkable phase effect (up to 300 mrad) could be observed with a maximum at 100 Hz. This phase effect is increasing with increasing electrode distances (equivalent to depth) and is associated with the buried antimonite sample, while the resistivity value does hardly show a significant change. For the highest level (green open square) the resistivity is overestimated probably because of the limited dimension of the sandbox, which was already observed for the measurements in the pure sand before. The next step is an inversion of the data that considers the correct dimensions of the sandbox.

Figure 8: First results from a buried antimonite in fully saturated quartz sandbox.

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CONCLUSIONS Our preliminary results show that probably reliable SIP measurements can be carried out using any of the three approaches. Previous studies (e.g., Binley et al., 2005; Kruschwitz, 2008; Martin, 2010; Weller et al., 2011) demonstrate that measurements at cylindrical core samples in a four-point cell can be considered to be the state-of-the-art for solid rocks. However, also measurements at rock samples with irregular geometry seems to be a promising tool, even if there is still potential to further develop the proposed approaches. SIP measurements at sand-filled boxes can also be a suitable way. However, the reliability of the SIP characterization of buried rocks inside a box must be verified in further studies. Our next steps are the comparison of the three approaches considering possible anisotropy effects and the verification of the measurement for a broader range of samples with irregular geometry. The electrode material for the measurements in the sandbox should be modified to avoid unwanted polarization effects. Also, alternative materials for coupling the electrodes directly to the rock surface will be tested in the future.

ACKNOWLEDGMENTS We thank the German Ministry of Education and Research (BMBF) for funding the project DESMEX (grant 033R130A) in which all the work is done. We also thank the BGR technicians for their great support.

REFERENCES Binley A., Slater L., Fukes M. and Cassiani G., 2005. The relationship between spectral induced polarization and hydraulic properties of saturated and unsaturated sandstone. Water Resources Research 41(12), W12417, doi: 10.1029/2005WR004202.

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Günther, T., Rücker, C., and Spitzer, K. (2006). Threedimensional modeling and inversion of DC resistivity data incorporating topography - Part II: Inversion. Geophys. J. Int., 166, 506-517. doi:10.1111/j.1365-246X.2006.03011.x. Kruschwitz, S., 2008, Assessment of the complex resistivity behaviour of salt affected building materials: Ph.D. Thesis, Federal Institute for Materials Research and Testing (BAM). Martin, T., 2010. Complex resistivity measurements on oak. European Journal of Wood and Wood Products 70, 45-53. Matter and Form, 2016, https://matterandform.net/scanner Radic, T., 1984. Bau und Programmierung eines mikrocomputergesteuerten digitalen Messgerätes zur Bestimmung des komplexen Gesteinswiderstandes durch induzierte Polarisation und dessen Erprobung im sandgefüllten Trog. Diploma Thesis (in German), Free University Berlin. Ronczka, M., Günther, T. and Stoeckl, L. (2014): Geoelectrical monitoring of freshwater-saltwater interaction in physical model experiments. Ext. Abstr., 23rd Saltwater Intrusion Meeting, Husum, Germany. Rücker, C., Günther, T. and Spitzer, K., 2006. 3-D modeling and inversion of DC resistivity data incorporating topography Part I: Modeling. - Geophys. J. Int., 166, 495-505. Weller A., Breede K., Slater L. and Nordsiek S., 2011. Effect of changing water salinity on complex conductivity spectra of sandstones. Geophysics 76(6), F315-F327. Zanetti, C., Weller, A., Vennetier, M. and Meriaux, P. (2011) Detection of buried tree root samples by using geoelectric measurements: a laboratory experiment. Plant and Soil, 339, 273–283. Zimmermann, E., Kemna, A., Berwix, J., Glaas, W., Münch, H., and Huisman, J., 2008. A high-accuracy impedance spectrometer for measuring sediments with low polarizability. Meas. Sci. Technol. 19. doi:10.1088/0957-0233/19/9/094010.

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Spectral induced polarization in a sandy medium containing semiconductor materials: study of the polarization mechanism ABDULSAMAD Feras

FLORSCH Nicolas

CAMERLYNCK Christian

Sorbonne Université, UPMC-CNRS UMR 7619 METIS, Paris, France [email protected]

Sorbonne Université, UPMC-IRD UMI 209 UMMISCO, Paris, France [email protected]

Sorbonne Université, UPMC-CNRS UMR 7619 METIS, Paris, France [email protected]

NTRODUCTION SUMMARY Induced polarization (IP) is useful for mineral exploration. In the presence of sulphides (more generally speaking: semi-conductors), the charge carriers inside particles are electrons and electron gaps. The inner diffusivity and the charge concentration are very high with respect to the background solution ones. Mechanisms of induced polarization are still under questioning in those cases. In order to improve our knowledge about the mechanisms controlling IP in such mediums, we propose new lab experiments on unconsolidated mineralized medium and begin numerical modelling by using the Poisson-NernstPlanck (PNP) equation set as well. Four different types of semi-conductors (graphite, pyrite, chalcopyrite and galena) are involved in the experiments. The polarization effect of grain size, mineral concentration as well as electrolyte salinity and type are investigated at the lab scale. We find that the total chargeability of the medium is a function of the mineral volume but is independent of the electrolyte salinity and electrolyte type. However, the time constant (τ) is highly dependent on the grain size and the electrolyte salinity, and is slightly dependent on the mineral type. These results appear to be in agreement with the classical Wong’s theory, but we assume here that no significant redox phenomenon does happen at the grain surface. The observed dependence of the chargeability and the time constant on the salinity could be explained by considering the mineral grain as a dipole impacting the potential and consequently charge distribution in its vicinity. This dipole is generated inside the particle to compensate the primary electrical field and the whole particle is –as a first approximation- a spherical boundary (and volume) with a constant potential on (and in) it. The distribution of the charged particles in the area around the dipole electric will respond accordingly to this boundary condition and is driven by the potential. Since the equations are coupled, the potential depends on return on the resulting ions distribution. Although the finiteelement numerical approach used here is still preliminary, it opens wide perspectives in the understanding of IP in more complex media. Key words: spectral induced polarization, electrolyte effect, mineralized medium.

One consensus does exist regarding the dependence of the time constant with the grain size and the diffusion coefficient (D in m2/s) of ions in the pore solution. However it seems not applicable in the case of semi-conductor particles: the diffusion coefficient as numerically derived from the time constant is some orders of magnitude larger than in the case of siliciclastic mediums (Gurin et al. 2015; Revil et al. 2015). In the presence of electronic semi-conductors, Gurin et al. (2015) and Hupfer et al. (2016) prefer to introduce the notion of specific surface area to model the time constant, and D is no more involved in the relationship providing the time constant.

METHOD AND EXPERIMENTAL RESULTS The complex resistivity of unconsolidated siliciclastic medium containing electron-based semi-conductors minerals were acquired over a frequency range from 91.5 mHz to 20 kHz using SIP Fuchs III electrical impedance spectrometer. We use Fontainebleau sand (consisting of 98 % of pure silica). The particle size lies between (0.1- 0.2 mm). According to our tests, this medium shows a weak polarization, in agreement with all previous works made on such samples. The measurements tank is rectangular with dimensions (28 cm long, 10 cm wide and 10 cm of height). We use a Wenner array with 6.5 cm spacing. Non-polarizable Cu/CuSO4 electrodes are used to measure the potential difference, whereas the current electrodes are made of stainless steel (Ag 316L) electrodes. The metallic grains are randomly scattered throughout the medium. We firstly vary the metal content (mass fraction) and the grain size, and secondly the electrolyte type (sodium chloride NaCl, potassium chloride KCl and sodium sulphate Na2SO4 separately). Finally the electrolyte concentration is also changed with 0.001, 0.01, 0.1 and 0.5 mol/l respectively. The chargeability M of the medium is calculated from the amplitude of the complex resistivity at higher and lower frequencies and the time constant τ is derived from the critical frequency (the frequency of the phase peak).

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For a long time, the interpretation of spectral induced polarization has been based on empirical models (Cole and Cole 1941), wherein the physical meanings of the model parameters are difficult to interpret physically. Pioneers like Pelton et al. (1978) showed relationships between chargeability and mineral content in sulphide deposits, but did not provide mechanistic approaches. However several theorists, for instance Schwarz (1962), Wong (1979) and more recently Revil et al. (2015) have proposed mechanistic approaches that light the micro-meso-macro IP in various cases.

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Increasing the mass fraction of metal (galena or chalcopyrite) leads to an increase of M and a decrease of the amplitude of the complex resistivity, while M is independent of the electrolyte type and concentration. Τhe time constant depends on the grain size and electrolyte concentration. The phase peak moves to higher frequencies while the electrolyte concentration increases. Accordingly, the time constant decreases with concentration and from the figure 1 we notice that the shape of the phase spectrum is not influenced by electrolyte concentration. That means that the shape of phase spectra is only controlled (actually: shifted along the frequency axe) by the grain size distribution.

Abdulsamad, Florsch, Camerlynck

The Poisson-Nernst-Planck (PNP) equation set is a theory (or model) which includes the two major determinisms involved in electrolytic solutions. Precisely, it takes into account the dispersion caused by the Brownian motion (as set by Einstein for each ion type as: the mobility,

, where D is the diffusivity, the Boltzmann constant, T the

temperature, and q the electrical charge of the ion) coupled with the Poisson equation. In the presence of several kinds of ions numbered (i), the system is written:

The figure 2 exhibits the dependence of the relaxation time with the solution conductivity. If we remove the distilled water point (which in reality may be acidified by carbonic acid), the relationship seems extremely linear with a slope of 0.85 s.m/mS.

,

where

is the concentration of ions (i),

e the elementary charge, involved ion species.

valence of ion (i),

the potential, and N the number of

The coupling of the concentrations

with the potential

leads the system to be nonlinear.

Figure 1: experimental phase with graphite (1% volume) for several electrolyte (KCl) concentrations.

We undertake computation by using the Finite Element Method as proposed by the free but powerful and convivial software named “freefem++” (see Hecht, 2012 and http://www.freefem.org/). Our modelling is preliminary 2-D. The figure 3 shows a typical mesh within a box of 2X2 mm2 including a 40 µm diameter particle, supposed to be very conductive. It assumes that the phenomenon inside the particle is rapid and anticipates the major phenomenon occurring outside the particle (later on we shall take into account the diffusion of charges inside the particle).

Figure 2: experimental relaxation time versus solution conductivity. Excluding the distilled water point, the slope is very close to -0.85 s.m/mS.

Figure 3: the mesh used to study the concentration and potential evolution in the vicinity of a conductive particle.

FINITE ELEMENT METHOD MODELLING

Only two kinds of ions (one cation and one anion) of equal diffusivity are involved in this preliminary modelling.

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REFERENCES At the beginning of the experiment, the potential is null everywhere and the ion concentration is homogeneous. Then we set potentials on the two opposite faces as depicted on figure 3 and run the software using finite differences in the time domain. The diffusivities D1 and D2 are close to 2.10-9 m2/s (K+ and Clstandard value). As expected, the resulting concentrations are just opposite through the experiment. On figure 4 we show the potential and cation concentration for two initial concentrations and after 1 s and 100 s. The potential evolution with time or concentration is so weakly perceptible, that we only show the potential one time. The concentration varies in the vicinity of the particle: the polarization phenomenon is mainly driven by the particle dipole at a distance of a few radiuses. The Gouy-Chapmann layer role is not taken into account here; actually we expect that its contribution is negligible when considering such conductive particles.

CONCLUSIONS The chargeability of the medium is a linear function of the concentration of the metallic particle (in volume), and it has a small and negligible dependence on the mineral type and solution conductivity. The phase of the complex resistivity is a direct indicator of the mineral content. The chargeability of the medium is slightly depending on the grain size and on the water conductivity. The relaxation time is depending on the grain size and electrolyte concentration: we find a clear logarithmic correlation between relaxation time and electrolyte conductivity. The polarization is at least partially controlled by the solution ions. The correlation between relaxation time and the resistivity of the medium is still one of the obstacles to use SIP in minerals discriminations. We expect that a good use of the numerical modelling by using the Poisson-Nernst-Planck model will improve our common understanding of IP in the future.

Cole, K, S., and Cole, H, R., 1941. Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics: The Journal of Chemical Physics, 9 (4), 341–51. Gurin, G., Titov, K., Ilyin, Y., and Tarasov, A., 2015. Induced Polarization of Disseminated Electronically Conductive Minerals: A Semi-Empirical Model: Geophysical Journal International, 200 (3), 1555– 65. Hecht, F., 2012. New development in freefem++. J. Numer. Math., 20 (3-4), 251–265. 65Y15. Hupfer, S., Martin,T., Weller, A., Günther, T., Kuhn, K., Ngninjio, N, D, V., and Noell, U., 2016. Polarization Effects of Unconsolidated Sulphide-Sand-Mixtures, Journal of Applied Geophysics, in Press. Pelton, W., Ward, S., Hallof, P., Sill, W., and Nelson, P., 1978. Mineral Discrimination and Removal of Inductive Coupling with Multifrequency Ip: Geophysics, 43 (3), 588–609. Revil, A., Florsch, N., and Mao, D., 2015. Induced Polarization Response of Porous Media with Metallic Particles — Part 1: A Theory for Disseminated Semiconductors, Geophysics, 80 (5), D525–D538. Schwarz G. 1962. A theory of the low-frequency dielectric dispersion of colloidal particles in electrolyte solution, J. Phys. Chem., 66, 2636-2642. Wong, J., 1979, An electrochemical model of the inducedpolarization phenomenon in disseminated sulfide ores, Geophysics, 44, 1245–1265.

ACKNOWLEDGMENTS We would like to thank Serena Delar for carrying on part of the measurements.

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Figure 4: potential and cation concentration: (a) potential; (b) cation concentration after 1 s with 0.001 mol/l; (c) after 1 s with 0.1 mol/l and (d) after 100 s with 0.1 mol/l. The potential modification is hardly perceptible, while the ion concentration varies in the vicinity of the particle.

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Quantification of Rock Structures with High Resolution X-Ray µ-CT for Laboratory SIP Measurements Matthias Halisch

Sabine Kruschwitz

Leibniz- Institut für Angewandte Geophysik (LIAG) Stilleweg 2, D-30655 Hannover, Germany [email protected]

Bundesanstalt für Materialforschung und –prüfung (BAM) Unter den Eichen 87, D-12205 Berlin, Germany sabine.krusc[email protected]

Mayka Schmitt

Andreas Weller

Federal University of Santa Catarina 88040-900 Florianópolis, Brazil [email protected]

Institut für Geophysik, Technische Universität Clausthal Arnold-Sommerfeld Str. 1, D-38678 Clausthal-Zellerfeld, Germany [email protected]

-

SUMMARY Spectral Induced Polarization (SIP) measurements are used in many different ways to characterize natural rocks and soils. Main foci of interest are the enhanced characterization of the causes of IP-effects in clastic rocks (especially sandstones), the interactions between the matrix-fluid-system and within the electrical double layers as well as the correlation with “classical” petrophysical parameters, such as specific surface area, permeability, mercury intrusion capillary pressure (MICP) and others. Nevertheless, for all of these investigations, knowledge of the inner structure of the sample material is essential in order to create reliable and validated models as well as to interpret and to assess the data most completely. Unfortunately, many of the methods used, to get access to the inner structure of rocks are destructive (e.g. MICP, thin sectioning, etc.) and the valuable sample is lost. In addition, data is either of volume integrated nature or only available for the 2D case and the usage of sister cores does not necessarily lead to reliable results. In this paper, the authors showcase the possibilities of non-destructive and three dimensional X-ray computed tomography and of enhanced image analysis capabilities for the quantification of rock structures at the pore scale. Key words: µ-CT imaging, rock structure, digital image analysis, pore geometry, grain geometry, SIP

INTRODUCTION Spectral induced polarization measurements are used in many ways to characterize natural porous rocks and soil material. In the last couple of years, there have been some efforts to correlate IP spectra and IP related data towards petrophysical and structural, i.e. pore scale quantities, such as: -

specific surface area (e.g. Börner et al., 1996; Slater et al., 2006; Weller et al., 2010); permeability and hydraulic conductivity (e.g. Börner et al., 1996; Weller et al., 2015);

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pore and pore throat sizes (e.g. Scott & Barker, 2003; Revil et al., 2014); general textural structures (Kruschwitz et al., 2010); fractal dimension of pore space geometries (Zhang & Weller, 2016).

Nevertheless, in many cases valuable core material is either destroyed during the measurements (e.g. by MICP experiments), or sister core plugs are used, which might not feature the same pore scale structures, or exact mineralogical composition. Hence, results of SIP and other measurements necessarily do not need to fit or correlate. This is where the imaging and image analysis techniques can contribute with an important part to pore scale research. In the following, the authors are giving a brief introduction of X-ray micro computed tomography (µ-CT), Digital Image Analysis (DIA) and Digital Rock Physics (DRP) at the pore scale. Afterwards, a selected variety of results from these different methods are showcased, in order to give an overview on the possibilities of non-destructive and three dimensional (3D) imaging procedures.

METHODS In this chapter, we would like to introduce the main technical background of high resolution X-ray computed tomography, followed by the extensive DIA and DRP workflow. X-Ray Computed Tomography Figure 1 showcases the basic principle of the µ-CT measurements. X-rays are emitted from a high power nanofocus source (Figure 1, left hand side) in form of a so called cone beam. As soon as they hit the sample material, which rotates stepwise in pitches 10 mrad). Ongoing work consists on the collection of aquifer materials to confirm the presence of NRZ in areas associated to high IP response

N

Doetsch, J., Ingeman-Nielsen, T., Christiansen, A. V., Fiandaca, G., Auken, E., and Elberling, B., 2015, Direct current (DC) resistivity and induced polarization (IP) monitoring of active layer dynamics at high temporal resolution: Cold Regions Science and Technology, 119, 1628. Flores Orozco, A., Kemna, A., Zimmermann, E.,. 2012, Data error quantification in spectral induced polarization imaging: Geophysics 77(3), E227-E237. Flores Orozco, A., Williams, K.H., Long, P.E., Hubbard, S. S., Kemna, A.,. 2011, Using complex resistivity imaging to infer biogeochemical processes associated with bioremediation of an uranium-contaminated aquifer: Journal of Geophysical Research: Biogeosciences 116(G3), 21562206. Flores Orozco, A., Williams, K.H., Kemna, A.,. 2013, Timelapse spectral induced polarization imaging of stimulated uranium bioremediation: Near Surface Geophysics: 11(5), 531-544. Gazoty, A., Fiandaca, G., Pedersen, J., Auken, E., & Christiansen, A. V., 2013, Data repeatability and acquisition techniques for time-domain spectral induced polarization: Near Surface Geophysics, 11(4), 391-406. Kemna, A., 2000. Tomographic Inversion of Complex Resistivity: Theory and Application, Der Andere Verlag, Osnabrück. Ntarlagiannis, D., Yee, N., and Slater, L., 2005, On the lowfrequency electrical polarization of bacterial cells in sands: Geophysical Research Letters 32, L24402.

Figure 7. Map of the Shiprock Site presenting the distribution of phase values in aquifer materials (at a depth of 4.5 m).

CONCLUSIONS We propose a new methodology for the processing of TDIP imaging data sets based on the analysis of the IP decay curve. Our approach reliably identifies outliers and provides an adequate quantification of the data error. Error parameters obtained with the proposed DCA and standard NRA are consistent, which clearly demonstrates the applicability of our approach. Imaging results obtained with the DCA resulted in images with enhanced contrasts and less artefacts compared to IP2016 – 6-8 June, Aarhus, Denmark

Slater, L., Ntarlagiannis, D., Personna, Y.R., and Hubbard, S., 2007, Pore-scale spectral induced polarization signatures associated with FeS biomineral transformations: Geophysical Research Letters 34. Wainwright, H. M., Flores Orozco, A.., Bücker, M., Dafflon, B., Chen, J., Hubbard, S. S., and Williams, K. H., 2015, Hierarchical Bayesian method for mapping biogeochemical hot spots using induced polarization imaging. Water Resources Research 52, 533-551. Williams, K.H., Kemna, A., Wilkins, M.J., Druhan, J., Arntzen, E., N'Guessan, A.L., Long, P.E., Hubbard, S.S., and Banfield, J.F., 2009, Geophysical monitoring of coupled microbial and geochemical processes during stimulated subsurface bioremediation: Environmental Science and Technology 43, 6717-6723.

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Advances in spectral inversion of time-domain induced polarization Gianluca Fiandaca

Esben Auken

Anders Vest Christiansen

HydroGeophysics Group Department of Geoscience Aarhus University (Denmark) [email protected]

HydroGeophysics Group Department of Geoscience Aarhus University (Denmark) [email protected]

HydroGeophysics Group Department of Geoscience Aarhus University (Denmark) [email protected]

SUMMARY The extraction of spectral information in the inversion process of time-domain (TD) induced polarization (IP) data is changing the use of the TDIP method. Data interpretation is evolving from a qualitative description of the subsurface, able only to discriminate the presence of contrasts in chargeability parameters, towards a quantitative analysis of the investigated media, which allows for detailed soil- and rock-type characterization. In this work a review of the recent advances in spectral inversion of TDIP data is presented, in terms of: supported IP parameterizations; modelling of transmitter waveform; support for buried electrodes; model regularization; computation of the depth of investigation. Keywords: spectral inversion, time-domain, Cole-Cole, CPA, transmitter waveform

INTRODUCTION Recently, the interpretation and inversion of TDIP data has changed from only inverting for the integral changeability to consider also the spectral information contained in the IP response curves (Fiandaca et al., 2012, 2013). Several examples of spectral TDIP applications have been presented, for landfill delineation (Gazoty et al., 2012b, 2013; Wemegah et al., 2016), lithotype characterization (Chongo et al., 2015; Gazoty et al., 2012a; Johansson et al., 2015, 2016; Maurya et al., 2016), time-lapse monitoring of CO2 injection (Doetsch et al., 2015a) and freezing of active layer in permafrost (Doetsch et al., 2015b). Furthermore, efforts have been made to achieve a wider time-range in TDIP acquisition, up to four decades in time (Olsson et al., 2016), for enhanced spectral content. In this work a review of the recent advances in spectral inversion of TDIP data is presented, in terms of: supported IP parameterizations; modelling of transmitter waveform; support for buried electrodes; model regularization; computation of the depth of investigation.

ADVANCES IN SPECTRAL TDIP INVERSION In the spectral inversion of TDIP data, the data space is composed by the apparent resistivity and the full voltage decays, while the model space is constituted by a parameterization of IP. The Cole-Cole model (Cole-Cole, 1941; Pelton et al., 1978) and the Constant Phase Angle (CPA) model (Van Voorhis et al., 1973) are the two parameterizations currently implemented in AarhusInv (Auken et al., 2015), the software in which the inversion algorithms described in Fiandaca et al. (2012,2013) are implemented. The complex resistivity ζCole-Cole of the Cole-Cole model takes the form:

𝜁𝐶𝑜𝑙𝑒−𝐶𝑜𝑙𝑒 = 𝜌 (1 − 𝑚0 (1 −

1 )) 1 + (𝑖𝜔𝜏)𝐶

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(1)

1

where ρ is the direct current resistivity, m0 is the intrinsic chargeability, τ is the time constant, C is the frequency exponent and i is the imaginary unit. The complex resistivity 𝜁𝐶𝑃𝐴 of CPA model is expressed as:

𝜁𝐶𝑃𝐴 = 𝐾(𝑖𝜔)−𝑏

(2) 𝜋

where b is a positive fraction, 𝜑 = − 2 𝑏 represents the phase shift and defines completely the IP response, K is a constant and i is the imaginary unit. In the CPA model, the DC resistivity cannot be defined, because the complex resistivity increases indefinitely at low frequencies. For this reason, Van Voorhis et al. (1973) introduced the Drake model:

𝜁𝐷𝑟𝑎𝑘𝑒 = 𝐾(𝑖𝜔 + 𝜔𝐿 )−𝑏

(3)

where in comparison with the CPA model a low frequency pole 𝜔𝐿 is introduced and the DC resistivity can be defined as 𝜌 = 𝐾𝜔𝐿 −𝑏 . In the AarhusInv implementation of the timedomain CPA forward response the Drake model of equation (3) is actually used, with a fixed value for the low frequency pole 𝜔𝐿 = 10−5 Hz. In this way, the CPA inversion is set up in terms of the model parameters 𝜌 and 𝜑, while the ColeCole inversion is set up in terms of ρ, m0, τ and C. Considering that the CPA and the Cole-Cole models are easily distinguishable in time-domain when more than 2 orders of magnitudes are acquired in the time-range (Lajaunie et al., 2016), the choice between the different supported IP parameterizations can be driven by the actual spectral content of the data. For both models it is also possible to invert directly for the normalized chargeability parameters 𝜑/𝜌 or 𝑚0 /𝜌, instead of 𝜑 or 𝑚0 . The forward modelling in AarhusInv, whatever parameterization is used for IP, takes into account the transmitter waveform and the receiver transfer function (Figure 1), for an accurate modelling of the IP response (Fiandaca et al., 2012,2013). The inversion is performed iteratively, by using the first term of the Taylor expansion of the nonlinear forward mapping of the model to the data space, as described in details in Auken et al. (2015). Figure 2 shows two typical forward responses for Cole-Cole and CPA homogeneous half spaces. The shape of the decays contains the spectral information of the IP phenomenon, which can be properly retrieved when the transmitter/receiver characteristics are properly modelled (Fiandaca et al., 2012; Fiandaca et al., 2013; Lajaunie et al., 2016; Madsen et al., 2016). Recently, the modelling of the IP response during the current on-time with a 100% duty cycle transmitter waveform has been implemented in AarhusInv (Figure 3). With the 100% duty cycle the current switches directly from positive to negative values, allowing for shorter acquisition times (because the offtime is skipped) and better signal-to-noise ratio (because the measured voltages are higher for the 100% duty cycle), but keeping equivalent spectral content when compared to the

Advances in spectral inversion of TDIP

50% duty cycle waveform (Olsson et al., 2015; Madsen et al., 2016).

Figure 1 (after Fiandaca et al, 2013). (a) Construction of the actual response by superimposing step responses; (b) IP percentage difference between decays with different number of stacks (a decay stacked six times is used as a reference) for the homogeneous half-space described by the Cole–Cole parameters (m0 = 100 mV/V, τ =2 s, C=0.5). (c) IRIS Syscal Pro filter effect (circles) measured in the time domain on a non-chargeable resistor. (d) Example of forward response with the filter implementation (black line) and without the filter implementation (grey line).

Fiandaca et al.

computing the response for buried electrodes, for inversion of 1-D borehole and 2-D cross-borehole data. The 1-D implementation computes the kernel following Sato (2000), with recursion formulas over the layers. Considering that in borehole data often hundreds of layers are modelled (Auken et al., 2016), the lateral-constrained approach has been implemented for speeding-up computations. The full 1-D model containing hundreds of layers is split into several submodels containing only a few tens of layers and the data are subdivided in subsets grouped by pseudodepth.

Figure 3. 50% duty cycle decays (circles) and 100% duty cycle decays (triangles) for Cole-Cole homogeneous halfspace (ρ=100 Ωm, m0=40 mV/V, τ=0.01 s, C=0.3, Ton/Toff =10 s, 4 stacked pulses). Black lines represent the normalized decays in mV/V, while red lines represent the actual voltages (see Olsson et al. (2015) for details).

Figure 2. Examples of Cole-Cole decay (red curve) and CPA decay (blue curve) for homogeneous half spaces and 50% duty cycle waveform (Ton= Toff =10 s, 4 stacked pulses). In addition to the 1-D and 2-D implementations described in Fiandaca et al. (2012,2013), the IP forward modelling in AarhusInv has been recently enriched by the possibility of

MRS2015 – 8-10 June, Aarhus, Denmark

Figure 4. Split of a 32-layers 1D model (grey model) in six 13-layers laterally-constrained sub-models for computational efficiency. The red arrows represent the lateral constraints.

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The inversion is then carried out in parallel on the split submodels/datasets and the full model is reconstructed stitching together the sub-models after inversion (Figure 4). This approach allows for gaining more than two order of magnitudes in run-time. The 2-D cross-hole computation has been implemented simply allowing the electrodes to be positioned at any node (on the surface or buried) of the finiteelement mesh (Bording et al., 2016). Compared to the implementations presented in Fiandaca et al. (2012,2013), new regularization schemes have been implemented for the spectral inversion of TDIP data, for vertical/horizontal constraints that favour sharp models (Vignoli et al., 2015) and for time-lapse constraints that promote compact time-lapse changes (Fiandaca et al., 2015a). In particular, two generalizations of the minimum support norm, namely 𝜑𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 and 𝜑𝑎𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 , have been developed for time-lapse inversion:

𝜑𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 (𝑥) = 𝛼 −1

(𝑥 2 ⁄𝜎 2 )𝑝 (𝑥 2 ⁄𝜎 2 )𝑝 + 1

𝜑𝑎𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 = 𝛼 −1 [(1 − 𝛽) ∙

+𝛽∙

𝛽=

(𝑥 2 ⁄𝜎 2 )𝑝1 (𝑥 2 ⁄𝜎 2 )𝑝1 + 1

(4)

(5a)

(𝑥 2 ⁄𝜎 2 )𝑝2 ] (𝑥 2 ⁄𝜎 2 )𝑝2 + 1

(𝑥 2 ⁄𝜎 2 )𝑚𝑎𝑥(𝑝1,𝑝2) (𝑥 2 ⁄𝜎 2 )𝑚𝑎𝑥(𝑝1,𝑝2) + 1

(5b)

where: 𝑥 = 𝑚 − 𝑚0 represents the difference between the reference value and the updated value in the time-lapse inversion for a given model parameter, i.e. the time-lapse change; 𝜎 represents the transition point of the minimum functional 𝜑 and controls the sharpness of time-lapse changes; 𝛼 controls the relative weight of data and model measures in the objective function and affects the size of time-lapse changes; 𝑝 (or 𝑝1 and 𝑝2 ) controls the transition sharpness of 𝜑 (Figure 5) and determines the way in which the overall focusing depends on 𝜎 and 𝛼 (Fiandaca et al., 2015a).

With the classic L2 norm 𝜑𝐿2 (𝑥) = 𝑥 2 ⁄𝜎 2 , the penalty in the objective function for a time-lapse change 𝑥 = 𝑚 − 𝑚0 increases with the square of 𝑥. With the norms of equation 4 and equation 5 the penalty does not increase indefinitely with 𝑥, but reaches a maximum when 𝑥 ≫ 𝜎 (Figure 5). This favours compact time-lapse changes, and the compactness can be easily and predictably controlled through the 𝜎, 𝛼 and 𝑝 settings. In many time-lapse experiments diffusive processes are monitored, and compact time-lapse changes do not necessarily represent the underlying physics/geochemistry. However, robust and easy-to-tune regularizations that favour the smallest model variation compatible with the data can be a very helpful tool for data interpretation, when used together with model measures that promote smooth variations. Finally, a new robust concept for the calculation of the depth of investigation (DOI) for inversion problems described by several intrinsic parameters, like the spectral inversion of time-domain induced polarization data, has been developed (Fiandaca et al., 2015b). A calculation of the DOI is crucial for interpreting the geophysical models, as the validity of the model varies considerably with data noise and parameter distribution. Without the DOI estimate, it is difficult to judge when the information in the model is data-driven or is strongly dependent on the constraints and/or on the starting value. The proposed method is based on an approximated covariance analysis applied to the model output from the inversion while considering the data standard deviations. Furthermore, the cross-correlations between intrinsic parameters are taken into account in the computations, which is crucial when strong cross-correlations are expected. Our new DOI implementation starts by subdividing the 2-D section in [𝑁𝐿𝑎𝑦𝑒𝑟𝑠 × 𝑁𝑐𝑜𝑙𝑢𝑚𝑛𝑠 ] cells, and summing the Jacobian elements of the 𝑁𝑐𝑜𝑙𝑢𝑚𝑛𝑠 model columns downwards. For each layer 𝑛 and each model column 𝑙 a cumulated [𝑁𝐷𝑎𝑡𝑎 × 𝑁𝑃𝑎𝑟 ] quasi-Jacobian matrix is defined (cumulated downward from the 𝑛𝑡ℎ layer to the last layer): 𝑗𝑘,𝑙 𝑛,𝑙 (𝑖, 𝑘) 𝐺𝐶𝑢𝑚

∶=



(6)

𝐺(𝑖, 𝑗)

𝑗=𝑗𝑘,𝑙 −𝑛+1

∀𝑖 ∈ [1, 𝑁𝐷𝑎𝑡𝑎 ], ∀𝑘 ∈ [1, 𝑁𝑃𝑎𝑟 ], ∀𝑛 ∈ [1, 𝑁𝐿𝑎𝑦𝑒𝑟𝑠 ], ∀𝑙 ∈ [1, 𝑁𝐶𝑜𝑙𝑢𝑚𝑛𝑠 ] where 𝑗𝑘,𝑙 represents the model index of the 𝑘 𝑡ℎ parameter of the last layer of the 𝑙 𝑡ℎ model column, 𝑁𝐷𝑎𝑡𝑎 is the number of data, 𝑁𝑃𝑎𝑟 is the number of intrinsic parameters (e.g. 4 for the Cole-Cole model), 𝑁𝐿𝑎𝑦𝑒𝑟𝑠 is the number of layers in the 2-D model and 𝑁𝐶𝑜𝑙𝑢𝑚𝑛𝑠 is the number of model columns in the 2D model. It is then possible to define a [𝑁𝑃𝑎𝑟 × 𝑁𝑃𝑎𝑟 ] cumulated approximate analysis for each model column 𝑙 and each layer 𝑛 of the 2D section: 𝑇

𝑛,𝑙 −1 𝑪𝑨𝑨𝑛,𝑙 ∶= [(𝑮𝑛,𝑙 𝐶𝑢𝑚 ) 𝑪𝑑 (𝑮𝐶𝑢𝑚 )]

Figure 5. Comparison of L2 norm, symmetric minimum support (equation 4) and asymmetric minimum support (equation 5) with varying norm settings. MRS2015 – 8-10 June, Aarhus, Denmark

−1

(7)

The cumulated approximate analysis 𝑪𝑨𝑨𝑛,𝑙 corresponding to the 𝑛𝑡ℎ layer does not contain information on the parameters of the 𝑛𝑡ℎ layer alone, but it cumulates the sensitivity from the 𝑛𝑡ℎ layer down to the last layer. This means that the cumulated approximate analysis gives information on all the layers below the 𝑛𝑡ℎ layer at once, for each model column 𝑙. In equation 7 the correlation between model parameters

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belonging to different model columns are neglected (lateral data correlation), but the correlation among the 𝑁𝑃𝑎𝑟 intrinsic parameters for each model column is considered. The inversion is carried out in logarithmic model space, and thus we use a standard deviation factor, 𝑆𝑇𝐷𝐹, for each parameter 𝑘:

bearing the implicit meaning that below this threshold the model structures are not data driven, but rather a result of the constraints and/or inversion properties. Figure 6 shows the 𝑆𝑇𝐷𝐹 values and the corresponding DOI computations for a typical 3-layers Cole-Cole model for a Schlumberger sounding (red lines). Furthermore, the results when disregarding the off𝑛,𝑙

𝑆𝑇𝐷𝐹

𝑛,𝑙 (𝑘)

∶=

𝑒𝑥𝑝 (√𝐶𝐴𝐴𝑛,𝑙 (𝑘, 𝑘))

(8)

The DOI-value is then defined for each parameter 𝑘 and each model column 𝑙 by imposing a threshold value for the 𝑆𝑇𝐷𝐹,

𝑇

𝑛,𝑙

diagonal elements in (𝑮𝐶𝑢𝑚 ) 𝑪𝑑 −1 (𝑮𝐶𝑢𝑚 ), i.e. the parameter correlations, are presented (blue lines): the DOI is significantly overestimated when neglecting the parameter correlations.

Figure 6. Depth of investigation (DOI) for an exemplary 3-layers Cole-Cole model for a Schlumberger sounding. Black dashed lines: layer interfaces. Continuous grey lines: vertical model subdivision for the 𝑺𝑻𝑫𝑭 computation (equation 8) as a function of depth. Green dashed lines: threshold value for the 𝑺𝑻𝑫𝑭 computation. Red lines: 𝑺𝑻𝑫𝑭 values as a function of depth taking into account the parameter correlations (continuous lines) and corresponding DOI values (dashed lines). Blue lines: 𝑺𝑻𝑫𝑭 values as a function of depth disregarding the parameter correlations (continuous lines) and corresponding overestimated DOI values (dashed lines).

CONCLUSIONS The spectral inversion of TDIP data has reached maturity. Different IP parameterizations can be modelled, i.e. the ColeCole and the CPA models, and the choice between the models can be made in function of the actual spectral content of the data. The forward modelling takes into account the transmitter waveform and the receiver transfer function for accurate computations, and the 100% duty cycle is supported for shorted acquisition time and better signal-to-noise ratio. Computation with buried electrodes for 1-D and 2-D modelling has been implemented, and advanced model regularizations have been developed, for sharp vertical/horizontal model variations and compact changes in time-lapse inversion. Furthermore, a new robust concept for the calculation of the depth of investigation has been developed, enabling judging when the information in the model is data-driven or is strongly dependent on the constraints and/or on the starting value. We believe that the MRS2015 – 8-10 June, Aarhus, Denmark

advances in spectral TDIP inversion significantly increase the potential of TDIP in (hydro)geophysical applications.

ACKNOWLEDGMENTS Support was provided by the research project GEOCON, Advancing GEOlogical, geophysical and CONtaminant monitoring technologies for contaminated site investigation (contract 1305-00004B). The funding for GEOCON is provided by The Danish Council for Strategic Research under the Programme commission on sustainable energy and environment. REFERENCES Auken E., Christiansen A.V., Kirkegaard C., Fiandaca G., Schamper C., Behroozmand A.A., Binley A., Nielsen E., Efferso F., Christensen N.B., Sorensen K., Foged N. & Vignoli G., 2015. An overview of a highly versatile forward and stable inverse algorithm for airborne, ground-based and borehole electromagnetic and electric data, Exploration Geophysics, 46, 223-235. 10.1071/eg13097.

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Auken E., Fiandaca G., Christiansen A.V., Maurya P.K., Holm H., 2016. Mapping lithotypes using in-situ measurement of time domain induced polarization: El-log. 4th IP Workshop, 6-8 June 2016, Aarhus, Denmark. Bording T.S., Fiandaca G., Maurya P.K., Auken E., Christiansen A.V., 2016. Mapping possible flowpaths of contaminants through surface and cross-borehole spectral time-domain induced polarization. 4th IP Workshop, 6-8 June 2016, Aarhus, Denmark. Chongo M., Christiansen A.V., Fiandaca G., Nyambe I.A., Larsen F. & Bauer-Gottwein P., 2015. Mapping localised freshwater anomalies in the brackish paleo-lake sediments of the Machile-Zambezi Basin with transient electromagnetic sounding, geoelectrical imaging and induced polarisation, Journal of Applied Geophysics, 123, 81-92. 10.1016/j.jappgeo.2015.10.002. Cole K.S., Cole R.H., 1941. Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys. 9 (4), 341. Doetsch J., Ingeman-Nielsen T., Christiansen A.V., Fiandaca G., Auken E. & Elberling B., 2015a. Direct current (DC) resistivity and induced polarization (IP) monitoring of active layer dynamics at high temporal resolution, Cold Regions Science and Technology, 119, 16-28. 10.1016/j.coldregions.2015.07.002. Doetsch J., Fiandaca G., Auken E., Christiansen A.V., Cahill A.G. & Jakobsen R., 2015b. Field-scale time-domain spectral induced polarization monitoring of geochemical changes induced by injected CO2 in a shallow aquifer, Geophysics, 80, WA113-WA126. 10.1190/geo2014-0315.1. Fiandaca G., Auken E., Christiansen A.V. & Gazoty A., 2012. Time-domain-induced polarization: Full-decay forward modeling and 1D laterally constrained inversion of Cole-Cole parameters, Geophysics, 77, E213-E225. 10.1190/geo20110217.1. Fiandaca G., Ramm J., Binley A., Gazoty A., Christiansen A.V. & Auken E., 2013. Resolving spectral information from time domain induced polarization data through 2-D inversion, Geophysical Journal International, 192, 631-646. 10.1093/gji/ggs060. Fiandaca G., Doetsch J., Vignoli G. & Auken E., 2015a. Generalized focusing of time-lapse changes with applications to direct current and time-domain induced polarization inversions, Geophysical Journal International, 203, 11011112. 10.1093/gji/ggv350. Fiandaca G., Christiansen A. & Auken E., 2015b. Depth of Investigation for Multi-parameters Inversions, Near Surface Geoscience 2015-21st European Meeting of Environmental and Engineering Geophysics, 1-4. 10.3997/22144609.201413797. Gazoty A., Fiandaca G., Pedersen J., Auken E., Christiansen A.V. & Pedersen J.K., 2012a. Application of time domain induced polarization to the mapping of lithotypes in a landfill site, Hydrology and Earth System Sciences, 16, 1793-1804. 10.5194/hess-16-1793-2012. Gazoty A., Fiandaca G., Pedersen J., Auken E. & Christiansen A.V., 2012b. Mapping of landfills using time-domain spectral induced polarization data: the Eskelund case study, Near

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Surface Geophysics, 10, 575-586. 10.3997/18730604.2012046. Gazoty A., Fiandaca G., Pedersen J., Auken E. & Christiansen A.V., 2013. Data repeatability and acquisition techniques for time-domain spectral induced polarization, Near Surface Geophysics, 11, 391-406. 10.3997/1873-0604.2013013. Johansson S., Fiandaca G. & Dahlin T., 2015. Influence of non-aqueous phase liquid configuration on induced polarization parameters: Conceptual models applied to a timedomain field case study, Journal of Applied Geophysics, 123, 295-309. 10.1016/j.jappgeo.2015.08.010. Johansson S., Sparrenbom C., Fiandaca G., Olsson P.-I., Dahlin T. & Rosqvist H., 2016. Investigations of a Cretaceous limestone with spectral induced polarization and scanning electron microscopy, Geophysical Journal International, Under Review. Lajaunie M., Maurya P.K., Fiandaca G., 2016. Comparison of Cole-Cole and Constant Phase Angle modeling in timedomain induced polarization. 4th IP Workshop, 6-8 June 2016, Aarhus, Denmark. Madsen L.M., Kirkegaard C., Fiandaca G., Christiansen A.V., Auken E., 2016. An analysis of Cole-Cole parameters for IP data using Markov chain Monte Carlo. 4th IP Workshop, 6-8 June 2016, Aarhus, Denmark. Maurya P.K., Fiandaca G., Auken E., Christiansen A.V., 2016. Lithological characterization of a contaminated site using Direct current resistivity and time domain Induced Polarization. 4th IP Workshop, 6-8 June 2016, Aarhus, Denmark. Olsson P.-I., Dahlin T., Fiandaca G. & Auken E., 2015. Measuring time-domain spectral induced polarization in the on-time: decreasing acquisition time and increasing signal-tonoise ratio, Journal of Applied Geophysics, 123, 316-321. 10.1016/j.jappgeo.2015.08.009. Olsson P.I., Fiandaca G., Larsen J.J., Dahlin T., Auken E., 2016. Doubling the spectrum of time-domain induced polarization: removal of non-linear self-potential drift, harmonic noise and spikes, tapered gating, and uncertainty estimation. 4th IP Workshop, 6-8 June 2016, Aarhus, Denmark. Pelton W.H., Ward S.H., Hallof P.G., Sill W.R., Nelson P.H., 1978. Mineral discrimination and removal of inductive coupling with multifrequency IP. Geophysics 43 (3), 588–609. Sato H.K., 2000. Potential field from a dc current source arbitrarily located in a nonuniform layered medium. Geophysics, 65 (6), 1726–1732. Van Voorhis G.D., Nelson P.H., Drake T.L., 1973. Complex resistivity spectra of porphyry copper mineralization. Geophysics 38 (1), 49–60 Vignoli G., Fiandaca G., Christiansen A.V., Kirkegaard C. & Auken E., 2015. Sharp spatially constrained inversion with applications to transient electromagnetic data, Geophysical Prospecting, 63, 243-255. 10.1111/1365-2478.12185. Wemegah D.D., Fiandaca G., Auken E., Menyeh A. & Danuor S.K., 2016. Spectral time-domain induced polarization and magnetic surveying – an efficient tool for characterization of solid waste deposits in developing countries, Near Surface Geophysics, Under Review.

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Examples of modelling IP in AEM data: synthetic and real data Viezzoli Andrea

Vlad Kaminski

Gianluca Fiandaca

Aarhus Geophysics Aps Lollandsgade 52, Aarhus, Denmark, DK-8000 [email protected]

Aarhus Geophysics Aps Lollandsgade 52, Aarhus, Denmark, DK-8000 [email protected]

HGG- Aarhus University Høegh-Guldbergs Gade 2 Aarhus, Denmark, DK-8000 [email protected]

SUMMARY There have been multiple evidences in the literature in the past several years of what has been referred to as IP effect in the Time Domain Airborne EM data (TDEM). This phenomenon is known to be responsible for incorrect inversion modelling of electrical resistivity, lower interpreted depth of investigation and lost information about chargeability of the subsurface as well as about other valuable parameters. Historically there have been many suggestions to account for the IP effect using the Cole-Cole model. In current paper we are showing the possibility to extract IP information from airborne TDEM data including inverse modelling of chargeability from airborne TDEM, both synthetic and actual VTEM data with a field example from Russia (Amakinskaya kimberlite pipe). The synthetic examples illustrate how it is possible to recover deep chargeable targets (depths to over 130 m) in association with both high electrical conductivity and in resistive environments. Furthermore, modelling of IP effects allows corrected resistivity models. The Amakinskaya kimberlite pipe results highlight the relevance of chargeability for kimberlite exploration. Key words: Airborne EM, IP, Cole-Cole, Kimberlite.

INTRODUCTION The IP effect in TDEM data can be observed in coincidentloop TDEM systems and is manifested as abnormally quick decay, which sometimes causes the measured voltage values in the receiver coil to demonstrate negative values. This phenomenon can significantly alter the shape of the transients and therefore may mislead the interpretation to recover false structures, with incorrect conductivity-thickness parameters. IP effect has been widely recognized in the ground-based Time Domain EM surveys, including work done by Kamenetsky et al. (2014). Nonetheless, for a long time it has been a standard practice within the geophysical community to neglect this effect in airborne data and eliminate any negative values, when inverting the TDEM data. There has been a recent and increasing interest in the IP effect in airborne data, as it carries potential for recovery of the Cole-Cole parameters (Cole and Cole, 1942), including chargeability information, which can be extracted from the airborne EM data, along with other Cole-Cole parameters. These recent attempts include work demonstrated in Kaminski et al. (2015), Viezzoli et al. (2013) and Viezzoli et al. (2015). IP2016 – 6-8 June, Aarhus, Denmark

1

The goal of the synthetic study, from which a short extract is presented here, is to address, under controlled conditions, the relevance of IP effect on heliborne TDEM data in different realistic scenarios, its impact on the data and the possibility of recovering the IP model parameters by means of multiparametric inversion. The results presented herein are currently under review in “Geophysics” The real case study deals with a classic geophysical target, i.e., kimberlite exploration. Even though it has long been known that, under certain conditions, the clay rich, altered kimberlite top faces can produce a measure chargeable signal, the examples of exploration exploiting IP effects in TDEM data are limited (e.g., Kamenetsky et al., 2014). In this paper we present results of IP modelling of VTEM data from Amakinskaya Kimberlite pipe, in Yakutia, eastern Russia. These results are under review in “Exploration Geophysics”.

METHOD AND RESULTS The synthetic models are used to simulate a series of VTEM full waveform (long pulse) data sets, which in turn are contaminated with noise and further inverted in order to study recoverability of various targets in different environments. In addition, some noise-contaminated data were artificially processed; replicating the advanced processing techniques required for optimal results of field data AIP modelling. In current study we present the results of the study of two synthetic models Kimberlite model: in this model, a synthetic kimberlite pipe was placed underneath 30 m overburden. The upper facies of the kimberlite (crater) was made chargeable and conductive, while the lower facies of kimberlite (diatreme) was made less conductive and non-chargeable. Recovery of depth to the bottom of chargeable target was studied. “Simple deep” chargeable model: in this model a series of conductive and chargeable targets were placed at increasing depths to the maximum depth of 150 m. Possibility to recover deep chargeable targets is studied in resistive and conductive host rock environments. The extraction of Cole-Cole parameters on both the synthetic and the field data is handled by means of Laterally Constrained Inversion (LCI) or Spatially Constrained Inversion (SCI). Both inversions (LCI and SCI) use similar forward mapping kernel, based on 1D considerations, in which the complex resistivity (dispersive model) is given by

the model of Cole and Cole. The inversion algorithm, modified as per Fiandaca et al. (2012) is providing combined estimation of all four parameters from equation (1) in two modes described above (LCI and SCI). The inversions are subject for regularization and user-defined constraints.

effects of duly pre-processing the data and of a-priori information (e.g., from boreholes).

Kimberlite model results: The true model is shown in Figure 1a and Figure 1b. As it can be seen from the figure the kimberlite model consists of 4 general rock types: Overburden (OB), Crater facies of kimberlite (S), Diatreme facies of kimberlite (M) and the host rock (HR).

Figure 1. Synthetic kimberlite true 2D model. (a) Electrical resistivity model (top 150 m). (b) Chargeability model (top 150 m). The next step was to invert the synthetic data in multiparametric mode with simultaneous recovery of four Cole-Cole parameters. The latter required testing different starting models. In general, the inverse problem is underdetermined and considering four varying parameters, the problem can become unstable and sensitive to starting models. Our objective was to test a wide selection of starting models, as well as different types of constraints (vertical and horizontal) imposed upon the  and C parameters to test which role locking  and C plays in ability to recover the true model. Starting resistivity values were tested from 10 to 1000 Ohm m; starting chargeability values were tested ranging from 10 to 100 mV/V; the starting time constant () values were tested from 10-4 to 10-2 s, which are consistent with range of this parameter in known airborne TDEM systems. Kamenetsky et al. (2014) showed that the frequency parameter C recovered from inversion of real TDEM data may reach 1. Based on this, the starting frequency parameter C was tested ranging from 0.3 to 0.7 values. These starting parameters yield 81 unique combinations. All of these combinations were used to generate starting model files. Two sets of constraints were used on  and C, first all 81 combinations were inverted using “soft” constraints (allowing  and C to vary rather freely spatially in the model space), then the same starting parameter combinations were inverted using “hard” constraints (locking the spatial variance in  and C to 1%). Therefore, a total of 162 realizations were carried out. The inversion results were then assessed by misfit values. Global misfit values, normalized by standard deviations produced misfits ranging from 0.82 to 313.20 (depending on the starting parameters and type of constraints). Figure 2 shows on of the inversion results that produce good data fit. No a-priori and “soft” constraints on  and C were used. The model recovered is generally in fair agreement with the true model. However, in this case, the C parameter for the overburden is not recovered. In order to recover the shallow C value, very loose vertical constraints were needed (not shown). We also assessed the relevance and

Figure 2. Inversion of synthetic kimberlite VTEM data with starting Cole-Cole parameters:  = 1000; m0 = 50,  = 10-3; C = 0.3 and “soft” constraints on  and C. Simple deep model results: a synthetic model is introduced with a series of conductive and chargeable targets, placed at increasing depth along the profile (Figure 3).

Figure 3. Left: synthetic “simple deep” true model ( and C parameters fixed to 10-3 and 0.5 respectively); top 150 meters are shown. Right: simulated noise-free transients. The inversion results (Figure 4) show that, in presence of favourable conditions (i.e., combinations of physical properties of the different strata) it is possible to recover information about chargeable targets in excess of 100 m depth straight from airborne data using the inversion in IP mode for the data simulated for the VTEM waveform. Other tests, which go beyond the scope of this abstract prove that, on the other hand, in some cases deep conductors can be masked by shallow chargeable layers.

In addition to strong IP effect, which made conventional inversion challenging, there was a strong electrified industrial infrastructure situated just 200 meters east of the Amakinskaya pipe, which seriously affected both EM and magnetic data. This cultural noise had to be removed from all data sets in order to proceed further with inverting the data. In general, the IP effect may be indicative of the clay alteration, which, in turn, may be present in upper (weathered) facies of a kimberlite. Interpretation of IP effect over kimberlites for ground TDEM surveys has been previously described in the literature (Kamenetsky et al., 2014) and becomes increasingly attractive in case with airborne TDEM data sets, as it allows extraction of chargeability, along with other parameters, such as time constant () and frequency parameter (C). Figure 4. Inversion of synthetic VTEM data for “simple deep” model in IP mode with the following starting model parameters:  = 1000; m0 = 10,  = 10-3; C = 0.5 and “hard” constraints on  and C. Amakinskaya Kimberlite pipe results: From the geological standpoint, the area surrounding Amakinskaya kimberlite pipe belongs to a sedimentary basin with widespread outcrops of clays and alevrolites of Jurassic age (J1or), which unconformably overlay Cambrean limestone complex (Є3hl). Triassic basalts (T1kt) are also widespread in the area, especially to the north from the pipe. Amakinskaya Kimberlite pipe shows a great deal of anisotropy in the vertical direction, shifting from weathered, clayish upper facies, affected by permafrost to consolidated hard kimberlite below 30 m depth. This obviously has reflection in the physical properties of the kimberlite. Resistivity and chargeability changes with depth, showing lowering resistivity and increasing chargeability values in the upper facies of the kimberlite, while magnetic susceptibility increases with depth, as kimberlite consolidates (Bondarenko and Zinchuk, 2004). The airborne survey was flown in late 2014 using a VTEM system and the data were seriously affected by the IP effect (Figure 5b). It should be noted however, that IP effect over the kimberlite, although evident in the transients, does not result in negative voltage measurements and therefore may not be instantly obvious in the data space at a first glance.

As a result of SCI inversion approach with IP modelling, all four Cole-Cole parameters were extracted. The target misfits of the inversions were achieved, producing distributions of Cole-Cole parameters, which were further interpolated to populate 3D volumes. The distributions of electrical resistivity and chargeability with depth are shown in Figure 6. Overall, the results of the inversions allow to clearly differentiate between the kimberlite and the host rock. The results are shown in Figure 7 as a compilation of all inversion results (including Mag), interpolated along VTEM flight line 9310 and shown as a depth section of electrical resistivity, chargeability and magnetic susceptibility.

Figure 6. 3D distribution of electrical resistivity and chargeability recovered by SCI inversion with IP modelling over Amakinskaya kimberlite pipe, shown as series of depth slices.

Figure 5. Location of Amakinskaya kimberlite pipe (northeastern Russia); (a): VTEM flight lines shown over Landsat image. (b): IP effect measured over the kimberlite, shown in VTEM individual transients.

The physical properties recovered through inversion of the VTEM data were compared to those derived from laboratory measurements on kimberlite samples (Figure 8). There is good agreement on the resistivity of the different facies, from the weathered kimberlite top to the deeper kimberlite breccia and carboniferous kimberlite. The clean limestones in the laboratory data display higher resistivities than those recovered by VTEM, due to the effect of saline water known to be present in the limestones, forming a confined aquifer in the area.

CONCLUSIONS A number of synthetic models are shown in current study, including those taken from real life scenarios (sulphides and kimberlite), as well as those models describing hypothetical but probable situations (“deep models”). It becomes evident from synthetic modelling that the multiparametric inversion of AEM in IP mode may be effective in cases, when no other approach can yield accurate results and in some cases drastically improve the results of inversions in real life. Such cases are: improved resistivity cross-sections, detection of chargeable targets based on only airborne TDEM data, detection of deep-seated chargeable targets (to the depth of approximately 150 m), under certain conditions, imaging targets at depth. Improved interpretation (e.g., differentiating between regolith and bedrock chargeable anomalies). It should also be stressed that, under certain conditions, shallow chargeable layers can effectively mask deep conductors that would have been otherwise resolvable by the given AEM system.

Figure 7. Compilation of inversion results over VTEM flight line 9310. Susceptibility is also in good agreement, even though is displays less vertical variability. No direct measurements on chargeability are available on the Amakinskaya pipe. However, Kamenetsky et al. (2014) report recovered Cole Cole models from ground TDEM soundings affected from IP from the nearby Baitakhskaya pipe. They report values (m0=210 mV/V, =800 s, c=1) close to those we obtained from the VTEM data.

The real case study shows that applying the Cole-Cole model in the inversions of TDEM data enables mapping the 3D distribution of physical parameters in the subsurface, which bring new value to mineral exploration. . It should be noted, that the greatest visibility of the pipe is evident in recovered chargeability, which was made possible by virtue of the SCI inversion with Cole-Cole modelling. REFERENCES Cole, K. S., and Cole, R. H., 1942, Dispersion and absorption in dielectrics: Journal of Chemical Physics 9-4, 341 – 351. Fiandaca, G., Auken, E., Christiansen, A. V. Gazoty, A., 2012, Time-domain-induced polarization: Full-decay forward modelling and 1D laterally constrained inversion of Cole-Cole parameters, Geophysics 77, E213 - E225. Kamenetsky, F., Trigubovich, G., Chernyshev, A., 2014, Three lectures on geological medium induced polarization, Ludwig-Maximilian University of Munich, ISBN: 978-3941352-65-0, 43 - 54. Kaminski, V., Oldenburg, D., 2012. The geophysical study of Drybones kimberlite using 3D Time Domain EM Inversion and 3D ZTEM inversion algorithms, 22-nd ASEG Intern. Geoph. Conf. and Exhib., Expanded Abstract, Brisbane, Australia, 4p. Kaminski, V., Viezzoli, A., Menghini, A., Fiandaca, G., 2015, Case studies of modelling IP effect in AEM data, EAGE 21-st Europ. Meet. of Envir. and eng. Geophys, Expanded Abstracts, Torino, Italy, 4p. Viezzoli, A., Christiansen, A.V., Auken, E., Sørensen, K., 2008, Quasi-3Dmodeling of airborne TEM data by spatially constrained inversion, Geophysics 73, 105–113.

Figure 8. 1D model of different physical properties above Amakinskaya pipe.

Viezzoli, A., Kaminski, V., Ley Cooper, Y., Hardy, L., Fiandaca, G., 2015, Improving modelling of AEM data affected by IP, two case studies, 24th Internat. Geophys. Conf. and Exhib., Extended Abstracts, 1, Perth, Australia, 5p.

Abstracts from poster session A

Effect of mineralogy on Spectral Induced Polarization of sediments: A conceptual model of membrane polarization Konstantin Titov

Daniil Chuprinko

St. Petersburg State University St. Petersburg State University 7-9 Universitetskaya naberezhnaya, 7-9 Universitetskaya naberezhnaya, 199034 St. Petersburg, Russia 199034 St. Petersburg, Russia [email protected] [email protected]

SUMMARY We discuss a membrane polarization effect produced by the difference in mineral composition of walls of two sequential pores, which can occur, for example when the first pore is encased in calcite and the second – in alumosilicate. We assume that the zeta potential values of these minerals differ from each other. This leads to a difference in the cation and anion transference numbers (even if the above two pores are of the same radius) and, therefore, to a membrane polarization when an electrical field is applied. We model this effect for two pores filled with water of low salinity (1 and 10 Mol.m3), and for three pore radius values (10-6, 10-7 and 10-8 m). We assume that one pore is “passive,” i.e., the interface potential is zero, and the other pore is “active”, with zeta potential of -75 mV. We calculate the maximum values of phase shift and the corresponding values of peak frequency as a function of lengths of the active and passive pores. We show that the maximum phase shift corresponds to a case where the pores have the same length. The shift values are between 13 and 210 mrad depending on the ion concentration in free water and on the pore radius. The peak frequency distributions for all modeled cases are very similar and, therefore, depend mostly on the pore length. We assume that the ratio of the pore length to its diameter can achieve values between 10 and 50. With this assumption, for the pore radius of 10-8, 10-7, and 10-6 m, the membrane polarization effect can be detected in the frequency range from 1.6 kHz to 1MHz, from 20 Hz to 1 MHz, and from 0.20 Hz to 1 MHz, respectively. Our modeling shows that the effect of mineral composition can appear superimposed on the polarization effect of the Stern layer, which coats the mineral grains.

the mobility difference or radius difference in a sequence of two pores (e.g., Marshall and Madden, 1959; Bücker and Hördt, 2013). Also, IP can be produced by the MaxwellWagner polarization when electrical field crosses materials of different electrical properties (e.g., Tabbagh et al., 2009). In this paper, we focus on the membrane polarization. In cases of both the mobility difference and the ion radius difference, the ion transference numbers in two pores differ from each other; therefore, an ion concentration gradient occurs when an electrical field is applied. This gradient leads to a secondary electrical field, which produces a phase shift between the electrical current and the tension. However, the same effect can occur in a case where the walls of the adjacent pores are built of different minerals, with different interface potentials, even if the radii of the two pores are equal. To the best of our knowledge, this effect has not yet been studied. In this paper, we analytically investigate its properties.

THEORY The theory of membrane polarization was first proposed by Marshall and Madden (1959). They postulated that the membrane polarization is produced by a concentration gradient resulting from an external electrical field along a sequence of pores with different ion mobility values. Fridrikhsberg and Sidorova (1961) and Kormiltsev (1963) proposed a different explanation of the membrane polarization, based on a difference in concentration of cations and anions in wide and narrow pores. Recently, Bücker and Hördt (2013) modified the Marshall and Madden’s theory to explicitly include the chemical parameters (zeta potential and partition coefficient), as well as the textural ones (pores radius and length). In this paper, we use the latter theory as a basis. We assume that ion concentrations in a cylindrical pore system ( c p and c n ) in the directions perpendicular and parallel to the pore axis, are independent of each other, c p,n ( x, r )  co ( x )  b p,n (r )

Key words: Spectral Induced Polarization, Membrane Polarization, Zeta Potential, Mineral composition.

where

c0 ( x)

Causes of induced polarization (IP) in sediments are primarily related to polarization of the Stern layer of the electrical double layer (EDL) coating mineral grains (e.g., Revil, 2012). The second cause of IP is the membrane polarization produced by IP2016 – 6-8 June, Aarhus, Denmark

1

(1)

is the concentration along the pore far from the

pore walls in Mol.m3,

INTRODUCTION

,

b p ,n ( r )

describes variations of the

dimensionless concentration across the pores, indices p and n stand for cations and anions, respectively. The current density averaged by the pore section is as follows,

Membrane polarization and mineralogy Titov and Chuprinko 

j p ,n   F

where

p ,n b p ,n

k BT c ( x) 0 x

e

 F

p ,n

b p ,n c 0 ( x ) E

(2)

96 485 is the Faraday constant in C .Mol-1,

F 

1.602.10-19 is the elementary charge in C, ion mobility in m2(V.s)-1, in m2.s-1,

,

kB

D

p ,n



p ,n



D

p ,n e

The ion concentration distributions in the diffuse layer along the pores radius are calculated,

e 

is the

k BT

is the ion diffusion coefficient

=1.38.10-23 is the Boltzmann constant in J.C-1,

r

2

b

p ,n

( )d

   

,

(7)

and numerically integrated by the pores section (Eq. (3)). According to Bücker and Hördt (2013), we include the Stern layer contribution to calculate the ion concentration in the pores:

r

2

 e (  ) b p , n  exp    k BT 

E

is the electrical field in V.m-1, and

b p ,n 

equilibrium with pore fluid produce a negligible SIP response due to very small surface charges”.

(3)

0

is the dimensionless concentration of ions averaged by section of the pore with radius r (  being the cylindrical coordinate). As was shown by Bücker and Hördt (2013), Eq. (2) is identical to Eq. (6) of Marshall and Madden (1959); therefore, their solution is applicable. However, the general form of the transference numbers,

t p ,n

,

includes not only the ion mobility (Marshall and Madden, 1959) but also the average ion concentrations (e.g., Bücker and Hördt, 2013): tp 

tn 

 pb p

where

fp

Z ( ) 

 pb p   nbn

.

(8)

is the partition coefficient defined as the ratio

L1



p 1b p 1 c 0 F

t p 2 tanh( X 1 (  ))

(5)

(t p1 

B A

( S 2  S1 ) X 1 ( ) S 1 2

 nbn

,

between the Stern layer charge density and the whole EDL charge density (e.g., Revil, 2012). Finally, the impedance of the pore sequence is calculated according to the Marshall and Madden (1959) equation,



(4)

 p b p   nbn

bp  fp ~ bp  1 fp



A

tp2 

,

2

X

B t2 t p 1 p 2 tanh( X

where  is the angular frequency, Therefore,

t p ,n

depend on the pore radii (see Eq. (1)). For

simplicity, we consider  p difference in

bp

and

bn

 n

and we focus on the

in the EDL. To obtain

values,

b p ,n

first the potential in the diffuse layer must be calculated:  ( )  

J 0 ( ik  )

,



is the zeta potential in V,

Bessel function,

i 

1

,

is the Debye length in m, relative permittivity, and

k   D

  80

0 

m,

,

A 

L1

L1

,

L2

 i X 1, 2 ( )    2D t p n1, 2 b p 1, 2 

 L1, 2   2 

(  ))

is the length of the pore S 1, 2 

t n1, 2

,

and

t p 1, 2

are dimensionless quantities,

and indices ”1” and “2” refer to the pore with smaller (“passive) and greater (“active”) interface potential, respectively.

(6)

J 0 ( ikr )

where

in

~ b p1 B  ~ b p2

2

(9)

)

2 ( ) S 2



1

J 0 (x)

in

is the zero order

m-1,  d 

2 c 0 eF

is the dimensionless water 8.54.10−12 is the vacuum

permittivity in F·m−1. The difference in zeta potential values in a sequence of two pores of the same radius can occur if the pores walls are built of different materials, with different interface potential values. An example can be a carbonate mineral in contact with silicate or alumosilicate. For silicates and alumosilicates, the zeta potential values (at pH about 7) are usually between -20 and 80 mV, depending on the water salinity (e.g., Revil 2003, Leroy and Revil 2004). For carbonate minerals, the zeta potential values are significantly lower in absolute values (e.g., Guichet et al., 2006), and can approach zero. Wu et al. (2010) argued that “calcium carbonates in thermodynamic

IP2016 – 6-8 June, Aarhus, Denmark

MODELING

 0 k B T

We model two parameters of spectral IP: maximum values of the phase shift,  max , and the corresponding peak phase frequency. The calculations are carried out for two values of the free pore water salinity, namely 1 Mol.m-3 and 10 Mol.m-3, and for the pore radius values of 10-8, 10-7, and 10-6 m. We consider the ion diffusion coefficient to be constant for cations and anions, D p  D n  10  9 m2.s-1, and the zeta potential to be -75 mV. For active pore we apply the average partition coefficient obtained for clays, q p  0.85 (see Revil, 2012, his Fig. 3). We calculate the phase shift, as well as the peak frequency, f c , as functions of the pore lengths. We present the data as the maps of calculated values vs. pore lengths (Fig. 1). In the maps, we also show values of three peak frequencies corresponding to two cases: (1) common limits of the spectral IP measurements (between 1 mHz and 20 kHz); and (2) limits of the wideband (see e.g., Volkmann and Klitzsch, 2015) measurements (between 1 mHz and 1MHz).

2

Membrane polarization and mineralogy Titov and Chuprinko radii and the electrical double layer: Geophysical Journal International, DOI: 10.1093/gji/ggt136.

DISCUSSION The maximum values of

 max

are found to be between 13 and

210 mrad depending on the ion concentration in free water and the pore radius (Fig. 1). The values increase with the decrease of the water salinity and the pore radius. This effect reflects the growth of the Debye length and, therefore, of the diffuse layer thickness relative to the pore size. The maximum values of  max correspond to the case of equal pore lengths. The behavior of

fc

is very similar in all cases (shown in Fig. 1 for

the case of the water salinity of 1 Mol.m-3 and the pore radius of 10-8 m only), which indicates that the main parameter determining f c is the pore length. The maximum curvature of the isocurves of For

 max

fc

corresponds to the case where

L1  L 2

.

Guichet, X., Jouniaux, L., and Catel, N., 2006, Modification of streaming potential by precipitation of calcite in a sand–water system: laboratory measurements in the pH range from 4 to 12: Geophysical Journal International, 445–460, DOI: 10.1111/j.1365-246X.2006.02922.x Fridrikhsberg, D.A., and Sidorova, M.P., 1961, Issledovanie sviazi yavlenia vyzvannoi polarizatsii s electrokineticheskimi svoistvami kapillarnyh sistem (A study of relationship between the induced polarization phenomenon and the electro-kinetic properties of capillary systems): Vestnik Leningradskogo Universiteta, Seria Chimia 4, 222– 226 (In Russian). Kruschwitz, S., Binley, A., Lesmes, D., and Elshenawy, A., 2010, Textural controls on low-frequency electrical spectra of porous media: Geophysics, vol. 75, issue 4, p.113, DOI: 10.1190/1.3479835

, we establish a threshold of 10 mrad, considering

that values below it would be under the detection limit because of the capacitive coupling and Maxwell-Wagner polarization. We assume that the pores can be elongated, i.e., their aspect ratio ( L / d ) can achieve the characteristic values of 10 and 50 (see Weber at al., 2014 for clay particles). In the phase maps, we show areas corresponding to these aspect ratio values by hatch. These hatches are also limited to isocurves corresponding to the higher frequency limit of the broadband IP measurements (1 MHz). Analysis of the maps shows that, for the narrowest pores (10-8 m), the effect is very strong (up to ~210 mrad), and can be detected in the frequency range between 1.6 kHz and 1 MHz. For larger pores (10-7 and 10-6 m), the effect is less pronounced (up to 130 and 13 mrad, respectively), and can be detected starting from the frequency values of 20 and 0.2 mrad, respectively. Therefore, it can be observed within the range of the common IP measurements. Our analysis shows that the studied effect, especially for the pore radii of 10-7 and 10-6 m, can be superimposed on the polarization effect of the Stern layer coating the mineral grains.

CONCLUSIONS Our modeling shows that the IP effect of mineral composition can be significant. It can be detected in cases of fresh water, large values of the zeta potential difference between the adjacent pores, and in elongated pores. For three modeled pore radius values, f c can be in the range between 1.6 kHz and 0.2 Hz; therefore, it can be observed in the range of typical spectral IP measurements, and can be superimposed on the polarization effect of the Stern layer coating the mineral grains.

ACKNOWLEDGMENT This paper was supported by St. Petersburg State University (grant # 3.37.134.2014).

REFERENCES Bücker, M., and Hördt, A., 2013, Analytical modelling of membrane polarization with explicit parametrization of pore IP2016 – 6-8 June, Aarhus, Denmark

Kormiltsev, V.V., 1963, O vozbuzdenii i spade vyzvannoi polarizatsii v kapillarnoi srede (On excitation and decay of Induced Polarization in capillary medium): Izvestia AN SSSR, Seria Geofizicheskaya (Solid Earth Physics) 11, 1658– 1666 (In Russian). Marshall, D.J., and Madden, T.K., 1959, Induced polarization, a study of its causes: Geophysics 24 (1), 790– 816. Revil, A., 2012, Spectral induced polarization of shaly sands: Influence of the electrical double layer: Water Resources Research, 48, p. 2517, DOI:10.1029/2011WR011260. Leroy, P., and Revil, A, 2004, A triple-layer model of the surface electrochemical properties of clay minerals: Journal of Colloid and Interface Science, 270, 371–380, DOI:10.1016/j.jcis.2003.08.007. Revil, A., Naudet, V., Nouzaret, J., and Pessel, M., 2003, Principles of electrography applied to self-potential electrokinetic sources and hydrogeological applications: Water Resources Research 39, 1114, DOI:10.1029/2001WR000916. Tabbagh, A., Cosenza, P., Ghorbani, A., Guérin, R., and Florsch, N., 2009, Modelling of Maxwell–Wagner induced polarisation amplitude for clayey materials: Journal of Applied Geophysics, 67, 109–113, DOI:10.1016/j.jappgeo.2008.10.002. Weber, C., Heuser, M., and Stanjek, H., 2014, A collection of aspect ratios of common clay minerals determined from conductometric titrations: Clay Minerals, 49, 495–498, DOI: 10.1180/claymin.2014.049.3.10. Volkmann, J., and Klitzsch, N., 2015, Wideband impedance spectroscopy from 1 mHz to 10 MHz by combination of fourand two-electrode methods: Journal of Applied Geophysics, 114, 191–201, http://dx.doi.org/10.1016/j.jappgeo.2015.01.012. Wu, Y., Hubbard, S. S., Ajo Franklin, J. B., Williams, K. H., 2010, Pore fluid chemistry and spectral induced polarization signatures of calcium carbonate: American Geophysical Union, Fall Meeting 2010, Abstract #NS33A-06.

3

Figure 1. Maximum phase shift (a, c, e, d, f) and peak frequency (b) as functions of the passive (L1) and active (L2) pore length. The phase shift threshold is 10 mrad. Colored lines in panels a, c, d, e, f are peak frequency values: red – 10 mHz, green – 20 kHz, and blue – 1 MHz. Cross-hatch shows areas when the pore aspect ratio, L/d, is less than 10, hatch – less than 50. Numbers indicate the minimum peak frequency values, corresponding to the assumed ratio. Panels a, b, c, d: water salinity is 1 Mol.m-3; e, f - 10 Mol.m-3; panels a, b, e: r is 10-8 m; c, f : r is 10-7 m; d: r is 10-6 m.

Evaluation of low frequency polarization models using well characterized sintered porous glass samples Jan Volkmann

Norbert Klitzsch

Applied Geophysics and Geothermal Energy, E.ON Energy Research Center RWTH Aachen University Mathieustr. 10, 52074 Aachen, Germany [email protected]

Applied Geophysics and Geothermal Energy, E.ON Energy Research Center RWTH Aachen University Mathieustr. 10, 52074 Aachen, Germany [email protected]

SUMMARY We assess the results of published theoretical and experimental findings regarding low frequency rock polarization for a reference system, consisting of sintered porous glass samples. Thereby, we benefit from well characterized samples, which allow for direct tests of theoretical predictions and empirical relations. We find that: (1) The correlation σ″~Sm is stronger than σ″~Spor for a wide range of fluid conductivities and frequencies above 1 Hz. (2) Correlation coefficients for the imaginary conductivity to inner surface area relations are strongly frequency dependent. (3) Normalized chargeability, obtained by fitting a Cole–Cole model to the spectral data, provides a fair alternative to single frequency information. (4) Salinity dependence of proportionality factors a1=Sm/σ″ and a2=Spor/σ″ due to a salinity dependent partition coefficient is confirmed qualitatively. Quantitative theoretic predictions of a1 or a2 fail due to the assumption of non-reduced Stern layer mobility for clay free silica. (5) Earliest grain size related models provide the best quantitative estimate of relaxation time. (6) Results agree well with published data for sands and sandstones with respect to (i) quantitative estimates of a1 or a2 and (ii) influences of rock structural parameters on relaxation time. The study introduced here was published by Volkmann and Klitzsch (2016).

rock samples has been analysed recently to verify theoretical and empirical relations (e.g. Weller et al., 2010;Weller et al., 2013). We assess the results of these published theoretical and experimental findings using a reference system, consisting of sintered porous glass samples. In particular, we address the following questions: 1.

2. 3.

4. 5.

Is the of correlation σ″ ~ Sm of the imaginary part of conductivity to specific surface area per unit mass stronger than the correlation σ″ ~ Spor of imaginary part of conductivity to specific surface area per unit pore volume? Does this correlation depend on salinity or frequency? Is there an advantage in frequency dependent measurement, e.g. by correlating normalized chargeability mn ~ Sm and mn ~ Spor instead of imaginary part of conductivity σ″ ~ Sm and σ″ ~ Spor to specific surface area? Are the quantitative relations σ″ = a1Spor and σ″ = a2Sm valid, using plausible model parameters? Which model provides the best quantitative estimate for Cole-Cole relaxation time τCC?

METHODS

Key words -Impedance spectroscopy -Spectral induced polarization -Low frequency polarization models

INTRODUCTION It is generally argued that low frequency electrical polarization is caused by charged mineral surfaces leading to an electrical double layer (EDL) in the vicinity of the inner rock surface. The counterions in the EDL, which compensate the surface charges of the rock in the electrolyte, interact with an external electric field and cause the polarization of rocks, i.e. lead to a frequency dependent complex conductivity of water saturated rocks. For rocks containing ore minerals or electronic conductors an additional polarization process occurs, often named electrode polarization (Pelton et al., 1978; Wong, 1979), which is not considered here. For a quantitative description of the complex, frequency dependent conductivity of ore-free rocks partially competing theories were published (e.g. Revil and Florsch, 2010; Revil, 2012; Bücker and Hördt, 2013a). Moreover, an extensive database for a wide range of IP2016 – 6-8 June, Aarhus, Denmark

1

Figure 1. Exemplary sintered porous borosilicate samples, manufactured by ROBU® Glasfilter-Geräte GmbH. (a): Dry sample with dpor,lm = 63.25 μm (Sample P2); (b): Saturated sample with dpor,lm = 12.65 μm (Sample P4). We used porous borosilicate samples (Fig. 1) as an experimental reference system as described by Volkmann and Klitzsch (2016). These are sintered porous ceramics, manufactured by ROBU® Sintered Glassfilters, of pure

borosilicate 3.3 standard glass according to ISO 4793 and DIN/ISO 3585. Main advantage, regarding the purpose of this study, is their well-known chemical composition and nominal pore size, both given in the above mentioned DIN/ISO norms. We used samples with nominal pore size ranges between 0.9 μm-1.4 μm and 100 μm-160 μm. The cylindrical samples had a length of 0.03 m and diameter of 0.02 m. We provide a summary of relevant sample properties in Table 1. Table 1. Nominal pore size dpor (MICP, given by ROBU® Glasfilter-Geräte GmbH, cf. ISO 4793), logarithmic mean of nominal pore size dpor,lm, logarithmic mean of (independently measured) grain diameter dgrain,lm, porosity (weighing), specific surface area Sm (BET, given by ROBU® Glasfilter-Geräte GmbH) Table modified according to Volkmann et al. (2013).

As described by Volkmann and Klitzsch (2015), it is advantageous to study Impedance Spectroscopy (IS) data over a wide frequency range, at least if subsequent model parameterizations shall be applied for further analysis. Thus, we follow the approach of Volkmann and Klitzsch (2015), using a combination of four- and two-electrode methods to enable wideband IS data from 1 mHz to 10 MHz. We conducted IS measurements under: 1.

2.

3.

4.

Variation of pore fluid salinity. We use NaCl solution in a conductivity range between 3⋅10-4 Sm-1 and 6⋅10-2 Sm-1. Variation of predominant pore diameter. We use 8 different sample types with pore diameters dpor,lm between 1.12 μm and 126.5 μm, cf. Table 1. Variation of grain diameter. We use 8 different sample types with (logarithmic mean) grain diameter dgrain,lm between 2.81 μm and 316.2 μm, cf. Table 1. Variation of Sm (BET) between 0.085 m2g-1 and 1.750 m2g-1 (Table 1) and corresponding variation of Spor, cf. Table 1.

The resulting IS data were processed according to Volkmann and Klitzsch (2015) and analysed using a Cole–Cole model (e.g. Dias, 2000).

Stern layer polarization models. Quantitatively, a1 and a2 agree with earlier experimental (sandstone sample) results, but imply a strongly reduced Stern layer mobility and/or partition coefficient. Another open question is, if there is any advantage in frequency dependent measurements compared to single frequency information regarding Spor/Sm determination. To resolve this issue, we studied the quality of σ″ ~ Sm and σ″ ~ Spor relations for a set of separate frequencies between 10 mHz and 100 Hz (Fig. 4). As measure of quality, we used the correlation coefficient R2 of the theoretically suggested linear fit. For comparison, we used the corresponding relation between normalized chargeability mn = m⋅σ0 (from Cole–Cole model) and Spor or Sm as typical parameter of frequency dependent measurements. Examples for mn at σf ≈ 3⋅10-4 Sm-1 are given in Figures 5 and 6. As a result, the correlation coefficients for σ″ are strongly frequency dependent and normalized chargeability provides a fair alternative to single frequency information.

Figure 2. Dependence of imaginary conductivity σ′′10 Hz (blue crosses) on specific surface area per unit pore volume Spor (from BET, Table 1 and equation 22). A linear correlation σ′′10Hz = a1 · Spor (red line) with a1 = 2.1 · 10−12 S is found (R2 = 0.84).

Figure 3. Dependence of imaginary conductivity σ′′10Hz (blue crosses) on specific surface area Sm (from BET, Table 1). A linear correlation σ′′10Hz = a2 · Sm (red line) with a2 = 5.2 · 10−9 S kg m−3 is found (R2 = 0.94).

RESULTS A main controversy is, if imaginary conductivity rather controlled by specific surface area per unit pore volume Spor (in m-1) or specific surface area per unit mass Sm (in m2g-1). In this respect, the quantitative model predictions have been made recently. Exemplary results at a selected single frequency of f = 10 Hz and fluid conductivity of σf ≈ 3⋅10-4 Sm-1 are shown in Figures 2 and 3. Here, we find a linear relation σ″10Hz = a1Spor with a1 = 2⋅10-12 S with a correlation coefficient of R2 = 0.84 and a relation σ″10Hz = a2Smwith a2 = 5.2⋅10-9 S kg m-3 with a correlation coefficient of R2 = 0.94. Thus, we find a stronger correlation of σ″10Hz to Sm than to Spor, which is suggested from recent

Figure 4. Dependence of correlation coefficient R2 on frequency f for σ″~Sm (red) and σ″~Spor (blue) relation at a fluid salinity of σf ≈ 3 · 10−4 Sm−1. Dotted lines show R2 for the corresponding mn ∼ Sm and mn ∼ Spor relations.

The slight difference in a1 and a2, e.g. compared to the data of Weller et al. (2010), may be explained by a salinity dependent partition coefficient as postulated by Leroy et al. (2008). To resolve this issue, we repeated our studies at the three additional fluid conductivities. We confirm the expected increase in a1 and a2 with salinity (Figs. 7 and 8), except for the highest salinity. Normalized chargeability mn increases with salinity up to the highest salinity. However, the salinity and pH dependent partition coefficient is not sufficient to explain the data quantitatively, if we do not assume a reduced counterion mobility at the same time. Numerous hypotheses exist on the predominant influence on relaxation time and/or characteristic time τ. As an advantage of our reference system, e.g. compared to the similar studies of Revil et al. (2012), we have independent information about pore and grain diameters (Table 1). A power law fit leads to a 1.3±0.2 dependence 𝜏𝐶𝐶 = 1.8 ⋅ 105 ⋅ 𝑑por,lm on logarithmic mean dpor,lm of nominal pore size (Fig. 9). Similarly, we find a 1.3±0.2 relation of 𝜏𝐶𝐶 = 5.3 ⋅ 104 ⋅ 𝑑grain,lm between relaxation time τCC and logarithmic mean dgrain,lm of the independently measured grain diameters (Fig. 10). These are results are in good agreement with earlier results (cf. Volkmann and Klitzsch, 2010, their Table 1). Following theoretic suggestions of a quadratic model, we find 𝜏𝐶𝐶 = (7.2 ± 3.2) ⋅ 108 ⋅ 2 2 𝑑por,lm and 𝜏𝐶𝐶 = (1.2 ± 0.5) ⋅ 108 ⋅ 𝑑grain,lm . These results support earliest grain size related model approaches (Schwarz, 1962) under the precondition of a non-reduced diffusion coefficient.

Figure 5. Dependence of normalized chargeability mn (blue crosses) on specific surface area per unit pore volume Spor (from BET, Table 1 and equation 22). A weak linear correlation mn = a1 · Spor (red line) with a1 = 1.07 · 10−11 S is found (R2 = 0.47).

Figure 6. Dependence of normalized chargeability mn (blue crosses) on specific surface area Sm (from BET, Table 1). A linear correlation mn = a2Sm (red line) with a2 = 2.75 · 10−8 S kg m−3 is found (R2 =0.78).

Figure 8. Dependence of the slope a1 at fopt = 10 Hz and the slope a1 of the linear mn ∼ Spor relation on fluid conductivity σf.

Figure 8. Dependence of the slope a2 at fopt = 10 Hz and the slope a2 of the linear mn ∼ Sm relation on fluid conductivity σf.

Figure 9. Dependence of Cole-Cole relaxation time (blue crosses) on pore diameter dpor,lm. A dependence of 𝟏.𝟑±𝟎.𝟐 𝝉𝑪𝑪 = 𝟏. 𝟖 ⋅ 𝟏𝟎𝟓 ⋅ 𝑑𝐩𝐩𝐩,𝐥𝐥 , R2 = 0.76 (red line) on pore diameter is found (Volkmann et al., 2013). A fit with fixed 𝟐 exponents leads to 𝝉𝑪𝑪 = (𝟕. 𝟐 ± 𝟑. 𝟐) ⋅ 𝟏𝟎𝟖 ⋅ 𝑑𝐩𝐩𝐩,𝐥𝐥 , 2 R = 0.31 (green line).

Figure 10. Dependence of Cole-Cole relaxation time (blue crosses) on grain diameter dgrain,lm. A dependence of 𝟏.𝟑±𝟎.𝟐 𝝉𝑪𝑪 = 𝟓. 𝟑 ⋅ 𝟏𝟎𝟒 ⋅ 𝑑𝐠𝐠𝐠𝐠𝐠,𝐥𝐥 , R2 = 0.76 (red line) on grain diameter is found. A fit with fixed exponents leads to 𝟐 𝝉𝑪𝑪 = (𝟏. 𝟐 ± 𝟎. 𝟓) ⋅ 𝟏𝟎𝟖 ⋅ 𝑑𝐠𝐠𝐠𝐠𝐠,𝐥𝐥 , R2 = 0.31 (green line).

CONCLUSIONS

REFERENCES

Regarding the recent developments in Stern layer polarization models, we find ambiguous results from our reference sample study. We can confirm the stronger correlation of imaginary part of conductivity to specific surface area (per unit mass), i.e. σ″ ~ Sm, compared to specific surface area per unit volume, i.e. σ″ ~ Spor, for a wide range of fluid conductivities and frequencies above 1 Hz. We find strongly frequency dependent correlation coefficients for both relations. A normalized chargeability mn to Sm correlation provides a fair alternative to the σ″ to Sm correlation, since the frequency fopt of optimal correlation of imaginary part of conductivity is typically unknown. We can qualitatively confirm the salinity dependence of the corresponding proportionality factor, arising from the salinity dependence of the partition coefficient parameter of recent Stern layer polarization models. However, quantitative theoretic suggestions for these factors do not agree with experimental evidence. In particular, the assumption that Stern layer mobility of counter ions is not reduced for TYPE II (clay free silica) material is incorrect with respect to the σ″ ~ Sm relation, if we assume the general model framework being correct and vice versa. On the other hand, exactly this assumption of a non-reduced mobility leads to good agreement for the relaxation time of the reference samples. Thus, different mobilities, e.g. bulk fluid versus Stern layer mobility, might be responsible for the different studied quantities. In conclusion, recent Stern layer polarization models comprise promising ideas on rock polarization physics. Nevertheless, in terms of quantitative relations we recommend further enhancement. Membrane polarization models on the other hand are very dependent on the particular geometric model conditions, predicting only the particular model impedance Z instead of conductivity σ. Nevertheless, these models prove falsifiability providing experimentally accessible differences to Stern layer polarization. In particular, relations between relaxation time and grain sizes (Stern layer polarization) or one the numerous imaginable pore size quantities (membrane polarization) have the potential to improve understanding. Unfortunately, we could not resolve any qualitative difference between the influence of independently measured (logarithmically mean) pore diameter and grain size using a power law fit on the reference sample data. Subsequently applying all sufficiently simple membrane polarization approaches, we could not challenge the earliest grain size related approach in a quantitative estimate of quadratic relaxation time behavior, but have to cope with numerous limiting assumptions. Thus, there is the potential to further improve these approaches in terms of universality, e.g. deduce the complex conductivity response, and reliable quantitative predictions for simple experimental cases.

Bücker, M., Hördt, A., 2013a. Analytical modelling ofmembrane polarization with explicit parametrization of pore radii and the electrical double layer. Geophys. J. Int.

ACKNOWLEDGMENTS The presented study was supported by the German Society for Petroleum and Coal Science and Technology (DGMK) - in particular by its members ExxonMobil Production Deutschland GmbH, GDF SUEZ E&P Deutschland GmbH, RWE Dea AG and Wintershall Holding GmbH - in the framework of the DGMK project 703 ”IS for assessing the wetting conditions of reservoir rocks”. Additional support was provided by the Collaborative Research Center 32 (TR32), funded by the German Research Foundation (DFG).

Dias, C., 2000. Developments in a model to describe lowfrequency electrical polarization of rocks. Geophysics 65 (2), 437–451. Leroy, P., Revil, A., Kemna, A., Cosenza, P., Ghorbani, A., 2008. Complex conductivity of water-saturated packs of glass beads. J. Colloid Interface Sci. 321 (1), 103–117. Pelton, W., Ward, S., Hallof, P., Sill, W., Nelson, P., 1978. Mineral discrimination and removal of inductive coupling with multifrequency IP. Geophysics 43 (3), 588–609. Revil, A., 2012. Spectral induced polarization of shaly sands: influence of the electrical double layer. Water Resour. Res. 48 (2). Revil, A., Florsch, N., 2010. Determination of permeability from spectral induced polarization in granular media. Geophys. J. Int. 181, 1480–1498. Schwarz, G., 1962. A theory of the low-frequency dielectric dispersion of colloidal particles in electrolyte solution. J. Phys. Chem. 66 (12), 2636–2642 Volkmann, J., Klitzsch, N., 2010. Frequency-dependent electric properties of microscale rock models for frequencies from one millihertz to ten kilohertz. Vadose Zone J. 9 (4), 858–870. Volkmann, J., Klitzsch, N., Mohnke, N., Schleifer, N., 2013. Rock properties influencing impedance spectra (IS) studied by lab measurements on porous model systems (Extended abstract), SCA2013-A039. Proceedings: International Symposium of the Society of Core Analysts held in Napa Valley, California, USA, pp. 419–424 (16–19 September, 2013). Volkmann, J., Klitzsch, N., 2015. Wideband impedance spectroscopy from 1 mHz to 10 MHz by combination of fourand two-electrode methods. J. Appl. Geophys. 114, 191–201. Volkmann, J., Klitzsch, N., 2016. Evaluation of low frequency polarization models using well characterized sintered porous glass samples. J. Appl. Geophys. 124 (2016): 39-53. Weller, A., Slater, L., Nordsiek, S., Ntarlagiannis, D., 2010. On the estimation of specific surface per unit pore volume from induced polarization: a robust empirical relation fits multiple data sets. Geophysics 75 (4), WA105–WA112. Weller, A., Slater, L., Nordsiek, S., 2013. On the relationship between induced polarization and surface conductivity: implications for petrophysical interpretation of electrical measurements. Geophysics 78 (5), D315–D325. Wong, J., 1979. An electrochemical model of the inducedpolarization phenomenon in disseminated sulfide ores. Geophysics 44 (7), 1245–1265.

SIP of the three-phase system CO2-brine-sand under reservoir conditions Jana H. Börner

Volker Herdegen

Jens-Uwe Repke

Klaus Spitzer

TU Bergakademie Freiberg Institute of Geophysics and Geoinformatics Gustav-Zeuner-Str. 12 D-09599 Freiberg [email protected]

TU Bergakademie Freiberg Institute of Thermal, Environmental and Natural Products Process Engineering

TU Bergakademie Freiberg Institute of Thermal, Environmental and Natural Products Process Engineering

TU Bergakademie Freiberg Institute of Geophysics and Geoinformatics

THEORY

SUMMARY We present laboratory measurements of the spectral complex electrical conductivity of water-bearing sand samples during exposure to and flow-through by carbon dioxide. Pressures up to 300 bar and temperatures up to 80°C were applied. Steady-state experiments serve for investigating the physicochemical equilibrium of the fluid phases. Dynamic experiments aim at analysing the impact of partial saturation and chemical interaction on complex conductivity. The steady-state dissolution experiments show that besides the conductivity-increasing dissociation a second opposing process may be observed, which results in a significant reduction of conductivity at high salinities despite the added CO2. We explain our observations with a semi-analytical formulation for the electrical conductivity taking into account the interactions of ion and neutral species. A significant reduction of saturation is observed during CO2 flow and drainage. The spectral complex conductivity maps both changes in saturation and chemical interaction. Including the semi-analytical correction for porewater conductivity allows for a good reconstruction of saturation from SIP-measurements. Additionally we get access to an indicator for changes of the inner surface area, which is related to mineral dissolution or precipitation processes. Key words: SIP, reactive gas, high pressure, monitoring

∗ The electrical rock conductivity 𝜎rock (ω) is generally complex and frequency dependent.

∗ ′ ′′ (𝜔) = 𝜎rock 𝜎rock + 𝒊𝜎rock

Complex quantities are marked with an asterisk, prime denotes the real and double prime the imaginary part, ω is the angular frequency. Several conductance mechanisms contribute to rock conductivity. They occur in parallel and are differently affected by, e.g., salinity and saturation: ∗ ∗ 𝜎rock = 𝜎electrolyte + 𝜎interface

The electrical rock conductivity is a sensitive indicator for CO2 migration processes (e.g. Börner et al., 2013). Due to their sensitivity to the pore fluids, electric and electromagnetic methods bear a great potential for monitoring CO2 injections and leakages. However, CO2 is a reactive gas which massively interacts with other pore fluids. Therefore, classic relationships do not necessarily apply to the three-phase system sand / pore water / CO2. We investigate the system with the spectral induced polarization method (SIP) at geologically relevant pressure and temperature conditions to get additional information on physical and chemical processes at the grain-water interface and evaluate the monitoring capabilities.

IP2016 – 6-8 June, Aarhus, Denmark

1

(2)

The electrolytic conductivity 𝜎electrolyte describes pure ohmic conduction caused by ions moving freely in the liquid. It contributes to the real part of conductivity only and is covered by Archie’s law (Archie, 1942). The interface layer, which forms at the contact of silicate grain and pore water, gives rise ∗ to an interface conductivity 𝜎interface acting similar to a lossy capacitor. It contributes to both real and imaginary part of conductivity and underlies multiple dependencies as well (e.g. Vinegar & Waxman, 1984; Revil & Skold, 2011; Skold et al., 2011; Weller & Slater, 2012). Especially changes in pore water conductivity 𝜎𝑤 and water saturation but also pH variations strongly influence all conductivity components. CO2 is a reactive gas and dissolves in water in great amounts depending on pressure, temperature and salinity (e.g. Duan et al. 2006). A small portion of the dissolved CO2, which forms carbonic acid, dissociates in two steps:

𝐶𝑂2 + 𝐻2 𝑂 ⇌ 𝐻+ + 𝐻𝐶𝑂3− 𝐻𝐶𝑂3− ⇌ 𝐻 + + 𝐶𝑂32− .

INTRODUCTION

(1)

(3)

Since the dissociation of CO2 adds considerable amounts of charged species to the fluid, the pore water conductivity should be affected by the presence of CO2 in pore space. Generally the electrolytic conductivity of an aqueous solution consists of contributions of each charged species i : 𝑛

𝜎𝑤 = ∑ Λ𝑖 𝛾𝑖 𝑐𝑖

(4)

𝑖=1

Here, 𝑐𝑖 is the concentration of species i and Λ𝑖 is the molar conductivity. The activity coefficient 𝛾𝑖 describes the change of ion mobility due to inter-species interactions:

ln(𝛾𝑖 ) = ln(𝛾𝑖o ) + 𝑓(𝑐𝑗≠𝑖 )

(5)

SIP of the system CO2 – brine – sand

Börner, Herdegen, Repke and Spitzer

Where 𝛾𝑖o is the activity coefficient of a solution of species i only and 𝑓(𝑐𝑗≠𝑖 ) is a function of all other species present in the solution.

METHOD AND RESULTS Laboratory set-up and procedure All experiments presented in this study were carried out with an experimental set-up based on the apparatus of Börner et al. (2013). It is possible to measure CO2 concentration with a wet chemical analysis method. Thereby, a defined sample volume can be taken and the concentration may be determined by back titration. Core of the experimental set-up is a steel autoclave (see Fig. 1), in which a maximum pressures of 300 bar at a maximum temperature of 80°C is generated. The autoclave can be equipped with different measuring cells. Static conditions or CO2 flow through the system may be realized.

Figure 1. Laboratory set-up with steel autoclave (green) in a hot-air cabinet (red). The measuring cell (yellow) may be adapted to the type of experiment. CO2 flow is plotted in blue. Two types of experiments have been carried out: steady-state dissociation and dynamic flow experiments. For static dissociation experiments, a salt solution of known salinity was filled in a 0.75 l measuring cell placed inside of the autoclave. The measuring cell completely consists of glass. Current electrodes are placed at the top and bottom of the measuring cell in form of wire meshes. 6 equidistant wire rings serve as potential electrodes. All electrodes were made of platinized platinum. For 135 pressure/ temperature / salinity / species combinations the equilibrium solution conductivity σw was determined. If related to the initial solution conductivity σow we get the conductivity contrast due to CO2:

𝜎𝑤norm =

𝜎𝑤 𝜎𝑤𝑜

(6)

For the dynamic flow experiments a different measuring cell is used, which is equipped with a permeable bottom to allow flow through the sample. The cell is filled with an initially fully saturated clean sand sample and the whole system is put under constant pressure and temperature. Then, pore water is driven out of the sample by a CO2 mass flow. During depressurization at the end of each experiment, no further drainage takes place. The spectral complex conductivity of the sample is monitored throughout the whole process. Repeated flow experiments have been carried out for 8 pressure / temperature / salinity combinations representing different depths within the Earth’s interior.

Results The static dissociation experiments revealed a partially unexpected behaviour (see Fig. 2). For small salinities, we observe an increase in the electrical pore water conductivity when pressure increases (see left subplot in Fig. 2), which strongly IP2016 – 6-8 June, Aarhus, Denmark

depends on the solution salinity. This is the expected effect, since the additional ions originating from the dissociation of carbonic acid contribute to the solution conductivity. However, when higher salinities are considered this effect is completely diminished. For increasingly saline solutions it is even overcompensated (right subplot in Fig. 2). To explain these observations we present a semi-analytical model, which is formulated in terms of a correction factor 𝜎𝑤norm (Eq. 6) and is based on Eqs (4) and (5) (see solid lines in Fig. 2):

𝜎𝑤norm =

ΛNaCl 𝛾NaCl 𝑐NaCl +ΛCO2 𝛾CO2 𝑐CO2(dis) 0 ΛNaCl 𝛾NaCl 𝑐NaCl

.

(7)

The remaining unknown quantities in Eq. (7) are derived by a least-squares inversion (for details, see Börner et al. 2015). Depending on salinity and the environmental conditions, either the additional conductivity from the dissociated CO2 or the decreased activity coefficient of the salt component dominates the solution conductivity.

Figure 2. Conductivity contrast due to CO2 dissociation for two salinities versus pressure (circles: measured data; 3% error bars). Solid lines represent the contrast predicted by the model (Eq. 7, Börner et al. 2015). Fig. 3 shows the experimental conditions (top) and the complex conductivity (bottom, in terms of real and imaginary part) for one flow experiment with nitrogen (N2, non-reactive) and one experiment with CO2 (reactive). Both real and imaginary part drop due to the drainage, as expected. The difference between the N2 and the CO2 experiment is caused by the reactive nature of CO2. The drop in the real part is dampened by the dissociation (cf. also Fig. 2, left). The disproportionate drop in the imaginary part may be associated with the low pH environment. We describe this effect with a second correction term 𝜎ifnorm , which is defined in analogy to 𝜎𝑤norm . The complex conductivity during interaction with CO2 may than be evaluated in terms of saturation. Since the imaginary part of conductivity strongly depends on the inner surface area of the porous medium (e.g. Börner et al., 1996; Weller et al., 2010) we can also deduce an indicator for the change in inner surface area. Such an indicator is of great interest during monitoring because a change in inner surface area is associated to mineral dissolution and/or precipitation processes.

CONCLUSIONS Our laboratory study shows that CO2 acts on the conductivity of a porous medium in several ways: By changing water saturation, by chemical interaction with the fluid phase and by mineral dissolution/precipitation processes. The chemical interaction with the pore water phase appears in different manifestations depending on salinity of the solution. We present a semi-analytical formulation to explain and predict these effects.

2

SIP of the system CO2 – brine – sand

The transition salinity between the regimes of conductivity increase and conductivity decrease is in the range of shallow clean aquifer salinities. Therefore, the observed effect is very important for leakage detection methods. Migrating CO2 might cause complex electrical anomalies with conductive and resistive areas. These effects have to be kept in mind when interpreting the flow experiments. The spectral complex conductivity maps both changes in saturation and chemical interaction. When the CO2-effects are taken into account a robust quantification of saturation and mineral dissolution and precipitation processes is possible.

ACKNOWLEDGMENTS This work has been funded by the German Research Foundation (DFG) (grant numbers SP 356/12-1 and RE 1705/9-1). Additionally, Jana Börner thanks the Christiane NüssleinVolhard-Foundation for their support.

REFERENCES Archie, G. E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers, 146, 54 – 62. Börner, F. D., Schopper, J. R. & Weller, A., 1996. Evaluation of transport and storage properties in the soil and groundwater zone from induced polarization measurements. Geophysical Prospecting, 44, 583-601.

Börner, Herdegen, Repke and Spitzer

Börner, J. H., Herdegen, V., Repke, J.-U. and Spitzer, K., 2013. The impact of CO2 on the electrical properties of water bearing porous media - laboratory experiments with respect to carbon capture and storage. Geophysical Prospecting, 61, 446 – 460. Börner, J.H., Herdegen, V., Repke, J.-U. und Spitzer, K., 2015. The electrical conductivity of CO2-bearing pore waters at elevated pressure and temperature: A laboratory study and its implications in CO2 storage monitoring and leakage detection. Geophysical Journal International: 203: 1072-1084. Duan, Z., Sun, R., Zhu, C. and Chou, I., 2006. An improved model for the calculation of CO2 solubility in aqueous solutions containing Na+, K+, Ca2+, Mg2+, Cl- and SO42-. Marine Chemistry, 98, 131-139. Revil, A. and Skold, M., 2011. Salinity dependence of spectral induced polarization in sands and sandstones. Geophysical Journal International, 187, 813-824. Skold, M., Revil, A. and Vaudelet, P., 2011. The pH dependence of spectral induced polarization of silica sands: Experiment and modeling. Geophysical Research Letters, 38, L12304. Vinegar, H. J. and Waxman, M. H., 1984. Induced polarization of shaly sands. Geophysics, 49, 1267-1287. Weller, A. and Slater, L., 2012. Salinity dependence of complex conductivity of unconsolidated and consolidated materials: Comparisons with electrical double layer models. Geophysics, 77, D185-D198. Weller, A., Slater, L., Nordsiek, S. and Ntarlagiannis, D., 2010. On the estimation of specific surface per unit pore volume from induced polarization: A robust empirical relation fits multiple data sets. Geophysics, 75, WA105-WA112.

Figure 3. Top: pressure, temperature and cumulative CO2 mass. Bottom: Real and imaginary part of conductivity at 11.7 Hz vs. time at 50 bar and 25°C with CO2 (reactive, red symbols) and N2 (non-reactive, blue symbols), respectively. The time period from 25 to 40 hours is skipped since no changes of the shown quantities occurred in this period. IP2016 – 6-8 June, Aarhus, Denmark

3

Predictive relationships for the permeability of unconsolidated sands based on SIP and pore surface fractal dimensions Malcolm Ingham

Sheen Joseph

Victoria University of Wellington PO Box 600 Wellington New Zealand [email protected]

Victoria University of Wellington PO Box 600 Wellington New Zealand [email protected]

is generally taken as the diameter of a nitrogen molecule (0.4 nm).

SUMMARY We present calculations of specific internal surface (Spor) and pore surface fractal dimension (D) based on measurements on unconsolidated sand samples. It is found that for these samples, for which the effective hydraulic radius is greater than 10 m, D  2 and the generalized PaRiS model of Weller et al. (2015) gives a good prediction of permeability both for the unconsolidated samples and for the sandstone samples reported by Zhang and Weller (2014). We use fitted relationships to Spor for both the SIP time constant () and the measured imaginary part of the conductivity at a frequency of 1 Hz (   ) to deduce predictive relationships for permeability based on and   , on the assumption that D = 2. These relationships both overestimate permeability but improved predictions are obtained by using a slightly lower value of D commensurate with the average of the calculated values. Key words: SIP, fractal dimension, specific internal surface, permeability.

INTRODUCTION Assuming equivalence of electrical and hydraulic tortuosity, the Kozeny-Carman equation can be expressed in a form that relates the permeability (k) of a natural porous medium to the electrical formation factor (F) and the specific internal surface (Spor) 1

k 

2 FS

8F

METHOD SIP and permeability measurements have been made on sand samples which have been sieved into different size fractions in the range  = 0.00 and  = 3.00 on the Krumbein scale. The method for SIP and permeability measurements has been described previously by Joseph et al. (2015). Measurements have been made on both individual size fractions and on samples consisting of mixtures of different size fractions. The specific internal surface has not been measured directly but, on the assumption of spherical grains, can be calculated using the measured value of the porosity () and a knowledge of the total masses and mean diameters of the components of the sample. Thus for a mixture of masses M1 and M2 of grains of median diameter D1 and D2, Spor can be expressed as S

2D 4

1

We find that for our unconsolidated samples, as long as the effective hydraulic radius (reff) is greater than 10 m, the fractal dimension is very close to 2. In contrast, as observed by Zhang and Weller (2014), if reff is smaller than this there is a linear relationship between D and Spor. Using D = 2 for unconsolidated samples generalized forms of the PaRiS model (equation (2)) using   or the SIP time constant ( )slightly overestimate the permeability.

(1)

2 por

The proportionality of Spor to both the surface conductivity (surf) and the imaginary part of the bulk conductivity (   ) as measured by spectral induced polarization (Weller et al, 2015) has led to predictive relations for permeability based on these parameters. For sandstone samples Zhang and Weller (2014) have also demonstrated a relationship between Spor and the fractal dimension (D) of the pore surface and incorporated D into a more general form of the PaRiS model k 

In this paper we present measurements made on unconsolidated sand samples and calculate values of both Spor and D and compare the relationships between these and permeability with those found by Zhang and Weller (2014).

( N ) 2

D 3

2

 S por   2 

   

D 3

(2)

originally proposed by Pape et al. (1987). In (2)  N represents 2

the minimal length scale over which self-similarity occurs and IP2016 – 6-8 June, Aarhus, Denmark

1

por



 M1 M 2      V  D1 D2 6

   

(3)

where V is the total volume of the sample and  is the density of a grain. From the calculated values of Spor estimates of the fractal dimension of the pore surface can be made using the relationship D  2 

log( S

por

)  log( 2 / r eff )

log( r eff /  H

2O

(4)

)

which is based on that given by Zhang and Weller (2014) but, as the measurement of Spor is based on measurement of the sample porosity, the minimal length scale is taken as the effective diameter of a water molecule (0.28 nm). In (4) reff can

SIP and fractal dimensions

Ingham and Joseph

be calculated from the measured permeability and formation factor using

r eff 

8 kF

.

RESULTS The measured values of k and F, and the calculated values of reff, Spor and D for each of the sand samples are listed in Table 1. Uncertainties in the calculated values of D are slightly less than 0.1, meaning that the fractal dimension is almost indistinguishable from 2 – the normal dimension for surface area.

Table 1 and for the sandstone samples discussed by Zhang and Weller (2014). Whereas equation (4) suggests a linear relationship between D and log (Spor), as indicated by Zhang and Weller, this appears only to hold for values of the effective hydraulic radius less than about 10 m. For larger values of reff, such as for the unconsolidated samples in this study, the fractal dimension is very close to 2. This is illustrated in Figure 2 which shows D plotted against reff. 3 2.8 2.6

2.4

0.00 0.50 1.00 1.50 2.00 2.50 3.00 Prop 100-0 90-10 80-20 60-40 20-80 0-100 Prop

33-3333-0 27-2727-20 20-2020-40 13-1313-60 6.7-6.76.7-80

D 1.918 1.920 1.946 1.955 1.942 1.948

D

2.2

D 1.915 1.948 1.953 1.937 1.950 1.956 1.946

1.6 1.4 1.2

1 1.E-08

1.E-06

1.E-05

1.E-04

1.E-03

Figure 2. Pore surface fractal dimension plotted against effective hydraulic radius. Circles – sand samples, crosses – sandstone data from Zhang and Weller (2014). Zhang and Weller (2014) presented equation (2) as a generalized form of the PaRiS model allowing for a variation in fractal dimension. The comparison of permeability predicted by (2) with the measured values is shown in Figure 3(a) in which kpred has been calculated using the values of D calculated for each individual sample.

D 1E-08

5.74E-11

4.25

44.2

13053

1.896

2.90E-11

6.09

37.6

30489

1.953

9.05E-12

5.84

20.6

41020

1.923

7.11E-12

5.28

17.3

46526

1.918

6.63E-12

4.84

16.0

56770

1.928

1E-09 1E-10

(a)

1E-11 1E-12 1E-13 1E-14 1E-15 1E-16 1E-17 1.E-17

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-12

1.E-11

1.E-10

1.E-09

k (m2) 1E-08

3.0

1E-09

2.8

1E-10

2.4

1E-11

kpred (m2)

2.6

2.2 2.0 1.8

(b)

1E-12 1E-13 1E-14

1.6

1E-15

1.4

1E-16

1.2 1.0 1.E+03

1.E-07

reff

Table 1. Measurements of k, F, reff, Spor and D for sand samples.

D

2 1.8

kpred (m2)



Sieved samples k (m2) F reff(m) Spor(m-1) 1.78E-10 4.22 77.5 9366 1.56E-10 4.48 74.8 14199 1.02E-10 3.47 53.2 17950 4.47E-11 3.58 35.8 22853 3.15E-11 3.80 30.9 32347 1.94E-11 3.86 24.5 47278 8.11E-12 3.83 15.8 66973 Mixtures of  = 0.25 and  = 2.50 k (m2) F reff(m) Spor(m-1) 1.39E-10 3.83 65.3 11094 5.83E-11 4.38 45.2 16958 5.70E-11 4.74 46.5 22355 2.82E-11 4.81 32.9 35874 9.80E-12 4.66 19.1 54820 1.19E-11 4.23 20.1 55550 Mixtures of  = 0.25, 0.50, 0.75 and  = 2.50 k (m2) F reff(m) Spor(m-1)

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

Spor (m-1)

Figure 1. Pore surface fractal dimension plotted against specific internal surface. Circles – sand samples, crosses – sandstone data from Zhang and Weller (2014). Shown in Figure 1 is a plot of fractal dimension against specific internal surface both for the sand samples listed in IP2016 – 6-8 June, Aarhus, Denmark

1E-17 1.E-17

1.E-16

1.E-15

1.E-14

1.E-13

k (m2)

Figure 3. Permeability predicted by equation (2) plotted against measured permeability. (a) Using measured/calculated values of D. (b) Assuming that D = 2 for sand samples and D = 2.307 for sandstone samples. Circles – sand samples, crosses – sandstone data from Zhang and Weller (2014).

2

SIP and fractal dimensions

Ingham and Joseph

Although the generalized form of the PaRiS model incorporating variable values of D gives highly accurate values of permeability across at least 7 orders of magnitude, the use of constant values of D for different kinds of samples, while not as accurate, still yields usable predictions of permeability. Nevertheless, use of (2) requires a knowledge of Spor which, for field measurements, is not readily available. Thus it is pertinent to seek parameters that can be measured in the field which may have a direct relationship with Spor In this regard parameters measurable through the technique of spectral induced polarization (SIP) are the most promising. Weller et al. (2015) have discussed the proportionality of the imaginary part of the conductivity (   ) measured at 1 Hz frequency with Spor. For the unconsolidated samples in this study if   at 1 Hz is treated as a function of Spor the best fitting relationship is    9 . 84 x 10

7

S

The comparison between measured values of permeability and those predicted by equation (6) is shown in Figure 6. As can be seen from Figures 4 and 6, both equations (5) and (6) overestimate the permeability. Additionally the permeability values predicted by equation (5) are very scattered reflecting the relatively low value of R2. The permeability values predicted on the basis of  , however, give a much better estimate of the measured values and are much less scattered. The overestimation of permeability by about half an order of magnitude comes partly from the use of D = 2 in deriving equation (6). The effect of this in increasing the estimate of k can be seen by comparing Figures 3(a) and 3(b). In the cases of predictions based on both   and , taking an average value of D from Table 1 and using 2.78 x 10-10 m for the minimal scale length produces a much closer fit between the predicted and measured permeability. This is shown for predictions based on  by the filled data points in Figure 6. 1.E+02 R² = 0.843 1.E+01

(s)

However, given that the fractal dimension is generally unknown, Zhang and Weller tested the predictive power of equation (2) by assuming their average value of D of 2.307. The predicted permeability given by (2) under this assumption for the sandstone samples and assuming a value of D = 2 for the unconsolidated samples in this study, is shown in Figure 3(b). Note that the assumption of D = 2 for the sand samples means that the term in the minimal scale length reduces to unity.

1.E+00

0 . 422 por

with a coefficient of determination (R2) of 0.38. Assuming D = 2 this leads to the predictive relationship for permeability of k 

1 . 357 x 10

1.E-01 1.E+03

 28

 

 4 . 739

1.E+04

1.E+05

1.E+06

Spor (m-1)

(5)

8F

in which   is in S/m. The permeability predicted by this equation for the sand samples (shown in Figure 4).

Figure 5. SIP time constant for sand samples plotted as a function of specific internal surface. 1E-08

1E-08 1E-09

kpred (m2)

kpred (m2)

1E-09

1E-10

1E-10

1E-11 1E-11

1E-12 1E-12

1E-12 1E-12

1E-11

1E-10

k

1E-09

Figure 4. Permeability of sand samples predicted by equation (5) plotted against measured permeability. The other frequently used parameter derived from SIP data is the time constant ( ) of the low frequency relaxation. For the sand samples listed in Table 1, as shown in Figure 5, there is a strong correlation between determined by fitting a ColeCole model to the measured complex conductivity spectrum, and Spor. This relationship can be represented by the expression   7 . 57 x 10 S

 1 . 797

8

5 . 247 x 10

 10



1E-10

1E-09

k (m2)

1 . 113

Figure 6. Open circles - permeability of sand samples predicted by equation (6), filled circles - predicted permeability derived from equation (2) using a value of D = 1.936.

CONCLUSIONS Measurements on unconsolidated sand samples, when compared to previous measurements on sandstones, demonstrate the following results. 

por

which, again assuming D = 2, leads to the predictive equation for permeability k 

1E-11

(m2)

(6)



For samples for which the effective hydraulic radius is greater than 10 m the calculated pore surface fractal dimension is close to, but just less than, 2. Using the recovered values of D in the generalized PaRiS model presented by Zhang and Weller (2014) gives

8F

IP2016 – 6-8 June, Aarhus, Denmark

3

SIP and fractal dimensions

 

excellent predictions of permeability. Using the constant value of 2 leads to a slight overestimation of permeability. Power law relationships between both   and  and Spor allow predictive relationships for permeability based on these parameters to be developed. Assumption of D = 2 for the unconsolidated samples in these relationships leads to an overestimation of k. However, use of an average value of D, slightly lower than 2, gives improved predictions using both   and 

It can be concluded that for unconsolidated samples such as those in this study, a pore surface fractal dimension of approximately 2 in the generalized PaRiS model of Weller et al. (2015) can be used to develop predictive equations for permeability. REFERENCES

Ingham and Joseph

dependence on fluid conductivity: Near Surface Geophysics, 13, 169-177 Pape, H., Riepe, L. and Schopper, J.R., 1987, Theory of selfsimilar network structures in sedimentary and igneous rocks and their investigation with microscopical methods: Journal of Microscopy, 148, 121-147. Weller, A., Slater, L., Binley, A., Nordsiek, S. and Shujie, X., 2015, Permeability prediction based on induced polarization: Insights from measurements on sandstone and unconsolidated samples spanning a wide permeability range: Geophysics, 80, D161-D173. Zhang, Z. and Weller, A., 2014, Fractal dimension of porespace geometry of an Eocene sandstone formation: Geophysics, 79, D377-D387.

Joseph, S., Ingham, M. and Gouws, G., 2015, Spectral induced polarization measurements on New Zealand sands –

IP2016 – 6-8 June, Aarhus, Denmark

4

Induced polarization of seafloor massive sulfides A. Hördt, K. Bairlein

G.Spagnoli

M.Jegen, M.Hannington, S.Petersen, T. Laurila

TU Braunschweig Mendelssohnstr. 3 38106 Braunschweig [email protected]

BAUER Maschinen GmbH BAUER-Str. 1 86529 Schrobenhausen [email protected]

GEOMAR Helmholtz Centre for Oceas Research Wischhofstr. 1-3 24148 Kiel [email protected]

METHODS AND RESULTS SUMMARY Sefloor massive sulfides (SMS) are believed to constitute an important future mineral resource. Nevertheless, little is known about the electrical properties of SMS, in particular under in-situ conditions. We measured electrical impedance spectra of 40 samples, 30 of which are sulfidebearing, and 10 are unmineralized host-rock. The samples were saturated with sodium chloride solution with 5 S/m conductivity. The resistivity magnitude shows a clear difference between mineralized and unmineralized samples, and also a weak grouping between the different types of mineralization. The imaginary conductivity at 1 Hz indicates a more pronounced discrimination between mineralized and unmineralized samples, suggesting that complex measurements might be useful for exploration purposes. We also measured spectra under dry conditions. Surprisingly, the sulfide-bearing samples exhibit significant phase shifts even for dry samples, indicating that the conducting minerals themselves cause a phase shift, and an interaction with an electrolyte might not be necessary. Key words: ore exploration, seafloor massive sulfidces, mineralization.

INTRODUCTION The electrical properties of continental ore-bearing rocks have been studied extensively with outcrops, in the laboratory, and with synthetic mixtures (e.g. Pelton et al., 1978; Vanhala and Peltoniemi, 1992, Nelson and van Voorhis 1983; Hupfer et al., 2015). However, except for some local studies (e.g. Iturrino et al., 2000; Bartetzko et al., 2006), little is known about the electrical properties of seafloor deposits. There is an increasing interest, in particular in seafloor massive sulfides (SMS), which are considered a new source of base metals with economic relevance (e.g. Hoagland et al. 2010; Hannington et al., 2011). Since seafloor rocks are saturated with significantly more conductive electrolyte compared to continental rocks, and have a different chemical history, it is not obvious that results obtained with continental studies can be transferred to seafloor conditions. Therefore, we measure electrical impedance spectra of 30 SMS samples and 10 unmineralized seafloor basalt samples and investigate potential relationships between SIP parameters and mineral content.

IP2016 – 6-8 June, Aarhus, Denmark

1

The samples consist of a selection from different seafloor locations representing different tectonic settings, and a variety of compositions, ranging from basalt host rock, non-ore mineralization to massive sulfide mineralizations with different dominant base metals. A detailed description can be found in Spagnoli et al. (2016). The 40 plugs with 25 mm diameter and 50 mm length were measured with the sample holder and impedance analyzer previously used for the investigation of sandstones and described in Hördt and Milde (2012). A highly conductive sodium chloride solution with 5 S/m conductivity was used to saturate the samples to simulate the seafloor conditions. Each samples underwent a well-defined cycle of saturation and drying, described in detail in Spagnoli et al. (2016). In order avoid a current bypass through at the interface between sample and acrylic glass cylinder, the samples were wrapped with teflon tape. Figure 1 shows the resistivity magnitude and imaginary conductivity at a frequency of 1 Hz, sorted by sample number, that corresponds to a grouping according to the dominant mineralization type. The unmineralized or non-ore mineralized samples, which include the basalt, Ba-rich and Si-rich samples, generally have higher resistivities compared to the sulfide samples. In particular the Fe-rich and Cu-rich samples have very low resistivities below 1m, and some even below the resistivity of the fluid used for saturation (0,2 m). The low resistivities cannot be explained with purely electrolytic conductivity and are most likely due to the conducting minerals. We conclude that the minerals are connected in these samples. This obervation is important because it means that the electrical spectra cannot be explained based on most of the existing theoretical models, which are exclusively designed for disseminated mineralization (eg. Wong, 1979; Revil et al., 2015).

IP of seafloor massive sulfides

Hördt, Bairlein, Spagnoli, Jegen, Hannington, Petersen, Laurila

Figure 1. Resistivity magnitude (top panel) and imaginary conductivity (bottom panel) sorted by sample number, indicating the dominating type of mineral content. Figure modified after Spagnoli et al. (2016). The imaginary conductivity (bottom panel of figure 1) shows a similar behaviour as the resistivity magnitudes: the nonmineralized samples have small imaginary conductivities, the sulfides have much larger values, with maxima for the Fe-rich and Cu-rich samples. However, compared to the resistivity magnitudes, the discrimination is considerably enhanced, the variation is more than 8 orders of magnitude in the imaginary conductivity compared to > 4 orders of magnitude for the resistivities. This is because the phase shifts are large for the mineralized samples and small for the unmineralized samples. Figure 2 shows 6 selected spectra, 3 of which are for unmineralized, and 3 for mineralized samples. The sulfide bearing samples generally have large phase shifts in the range of several 100 mrad, and low resistivites, whereas sulfide-free samples have small phase shift and high resitivites. This was qualitatively expected and means that the principle idea, using IP to explore for ores, might work also under highly saline conditions met at the seafloor.

IP2016 – 6-8 June, Aarhus, Denmark

Figure 2. Selected spectra of three samples with no significant sulfide content (basalt samples) and three samples with significant sulfide content, saturated with 5 S/m sodium chlorite solution. Top panel: resistivity magnitudes. Bottom panel: phase shift. The samples were also measured under dry conditions, after drying in a vacuum chamber at 10 mbar and 40°C for at least 24 hours. As expected, the resistivity magnitudes (figure 3, top panel) have considerably increased compared to the saturated samples. However, the resistivities of two mineralized samples are still small (below 10 m), confirming that the conducting minerals are connected and thus contribute significantly to the bulk conductivity. The phase shifts of the dry samples (figure 3, bottom panel) are large and reach up to several 100 mrad. This is unexpected, because it is generally assumed that the elctrolyte is essential to generate an IP effect. One hypothesis is that the phase shifts are an artefact caused by EM coupling effects or by the electrode impedance that might be relevant at high impedances. This is particularly apparent for the basalt samples, where the phase shift is large only at high frequencies. However, the mineralized samples do not have a particularly large resistance, and exhibit large phase shifts also at low frequencies. Therefore, an alternative hypothesis might be that the phase shift is caused by the conducting minerals themselves, without an electrolyte.

2

IP of seafloor massive sulfides

Hördt, Bairlein, Spagnoli, Jegen, Hannington, Petersen, Laurila

ACKNOWLEDGMENTS The authors thank the Future Oceans research and technology transfer program MaTeP of The Future Ocean Cluster (GEOMAR and CAU Kiel) and BAUER Maschinen GmbH for the financial support for this project and for the permission to publish the results. REFERENCES Bartetzko A., Klitzsch, N,, Itturino, G., Kaufhold, S., and Arnold, J., 2006, Electrical properties of hydrothermally altered dacite from the PACMANUS hydrothermal field (ODP Leg 193): Journal of Volcanology and Geothermal Research 152, 109-120. Hannington, M., Jamieson, J., Monecke, T., Petersen S., Beaulieu, S. 2011. The abundance of seafloor massive sulfide deposits: Geology 39. 1155–1158. Hoagland, P., Beaulieu, S., Tivey, M.A., Eggert, R.G, German, C., Glowka, L., Lin, J., 2009, Deep-sea mining of seafloor massive sulfides: Marine Policy 34: 728–732. Hördt, A., and Milde, S., 2012, Studies on the origin of induced polarisation with gel-filled sandstone samples: Near-surface Geophysics, 6, 469-478. Hupfer, S., Martin, T., Weller, A., Günther, T., Kuhn, K., Djotsa Nguimeya Ngninjio, V., Noell, U., 2015, Polarization effects of unconsolidated sulphide-sand-mixtures: Journal of Applied Geophysics, in press.

Figure 3. Spectra of the same samples shown in figure 2, after drying under vacuum and 40°C. Top panel: resistivity magnitude vs. frequency. bottom panel: phase shift vs. frequency.

CONCLUSIONS Seafloor massive sulfides show a strong IP effect, i.e. large imaginary conductivities and phase shifts, even under highly saline conditions. This is not unexpected, considering previous results with continental ores, but is nevertheless considered an important experimental observation.

Iturrino, G.J,, Davis, E., Johnson, J., Gröschel-Becker, H. M., Lewis, T.J., Chapman, D., Cermak, V., 2000, Permeability, electrical, and thermal properties of sulfide, sedimentary, and basaltic units from the Bent Hill area of Middle Valley, Juan de Fuca Ridge. In: Zierenberg RA, Fouquet Y, Miller, Normark WR (ed), Proceedings of the Ocean Drilling Program, Scientific Results, 1-42, doi:10.2973/odp.proc.sr.169.115.2000. Nelson, P.H., Van Voorhis, G.D., 1983, Estimation of sulfide content from induced polarization data: Geophysics, 48 (1), 6275. Pelton, W.H., S.H. Ward, G. Hallof, W.R. Sill, and P.H. Nelson, 1978, Mineral discrimination and removal of inductive coupling with multifrequency IP: Geophysics 43, 588-609.

The results indicate that using the imaginary conductivity, even different types of mineralization (e.g. Cu-rich and Fe-rich) might be discriminated. According to previous studies, this discrimination would be due to texture of the minerals rather than their chemistry (e.g. Pelton et al., 1978). Many of the samples investigated here have resistivities so small that they can not be explained by electrolytic conductivity. This is confirmed by the measurements with dry samples, which also show low resistivites. We conclude that the minerals in those samples must be connected, and thus the spectra cannot be understood with existing theories, which are based on disseminated minerals.

Revil, A., Florsch, N., Mao, D. 2015, Induced polarization response of porous media with metallic particles -Part 1: A theory for disseminated semiconductors: Geophysics, 80 (5), D525-D538.

We also observe large phase shifts for the dry samples. These results must be treated with caution, because they might be distorted by electrode effects. However, if confirmed, the consequences could be important because existing theories assume the elctrolyte as essential to explain IP effects.

Wong, J., 1979, An electrochemical model of the induced polarization phenomenon in disseminated sulfide ores: Geophysics, 44, 1245-1265.

IP2016 – 6-8 June, Aarhus, Denmark

Spagnoli, G., Hannington, M., Bairlein, K., Hördt, A., Jegen, M., Petersen, S., and Laurila, T., 2016, Electrical properties of seafloor massive sulfides: Geo-marine letters, DOI 10.1007/s00367-016-0439-5. Vanhala, H., Peltoniemi, M, 1992: Spectral IP studies of Finnish ore prospects: Geophysics, 57 (12), 1545-1555.

3

On the α-polarization of bacterial suspensions: SIP measurements on E. coli K12 and Rhodococcus erythropolis T902.1 Tamara PILAWSKI

Wolfgang TAPPE

Egon ZIMMERMANN

Applied Geophysics Research Unit Department ArGEnCo Faculty of Applied Sciences University of Liège Allée de la Découverte 9 (B52) 4000 Liège Belgium [email protected]

Institute of Bio- and Geosciences Agrosphere (IBG-3) Forschungszentrum Jülich GmbH 52425 Jülich Germany [email protected]

Central Institute for Engineering, Electronics and Analytics (ZEA-2) Forschungszentrum Jülich GmbH 52425 Jülich Germany [email protected]

Johan Alexander HUISMAN

Frank DELVIGNE

Frédéric NGUYEN

Institute of Bio- and Geosciences Agrosphere (IBG-3) Forschungszentrum Jülich GmbH 52425 Jülich Germany [email protected]

Microbial Processes and Interactions Gembloux Agro-Bio Tech University of Liège Passage des Déportés 2 5030 Gembloux Belgium [email protected]

Applied Geophysics Research Unit Department ArGEnCo Faculty of Applied Sciences University of Liège Allée de la Découverte 9 (B52) 4000 Liège Belgium [email protected]

SUMMARY The influence of bacteria on the electrical properties of porous media has been explained by different mechanisms. A few studies have also reported direct bacterial polarization using measurements on bacterial suspensions at frequencies below 10 kHz, so-called αpolarization. These measurements were performed by dielectric spectroscopy techniques relying on two electrodes and models to correct for electrode polarization at low frequencies. We performed complex conductivity measurements on bacterial suspensions from 0.01 to 45,000 Hz with an impedance spectrometer (phase accuracy better than 0.1 mrad below 1 kHz for a measurement on water) that used four-point measurements and thus does not require large corrections for electrode polarization). Two strains were studied: Escherichia coli (Gram-negative bacterium) and Rhodococcus erythropolis (Gram-positive bacterium). The imaginary parts of the complex conductivity of suspensions of both strains were very similar to the one of water. These preliminary results suggest that microbial alterations of the complex electrical conductivity measurements of porous media observed in previous studies are more likely related to other mechanisms than α-polarization of the bacteria, such as bioclogging, biomineralization, and growth and attachment of microbial cells to the sediment grains. We are planning to test additional strains to verify these results. Key words: SIP, biogeophysics, bacteria, α-polarization

INTRODUCTION

IP2016 – 6-8 June, Aarhus, Denmark

1

For the last decade, numerous studies have shown geophysical changes in geological media affected by bacterial activity (Atekwana and Slater, 2009; Davis et al., 2010; Masy et al., 2016). Among the different geophysical techniques, spectral induced polarization was shown to be particularly sensitive to subsurface bacterial processes and microbially-induced alterations. Different mechanisms were proposed to explain the influence of bacteria on the electrical properties: bioclogging (Ntarlagiannis et al., 2005; Abdel Aal et al., 2010a), biomineralization (Atekwana and Abdel Aal, 2015; Personna et al., 2008; Williams et al., 2005), growth and attachment of microbial cells to the sediment grains (Abdel Aal et al., 2004, 2009 and 2010b; Davis et al., 2006), and mineral weathering (Atekwana et al., 2004). A few studies have also reported bacterial polarization at frequencies below 10 kHz, often referred to as α-polarization (Prodan et al., 2008; Bot and Prodan, 2009; Zhang et al., 2013). αpolarization has been mainly explained by a reversible storage of electrical charges moving under the influence of the external electrical field and being stored at some polarization length scales (Revil et al., 2012). To our knowledge, all published measurements on bacterial suspensions have been measured using two-electrode setups that require correction for electrode polarizations in the kHz frequency range and below. To date, α-polarization measurements on bacteria remain difficult because of the considerable uncertainty in the correction of the large electrode polarization that occurs in the same frequency range as α-polarization (Asami, 2014). The main purpose of this study was to measure the complex conductivity of bacterial suspensions at frequencies from 0.01 to 45,000 Hz with a high-accuracy impedance spectrometer (phase accuracy better than 0.1 mrad below 1 kHz for a measurement on water) and to determine the polarization associated with bacterial cells at this frequency range. Two strains were studied: Escherichia coli K12 and Rhodococcus erythropolis T902.1. E. coli is a rod-shaped Gram-negative bacterium found in the lower intestine of warm-blooded

On the α-polarization of bacterial suspensions

organisms. R. erythropolis is a Gram-positive microorganism known to degrade hydrocarbons and has therefore been used in bioremediation.

MATERIALS AND METHODS Bacteria cultivation and preparation E. coli K12 wild type and R. erythropolis T902.1 were obtained from the Bio-Industries Research Unit of Gembloux Agro-Bio Tech and the Walloon Center of Industrial Biology of the University of Liège, respectively. Cultures were prepared in duplicate in 1 L flasks containing 500 ml of 8 g/l nutrient broth (Merck, 5443) consisting of 5 g/l of peptone and 3 g/l of meat extract. Bacteria were incubated at lab temperature (20°C) and 100 rpm orbital agitation until they reached the early stationary phase. Growth was monitored by optical density (OD) measurements at 570 nm. The cells were pelleted at 3345 x g for 30 minutes, and washed twice in M284 minimal medium (0.0275 mol/l KH2PO4, 0.0391 mol/l Na2HPO4.12H20, 0.02 mol/l NH4Cl, 0.003 mol/l N2SO4, 0.00098 mol/l MgCl2.6H20, 0.0002 mol/l CaCl2.2H2O, 0.000011 mol/l C6H5FeO7.H2O and trace elements) diluted 20 times with milli-Q water (electrical conductivity of 612 µS/cm at 20°C). They were then resuspended in M284 minimal medium diluted 20 times so that the final OD at 570 nm was 0.40. Petri plates were prepared to count the colony-forming units (CFU) in order to estimate the number of viable cells of the samples. Experimental setup Low frequency electrical measurements (0.01 – 45,000 Hz) were performed in a 40 cm long polycarbonate column with an inner diameter of 3.4 cm. The measurement system developed in the Forschungszentrum Jülich is based on a four point measurement method as described in Zimmermann et al. (2008). It can measure the spectral induced polarization response of the bacteria suspensions with a phase accuracy better than 0.1 mrad up to 1000 Hz. Two brass electrodes were used as current electrodes and were fully inserted into the sample holder (perpendicular to the main axis of the column). Two brass potential electrodes were installed between the current electrodes. They were placed outside the sample to minimize electrode polarization at the surface of the electrodes. The spacing between the different electrodes was 12 cm.

RESULTS Figure 1 shows the imaginary parts of the complex electrical conductivity (σ’’) of E. coli and R. erythropolis. They were obtained by averaging two independent measurements. For comparison, σ’’ of the water used to resuspend the bacteria is also plotted on the graph. No significant difference is observed between the two strains and the water, which strongly suggests that no α-polarization is observed for the two bacterial strains. The viability of the cells was assessed by CFU counting on Petri plates. The CFU of E. coli and R. erythropolis were (6.2±4.3)*108 and (9.2±0.4)*107 CFU/ml, respectively.

CONCLUSIONS

IP2016 – 6-8 June, Aarhus, Denmark

Pilawski, Tappe, Zimmermann, Huisman, Delvigne and Nguyen

α-polarization has been postulated to explain changes in the complex electrical conductivity below 10 kHz observed in geological media affected by bacterial activity. This polarization was measured in a few dielectric spectroscopy studies where strong electrode polarization required large corrections (Bot and Prodan, 2009; Zhang et al., 2013). We performed complex electrical conductivity measurements on two bacterial suspensions using an impedance spectrometer at frequencies from 0.01 to 45,000 Hz and we did not observe any polarization. Therefore, we conclude that at lower frequencies other mechanisms are more likely to explain the influence of bacteria on the electrical properties of porous media: bioclogging, biomineralization, growth and attachment of microbial cells on the sediment grains. We are planning to confirm these results by repeating these measurements (to get triplicates) and to test two other strains: Pseudomonas putida (Gram-negative bacterium) and Bacillus subtilis (Gram-positive bacterium).

ACKNOWLEDGMENTS This work was supported by a Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (F.R.I.A.) grant funded by the Belgian National Fund for Scientific Research (Fonds National de la Recherche Scientifique, FNRS) and attributed to T. Pilawski. REFERENCES Abdel Aal, G., Atekwana, E., Slater, L., and Atekwana, E., Effects of microbial processes on electrolytic and interfacial electrical properties of unconsolidated sediments: Geophysical Research Letters, 31 (12), L12505. Abdel Aal, G., Atekwana, E., Radzikowski, S., and Rossbach, S., 2009, Effect of bacterial adsorption on low frequency electrical properties of clean quartz sands and iron-oxide coated sands: Geophysical Research Letters, 36 (4), L04403. Abdel Aal, G., Atekwana, E., and Atekwana, E., 2010a, Effect of bioclogging in porous media on complex conductivity signatures: Journal of Geophysical Research, 115, G00G07. Abdel Aal, G., Atekwana, E., Rossbach, S., and Werkema, D., 2010b, Sensitivity of geoelectrical measurements to the presence of bacteria in porous media: Journal of Geophysical Research, 115, G03G017. Asami, K., 2014, Low-frequency dielectric dispersion of bacterial cell suspensions: Colloids and Surfaces B: Biointerfaces, 119. Atekwana, E., and Abdel Aal, G., 2015, Iron biomineralization controls on geophysical signatures of hydrocarbon contaminated sediments: Journal of Earth Science, 26 (6), 835-843. Atekwana, E., and Slater, L., 2009, Biogeophysics: A new frontier in Earth science research: Reviews of Geophysics, 47 (4), RG4004. Atekwana, E., Atekwana, E., Werkema, D., Allen, J., Smart, L., Duris, J., Cassidy, D., Sauck, W.,and Rossbach, S., 2004, Evidence for microbial enhanced electrical conductivity in

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On the α-polarization of bacterial suspensions

hydrocarbon-contaminated sediments: Geophysical Research Letters, 31, L23501 Bot and Prodan, 2009, Probing the membrane potential of living cells by dielectric spectroscopy: European Biophysics Journal, 38 (8), 1049-1059. Davis, C., Atekwana, E., Atekwana, E., Slater, L., Rossbach, S., and Mormile, M., 2006, Microbial growth and biofilm formation in geologic media is detected with complex conductivity measurements: Geophysical Research Letters, 33, L18403. Davis, C., Pyrak-Nolte, L., Atekwana, E., Werkema, D., and Haugen., M., 2010, Acoustic and electrical property changes due to microbial growth and biofilm formation in porous media: Journal of Geophysical Research, 115, G00G06. Masy, T., Caterina, D., Tromme, O., Lavigne, B., Thonart, P., Hiligsmann, S., and Nguyen, F., 2016, Electrical resistivity tomography to monitor enhanced biodegradation of hydrocarbons with Rhodococcus erythropolis T902.1 at a pilot scale: Journal of Contaminant Hydrology, 184. Naudet, V., and Revil, A., 2005, A sandbox experiment to investigate bacteria-mediated redox processes on self-potential signals: Geophysical Research Letters, 32, L11405. Ntarlagiannis, D., Yee, N., Slater, L., 2005, On the lowfrequency electrical polarization of bacterial cells in sands: Geophysical Research Letters, 32, L24402.

Pilawski, Tappe, Zimmermann, Huisman, Delvigne and Nguyen

Personna, Y., Ntarlagiannis, D., Slater, L., Yee, N., O’Brien M., and Hubbard, S., 2008, Spectral induced polarization and electrodic potential monitoring of microbially mediated iron sulfide transformations: Journal of Geophysical Research, 113, G02020. Prodan, E., Prodan, C., and Miller, J.H., 2008, The Dielectric Response of Spherical Live Cells in Suspension: An Analytic Solution: Biophysical Journal, 95 (9), 4174-4182. Revil, A., Atekwana, E., Zhang, C., Jardani, A., and Smith S., 2012, A new model for the spectral induced polarization signature of bacterial growth in porous media: Water Resources Research, 48, W09545. Williams, K., Ntarlagiannis, D., Slater, L., Dohnalkova, A., Hubbard, S., and Banfield, J., Geophysical Imaging of Stimulated Microbial Biomineralization: Environmental Science & Technology, 39 (19), 7592-7600. Zhang, C., Salter, L. and Prodan, C., 2013, Complex Dielectric Properties of Sulfate-Reducing Bacteria Suspensions: Geomicrobiology Journal, 30 (6), 490-496. Zimmermann, E., Kemna, A., Berwix, J., Glaas, W., Münch, H.M., and Huisman, J.A., 2008, A high-accuracy impedance spectrometer for measuring sediments with low polarizability: Measurement Science and Technology, 18, 105603.

Figure 1. Imaginary parts of the complex electrical conductivity (σ’’) measured on suspensions of E. coli and R. erythropolis between 0.1 and 45,000 Hz. They were obtained by averaging two independent measurements. The

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vertical error bars represent the standard deviation of the data. For comparison, σ’’ of the water used to resuspend the bacteria is also shown on the graph.

www.sip-archiv.de – an internet based, interactive archive and database for SIP data Matthias Halisch, Jens Gramenz, Lothar Gorling, Klaus Krause, Iakov Bolotovski Leibniz Institute for Applied Geophysics (LIAG) Stilleweg 2, D-30655 Hannover, Germany [email protected]

SUMMARY Long-term storage of scientific data has become a topic of utmost importance for the scientific community. Due to European and national (here: German) initiatives, new guidelines and laws have been validated to ensure a reliable storage and documentation of scientific primary data. As a result of a workshop and discussion round of the working committee induced polarization (AK-IP) of the German Geophysical Society (DGG), the Leibniz Institute for Applied Geophysics (LIAG) accepted the challenge to develop and create a safe, free and easy to use, internet based database and archive for SIP measurements. Key words: archive, database, data storage, internet, SIP, SQL

The backend of the application is developed in PHP (PHP: Hypertext Preprocessor), using a model-view-controller (MVC; Krasner and Pope, 1988) related approach that is based on the framework “CodeIgniter” (https://codeigniter.com). This tool has been chosen to reduce developing time by making use of some handy features like form validation or predefined internationalization routines. Additionally, the built-in abstraction layers make the application more portable, in case of server-side software, i.e. operating system or database engine change. The web frontend uses “Bootstrap” (www.getbootstrap.com) to obtain a responsive layout and enhanced cross browser compatibility. The web pages are served by Microsoft’s Internet Information Services (IIS) running on Windows Server. The data is stored in a Structured Query Language (SQL) server database, which is the default relational database management system (RDBMS; Date and Darwen, 1997) in the local data centre. Figure 1 shows a generalized entity-relationship-model of the database. Figure 2 highlights the general architecture and infrastructure.

INTRODUCTION Long-term storage of scientific data has become a topic of utmost importance for the scientific community. Due to European and national initiatives, new guidelines and laws have been validated to ensure a reliable storage and documentation of scientific primary data (e.g.: Kuder and Kühne, 2006; EU, 2007; DFG, 2009; Ludwig & Enke, 2013). Due to more than ten years of experience with the development of scientific database structures (Kühne, 2006), the LIAG decided to create a new database system for a reliable and safe storage of data from SIP measurements. In the following, the authors would like to briefly introduce the main concept of the new database www.sip-archiv.de, to give a short technical report as well as to provide an outlook about the ongoing development.

CONCEPT & TECHNIQUE The SIP database has been planned with respect to the needs and wishes of the German IP community that have been evaluated between October 2014 and March 2015. Accordingly, the following requirements form the main concept of this database: to provide a safe, long term archive and database structure for SIP data, web based, easy and free to use and self administrated, in order to ensure maximum control over individual and institutional data sets. In addition, this data base provides functionalities to exchange and provide data and metadata with respect to the guidelines of good scientific practice (DFG, 2013). IP2016 – 6-8 June, Aarhus, Denmark

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Figure 1. A generalized entity-relationship-model of the database. At the current stage of the development, only data of SIP measurements on hardrock samples are supported. This model will be extended in the near future, to provide storage capabilities for unconsolidated sample and field scale data.

www.sip-archiv.de

M. Halisch et al.

CONCLUSIONS & OUTLOOK With this archive and database structure, the national and international SIP community gets a powerful tool to store and manage their data from SIP measurements on a long time scale. Additionally, this archive is specifically designed to enhance national and international research collaborations, to initiate systematic round robin tests and / or projects, and to exchange data safely and self-controlled. As an ongoing development, existing functionalities are permanently evaluated and adopted. New functionalities and storage capacities are planned, e.g. the implementation of laboratory SIP measurements on soil and other unconsolidated sample materials, as well as implementing upload and storage capabilities for field and large scale measurements (SIP profiles, 2D pseudo-sections, SIP soundings, etc.).

ACKNOWLEDGMENTS The authors would like to thank the members of the working committee induced polarisation (AK-IP) of the German Geophysical Society (DGG) for their support and constructive feedback during the evaluation and beta testing phase of this archive and database. As an ongoing development, continuous feedback from the community concerning functionalities, structure and design towards the developers is highly recommended and greatly appreciated!

Deutsche Forschungsgemeinschaft (DFG), Ausschuss für Wissenschaftliche Bibliotheken und Informationssysteme, Unterausschuss für Informationsmanagement, 2009, Empfehlungen zur gesicherten Aufbewahrung und Bereitstellung digitaler Forschungsprimärdaten: www.dfg.de/download/pdf/foerderung/programme/lis/ua_inf_ empfehlungen_200901.pdf Deutsche Forschungsgemeinschaft (DFG), 2013, Momorandum on safeguarding good scientific practice: http://www.dfg.de/download/pdf/dfg_im_profil/reden_stellun gnahmen/download/empfehlung_wiss_praxis_1310.pdf EU Guideline 2007/2/EC, 2007, Infrastructure for Spatial Information in the European Community (INSPIRE): EU Guideline 2007/2/EC, Brüssel. Kuder, J., and Kühne, K., 2007, GeoMind: Ein europäisches Internetportal für geophysikalische Daten: Mitteilungen der Deutschen Geophysikalischen Gesellschaft, Ausgabe 1+2/2007, S. 1-8, ISSN 0934-6554; Hannover.

REFERENCES

Kühne, K., 2006, Das Fachinformationssystem Geophysik und seine Nutzung über das Internet: GIS - Geowissenschaftliche Anwendungen und Entwicklungen, 57. Berg- und Hüttenmännischer Tag, Wiss. Mitteilungen des Instituts für Geologie, 31: 227-231; Freiberg. Krasner, G.E., and Pope, T.A., 1988, A cookbook for using the model-view controller user interface paradigm in smalltalk-80", J. Object Oriented Program., vol. 1, no. 3, pp. 26-49, Aug. 1988.

Date, C.J., and Darwen, H., 1997, A guide to the SQL standard: a users guide to the standard database language SQL, 4th edition, Addison Welsey Publishing, USA, 1997.

Ludwig, J., and Enke, H., 2013, Leitfaden zum Forschungsdaten-Management: 122 pp., Verlag Werner Hülsbusch, Glückstadt, 2013.

Figure 2. General architecture and infrastructure of www.sip-archiv.de.

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SIP investigation at historical mining slag heaps Tina Martin

Thomas Günther

Federal Institute for Geosciences and Natural Resources (BGR) Wilhelmstr. 25-30, D-13593 Berlin/Germany [email protected]

Leibniz Institute for Applied Geophysics (LIAG) Stilleweg 2, D-30655 Hannover/Germany [email protected]

with the synthetic mineral-sand conclusions. Additionally some (in situ) examples from the heap were investigated in laboratory and show the complexity of a further interpretation.

SUMMARY Geophysical investigations at historical slag heaps are increasingly in focus due to economic, environmental or archaeological reasons. We present in this study the investigation of a historical slag heap in the Harz Mountains, Germany, where laboratory and field measurements were conducted. Previous detailed laboratory measurements of different synthetic mineral-sand mixtures have shown that there is a relationship between chargeability and mineral concentration as well as between relaxation time and mineral grain size. With the development of a new approach for the simultaneous fitting of the whole spectral field data set to different models we are now able to interpret the field measurements further. We started to show that the relationships found in laboratory can be in principle transferred to the field data. However, in situ samples also show that the SIP response can be very different between samples from the same heap. So a general statement of the mineral content/grain size of a slag heap only from some field profiles is not possible. With the help of additional mineralogical, chemical and optical methods we try to characterize the different SIP response with the aim of rough classification of slag heap areas. Key words: slag heap; SIP; field measurements, mineralogical results

INTRODUCTION For a long time, retrieving residual from historical mining waste dumps was considered economically inefficient. Rising prices and a growing demand have corrected this estimation even for less productive material sources. So in the last few years different own geophysical investigations at abandoned mining heaps were conducted to determine the potential of the raw material. Also for the archaeological application investigation of historical slag heap sites in France were increasingly conducted (Florsch et al., 2011; 2012) From own laboratory measurements at synthetic mineral-sand mixtures it is known (Hupfer et al., 2015) that concentration and mineral grain size of different minerals can be estimated with the spectral induced polarization (SIP) method by using the Cole-Cole equation (e.g. Cole & Cole, 1941; Pelton et al., 1978). With the newest two dimensional inversion algorithm (Günther & Martin, 2016) the analysis of the field SIP results at mining slag heaps can also improve the interpretation of the residual mineral content so that spatial information about the mineral content of historical heaps seems to be possible. In this study the results of different profiles at a mining slag heap measured with the SIP technique are shown and compared IP2016 – 6-8 June, Aarhus, Denmark

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METHOD AND MATERIAL A historical slag heap in the south-west part of the Harz mountains/Germany was investigated with several 2D profiles. Starting in the middle ages, copper, lead, silver and zinc ores were mined at different periods before it was abandoned more than 200 years ago. As a result, these dumps exhibit heterogeneous structures, i.e. variations in mineral composition and content, but also dominant grain size are expected. The total extension of the heap is about 600 m x 200 m but it is probably not continuous. The used SIP device was the multi-channel and PC-controlled instrument SIP 256C (Radic, 2004). As configuration we used the dipole-dipole array as it reduces coupling between the current and voltage cable near the electrodes. Although non-polarizable electrodes were recommended to measure small IP effects (e.g. Kemna et al. 2012) we used standard stainless steel electrodes because we expected large polarization effects from the slag. Nevertheless we tried to reduce the electrode influences by using two different electrodes at each measurement point (one for current injection, one for potential measurement). For the profiles we used up to 41 channels with an electrode distance of 1 m. We measured at 14 frequencies between 0.16 and 1000 Hz. A detailed description can be found in Günther & Martin (2016). The in situ (at the surface) collected slag chunks of two profiles were cut into cylindrical shapes in order to fit into the four-point measuring cell. The samples were fully saturated with tap water ( = 700 S/cm) and measured under controlled laboratory conditions with the instrument SIP-ZEL (Zimmermann et al., 2008). As coupling agent we used an Agar-Agar gel. Parts of the slag chunks were also investigated with the XRF (X-ray fluorescence) spectroscope to analyze the element content. To estimate the porous nature of the slag samples the MIP method (mercury intrusion porosimetry) was applied.

RESULTS Synthetic mineral-sand-mixtures Hupfer et al. (2015) showed in their study that there is a strong relationship between the SIP signature and ore concentration, grain radius and pore fluid conductivity. They observed that the polarization increases with increasing ore concentration and with decreasing grain radius. Fitting these data with a ColeCole model clear relationships between chargeability and mineral concentration, as well as between relaxation time and grain size, could be found. For different pyrite grain sizes and concentrations the results can be seen in Figure 1.

SIP at historical mining slag heaps

Figure 1: Relationship between chargeability and mineral concentration (left) and time constant and mineral grain size (right) for the synthetic mineral-sand-mixture samples after Hupfer et al. (2015). The green circle shows the expected grain sizes/mineral content from the SIP field measurements.

Field SIP measurements In this study the results from two field profiles are shown. Profile 3 (Figure 2) was a 32 m long profile with 33 electrodes with an electrode distance of 1 m. The first 7 m of the profile were covered by grass followed by approx. 9 m of slag layer right on top. Further back we found a slag/grass layer sequence. Close to the surface the amplitudes for the frequency of f = 1.25 Hz correlate well with the slag/grass layers (Figure 2, top). So the slag shows typically resistivities above 600 m whereas the soil layer and the surrounding material is defined by smaller resistivities (< 100 m). In phase (Figure 2, bottom) the slag layer correlates with high phase values (> 7°). In contrast, both soil layer and non-slag material shows phase values < 1°.

Martin and Günther

Figure 3: SIP results from profile 5 for 1.25 Hz. Top: amplitude, bottom: phase. The covered slag material is defined by higher resistivities and high phases. Both profiles show that the slag material here is characterized by higher resistivities and very high phase values. With the development of a new approach for the simultaneous fitting of the whole spectral field data set to different models (here ColeCole for example) we are now in a position to obtain chargeability and time constant for both profiles (Günther & Martin, 2016). With the relationship found in the laboratory data, conclusions about mineral concentration and grain size should now be possible. In Figure 4 the results for profile 5 can be found for the chargeability m (top), time constant  (middle) and the relaxation exponent c (bottom)The chargeability of the supposed slag layer is around 0.7-0.8. The very noticeable layer with higher time constants shows values around 3 s.

Figure 2: SIP results from profile 3 for 1.25 Hz. Top: amplitude, bottom: phase. The slag material is defined by higher resistivities and high phases. Profile 5 was conducted approx. 150 m south of profile 3 and directed perpendicular. This profile was 40 m in length with an electrode distance of 1 m. A detailed description of these profiles can be found in Günther & Martin (2016). In the field, this profile was fully covered by grass. Figure 33 shows the results of profile 5 for f = 1.25 Hz. In resistivity (top) a high resistive layer can be found in a depth of approx. 1.5 - 2 m. This layer seems too thin out to the right hand part of the profile. In the phase section (bottom) a zone of high phase (up to 16°) in approx. 3 m depth can be seen through the whole profile. This layer has a phase maximum for the lowest fully observed frequency of 0.16 Hz. To higher frequencies these layer decrease in phase.

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Figure 4: Fit of Cole-Cole parameters for each model cell of profile 5. Top: chargeability m; middle: time constant ; bottom: relaxation exponent c. Laboratory results of the slag samples From the collected slag chunks various samples were cut and measured. In Figure 5 two samples from profile 3 (SK 1 - red) and two samples from a further profile (SK 2 - blue) can be seen. Analogue to the field results the red samples show high

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resistivities (> 1000 m). The phase values are significant (~ 5-6°) but not as high as in the field measurements. In contrast, the blue samples behave differently. Although only 50 m away from profile 3, the SIP characteristics are very different. These samples show much lower resistivities (< 50 m) and very high phases (up to ~ 40°) with a clear maximum at 0.1 Hz resp. 0.01 Hz. In Table 1 some selected results from the XRF analysis for both chunks can be seen. The slag residuals show still relatively high minerals content. In Table 2 some results from the MIP measurement are listed. Although the porosity is twice for sample SK 1, an explanation for the different SIP characteristic could not be found until now.

The results from the laboratory measurements of slag samples, gathered in-situ from the profile, indicate that both resistivity and phase are in the same range although we also find samples at the same slag heaps (but few meters away from the profile) which shows very different SIP characteristics. Generally it seems very promising to investigate historical slag heaps with the SIP method to get information about the residual mineral content and grain size. The investigations of more slag samples from other parts of the slag heaps or/and other slag mining dumps demonstrate that a lot of different slag types exist and according to this very different SIP results could be observed. By ongoing further analysis with mineralogical, optical and chemical methods we try to characterize these differences. ACKNOWLEDGMENTS We thank the German Ministry of Education and Research (BMBF) for funding the project ROBEHA (grant 033R105) in which all the work was done. We also thank Kerstin Kuhn/BGR for the mineralogical investigation and background as well as Dr. Sabine Kruschwitz/BAM/TU Berlin for the MIP results.

REFERENCES Figure 5: SIP laboratory results for different samples from two slag chunks. Similar to the field results, samples from SK 1 (profile 3 - red) show higher resistivities (> 800 m) and high phase effects (around 5-6°). The blue samples are from another slag chunk (SK 2, but from the same heap) and show different SIP response.

Table 1: Selected results from the XRF Analysis sample SK 1 SK 2

Ba [%] 2.65 3.80

Pb [%] 1.78 3.83

Zn [%] 8.14 8.57

Cu [%] 0.68 0.51

Fe2O3 [%] 53.59 43.55

SiO2 [%] 18.53 25.30

Table 2: Selected results from the MIP. sample SK 1 SK 2

Porosity [%] 7.39 3.36

Density [g/cm³] 3.62 3.75

Avg. Pore diameter [m] 10.14 14.42

CONCLUSIONS In field measurements at a historical slag heap the SIP results show that slag material, which traditionally contains the left over parts, showed high resistivities and high phase values at least for low frequencies. Using the whole spectral information and fitting these data to a Cole-Cole-model allows us to determine chargeability and relaxation time similar to the parameters from Hupfer et al. (2015). Their results show a strong relationship between chargeability and mineral concentration as well as between relaxation time and grain size for pyrite-sand samples. If we extend the fit and locate the parameter values obtained from the field measurements (Figure 1) we calculate mineral concentration of about 10-15% what is conceivable in this area (compare Table 1). The obtained grain sizes in the dm/m area seem much too high for a pure mineral grain but the slag might act as a compact body. IP2016 – 6-8 June, Aarhus, Denmark

Cole, K.S. & Cole, R.H., 1941. Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys. 9, 341–351. doi:10.1063/1.1750906. Florsch, N., Llubes, M., Tereygeol, F., Ghorbani, A. & Roblet, P., 2011. Quantication of slag heap volumes and masses through the use of induced polarization: application to the Castel-Minier site. Journal of Archaelogical Science, 38, 438{451. doi:10.1016/j.jas.2010.09.027. Florsch, N., Llubes, M., & Tereygeol, F. (2012). Induced polarization 3D tomography of an archaeological direct reduction slag heap. Near Surface Geophysics, 10, 567{574. doi:10.3997/1873-0604. 2012042. Günther, T. & Martin, T. (2016). Spectral two-dimensional inversion of frequency-domain induced polarisation data from a mining slag heap. Journal of Applied Geophysics, doi:10.1016/j.jappgeo.2016.01.008. Hupfer, S., Martin, T., Weller, A., Kuhn, K., Günther, T., Ngninjio,V., & Noell, U. (2015). Laboratory SIP measurements at unconsolidated sulphide-sand-mixtures. Journal of Applied Geophysics, doi:10.1016/j.jappgeo.2015.12.003. Kemna, A., Binley, A., Cassiani, G., Niederleithinger, E., Revil, A., Slater, L., Williams, K. H., Orozco, A. F., Haegel, F.-H., Hördt, A., Kruschwitz, S., Leroux, V., Titov, K., & Zimmermann, E. (2012). An overview of the spectral induced polarization method for near-surface applications. Near Surface Geophysics, 10, 453-468. doi:10.3997/1873-0604.2012027. Pelton, W., Ward, S., Hallof, P., Sill, W., & Nelson, P. (1978). Mineral discrimination and removal of inductive coupling with multifrequency IP. Geophysics, 43, 588-609. Radic, T. (2004). SIP256C - Users manual. Radic Research http://www.radic-research.de. Zimmermann, E., Kemna, A., Berwix, J., Glaas, W., Münch, H., & Huisman, J., 2008. A high accuracy impedance 3

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spectrometer for measuring sediments with low polarizability. Meas. Sci. Technol. 19. doi:10.1088/0957-0233/19/9/094010.

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Influence of plant roots on induced polarization of cultivated soil columns Sophie Maloteau

Guillaume Blanchy

UR TERRA, Gembloux Agro-Bio Tech, ULg 2, passage des Déportés 5030 Gembloux Belgique [email protected]

Gembloux Agro-Bio Tech, ULg 2, passage des Déportés 5030 Gembloux Belgique [email protected]

Frédéric Nguyen

Sarah Garré

Bât. B52/3 Géophysique appliquée, Quartier Polytech 1 allée de la Découverte 9 4000 Liège Belgique [email protected]

UR TERRA, Gembloux Agro-Bio Tech, ULg 2, passage des Déportés 5030 Gembloux Belgique [email protected]

SUMMARY Here the influence of plant roots on geophysical measurements is tested. For this purpose, electrical resistivity (ER) and induced polarization (IP) measurements are conducted on cultivated soil columns with one plant of Brachypodium. The preliminary results in known media show that acceptable values are obtained from the IP measurements. Even though, we are still testing the specific impact of the electrodes and the column layout on the IP measurements, the decay curves display the expected form and behaviour. The results from this experiment will give us a first idea of the ability of IP to serve as a proxy for the presence of roots in a column. This, combined with ERT and TDR measurements, should lead us to a better understanding of the electrical signature of bulk soil with roots at different soil moisture levels. Key words: TDIP; roots; relationship; Brachipodium

soil;

activity (by transporting ions, releasing exudates, changing the soil structure,…) will cause changes in rhizosphere sufficient to be detected by geophysical measurements. This experiment is included in a bigger research project, eROOT, about the influence of roots system on geophysics measurements. In this experiment, 6 cylindrical columns (Φ=20 cm, h=45 cm) are filled with repacked saturated loam: Two columns are made of transparent plexi in which 40 electrodes are inserted (5 levels of 8 electrodes) and connected to the MPT-DAS machine (Figure 1).

pedo-physical

INTRODUCTION Geo-electrical methods have been widely used for the last 40 years in many fields: mineral investigation, soil and water pollution, engineering application for subsurface surveys, etc (Reynolds, 2011). Many factors can influence the electrical properties of a media, and thus influence the electrical resistivity (ER) and induced polarization (IP) measurements. Among those factors, it has been observed occasionally that plant roots affect bulk electrical resistivity and electrical induced polarization(Waisel et al., 2002; Kemna et al., 2011; Vanderborght et al., 2013). However, this impact is not yet well understood. The goals of this experiment are to quantify the effect of plant roots on electrical properties of the soil subsurface and particularly on IP measurements.

METHOD AND RESULTS For this research, it is assumed that roots system affect the electrical properties of the rhizosphere. Indeed the root

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Figure 1. One column of soil connected to 40 electrodes for ERT and IP measurements.

Plant roots influence on ER and IP

eg: Maloteau, Blanchy, Nguyen and Garré

CONCLUSIONS Each of those 2 columns is placed on a scale. Resistivity and chargeability (with 11 time windows) are measured on the first column, whereas only resistivity is measured on the second column because 4 TDR probes are inserted between each level of electrodes. The 4 other columns are made of grey plastic cylinders pre-cut in 5 pieces corresponding to the 5 electrodes levels and for which the RLD (Root Length Density) is measured at each development stage of the plant (Figure 2). The experiment takes place in a container where the air temperature, the photosynthetically active radiation (PAR), the photoperiod and the relative humidity are controlled and measured. We have sown one seed of Brachipodium distachyon (L.) Beauv. in each column. When the plant is big enough to support saturated conditions, the columns are irrigated till saturation (Day 1). From that day, no irrigation will be applied until the end of the experiment in order to observe a drying cycle. Measurements begin at Day 1 and will continue for 2 months. ERT and IP measurements (vertical and horizontal dipoledipole array) are conducted twice a day while TDR probes and scales are measuring continuously. Parameters of the controlled environment of the container are also measured permanently. Preliminary results of electrical resistivity (Ohm m) and phase angle of IP measurements (mrad) for columns obtained during the testing phase with (1) saturated sand, (2) ½ saturated loam and ½ water, and (3) only water and one submerged root system of Brachipodium, are shown in Figure 3 and Figure 4.

The preliminary results in known media show that acceptable values are obtained from the IP measurements. Even though, we are still testing the specific influence of the electrodes and the column layout on the IP measurements, the decay curves display the expected form and behaviour. The results from this ongoing experiment will give us a first idea of the ability of IP to serve as a proxy for the presence of roots in a column. This, combined with ERT and TDR measurements, should lead us to a better understanding of the electrical signature of bulk soil with roots at different soil moisture levels.

ACKNOWLEDGMENTS We thank Guillaume Blanchy for his exceptional motivation during his MSc thesis project and the partners from Forschungszentrum Jülich GmbH, Germany and UCL, Belgium for their valuable support. This project is funded by FRS-FNRS (Belgian National Scientific Research Fund). REFERENCES Kemna, A., Kelter, M., Pfeifer, J., Zimmermann, E., Walter, A., 2011. Imaging and characterizing root systems using electrical impedance tomography. Presented at the AGU Fall Meeting 2011, San Francisco, California, USA. Reynolds, J.M., 2011. An introduction to applied and environmental geophysics, 2nd ed. Wiley. Vanderborght, J., Huisman, J.A., Kruk, J. van der, Vereecken, H., 2013. Geophysical Methods for Field-Scale Imaging of Root Zone Properties and Processes. Soil–Water–Root Process. Adv. Tomogr. Imaging, 247–282. Waisel, Y., Eshel, A., Beeckman, T., Kafkafi, U., 2002. Plant Roots: The Hidden Half, Third Edition. CRC Press.

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Plant roots influence on ER and IP

eg: Maloteau, Blanchy, Nguyen and Garré

4

9

45 cm

8

9

20 cm

ERT and IP measurements

TDR probes and ERT measurements

Root length density (RLD) measurements

electrode TDR pre-cut line

Figure 1. Scheme of the container experiment set up. Figure 2. Scheme of the experiment set up.

Figure 3. Electrical resistivity tomography (Ohm m) of columns with (1) saturated sand, (2) 1/2 saturated loam and 1/2 water, and (3) water only with 1 plant of Brachipodium.

Figure 4. Phase angle tomography (mrad) of columns with (1) saturated sand, (2) 1/2 saturated loam and 1/2 water, and (3) water only with 1 plant of Brachipodium.

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Concept of our New Multi-Channel SIP Instrument: SIP256D Tino Radić www.radic-research.de Zehntwerderweg 188A, 13469 Berlin, Germany [email protected]

SUMMARY The quality of SIP measurements is largely determined by the hardware concept of the measuring instrument. High frequency impedance measurements are only possible with the shortest possible current and potential cables. For this, the transmitter should always be located at the electrodes. The current and potential measurement should also be carried out directly at the corresponding electrodes. Our newly developed instrument SIP256D satisfies all these requirements. Key words: Spectral Induced Polarization, Minimizing Systematic Errors, Expanding Frequency Range.

INTRODUCTION In the last few years, the number of possible applications of the method of spectral induced polarisation (SIP) has had a notable sharp increase. An example of one such application is the determination of the coefficient of permeability of sand and sandstone, which is important for hydrogeologists (Weller et al, 2010). The assessment of the health of a tree through characteristic features in the impedance spectrum should also be mentioned (Martin et al., 2013). The basis for this was indepth knowledge gained in the laboratory in the last few years about the connection between petrophysical attributes such as pore space geometry, pore fluid conductivity (Hoerdt et al, 2014) and temperature (Bairlein et al, 2014) of nonmineralised rocks and their resulting frequency dependent electrical impedance. The size of the formation is closely linked with the frequency, at which it is represented in the spectrum. This means that impedance measuring devices must be able to deliver a high quality of data in a wide frequency range. For example, our Chameleon instrument (Radić, 2014) gives measurements between 0.001 Hz and 250.000 Hz 81/2 decades (Figure 1).

Figure 1. The impedance spectrum of a sandstone (Baumberger R18) shows that IP effects appear in a wide area of frequency. Laboratory measurement with our Chameleon instrument. For geoelectric direct current measurements the concept of a multi-channel multi-electrodes instrument has established itself. (Figure 2). This concept has, however, for IP measurements limited suitability. Measurement results are already systematically and irreversibly biased at frequencies from ~10 Hz. An analysis of this concept shows that the cause of this is not the electronics themselves, but is the cable, which connects the electrodes with the electronics. (Dahlin, 2012). There is a multitude of coupling effects because of the capacity of the cable. These increasingly bias the impedance measurements with a higher frequency. With our SIP256C Multi-Receiver instrument (Figure 3), the most important of these coupling effects can be avoided, thus extending the area of frequency to 1 kHz. The most effective method to minimise the effects of cable coupling is therefore to avoid them altogether. This means concretely that one reduces the length of each cable to its necessary minimum. Additionally, it is necessary to avoid a parallel cable run. We have already made an important first step with our SIP256C instrument by establishing the current and voltage measurements directly at the electrodes.

THE CHALLENGE In order to be able to widely use the knowledge gained in the laboratory also in the field, the range of measurement has to be increased to include higher frequencies. Measuring devices for use in the field have to, however, meet further requirements. In this way, a higher progress in measurement and a higher degree of automation are expected of a modern measuring instrument.

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Figure 2. Schema of a typical multi-electrode instrument for geoelectric measurements. The electronics for voltage and current measurements are located together with the transmitter in one casing. A multicore cable is used to connect the electrodes (P, C) with the electronics. Typical cable lengths are tens up to hundreds of meters. Capacitive coupling between the cables and the soil results in systematic data errors.

Features of our Next Generation Multi-Channel SIP Instrument.

Tino Radić

THE NEW HARDWARE: SIP256D

Figure 3. Schema of our multi-receiver instrument SIP256C. Remote Units are used to measure currents and voltages direct at the electrodes. Thanks to the short potential cable, undesired coupling effects are significantly smaller as with a multi-electrode instrument (Figure 2). For this, a Remote Unit is located at each electrode. Thus, the lengths of the potential lines are reduced to a minimum; namely to the distances between the pairs of potential electrodes. Furthermore, with this concept configurations of measurements (dipole-dipole) can be chosen with which the current and potential cables do not run parallel. This fundamentally distinguishes our concept from most other multi-electrodes instruments, which assemble the entire measuring electronics in one place, and which connect to the electrodes via long multicore cables. With our SIP256C, it was possible for the first time to obtain high value measurements up to 1kHz with medium size arrays and moderate soil conductivity conditions. With worse conditions (larger cable lengths, variable contact resistance of electrodes), measurement results at the highest frequencies still turn out unsatisfactory. The course of this is the capacitive coupling of the electrical cable with the ground. We were able to solve this problem by actively shielding the current cable. A modified SIP256C instrument (Figure 4a), which we created for Aachen University (Germany), shows that with it this coupling effect can be extensively suppressed (Radić et al., 2012). A separation of the current cable and the potential cable is not, however, necessary (Figure 4b).

Our current concept has to be further developed to achieve even higher frequencies (20 kHz). In particular it is essential to minimise the length of the electrical cable. This, however, cannot be realised with a central transmitter, as used in the SIP256C. Instead, each of our Remote Units have to be equipped with their own transmitter (Figure 5). The length of the current cable is then identical to the distance of both current electrodes, and for this reason it is as short as possible. However, also the remaining short current cable exhibits a low capacitive coupling with the ground. The resulting parasitic leakage current is dependent on the voltage difference compared to the ground. If the potential difference was successfully minimised then the leakage current would be minimal and would no longer bias the impedance measurement. To achieve this, both transmitters located at the current electrodes are connected in series. Now the current strengths are compared just as with the CE-compensation with a shielded current cable and are measured by both the RUs, which are located at the current electrodes. If they do not match, then the voltage of one the transmitters is increased and the voltage of the other is decreased. The overall voltage stays the same. An automatic algorithm calculates in a few steps the setting for matching the current strengths. Now the electrical cable exhibits approximately the level of the ground and systematic mistakes caused by the current cable capacity are minimised. The increased hardware in the Remote Units comes with less hardware in other places. Instead of a Base Unit with an integrated transmitter, only an interface is needed which connects PC and the chain of Remote Units. In addition, the connecting cable between the Remote Units contains just one single unshielded wire for the current. Both of these features save on money, volume and weight.

Figure 5. Schema of our new SIP256D instrument. A transmitter is located in each Remote Unit. With this, the length of the electrical cable is reduced to a minimum. Figure 4a. Schema of the modified SIP256C instrument. The electrical cables (pink) are actively shielded and furthermore separated from the potential cables (green) with a distance of 1m.

Figure 4b. The same schema as in Figure 4a, however, here the shielded cables are not set-up separately from the potential cables.

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BUILT-IN TRANSMITTER To equip each Remote Unit with its own transmitter presents a challenge in various ways. The transmitter has to be cost effective, compact, light and equipped with a high degree of efficiency. Unfortunately, transmitters for sinusoidal signals, such as the ones that we have successfully used for many years, do not exhibit these features. The above challenges would at best be satisfied with a transmitter that is especially constructed to generate rectangular signals. From a theoretical viewpoint, rectangular signals should be just as suitable for high value SIP measurements. The fact that rectangular signals exhibit a large harmonic wave spectrum urges caution.

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Features of our Next Generation Multi-Channel SIP Instrument.

Tino Radić

For this, both transmitters are to be connected to both Remote Units respectively, which are currently responsible for the power input. We can provide an external transmitter with up to 600 watt, while the performance of a built-in transmitter is limited to only 25 watt. A higher performance is also possible if needed. For this, the power input is not longer realised via the Remote Units, but via separate electrodes.

CONCLUSIONS

Figure 6. Amplitude and Phase of the resistivity at 80 Hz. Top: Sinusoidal Signal, Bottom: Rectangular Signal. Location: Lübars (Berlin, Germany). Configuration: Dipole-Dipole, a=0.5 m. On the one hand, the requirements for the linearity, speed and stability of the signal processing electronics are even higher with a rectangular signal. On the other hand, with the appearance of EM-effects, the amplitudes of the harmonic waves decrease more slowly with the distance as those of the fundamental frequency. The result is distinct overshooting at the flanks of the receiver signals. Field measurements with a modified SIP256C instrument show, however, that at least with small and medium distances between electrodes, a moderate specific conductivity of the ground and frequencies at least up to 1kHz show no loss of quality (Figure 6). A further challenge results from the necessity to power the transmitters from the Remote Units' internal batteries. Until now, the concept envisaged a single 50 watt transmitter, which is used for all current dipole configurations. Power for 10 hours requires 500 watt*h of energy. If one divides this energy between typically 20 Remote Units then the result is an energy requirement of 25 watt*h for each Remote Unit. This energy can, for example, be provided by a 12 V NiMh battery pack with 2.1 Ah. Due to the fact that two built-in transmitters are normally connected in series, the aimed for total power of 50 watt is reached.

EXTERNAL TRANSMITTER The use of two mobile transmitters presents a cost effective alternative to using built-in transmitters (Figure 7). This variation requires, however, that the user personally moves the transmitters step for step along the profile.

Figure 7. Same schema as in Figure 5, but instead of a built-in transmitter, two mobile transmitters are used. This variation costs less and allows the use of stronger transmitters. However, it requires that the user themselves changes over the transmitters.

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Laboratory measurements prove that the structure of the porosity of non-mineralised rock is shown in the impedance spectrum. Measuring instruments have to be able to deliver high value IP data in a broad frequency area in order to record as much information as possible about the structure of the substrate also in field use. Alternating current measurements with multi-channel instruments are, however, biased through capacitive coupling effects between the measuring cable and the ground. An improved measuring concept avoids the most frequent sources of error and thus allows SIP measurements of up to 20 kHz.

REFERENCES Bairlein, K., Hoerdt, A., Buecker, M. and Nordsiek, S., 2014, Experimental and theoretical studies of the temperature dependence of the spectral induced polarization (SIP) based on a membrane polarization model: Ext. Abstract, 3rd International Workshop on IP, Oleron Island, France, 6-9 April 2014. Dahlin T. and Leroux V., 2012, Improvement in time-domain induced polarization data quality with multi-electrode systems by separating current and potential cables: Near Surface Geophysics, 2012, 10, 545-565. Hoerdt, A. and Buecker, M., 2014, The salinity dependence of SIP parameters studied with an extended model of membrane Polarization: Ext. Abstract, 3rd International Workshop on IP, Oleron Island, France, 6-9 April 2014. Martin, T. and Guenther, Th., 2013, Complex Resistivity Tomography (CRT) for fungus detection on standing oak trees: European Journal of Forest Research (2013) 132 (5-6), 765-776. Radić, T. and Klitzsch, N., 2012, Compensation Technique to Minimize Capacitive Cable Coupling Effects in MultiChannel IP Systems: Ext. Abstract, P81, Near Surface Geoscience 2012 - 18th European Meeting of Environmental and Engineering Geophysics, Paris, France, 3-5 September 2012. Radić, T., 2014, Measuring IP Effects at high frequencies. First lab and field data from 0.001 Hz - 250 kHz: Ext. Abstract, 3rd International Workshop on IP, Oleron Island, France, 6-9 April 2014. Weller, A., Nordsiek, S. and Debschütz, W., 2010, Estimating permeability of sandstone samples by nuclear magnetic resonance and spectral-induced polarization: Geophysics 75, 215-226.

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Spectral Inversion of SIP field data using pyGIMLi/BERT Thomas Günther

Tina Martin

Carsten Rücker

Leibniz Institute for Applied Geophysics (LIAG) Stilleweg 2 D-30655 Hannover, Germany [email protected]

Federal Institute for Geosciences and Natural Resources (BGR) Wilhelmstr. 25-30 D-13593 Berlin, Germany [email protected]

Berlin Institute of Technology Institute f. Applied Geosciences Ernst-Reuter-Platz 1 D-10623 Berlin, Germany [email protected]

SUMMARY With the developing SIP instruments there are increasing applications of spectral induced polarization in the field. The spectral content of the electric parameters has the potential of characterizing the subsurface and must therefore be retrieved from inversion. Up to now there is no open available inversion package for researchers. We present the open-source library pyBERT, a C++Python library for inversion of field resistivity data. It is able to analyse the measured spectra with a variety of different approaches. A Python manager class allows nonprogrammers to access and visualize in different ways and includes pre-processing of the data as well as postprocessing of results, e.g. fitting Cole-Cole models. We give an impression on how to use these codes and present results based on a synthetic model demonstrating that spectral parameters can be reliably retrieved. Key words: field SIP, spectral inversion, programming, open-source software, slag heap.

INTRODUCTION Resistivity is a key parameter in many applications in the field of hydrology, engineering geology or exploration. Besides resistivity, i.e. energy loss, the ability of polarization, i.e. energy storage, can reveal important properties like mineral content or dominant pore size. Laboratory measurements are usually done in the frequency domain over a wide frequency range from mHz to kHz. The magnitude and phase spectra are either fitted with Cole-Cole models (Pelton et al., 1978) or decomposed using Debye or Warburg models (Nordsiek & Weller, 2008; Florsch et al., 2014). Contrary to the laboratory measurements, field measurements are usually conducted in time domain (TD), i.e. the full wave form of the voltage is recorded. Traditionally, only an integral value, the total chargeability, was used for imaging. However, the spectral inversion on dominant relaxation time is lost then. Fiandaca et al. (2013) presented a method to retrieve Cole-Cole parameters from inverting the full decay. However, the resolvable bandwidth of available time-domain instruments is restricted by limitations of the source signal and the recording gates. Frequency-domain (FD) instruments are able to cover much wider ranges, however at the cost of significantly increased measuring time. Up to now, there is only a limited number of publications on FD field SIP.

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In this work we focus on the analysis of frequency-domain data, i.e. data sets of magnitude and phase for a number of measured frequencies. The easiest approach is to treat each data set independently. An improvement could be made by subsequent inversion using the preceding frequency as a starting or reference model. Other ways are simultaneous inversion of all data with smoothness constraints along frequency or with respect to Cole-Cole parameters (e.g. Routh et al., 1998; Loke et al., 2016). While before mostly approximations for small phases have been used, Kemna (2000) proposed fully complex calculation of the governing partial differential equation and solved the inverse problem in two steps, first for magnitude and then improving the phase. Up to now, there is no open available code that includes spectral inversion of SIP data. We present a code within the BERT software, is based on the software library GIMLi, that uses a variety of different inversion approaches and includes pre- and post-processing of data and models.

SIP INVERSION METHODS Single-frequency inversion We use the triple-grid inversion approach described by Günther et al. (2006). In 2D, the subsurface is discretised by using triangular meshes with the advantage that including arbitrary topography can be described. Whereas a coarse mesh is used for inversion, a refined mesh is used for the forward calculation using the secondary field approach (Rücker et al., 2006). On a highly-refined mesh the primary potentials are computed by using quadratic shape functions. A Fourier transform is used to solve the 3D source problem into 2D (Loke et al., 2006) using Gauss-Legendre and Gauss-Laguerre wavenumber integration (Kemna, 2000). A Gauss-Newton algorithm is used to minimize the errorweighted data misfit along with the roughness of the model (Günther et al., 2006). Weighting of the two terms is achieved by a regularization parameter that is determined such that the smoothest model that is able to fit the data is found. After resistivity inversion, the measured phase is inverted using a low-phase approximation as done by Martin & Günther (2013), i.e. the imaginary resistivity is the model parameter. Alternatively, a fully complex calculus (e.g. Kemna, 2000) can be used for calculating of the forward response and also the Jacobian matrix. Logarithmic transforms are used to keep both data and model positive (Kim & Kim, 2011). In time domain, where apparent chargeability is measured by integrating the voltage curve, one could also use the low-phase approximation. Another way incorporates a second real-valued inversion of higher-frequency data with the first model as reference model, which are the only TD implementations so far.

Spectral frequency-domain SIP inversion

Günther, Martin & Rücker

Multi-frequency inversion An example code looks as follows The data of the individual frequencies could be independently inverted. However, the ambiguity inherent in the inversion leads to artifacts so that the spectral information can easily be lost. We use the fact that all underlying relaxation processes (as described by Debye, Warburg or Cole-Cole models) generally exhibit smooth spectra and apply smoothness constraints along the frequency axis. The apparent resistivities of all frequencies are inverted simultaneously for frequency-dependent resistivity as described in detail by Günther & Martin (2016). The data vector comprises all sub-vectors and the model vector accordingly. The Jacobian matrix has a block-diagonal behaviour. 𝐽1 𝐽 =[⋮ 0

⋯ 0 ⋱ ⋮ ] (1) ⋯ 𝐽𝑁

where the matrices Ji are the Jacobian matrices for a number of N individual frequencies. The regularization is applied on both the spatial and the spectral axis, i.e. neighbouring cells of the same frequency and the same cells with neighbouring frequencies are involved by the derivative operator. After magnitudes, the same is done for the phases and another coupled inverse problem is solved, before further analysis of the results follows. A completely different way of discretization consists in describing each model by a sum of Debye (or Warburg) terms, i.e. a Debye decomposition (Nordsiek & Weller, 2008) 𝐾

𝜌 = 𝜌0 (1 − ∑

𝑘=1

𝑚𝑘 (1 −

1 1+𝑖𝜔𝜏𝑘

1 1+(𝑖𝜔𝜏)𝑐

)) (3)

IMPLEMENTATION The pyGIMLi framework We use the open-source framework GIMLi (Geophysical Inversion and Modelling Library), a C++ library that includes performance-critical parts as finite element analysis and equation solvers. Boost is used to bind the whole library to the modern and flexible free programming language Python, in which most of the logical code is written. See www.pygimli.org for a documentation of the individual modules consisting of mesh generation, solvers and different geophysical methods. pyGIMLi includes a class for handling SIP spectra (as they arise in the lab or in the field) that comprises different ways of plotting, removal of electromagnetic coupling, or fitting. Although all important part are available as functions, data are organised in a class which makes using the individual methods easy and intuitive.

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pyGIMLi is able to do fully constrained models, e.g. for timelapse or laterally constrained inversion in an efficient way. The Jacobian matrix (1) is a block diagonal matrix that stores only references to the Jacobians of the individual forward operators, whose forward responses are pasted together to yield the model response. So if a single inversion comprises a number of D data and a number of M model cells, only NxDxM entries are stored instead of NxDxNxM. pyBERT and SIP inversion BERT (Boundless Electrical Resistivity Tomography, Günther & Rücker, 2012) is a package built upon GIMLi. Besides the classical command line based inversion with configuration files there are also Python bindings called pyBERT. They include a resistivity class that handles single frequency (FD) or total chargeability (TD) data. On top of this, a specialized class SIP2d was designed for handling complete multi-frequency data. Up to now it reads the format of the Radic instruments (www.radic-research.de) and can visualize spectra or pseudosections (and export multipage pdf files of it), run different inversion approaches and do post-processing and model output. An example code reads as follows:

)) (2)

with a number of K predefined relaxation constants k and associated spectral chargeabilities mk that are inverted for. Each model cell owns a Debye spectrum that is used to derive mean relaxation times and total chargeability values. The size of the model space is comparable, but the Jacobian matrix involves further derivatives. This is also the case for a direct inversion for Cole-Cole parameters where the resistivity of each model cell is described as follows: 𝜌 = 𝜌0 (1 − 𝑚 (1 −

from pygimli.physics import SIP sip = SIP(‘example.txt’) # read data sip.showData(norm=True, KramersKronig=True) sip.removeEM(epsilon=True) sip.fitColeCole() sip.showAll(savePDF=True)

from pybert.SIP import SIP2d sip = SIP2d(‘example.res’) # SIP256C file sip.generateSpectraPDF(maxdist=20) sip.generateDataPDF(kmax=50000) sip.removeEMTerms(Pelton=True) sip.invertSingleFrequency(f=0.625) sip.invertSimultaneous(maxF=200) sip.fitColeColeModel(show=True) sip.saveResults() We test the approach by using a synthetic model.

SYNTHETIC MODEL We make use of a synthetic model consisting of a shallow slag heap body with two different relaxation constants (Fig. 1). The resistivities are quite homogeneous in the subsurface. Only the slag bodies are highly polarisable with different relaxation constants of 0.1 and 1.0 s and a common c of 0.5.

Figure 1. Synthetic model of a shallow slag heap, divided into two parts (r=200 m, m=0.8/0.7 and =0.1/10 s) over a 500m bedrock and partially covered by a 100 m topsoil (after Günther & Martin, 2016).

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Spectral frequency-domain SIP inversion

We show inversion results of noisified synthetic data for four frequencies (Fig. 2). The bottom of the slag is well found from resistivity which does otherwise not distinguish more.

Günther, Martin & Rücker

spectral behaviour is determined very well by the phases, whereas the resistivity spectra show undulations and make it hard to retrieve spectral properties. After all model cells have been fitted by the same routine, we obtain images for chargeability, time constant and relaxation exponent (Fig. 4). The chargeability shows increased values at the centre, but also at the surface and at depth. The time constant shows the correct values for the two slag bodies, but the anomalies are smeared towards the bottom. Interestingly, the exponent also delineates the slag body (with a too deep lower boundary) with correct values of about 0.5 whereas the other cells show values of about 0.25 (the starting values).

Figure 2. Resistivity (left) and phase (right) from inversion of synthetic data for four selected frequencies (156 mHz, 1.25 Hz, 10 Hz, and 80 Hz). The phase delineates the slag body and shows maximum values for the right part at low frequencies, whereas the left part shows up for higher frequencies.

In total, looking at all properties simultaneously the slag can be delineated and the two parts can be clearly distinguished by their relaxation constant. The curves are very smooth in contrast to individual inversion results. Simulations with much lower synthetic chargeability increase the undulations in the phase and improve the chance that the spectral behaviour is retrieved by resistivity only. However, these results are highly depending on the used error models. Further systematic parameter studies are needed to fully assess potential and limits.

We test the method by extracting the resistivity and phase values of selected model cells inside the slag body (see markers in Fig. 2). The general trend of decreasing resistivity and phase maxima at low frequencies is obvious (Fig. 3). The values are then fitted by a Cole-Cole model.

Figure 4. Result of Cole-Cole fit for all model cells showing chargeability (top), time constant (middle) and exponent (bottom). White lines denote the synthetic model boundary.

CONCLUSIONS

Figure 3. Cole-Cole fit for synthetic inversion results of three slag model cells (see markers in Fig. 2 for positions).

The presented software pyGIMLi/BERT is an open-source framework for resistivity inversion that also includes the processing of spectral induced polarization data in the frequency domain. As a generally applicable model, it includes constrained inversion of all frequencies simultaneously which is efficiently achieved by using block matrices.

Whereas the resistivity of the first cell is retrieved correctly, the other two are underestimated by about 30% due to the low contrasts in the model and the used smoothness constraints. However, the retrieved values for chargeability are quite close to the synthetic values given in Fig. 1, although the time constant of point 3 is too high. In general it reveals that the

Synthetic models based on Cole-Cole parameters show that the spectral parameters chargeability and time constant can be reliably retrieved by a fit of the obtained resistivity or phase spectra. Inversion of field data from a historic slag heap demonstrates the applicability to field data (Günther and Martin, 2016).

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Spectral frequency-domain SIP inversion

Further development could be achieved by extension to time domain SIP data. The tool could be used for extensive modelling studies for rigorous comparison between both approaches or to design optimum survey design for a given target. Although spectrally constrained inversion or discretisation by Debye or Warburg models are general approaches that do not require a specific behaviour, direct inversion for ColeCole parameters potentially yields the most reliable results in specific cases. However, the presented spectrally constrained inversion can present suitable starting models.

ACKNOWLEDGMENTS We like to thank all developers of the used open-source software packages (Triangle, SuiteSparse, Python, numpy, matplotlib) that made this software possible.

REFERENCES Fiandaca, G., Ramm, J., Binley, A., Gazoty, A., Christiansen, A. V. & Auken, E. (2013). Resolving spectral information from time domain induced polarization data through 2-D inversion. Geophysical Journal International, 192, 631–646.

Günther, Martin & Rücker

Günther, T. & Martin, T. (2016). Spectral two-dimensional inversion of frequency-domain induced polarisation data from a mining slag heap. Journal of Applied Geophysics, doi:10.1016/j.jappgeo.2016.01.008. Kemna, A. (2000). Tomographic inversion of complex resistivity. Ph.D. thesis. Ruhr-Universität Bochum. Kim, H.J. & Kim, Y.H. (2011): A unified transformation function for lower and upper bounding constraints on model parameters in electrical and electromagnetic inversion. Journal of Geophysics & Engineering 8, 21-26. doi:10.1088/17422132/8/1/004 Loke, M., Chambers, J. & Ogilvy, R. (2006). Inversion of 2D spectral induced polarization imaging data. Geophysical Prospecting 54, 287–301. Martin, T. & Günther, T. (2013). Complex resistivity tomography (CRT) for fungus detection on standing oak trees. European Journal of Forest Research, 132, 765–776. Nordsiek, S. & Weller, A. (2008). A new approach to fitting induced polarization spectra. Geophysics 73(6), F235-F245.

Florsch, N., Revil, A. & Camerlynck, C. (2014). Inversion of generalized relaxation time distributions with optimized damping parameter. Journal of Applied Geophysics, 109, 119-132.

Pelton, W., Ward, S., Hallof, P., Sill, W. & Nelson, P. (1978). Mineral discrimination and removal of inductive coupling with multifrequency IP. Geophysics, 43, 588–609.

Günther, T., Rücker, C. & Spitzer, K. (2006). Three-dimensional modeling and inversion of DC resistivity data incorporating topography - Part II: Inversion. Geophys. J. Int., 166, 506517.

Routh, P.S., Oldenburg, D.W. & Li, Y. (1998). Regularized in ersion of spectral IP parameters from complex resistivity data. SEG Expanded Abstracts 1998. doi:10.1190/1.1820608.

Günther, T. & Rücker, C. (2012): Boundless Electrical Resistivity Tomography (BERT) v. 2.0 - Open Access Software for Advanced and Flexible Imaging. Ext. Abstr., Schlumberger Symposium of 100 years ERT, Paris 10/07/10.

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Rücker, C., Günther, T. & Spitzer, K. (2006). 3-D modeling and inversion of DC resistivity data incorporating topography Part I: Modeling. Geophys. J. Int., 166, 495-505.

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On the Effectiveness of 1D Inversions of TEM Data affected by Induced Polarization Marc Seidel

Bülent Tezkan

Institute of Geophysics and Meteorology University of Cologne Albertus-Magnus-Platz, 50923 Cologne, Germany [email protected]

Institute of Geophysics and Meteorology University of Cologne Albertus-Magnus-Platz, 50923 Cologne, Germany [email protected]

SUMMARY In case of a polarizable subsurface, effects of inductively induced polarization (IP) can have an impact on timedomain electromagnetic measurements (TEM) and may lead to nonmonotonous voltage responses or even sign reversals in the recorded transients. For this reason, we developed a new 1D inversion algorithm for the centralloop and the separate-loop TEM configurations using the Cole-Cole relaxation model. 1D forward calculations for a polarizable homogeneous half-space were conducted with the aim of analyzing the impacts of varying Cole-Cole parameters on TEM transients with respect to possible sign reversals. Additionally, we considered the variation of geometrical parameters like the transmitter size and the receiver offset. For the inversion of TEM data, one consequence of these modelings is the large number of equivalences that arise from the additional Cole-Cole parameters. Subsequently, 1D inversions of synthetic data were performed to study the potentials and limitations of the new inversion algorithm regarding the resolution of the Cole-Cole parameters. The obtained findings were eventually adopted on the inversion of real TEM field data that contained considerable IP signatures such as sign reversals. One field dataset was recorded at the Nakyn kimberlite field in Western Yakutiya, Russia in the central-loop configuration. The second field dataset originates from a waste site in Cologne, Germany, and was measured utilizing the separate-loop configuration. Key words: TEM, IP, Inversion, Cole-Cole model

INTRODUCTION While interpreting time-domain or transient electromagnetic (TEM) data, effects of inductively induced polarization (IP) are often neglected. This might lead to misinterpretations of TEM results in case of a polarizable subsurface. These effects vary from nearly imperceptible influences on the transients to the distortion of monotony or even to one or more sign reversals. Spies (1980) and Smith and West (1989) reported the appearance of sign reversals in transient electromagnetic data obtained by a coincident-loop configuration. These features cannot be interpreted using common 1D interpretation techniques. According to Weidelt (1982), local inhomogeneities or 3D effects can be ruled out as a source of negative voltages when the data is taken in the coincidentalloop configuration. However, these signatures can be explained through dispersive conductivities. IP2016 – 6-8 June, Aarhus, Denmark

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Flis et al. (1989) showed that a polarizable subsurface can trigger polarization currents due to the separation of charges during the downward transit of the inductive currents. The direction of these relaxing currents is opposite to the direction of the induced currents and may therefore lead to sign reversals in the recorded transients. Whether these IP effects can be observed, and to what extent, depends strongly on the intensity of the polarization currents compared to the measured induction currents. A possible polarizability leads to a capacitor-like behavior of the subsurface which is commonly described through the Cole-Cole relaxation model (Pelton et al., 1978). In that, one or more layers are assigned with a complex and frequencydependent resistivity ρ(ω):

1 [ ( 1+ iωτ )]

ρ ( ω ) =ρ0 1−m

(

)c

,

(1)

where ω is the angular frequency in s -1, ρ0 is the direct current resistivity in Ωm, m the chargeability, c the frequency exponent (both dimensionless) and τ the relaxation time in s. The forward modeling of IP effects in transient electromagnetics using the Cole-Cole model has been the studied in several publications over the last decades. The history of the inversion of IP-affected TEM data deploying the Cole-Cole model is much briefer and only a few scientific papers were published so far. Kozhevnikov and Antonov (2006) successfully inverted IP-affected central-loop TEM data recorded over a kimberlite mine in Western Yakutia, Russia (this dataset is furthermore subject to this work). The same authors studied the inversion potentials of synthetic TEM data affected by fast-decaying induced polarizations for a homogeneous half-space and a two-layered earth (Kozhevnikov and Antonov, 2008 and 2010) and successfully applied an inversion algorithm on central-loop TEM data in permafrost areas providing fast-decaying IP effects (Kozhevnikov and Antonov, 2014). Any aforesaid publication concentrated on the inversion of data measured or calculated in the central- or coincidental-loop configuration. In this work, we discuss the results of a newly developed 1D TEM inversion algorithm for IP-affected synthetic and field data utilizing the central- and separate-loop configuration. For this, we employed a 1D forward algorithm based on former works of P. Weidelt using the Cole-Cole relaxation model for dispersive resistivities. 1D forward calculations for a homogeneous half-space were conducted with the aim of analyzing the impacts of the Cole-Cole parameters on TEM transients regarding the time and the negative amplitude of possible sign reversals. Subsequently, 1D inversions of synthetic data were performed using the Cole-Cole model to

study the potentials of such an algorithm with respect to the resolution of the Cole-Cole parameters. The obtained findings were eventually adopted on real field data which provided considerable IP signatures such as sign reversals. One examined field dataset was recorded in the central-loop configuration on the Nakyn kimberlite field in Western Yakutiya, Russia (Kozhevnikov and Antonov, 2006). A second field dataset, measured in the separate-loop configuration, origins from a waste site in Cologne, Germany (Schaumann, 2001).

FORWARD MODELING STUDIES For the forward modeling studies, a new 1D forward algorithm deploying the Cole-Cole relaxation model was used. Here, the resistivity ρ is replaced by the dispersive resistivity ρ(ω) (see equation 1). The electromagnetic fields are calculated in the frequency domain for a given transmitter/receiver configuration. Afterwards, the fields are Fourier-transformed into the time domain using digital filters. The numerical solution of the Bessel integrals was conducted by a fast Hankel transform (Johansen and Sørensen, 1979). In our studies, we always vary one parameter and keep the remaining ones fixed. The Cole-Cole parameters were chosen in the way that they provide considerable IP effects. Partially, they are slightly exaggerated to facilitate proper studies of these effects. The introduced current was a 1 A step-off function with no ramp. The calculated induced voltage response is proportional to the time derivative of the z-component of the secondary magnetic flux density integrated over a receiver area of 1 m². All calculations were performed for the times from 1 μs to 10 ms using 61 sampling points for each transient.

INVERSION OF SYNTHETIC DATA Regarding the inversion of synthetic data, we primarily investigated the homogeneous half-space but also examined two and three layer cases. Due to the additional Cole-Cole parameters per layer (m, c and τ), the total number of free parameters in the inversion process increases rapidly making a structured analyses of the inversion results rather complex. An additional challenge is the ambiguity between IP-affected and non IP-affected data. Kozhevnikov and Antonov (2008) showed that the inversion results for synthetic data from a polarizable half-space can also be explained through a multilayer subsurface model without IP effects. Figure 2 shows an exemplary successful inversion result of synthetic separate-loop data for a three layer model which consists of a polarizable layer (ρ 0 = 3 Ωm, m = 0.5, c = 0.5, τ = 0.001 s) between two non-polarizable layers (both ρ 0 = 30 Ωm). The thicknesses are 5 m for first layer and 10 m for the second layer. For the starting model we varied the resistivity of the first layer to 20 Ωm and its thickness to 7 m. The polarizable second layer in the starting model has the values ρ0 = 1 Ωm, m = 0.6, c = 0.5, τ = 0.001 s and its thickness was defined as 8 m. The forward calculated data for the starting model is shown as a dashed line in Figure 2, the inversion result as a solid line. Before the inversion, the synthetic data was imposed with 2% Gaussian noise. The first sign reversal is due to the geometry of the separate-loop configuration, the second sign reversal is attributed to IP effects.

The most prominent features of IP-affected data are sign reversals and the following negative amplitudes. Therefore, we concentrated on the study of the impacts of the Cole-Cole parameters on the times of possible sign reversals (SR) and the maximum of the subsequent negative response (NR), see Figure 1. Figure 2. Synthetic data, forward calculated starting model and inversion result of a three-layer case (separateloop configuration).

INVERSION OF FIELD DATA

Figure 1. Forward calculated transient data with a sign reversal (central-loop configuration) of the homogeneous half-space with Cole-Cole parameters: ρ0 = 100 Ωm, m = 0.5, c = 0.5, τ = 0.001 s, transmitter loop size 50 m x 50 m.

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To test our new inversion algorithm with field data taken in the central-loop configuration, the group of N.O. Kozhevnikov from the Institute of Geophysics of the SB RAS, Novosibirsk, Russia, granted us access on TEM data which was recorded during a diamond prospection in Western Yakutiya, Russia (Kozhevnikov and Antonov, 2006). This dataset consists of 25 TEM soundings taken with a 200 x 200 m² transmitter loop and a 100 x 100 m² receiver loop along a 5 km profile. Some of these soundings contain two sign reversals while others have no sign reversal but provide a break of monotony and a local minimum. According to Kozhevnikov and Antonov (2006), these IP-like patterns can be attributed to a few meters thin and shallow layer consisting of frozen quartz sands. Therefore, the observed IPeffects occur at very early times and decay very fast. Furthermore, this fast decay is the reason for a second sign

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reversal observed on some soundings. Figure 3 shows the data and the inversion result of one exemplary TEM sounding from that dataset.

electromagnetics applying the Cole-Cole relaxation model. For a polarizable homogeneous half-space, the influence of variations of the Cole-Cole parameters and geometrical factors like transmitter size and receiver offset on synthetic transients have been studied utilizing the central-loop and the separate-loop configuration. One consequence of including the Cole-Cole model in the inversion of TEM is the large number of equivalent models that result from the different parameters. Without the ColeCole model (or any other model describing IP-effects), the interpretation of IP-unaffected TEM data already encounters the issue of possible equivalences. With the Cole-Cole model applied, this issue becomes more complex. The inversion algorithm was tested successfully on synthetic data. We point out that the success of the inversion strongly depends on the choice of a starting model which is inherent to the implemented damped least squares approach. This dependency increases when applying the Cole-Cole model to one or more layers of the starting model. We successfully carried out inversions of central-loop field data which provided considerable IP patterns. The inversion of separate-loop field data turned out to be more challenging on the available field data which can be traced back to lateral inhomogeneities.

ACKNOWLEDGMENTS We would like to thank Gerlinde Schaumann from the BGR Hannover, Germany, and Nikolay Kozhevnikov of the SB RAS, Novosibirsk, Russia, for granting access on their field data. REFERENCES

Figure 3. a) Field data and inversion result of one station from the central-loop TEM dataset from Western Yakutiya (Kozhevnikov and Antonov, 2006). b) Resulting model and Cole-Cole parameters of the second, polarizable layer. The inversion of IP-affected separate-loop TEM data is of greater complexity due to the additional sign reversal. Gerlinde Schaumann of the BGR, Germany, permitted us to use data which was recorded in the separate-loop configuration on top of a former waste site in Cologne Ossendorf, Germany (Schaumann, 2001). The examined dataset consists of 20 TEM soundings taken with a transmitter loop size of 25 x 25 m² and a receiver offset of 25 m. Some of the recorded transients comprise 2 or even 3 sign reversals which may originate from a shallow, polarizable layer. The inversion of this dataset was challenging and the algorithm was nearly unable to find sound data fittings. These difficulties originate probably from lateral inhomogeneities in the subsurface.

CONCLUSIONS We investigated the capabilities of a 1D forward and inversion algorithm for IP-affected data in time-domain IP2016 – 6-8 June, Aarhus, Denmark

Flis M. F., Newman G. A. and Hohmann G. W., 1989, Induced Polarization Effects in Time-Domain Electromagnetic Measurements: Geophysics 54, 514–523. Johansen H.K. and Sørensen K., 1979, Fast Hankel Transforms: Geophysical Prospecting 27, 876-901. Kozhevnikov N. O. and Antonov E. Y., 2006, Fast-decaying IP in frozen unconsolidated rocks and potentialities for its use in permafrost-related TEM studies: Geophysical Prospecting 54, 383–397. Kozhevnikov N. O. and Antonov E. Y., 2008, Inversion of TEM data affected by fast-decaying induced polarization: Numerical simulation experiment with homogeneous halfspace: Journal of Applied Geophysics 66, 31–43. Kozhevnikov N. O. and Antonov E. Y., 2010, Inversion of IPaffected TEM responses of a two-layered earth: Russian Geology and Geophysics 51, 708–718. Kozhevnikov N. O. and Antonov E. Y., 2014, TEM Surveys for seach of taliks in areas of strong fast-decaying IP effects: Russian Geology and Geophysics 55, 1428–1436. Pelton W. H.,Ward S. H., Hallof W. R., Sill W. R. and Nelson P. H., 1978, Mineral Discrimination and Removal of Inductive Coupling with Multifrequency IP: Geophysics 43, 588–609.

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Schaumann G., 2001, Transientenelektromagnetische Messungen auf Mülldeponien - Untersuchung des Einflusses von 3D-Leitfähigkeitsvariationen und 1D-frequenzabhängiger Polarisierbarkeit: PhD thesis, University of Braunschweig, Braunschweig, Germany. Smith R. S. and West G. F., 1989, Field examples of negative coincident-loop transient electromagnetic responses modeled with polarizable half-planes: Geophysics 54, 1491-1498.

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Spies B. R., 1980, A field occurrence of sign reversals with the transient electromagnetic method: Geophysical Prospecting 28, 620–632. Weidelt P., 1982, Response characteristics of coincident loop transient electromagnetic systems: Geophysics 44, 1325– 1330.

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Characterization of Abandoned Mine Tailings by means of Timeand Frequency-Domain Induced Polarization Imaging Jakob Gallistl

Adrian Flores Orozco

TU-Wien [email protected]

TU-Wien Gusshausstraße 27-29, 1040-Vienna Austria [email protected]

SUMMARY Induced Polarization (IP) imaging datasets were collected in both time domain (TDIP) and frequency domain (FDIP) for the characterization of abandoned minetailings and in order to assess possible down-gradient transport of sulphide minerals. The study area is characterized by measurable iron and copper concentrations of fine-grained minerals (gain size < 1 mm), which are expected to cause a distinct IP response. This study aims at the evaluation of the applicability of TDIP and FDIP at the field scale, its capability to quantify metallic volumetric content and to discriminate between different metallic minerals. Furthermore, the analyses of water samples down gradient from the tailings have revealed significant concentrations of heavy metals, such as arsenic and mercury. Hence, imaging results of an extensive mapping campaign were used to delineate preferential flow paths of sulphides and the extensions of the contaminated volume. Key words: frequency domain; time domain; field measurements; imaging; metallic minerals.

INTRODUCTION There is a growing interest in the characterization of abandoned mine-tailings – on one hand, because of the possible economic value of metal-rich tailings, on the other hand, because of the need to evaluate the environmental impact due to the leaching and migration of heavy metals. Although the analysis of soil and groundwater samples provides direct information about the parameters of interest (e.g., chemical composition, concentration), such characterization is time consuming and does often not provide the required spatial resolution to evaluate the geometry and extension of mineral deposits or contaminated volumes. Furthermore, the relatively high costs of ex-situ characterization methods often render detailed site investigations prohibitively expensive. To overcome these limitations, recent studies (e.g., Jang M, 2009; Peinado et al., 2010) have suggested the use of portable X-Ray Fluorescence Spectrometry (XRFS) devices to determine in-situ concentrations of heavy metals and permit the assessment of extensive areas. Although promising, the XRFS technique has a limited investigation depth of a few millimetres. Geophysical methods are well suited for collecting spatially continuous data. Given the strong induced polarization response observed in presence of electronic conductors (e.g., IP2016 – 6-8 June, Aarhus, Denmark

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Matthias Bücker TU-Wien [email protected]

metallic minerals), the Induced Polarization (IP) method has been established as a standard tool for the exploration of metallic ores (e.g., Pelton et al., 1978). Recent studies have also demonstrated the capability of the IP method to assess changes in the chemical composition of groundwater (Flores Orozco 2011: 2013; Placencia-Gómez, 2014; 2015). Furthermore, petrophysical models have been suggested to quantify the grain size of metallic minerals based on the frequency dependence of the IP response (e.g. Wong, 1979). In this study we present the application of the IP imaging method for the characterization of an abandoned mine tailing. Extensive field measurements were collected to delineate the geometry of the lithological contacts with high spatial resolution, identify zones at which metallic minerals accumulate and extend the interpretation of IP images towards the quantification of the metallic volumetric content. Measurements were collected in both frequency and time domain (FDIP and TDIP) in order to evaluate the applicability of existing petrophysical models to discriminate between metallic minerals, and to infer dominating grain sizes of the metallic minerals.

METHOD Initial characterization of the site was done by means of frequency-domain measurements (FDIP). To minimize acquisition time and rapidly assess the main structures at the site, these measurements were collected at a single frequency (1 Hz). FDIP measurements were collected with a DAS-1 system (Multi-Phase Technologies, LLC). Based on the initial characterization, particular areas were selected for the collection of FDIP measurements over a broader frequency bandwidth (0.05 to 200 Hz). For comparison, the same profiles were re-collected in the time domain (TDIP) using a square wave form with 50% duty cycle, a pulse length of 2 s, and 35 linearly distributed IP windows. Selected TDIP profiles were also measured with a Syscal Pro (Iris Instruments) using a 2 s pulse length and 50% duty cycle, but sampling the entire wave form by means of voltage readings every 10 ms. The data were collected using multiple-gradient configurations, similar to those proposed by Dahlin and Zhou (2006). These configurations consist in potential measurements collected between electrodes located within the current dipole. In particular, we collected potential measurements using skip-0, skip-1, skip-2, skip-3 and skip-4 schemes (i.e., increasing the length of the potential dipole by increasing the number of skipped electrodes within the potential dipole). In order to use all eight channels of the DAS-1 equipment, the length of the current dipole was ten times the length of the potential dipole. For the evaluation of data error, selected profiles were also measured as normalreciprocal pairs using a dipole-dipole configuration with

IP imaging of abandoned mine tailings

dipole lengths varying from skip-0 to skip-6. Data error was quantified by means of the statistical analysis of normalreciprocal readings as described by Flores Orozco et al. (2012a). The inversion of the data was performed with CRTomo, a smoothness-constraint algorithm by Kemna (2000). For the sake of comparability, the inversion of TDIP datasets was performed using a linear conversion of the measured integral chargeability to apparent phase values (at the fundamental frequency of 0.125 Hz), which assumes a constant-phase response (Kemna, 2000).

Gallistl, Flores Orozco, Bücker

m below the surface), which explains the high polarization response (-φ> 15 mrad). XRFS measurements on the sediment cores recovered from drillings at this location reported values between 2000 and 3000 ppm copper. The anomaly observed at the beginning of the profile A, characterized by low resistivity values ( 104 Ωm) and low phase shifts can be observed; and 3) an anomaly characterized by low resistivity values (< 1000 Ωm) and high polarization response (-φ > 15 mrad) appears approximately between 60 and 120 m along the profile. The electrical images presented in Figure 2 were intriguing, particularly the anomaly characterized by the extremely high electrical resistivity values. Excavations at the location of the resistive anomaly between 30 and 60 m along the profile revealed a construction waste dump that mainly consists of large rocks and bricks. This was an important finding of the exploratory campaign, as this dump is not described in any of the records of the mine and might have a strong impact on the hydrogeology of the site. However, the shallow anomaly observed between 80 and 120 m, which is also characterized by high resistivity values (~1000 Ωm), is not related to construction waste, but to fine grained sand. Collection of samples at the site revealed the presence of fine-grained metallic minerals at depth (~ 1.5 - 3 IP2016 – 6-8 June, Aarhus, Denmark

Figure 2. Electrical imaging results for FDIP data collected at 1 Hz along profile A. The complex electrical resistivity is expressed in terms of electrical resistivity (top) and phase shift (bottom). The positions of the electrodes are indicated by black dots. To better understand the response down gradient the mine tailing and to characterize possible transport and accumulation of metallic sulphides at the foot of the mountain, extensive measurements were collected down gradient the tailings. Figure 3 shows the imaging results for data collected along profile B located in this area revealing low electrical conductivity values, which are likely related to the increase of the metallic content. XRFS measurements on recovered sediments (down to 3 m depth) revealed values varying between 1400 and 10,000 ppm copper and 2.2 ppm mercury. However, such concentrations are a consequence of the downgradient transport of metallic sulphides. Besides the occurrence of metallic minerals in the subsurface, the low electrical resistivity values are also a consequence of the high clay content observed in collected sediments. Nonetheless, the resistivity image (Figure 3, top panel) exhibits an anomaly characterized by slightly higher resistivity values (~ 100 Ωm),

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IP imaging of abandoned mine tailings

which is related to sandy materials. At both edges of this resistive anomaly we also observe two anomalies characterized by high phase-shift values (-φ> 15 mrad), which are correlated with an increase of the metallic content reported by XRFS measurements. Plots in Figure 3 also reveal an increase in the IP response for measurements collected at the lowest frequencies (0.25 Hz), with negligible values observed at higher frequencies (not shown here for brevity). We hypothesize that the increase of the phase shift at the lower frequencies corresponds to the presence of larger grain sizes as predicted by the model of Wong (1979).

Gallistl, Flores Orozco, Bücker

parameters) to describe the frequency dependence of the observed IP responses. We believe that maps representing the distribution of spectral parameters at the study area, and their correlation with XRFS data, will permit an improved characterization regarding the changes in the composition and grain size of the metallic minerals. Furthermore, we are planning the inversion of the extensive datasets using a fullwave form approach (e.g., Fiandaca et al., 2012) in order to extract spectral parameters also from TDIP measurements.

CONCLUSIONS Our results confirm the potential of the IP method to characterize the occurrence of metallic minerals in the subsurface, even if the size and concentration of such minerals in mine tailings is much lower than those observed in mining exploration. However, results presented here reveal the large degree of heterogeneity typically observed on mine tailings. Although not a primary objective of the study, IP images permitted the identification of a secondary deposit associated to construction waste, linked to high electrical resistivity values. The characterization of such heterogeneities is critical to fully understand the fate and transport of metallic sulphides. For data collected at 1 Hz, the sediments at the mine tailing presented only a modest polarization response (-φ~ 15 mrad); whereas down gradient, the polarization response was larger (-φ> 20 mrad), with a stronger response observed at lower frequencies ( 500.000 models, respectively, before reaching convergence. Using the scaled model proposer reduces the computation time for simple models from approximate one hour to 20 sec on 10 cores.

As the proposal distribution is symmetric in the logarithmic space, the equation reduces to:

(7)

So, the model mnew is always accepted if its probability is larger than the probability of the current model. If its probability is smaller, then the model is accepted with probability α.

SYNTETIC DATA Given a layered medium described by the Cole-Cole model, the 1D forward TDIP response is calculated using the algorithm presented by Fiandaca et al. (2012). Single quadrupolar measurements (geometric factor of approximately 470 m) and Schlumberger soundings (20 quadrupoles) are simulated for homogenous half spaces and three-layer models, respectively. The Cole-Cole parameters range between ρ = 10 - 1000 Ωm, m0 = 5 - 800 mV/V, τ = 0.001 - 10 sec and C = 0.1 - 0.6. Three stacks are considered

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Figure 1: The normalised posterior distributions of ColeCole parameter τ resulting from two different model proposers: A covariance-scaled proposer (A) and a Gaussian proposer (B). The figure illustrates the faster convergence rate of the covariance-scaled model proposer, where we see convergence after just 5000 model proposes.

RESULTS 2

MCMC analysis of TDIP data

Madsen et al.

Figure 2 (last page) shows the posterior distribution of the DC resistivity and the IP parameters for the homogeneous half space defined earlier. 100,000 models are proposed and 33 % are accepted and added to the posterior distribution. The histograms along the diagonal show the distributions of parameter values in log space with the true model values indicated in red. The off-diagonal are cross-plots of all combinations of the four parameters.

confirming the equivalence of the 50% and 100% duty cycle waveforms for spectral resolution.

The distributions are all bell-shaped, which means they are all approximately log-normal. The parameters show a single maximum and are resolved to a different extent. However skewness is evident for m0 and τ. The DC resistivity is almost uncorrelated to the Cole-Cole parameters. The chargeability shows a negative correlation to τ and C with a Person’s correlation coefficient of 0.77 and 0.70 respectively. The correlation between to τ and C is positive with a correlation coefficient of 0.86. It is possible to compute the standard deviation (STD) on the model parameters from the posterior distributions. A relative standard deviation factor (STDF) is used here, where the 68% confidence interval for parameter p then lies between:

(9)

A perfect resolution will give STDF = 1. Using the terminology from Auken et al., (2005), STDF < 1.2 is a wellresolved parameter, 1.2 < STDF < 1.5 is a moderately resolved parameter, 1.5 < STDF < 2 is a poorly resolved parameter and STDF > 2 is an unresolved parameter. For the MCMC posterior distribution the standard deviation is calculated over all accepted models. The STDF values are shown in Figure 3 for a varying value of the frequency exponent C. Together with the MCMC STDFs, we show the STDFs obtained from the linearized approach. Figure 3 shows that the uncertainty increases if the value of C is decreased. This holds for both the MCMC- and the linearized approach. For C = 0.6 all parameters, except τ, is well resolved with STDF < 1.2 for both MCMC- and linearized inversion. For C = 0.2, only the resistivity value is well resolved. The linearized estimations of the STDFs are reasonable for well resolved parameters, but are underestimated for poorly resolved parameters. As the Cvalue decreases the posterior distribution of the Cole-Cole parameters resulting from the MCMC analysis become more non-loglinear and the correlation between the model parameters becomes stronger. More complex three-layer models verify the results with resolved bell-shaped posterior distributions for all the ColeCole parameters and linear correlations. Synthetic data are simulated on the same homogenous half space with a minimum acquisition range. The MCMC result shows nearly bell-shaped posterior distributions, but with nonlinear correlations between the parameter C and m0 and between C and tau. The STDFs of the DC resistivity and C are almost unchanged compared to the result of the maximum range, but τ and m0 are unresolved. The maximum of the posterior distribution and the true model is not consistent as well. Similar results are obtained for the 100% duty cycle data, IP2016 – 6-8 June, Aarhus, Denmark

Figure 3: Standard deviation factor (STDF) as a function of the Cole-Cole parameter C. The STDF is computed for the results of a linearized approach and the MCMC results. NB: If the STDF value is above 5, it is put to 5.

CONCLUSIONS The results of running a MCMC inversion of synthetic TDIP data show that it is possible to extract the spectral Cole-Cole parameters from time-domain data. The sampled posterior probability distributions of the ColeCole parameters are all bell-shaped with one maximum. Strong correlations are present between the IP parameters and for more complex models correlations can also been seen between these and the DC resistivity. The uncertainties of the model parameters increase with decreasing values of C, which makes it more difficult to resolve parameters. This holds for the MCMC and the linearized approach. However the linearized standard deviations work well for well resolved parameters. If the acquisition range is too short (2 decades or less), then the Cole-Cole parameters become poorly- or completely unresolved, and the correlations become nonlinear. In general, all the results justify the linearized inversion of TDIP data for resolved Cole-Cole parameters, when the necessary acquisition range is used. REFERENCES Auken, E., A. V. Christiansen, B. H. Jacobsen, N. Foged, and K. I. Sørensen, 2005, Piecewise 1D laterally constrained inversion of resistivity data: Geophysical Prospecting, 53, 497–506. Chongo M., Christiansen A.V., Fiandaca G., Nyambe I.A., Larsen F. & Bauer-Gottwein P., 2015. Mapping localised freshwater anomalies in the brackish paleo-lake sediments of the Machile-Zambezi Basin with transient electromagnetic sounding, geoelectrical imaging and induced polarisation, Journal of Applied Geophysics, 123, 81-92. 10.1016/j.jappgeo.2015.10.002. Doetsch J., Ingeman-Nielsen T., Christiansen A.V., Fiandaca G., Auken E. & Elberling B., 2015a. Direct current (DC) resistivity and induced polarization (IP) monitoring of active

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MCMC analysis of TDIP data

layer dynamics at high temporal resolution, Cold Regions Science and Technology, 119, 16-28. 10.1016/j.coldregions.2015.07.002. Doetsch J., Fiandaca G., Auken E., Christiansen A.V., Cahill A.G. & Jakobsen R., 2015b. Field-scale time-domain spectral induced polarization monitoring of geochemical changes induced by injected CO2 in a shallow aquifer, Geophysics, 80, WA113-WA126. 10.1190/geo2014-0315.1. Fiandaca, G., Auken, E., Christiansen, A. V. and Gazoty, A., 2012, Time-domain-induced polarization: Full-decay forward modelling and 1D laterally constrained inversion of Cole-Cole parameters: Geophysics, 77, 3, E213-E225.

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techniques for time-domain spectral induced polarization: Near Surface Geophysics, 11, 391-406. Ghorbani, A., C. Camerlynck, N. Florsch, P. Cosenza, and A. Revil, 2007, Bayesian inference of the Cole-Cole parameters from time- and frequency-domain induced polarization: Geophysical Prospecting, 55, 589–605. Johansson S., Fiandaca G. & Dahlin T., 2015. Influence of non-aqueous phase liquid configuration on induced polarization parameters: Conceptual models applied to a timedomain field case study, Journal of Applied Geophysics, 123, 295-309. 10.1016/j.jappgeo.2015.08.010.

Fiandaca G., Ramm J., Binley A., Gazoty A., Christiansen A.V. & Auken E., 2013. Resolving spectral information from time domain induced polarization data through 2-D inversion, Geophysical Journal International, 192, 631-646. 10.1093/gji/ggs060.

Olsson P.I., Fiandaca G., Larsen J.J., Dahlin T., Auken E., 2016. Doubling the spectrum of time-domain induced polarization: removal of non-linear self-potential drift, harmonic noise and spikes, tapered gating, and uncertainty estimation. 4th IP Workshop, 6-8 June 2016, Aarhus, Denmark.

Fiandaca G., Doetsch J., Vignoli G. & Auken E., 2015a. Generalized focusing of time-lapse changes with applications to direct current and time-domain induced polarization inversions, Geophysical Journal International, 203, 11011112. 10.1093/gji/ggv350.

Olsson, P.-I., Dahlin, T., Fiandaca, G., and Auken E., 2015. Measuring time-domain spectral induced polarization in the on-time: decreasing acquisition time and increasing signal-tonoise ratio, Journal of Applied Geophysics, 123, 316-321. 10.1016/j.jappgeo.2015.08.009.

Gazoty A., Fiandaca G., Pedersen J., Auken E., Christiansen A.V. & Pedersen J.K., 2012a. Application of time domain induced polarization to the mapping of lithotypes in a landfill site, Hydrology and Earth System Sciences, 16, 1793-1804. 10.5194/hess-16-1793-2012.

Hastings, w. K., 1970, Monte Carlo sampling method using Markov Chains and their appllications: Biometrika, 57, 97109.

Gazoty, A., Fiandaca, G., Pedersen, J., Auken, E. and Christiansen, A. V., 2012b. Mapping of landfills using timedomain spectral induced polarization data: the Eskelund case study: Near Surface Geophysics, 10, 575-586. Gazoty A., Fiandaca G., Pedersen J., Auken E. and Christiansen A.V., 2013. Data repeatability and acquisition

Pelton, W. H., S. H. Ward, P. G. Hallof, W. R. Sill, and P. H. Nelson, 1978, Mineral discrimination and removal of inductive coupling with multifrequency IP: Geophysics, 43, 588–609. Metropolis, N., Rosenbulth, A., Rosenbulth, M., Teller, A. and Teller, E., 1953, equation of state calculations by fast computing machines: Journal of Chemical Physics, 21, 10871092.

Figure 2: The posterior probability distribution of the Cole-Cole parameters for a homogenous half space: ρ = 100 Ωm, m0 = 200 mV/V, τ = 0.01 sec, C = 0.6. The diagonal shows histograms of the distribution of each Cole-Cole parameter. The offdiagonal shows the correlation between the parameters. The true model parameters are indicated in red. Note the figure is symmetric about the diagonal.

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Simulation of membrane polarization for 2D and 3D pore networks Hermann Stebner

Andreas Hördt

TU Braunschweig TU Braunschweig Mendelssohnstr. 3 Mendelssohnstr. 3 38106 Braunschweig 38106 Braunschweig [email protected] [email protected]

SUMMARY We extend an existing membrane polarization model to 2D and 3D pore combinations networks, which are numerically solved to obtain an overall SIP response. We investigate the behaviour of these networks by varying the distribution function of the pore combinations and the size of the network. Equally distributed pore combinations show a dominance of high phase shifts. For empirically distributed combinations, obtained from measured pore radii distributions, high phase shifts tend to dominate only in big 3D networks. Our simulations show that for networks, which are comparable to real rocks, higher maximum phase shifts than the mean of the original pore combinations are possible. The results suggest that networks may allow a simulation of more realistic pore geometries than the original 2-pore system.

Schwarz (1962), and subsequently extended by several authors (e.g. Leroy et al. 2008; Revil and Florsch 2010), and the theory of membrane polarization, first suggested by Marshall and Madden (1959) and extended by Bücker and Hördt (2013), are both based on the ion movement in the electrical double layer. The fundamental difference between the both models is expressed in the definition of the mineral geometry. The electrochemical polarization is based on mineral grains where the polarization effect is based on a local concentration of charge on the grain. The membrane polarization is based on sequences of narrow and wide pores where the polarization effect is caused by narrow throats between the pores (FIGURE 1).

Key words: membrane polarization, pore networks, measured pore radii distribution.

INTRODUCTION The characterization of porous media (e.g. unconsolidated sediment or rocks) by geophysical methods is a research topic of fundamental importance in environmental and economic issues like the investigation of water reservoirs or the evaluation of waste deposits. The spectral induced polarization (SIP) method is supposed to have big potential to provide useful information based on relationships between electric and hydraulic parameters. Several empirical approaches for the interpretation of the measured SIP response exist. Attempts have been made to correlate a characteristic time scale, derived from the phaseshift spectra, with measured material parameters like hydraulic conductivity or pore radii (Titov et al., 2010; Binley et al., 2005). Another approach is to compare the imaginary conductivity at a single frequency (Weller et al., 2010) to the specific surface of the pore space. Although both methods are based on different assumptions they are supported by examples of reasonable agreement with laboratory experiments. The formulation of a comprehensive theoretical model is difficult because the underlying physical processes on the pore scale are not yet fully understood. The two main models, the theory of electrochemical polarization, first suggested by IP2016 – 6-8 June, Aarhus, Denmark

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Figure 1: Marshall and Madden polarization. Overlapping cation layers in pore throats (grey) lead to decreased anion mobility. An applied electric field causes concentration gradients which relax with a characteristic time after switch-off. While the original membrane polarization model was (besides the pore fluid properties) primarily parametrized by pore lengths and differing ion mobilities, the expansion by Bücker and Hördt (2013) introduced a parametrization by pore radii instead of ion mobilities. This allowed to describe the pore geometry by a sequence of narrow and wide cylinders (FIGURE 2). With subsequent development on the electrolyte parametrization and on the pH, salinity and temperature dependence the model had some success in reproducing features also observed with experimental data (e.g. Hördt et al. 2016a; Bairlein et al. 2016).

Figure 2: 2D-extension of the model. Parameterizing the narrow and wide pores through pore radii allows to

Simulation of membrane polarization for 2D and 3D pore networks

calculate the Marshall and Madden ion mobilities by taking into account the electrical double layer (dark-blue layers). The combination of a narrow and a wide pore is a simplified model that does yet not account for the complexity of macroscopic porous media. A basic study on geometrical parameters of the model showed generally reproducibility of phase shifts and characteristic time scales in the range typically measured with natural sandstones (Hördt et al., 2016b). As a next step towards the simulation of realistic pore space geometries, we present an approach to merge different pore combinations to 2D and 3D network grids. The aim of this work is to examine possible differences of the response behaviour of such networks in comparison with the simplified model and to determine minimum size and necessary complexity requirements.

H. Stebner and A. Hördt

In FIGURE 4, we investigate 100 equivalent random 2D networks constructed from 4 representative pore combinations. The simulations show unexpected behaviour. The total maximal phase shifts of the networks concentrate in two bins. The higher one (~70 mrad) corresponds with pore combination 2 and the lower one (~30 mrad) with pore combination 3. Both bins are higher than the weighted mean of the 4 pore combinations (red line in figure 4). The two pore combinations 1 and 4 with very small maximal phase shifts (< 1 mrad) are not represented at all. This dominance of high phase shifts is more pronounced in 2D networks but can also be observed in 3D networks.

METHODS Each pore combination of a narrow and a wide pore (e.g. FIGURE 2) can be treated as an impedance component which we merge to a resistor network (FIGURE 3). We obtain the SIP response of this network by numerically solving a linear equation system corresponding to the finite differences method.

Figure 3: 3D impedance network with 64 nodes. Different colors correspond to different pore radii combinations with random distribution. In a first approach, we use equally distributed pore combinations to obtain on overview over the behaviour of such networks. In order to match realistic pore space geometries, we use measured pore radii distributions of real rocks (e.g. Weller et al. 2011). First, we approximate the distributions by a fractal relationship. Then, we chose the pore combinations such that the overall radii distribution in our model matches the fractal distribution.

RESULTS

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Figure 4: Top: Phase shift vs. angular frequency of 4 representative pore combinations. Bottom: Maximum phase shift of 100 equivalent random 2D networks (each of 100 nodes), constructed from equally distributed pore combinations 1-4. Red line: Mean of the maximum phase shifts of the combinations 1-4, weighted with the appearance in the network. Due to the large number of possible pore combinations, networks with empirically distributed pore combinations, obtained from measured pore radii distributions, do not show any strict binning of their maximum phase shifts. In contrast to equally distributed combinations, the maximum phase shifts here spread about the weighted mean (FIGURE 5). First simulations with big networks (up to 5000 nodes) and empirically distributed pore combinations show a small tendency of the dominance of above-average maximum phase shifts for 3D networks and below-average maximum phase shifts for 2D networks.

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Simulation of membrane polarization for 2D and 3D pore networks

H. Stebner and A. Hördt

REFERENCES Bairlein, K., Bücker, M., Hördt, A., Hinze, B., and Nordsiek, S. (2016). Temperature dependence of spectral induced polarization data: experimental data and membrane polarization theory. Geophysical Journal International. Accepted. Binley, A., Slater, L. D., Fukes, M., and Cassiani, G. (2005). Relationship between spectral induced polarization and hydraulic properties of saturated and unsaturated sandstone. Water Resources Research, 41(W12417).

Figure 5: Maximum phase shift of 100 equivalent random 3D networks (each of 125 nodes), constructed from empirically distributed pore combinations. Red line: Mean of the maximum phase shifts of the empirical combinations, weighted with the appearance in the network.

CONCLUSIONS In order to get closer to a realistic description of real rocks we extended an existing membrane polarization model to impedance networks. We investigated the behaviour of 3D and 2D networks of different size and different pore combination distributions. The choice of the distribution function influences the SIP response behaviour. While equally distributed pore combinations in small networks (~100 nodes) show dominance of high phase shifts, this behaviour cannot be confirmed with empirically distributed combinations. In big networks (> 1000 nodes) the behaviour tends to split between the dominance of high phase shifts for 3D and low phase shifts for 2D networks. Our results show that for impedance networks, higher maximum phase shifts than the mean are in general possible. This is more pronounced with equally distributed combinations, but can also be shown, although with much smaller evidence, for big 3D networks with empirically distributed combinations. Big empirically distributed networks are most comparable to real rocks, which allows us to get closer to realistic SIP response modelling than with the simplified 2-pore model only.

ACKNOWLEDGMENTS We thank Klaus Spitzer, Ralph-Uwe Börner, Jana Börner, Julia Weißflog and Wenke Wilhelms from Institute of Geophysics and Geoinformatics, TU Freiberg, for useful discussions on the numerical implementation. The work is sponsored by the German Science foundation (Project Ho1506/23-1).

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Bücker, M. and Hördt, A. (2013). Analytical modelling of membrane polarization with explicit parametrization of pore radii and the electrical double layer. Geophysical Journal International., 194:804–813. Hördt, A., Bairlein, K., Bielefeld, A., Bücker, M., Kuhn, E., Nordsiek, S., and Stebner, H. (2016a). The dependence of induced polarization on fluid salinity and ph, studied with an extended model of membrane polarization. Journal of Applied Geophysics, accepted. Hördt, A., Bairlein, K., and Stebner, H. (2016b). Constraints on pore space geometries with membrane polarization, this issue. Leroy, P., Revil, A., Kemna, A., Cosenza, P., and Ghorbani, A. (2008). Complex conductivity of water-saturated packs of glass beads. Journal of Colloid and Interface Science, 321:103– 117. Marshall, D. J. and Madden, T. R. (1959). Induced polarization, a study of its causes. Society of Exploration Geophysicists, 24(4):790–816. Revil, A. and Florsch, N. (2010). Determination of permeability from spectral induced polarization in granular media. Geophysical Journal International, 181:1480–1498. Schwarz, G. (1962). A theory of the low-frequency dielectric dispersion of colloidal particles in electrolyte solution. The Journal of Physical Chemistry, 66:2636–2642. Titov, K., Tarasov, A., Ilyin, Y., Seleznev, N., and Boyd, A. (2010). Relationships between induced polarization relaxation time and hydraulic properties of sandstone. Geophysical Journal International, 180:1095–1106. Weller, A., Breede, K., Slater, L., and Nordsiek, S. (2011). Effect of changing water salinity on complex conductivity spectra of sandstones. Geophysics, 76(5):F315–F327. Weller, A., Slater, L., Nordsiek, S., and Ntarlagiannis, D. (2010). On the estimation of specific surface per unit pore volume from induced polarization a robust empirical relation fits multiple data sets. Geophysics, 75(4):WA105–WA112.

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Lithological characterization of a contaminated site using Direct current resistivity and time domain Induced Polarization Pradip Kumar Maurya Department of Geoscience Aarhus University C.F. Møllers Allé 4, 8000 Aarhus C [email protected]

Gianluca Fiandaca Department of Geoscience Aarhus University C.F. Møllers Allé 4, 8000 Aarhus C [email protected]

Esben Auken Department of Geoscience Aarhus University C.F. Møllers Allé 4, 8000 Aarhus C [email protected]

Anders Vest Christiansen Department of Geoscience Aarhus University C.F. Møllers Allé 4, 8000 Aarhus C [email protected]

METHODS AND RESULTS

SUMMARY Characterization tools for contaminated sites have become advanced with the continued development of geophysical methods. Resistivity methods and timedomain induced polarization methods have proven their capability to delineate the subsurface properties by complementing each other. In the present study a large contaminated site in Denmark was investigated using direct current resistivity and time domain induced polarization (DCIP). For this purpose 14 profiles were collected alongside a stream in order to investigate the contamination and delineate the lithological units. 2D inversion using a cole-cole model of two selected profiles are presented. They show that the resistivity model alone cannot depict the geology as inferred in the borehole. However, when including the models of chargeability and mean relaxation time the geological units are clearly defined, which helps in identifying the possible contaminations. Key words: Time Domain Induced Polarization, ColeCole model

INTRODUCTION Groundwater and surface water can be contaminated due to various types of human activities e.g. waste from residential, commercial, industrial, and agricultural activities. Especially in cities with an industrial history this is often a severe problem. In order to evaluate the risks, characterization of the contaminated sites in terms of geology and contaminant leachate is needed. This characterization is often carried out using limited drill hole information, but a much more detailed picture of the subsurface can be obtained by dense surfacebased geophysical methods. Multi-electrode direct current (DC) resistivity and induced polarization(DCIP) methods have proven their capability to delineate the contaminant mass from the host geology, as contamination strongly influences the resistivity and chargeability of the subsurface (Gazoty et al., 2012). The method has recently advanced in terms of data acquisition techniques (Dahlin et. at., 2002) and processing and inversion optimizations (Auken et al., 2009). In this study we investigated a contaminated site using DCIP measurements along a stream in the city of Grindsted (southern part of Denmark) where a pharmaceutical industry deposited massive amounts of chemicals on a number of sites.

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DCIP Methodology Direct current resistivity and Induced polarization methods (DCIP) have been extensively used in environmental studies. The resistivity method is based on the fact that distribution of electrical potential in the subsurface depends on the resistivities around a current injecting electrode. In normal practice two electrodes are used for injection and another pair of electrodes measures the potential. The IP method is based on the chargeability effects of the subsurface. When measuring in the time-domain and when the subsurface is chargeable, the voltage does not drop immediately to zero following the current shut down, but rather it decays slowly over a few seconds. The magnitude of the polarization and the shape and length of the decay depend on subsurface parameters such as ion content and type, clay content, and pore structure to mention a few. Time-domain IP data are recorded along with the traditional DC data using the same measurement setup. Recent developments in the field of data acquisition such as multichannel measurements (Dahlin et al., 2002) have made the time-domain DCIP method more robust, faster and more convenient to perform in the field. Combined with advancements in the numerical modelling of IP data including modelling of transmitter waveform and low-pass filters enable us to retrieve the Cole-Cole parameters from time-domain measurements of the entire decaying IP signal (Fiandaca et al., 2012). The cole–cole model (Pelton et al., 1978) is a commonly used empirical model which involves the parameters resistivity, chargeability, relaxation time, and frequency exponent. Field Site and Geological Settings The investigated study area is located in the region of southern Denmark, Grindsted. Two of Denmark’s 122 locations classified as "large contaminated sites" are located here (Grindsted factory and Grindsted landfill). Contamination from the landfill and factory site is posing great risks to Grindsted stream and a large impact from contaminations have been observed in the stream (Nielsen et al., 2014). The geology of the Grindsted area consists of an upper 10-12 m quaternary sand layer and a lower tertiary sand layer, locally separated by silt and clay layer (Heron et al., 1998). Below this layer, we have a regional micaceous sandy layer approximately 65 m thick, which is underlain by a clay layer at 80 m depth.

delineate the major lithological boundaries observed in a borehole. Identification of the geological units allows for speculations on possible contaminations identified in the resistivity section.

Data Acquisition The site was investigated with the collection of 14 DCIP profiles (Figure 1) covering both the north and the south bank of the river. The profiles are will be treated in a full 3D framework, but here we will present selected 2D results. Out of the 14 profiles, seven profiles were 410 m long with 5 m electrode spacing and other seven profiles were 126 m long with 2 m electrode spacing. The survey was performed using the gradient array (Dahlin and Zhou, 2006) and we used the ABEM Terrameter LS for the data acquisition.

ACKNOWLEDGMENTS The authors are thankful to the Danish Council for Strategic Research for funding the GEOCON project under which the present study has been carried out.

REFERENCES Results The processing and inversion of the DCIP data were carried out using Aarhus Workbench (Auken, 2009). Processing of DCIP data involves removal of outliers from apparent resistivity data and culling of disturbed IP decays. Data were inverted using the 2D DCIP inversion code developed by Fiandaca et al. (2013) .This inversion routine uses the colecole model to invert the DCIP data, which gives four model parameters namely resistivity (ρ), chargeability (m0), relaxation time (τ) and frequency exponent (C). The inversion code also models the full waveform and stack sizes. Figure 2 presents the inversion results of two representative profiles (profile 3 and 6) located at the northern bank of the river. The cole-cole parameters shown from top to bottom are resistivity (ρ), chargeability (m0), relaxation time (τ) and frequency exponent (C). The borehole located on profile 6 (shown as blue dot in figure 1) is presented as a bar with the different geological units indicated. The bar colour code represents major lithological unit identified in borehole (Brown: sand, light blue: sand mixed with clay, blue: clay). It can be seen that the low resistivity anomaly in both profiles does not clearly represent the clay rich layers seen in the borehole. This could be attributed to the combined response of clay layer and the contamination present in the sandy aquifer above and below the clay layer in the north western part of the profile. However, in the chargeability section a high chargeability layer agrees very well with the clay layers. This layer clearly stands out also in the tau section. The bottom of the high chargeable layer indicates the lower boundary of the clay layer. To show this boundary in the resistivity section, a red dashed line is drawn in both profiles. We can see that in the northwestern part of both profiles the low resistivity signature is continuing in the sandy aquifer, which possibly indicates the presence of contaminations. These observations indicate that the IP response is mostly dominated by the clay rich layers, which helps in identifying the lithological units more adequately than the resistivity section alone. In the presentation we will show results in 3D combining the results of all the lines to visualize the delineation of a possible contamination.

Auken, E., A. Viezzoli, and A. V. Christiansen, 2009, A Single Software For Processing, Inversion, And Presentation Of Aem Data Of Different Systems: The Aarhus Workbench, Adelaide, ASEG. Dahlin, T., V. Leroux, and J. Nissen, 2002, Measuring techniques in induced polarisation imaging: Journal of Applied Geophysics, v. 50, p. 279-298. Dahlin, T., and B. Zhou, 2006, Multiple-gradient array measurements for multi-channel 2D resistivity imaging: Near Surface Geophysics, v. 4, p. 113-123. Fiandaca, G., E. Auken, A. Gazoty, and A. V. Christiansen, 2012, Time-domain induced polarization: Full-decay forward modeling and 1D laterally constrained inversion of Cole-Cole parameters: Geophysics, v. 77, p. E213-E225. Fiandaca, G., J. Ramm, A. Binley, A. Gazoty, A. V. Christiansen, and E. Auken, 2013, Resolving spectral information from time domain induced polarization data through 2-D inversion: Geophysical Journal International, v. 192, p. 631-646. Gazoty, A., G. Fiandaca, J. Pedersen, E. Auken, and A. V. Christiansen, 2012, Mapping of landfills using time-domain spectral induced polarization data: The Eskelund case study: Near Surface Geophysics, v. 10, p. 575-586. Heron, G., P. L. Bjerg, P. Gravesen, L. Ludvigsen, and T. H. Christensen, 1998, Geology and sediment geochemistry of a landfill leachate contaminated aquifer (Grindsted, Denmark): Journal of Contaminant Hydrology, v. 29, p. 301-317. Nielsen, S. S., Tuxen, N., Frimodt Pedersen, O., Bjerg, P. L., Sonne, A. T., Binning, P. J., Fjordbge, A. S., and Aabling, J. (2014). Risikovurdering af over adevand, somer påvirket af punktkildeforurenet grundvand, miljøprojekt nr 1572. Technical report, Miljøministeriet. Miljøstyrelsen Pelton, W. H., S. H. Ward, P. G. Hallof, W. R. Sill, and P. H. Nelson, 1978, Mineral discrimination and removal of inductive coupling with multifrequency IP: Geophysics, v. 43, p. 588-609.

CONCLUSIONS DC resistivity and the time domain induced polarization method were used at a contaminated site for characterizing the contaminants and lithology. The results are presented in terms of Cole-Cole parameters. The major lithological unit could not be interpreted from the resistivity section alone, but the chargeability section clearly

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Figure 1 Location of DCIP profiles. Location of the borehole is shown as blue dot on profile 6.

Figure 2 DCIP inversion results from profile 3 and 6. Cole -Cole parameter shown from top to bottom are resistivity (ρ), chargeability (m0), relaxation time (τ) and frequency exponent(C). DOI is shown by continuous black lines and dotted line in resistivity section shows the interpreted lower boundary of the clay layer.

Spectral induced polarization of sand-biochar mixtures: experiments and modeling Z. Gao

F.-H. Haegel

J.A. Huisman

H. Vereecken

Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, Germany [email protected]

Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, Germany [email protected]

Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, Germany [email protected]

Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, Germany [email protected]

SUMMARY Biochar attracts increasing research interest due to its potential for agricultural and environmental purposes such as soil amendment and greenhouse gas reduction. To better monitor and investigate biochar in soil, noninvasive measurement approaches that can be applied in the laboratory and at field scale are needed. The goal of this work is to examine the sensitivity of the spectral induced polarization (SIP) method to the presence of disseminated biochar in sand. We investigate the complex electrical conductivity of saturated mixtures of sand and sieved biochar, and use a mechanistic SIP model that accounts for the redox reactions at the surface of the polarized particles to invert the measured data. The magnitude of the measured complex electrical conductivity showed a positive correlation with the mass fraction of biochar, while the peak frequency of the imaginary part showed a negative correlation with the particle size of the biochar. The model provides reasonable fitting results for low mass fraction of biochar in the mixtures. Key words: SIP, biochar, electrochemical model

INTRODUCTION Biochar is the by-product of biomass pyrolysis and gasification. It is derived from a wide variety of sources, including wood (Cheng et al., 2014), green waste (Chan et al., 2007), poultry litter (Chan et al., 2008), agricultural residues (Demirbas et al., 2006), and a wide range of additional sources. The application of biochar to farmland can increase plant growth, reduce leaching of nutrients, and increase water retention and microbial activity (Hunt et al., 2010). Furthermore, biochar seems to be a promising option for longterm sequestration of carbon to offset CO2 emissions (Sohi et al., 2009). Long-term effects of biochar in soil, however, are not yet sufficiently investigated. Therefore suitable methods of monitoring and investigating biochar in soil are still required to better evaluate the true agronomic and environmental value of biochar as a soil amendment. The physical and chemical properties of biochar vary largely owing to different feedstocks and production processes. Characterizing biochar and its properties in soil media by using traditional physico-chemical methods is therefore difficult and time consuming. SIP is a promising method to overcome these problems due to its real-time and non-invasive IP2016 – 6-8 June, Aarhus, Denmark

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features and the relatively large monitoring volumes or areas in the field. However, modeling and understanding the SIP signal related to the physical nature of the samples are still challenging. Existing mechanistic models are mostly based on the theory of the polarization of the charges in the electrical double layer (EDL) at the solid-liquid interface. These models, however, cannot be directly applied to the polarization that is observed in the presence of disseminated materials with electronic conductance (Gurin et al., 2013). Wong (1979) developed a model that we refer to as the electrochemical SIP model in the following. This model was originally proposed to describe the SIP response of disseminated sulfide ores, which show similar electronic conductance as particles of biochar. In this work, we study the spectral induced polarization of disseminated biochar in sand media, and test the ability of the electrochemical SIP model to describe the measured SIP data.

METHOD AND RESULTS SIP Measurement We used the SIP method to measure the complex electrical conductivity σ* = σ’ + iσ” of mixtures of sand and sieved biochar. The experimental set-up is shown in Figure 1. The sample holder has a height of 18 cm and an inner diameter of 3 cm. Water can flow through the sample from the bottom to the top of the sample holder. Flushing with electrolyte solution was used to saturate the material inside the column and to remove excess salts released from the biochar after sample preparation. Two porous bronze plates were used as current electrodes at the top and bottom of the column to inject current. Two metal potential electrodes were used at a distance of 6 and 12 cm from the bottom of the sample holder. To avoid electrode polarization, the potential electrodes were retracted about 1.2 cm (2 times of the diameter of the potential electrodes) into their borings.

Figure 1. Sketch of the experimental set-up. A water tank is connected with the bottom of the column for flushing the sample.

SIP on biochar

Z.Gao

Particle Size of biochar (d) (mm)

1 2 3 4

1% 2% 3% 4%

0.5-1 0.5-1 0.5-1 0.5-1

1 2 3

2% 2% 2%

0.25-0.5 0.5-1 1-2

Modeling Method

𝑒 ( ) 0

=

1+2 ∑ 𝑣𝑖 𝑓( ;𝑎𝑖 ) 1−∑ 𝑣𝑖 𝑓( ;𝑎𝑖 )

,

(1)

where  is the angular frequency, 𝑣𝑖 is the volume fraction of spheres with radius 𝑎𝑖 = 0.5 𝑑𝑖 , 𝑒 is the complex electrical conductivity of the sample and 0 is the electrical conductivity of the electrolytic medium. In addition, the reflection coefficient (f()) is given by: 𝑓( ) = 1 +

𝛽𝑎

3𝑐 𝛼 ( − 1) 𝑐−2𝑐 0 𝜇 𝛽𝑎𝜆2 𝛼 𝑐 1 +2]−(2+ 𝑓 )(1+ 𝛽𝑎 𝑓 ) [𝑓 + (𝑓 −2)+ 1 𝐷 3 𝐷2 2 𝑐−2𝑐 0 1 𝜇 2

3(1 +

𝐷

𝑓3 ) +

(2),

with 𝑓1 = 𝑓3 =

𝜆21 𝑎2 +2𝜆1 𝑎+2 (𝜆1

𝑖𝜔/𝐷, 𝑓2 =

𝑎+1)22

𝜆2 𝑎+1

𝜆21 𝑎2 +2𝜆1 𝑎+2 (𝜆1 𝑎+1)

,

,

𝜆22 𝑎2 +2𝜆2 𝑎+2

𝜆21 = 22 + 𝑖𝜔/𝐷, 𝜆22 = 𝑖𝜔/𝐷, 22 = 𝜎0/(𝜀𝐷), where 𝛼 - electrochemical reaction parameter (A s2 kg −1 mol−1)  - electrochemical reaction parameter (m mol−1 s−1) c - concentrations of active cations (n/m3) c0 - total concentration of cations and anions (n/m 3) D - diffusivity of cations and anions (m2/s) ɛ - dielectric constant (F/m) 𝜇 - mobility of ions (m2 V−1 s−1). Measurement Results The SIP spectra of sand-biochar mixtures were analyzed in terms of the real part σ’(ω) and the imaginary part σ”(ω). Figure 2 presents the frequency-dependent complex electrical conductivity as a function of frequency for different mass fraction (ξ) and particle size (d) of biochar, respectively. Figure 2a shows that σ’(ω) increases within the whole frequency range, and this increase is stronger when the amount of biochar increases. Figure 2b shows that σ”(ω) first increases and then decreases with increasing frequency. A IP2016 – 6-8 June, Aarhus, Denmark

0.025 -1

0.015 0.010 0.005

d = 0.25 - 0.5 mm d = 0.5 - 1 mm d = 1 - 2 mm  2%

0.000 -3 -2 -1 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 frequency (Hz)

0.0040 b) 0.0035 0.0030 0.0025 0.0020 0.0015 0.0010 0.0005 0.0000 -3 -2 -1 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10

0.0020

c)

0.020 ' / S m

The electrochemical SIP model is based on a combination of electrochemical principles and electrical potential theory. In Wong’s model, the complex electrical conductivity of the particles is determined by the sum of surface conductivity and the conductivity produced by the redox reaction. We used an extended form of the model that is able to consider the particle size distribution:

0.035 1% a)  2% 0.030  3% 0.025  4% 0.020 0.015 0.010 d = 0.5 - 1mm 0.005 0.000 -3 -2 -1 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10

-1

Fraction of biochar (ξ)

" / S m

Set B Sample No.

-1

Particle Size of biochar (d) (mm)

" / S m

Fraction of biochar (ξ)

-1

Table 1: Mass fraction and particle size of biochar in samples Set A Sample No.

H.Vereecken

peak with an increasing maximum value related to the increasing fraction of biochar is observed for each of the spectra in a similar frequency range. Figures 2c and 2d show that there is no obvious influence of the particle size distribution on the magnitude of σ’(ω) and σ”(ω). The larger biochar particles show the increase of σ’(ω) at lower frequency. The peak frequency of σ”(ω) clearly moves to lower frequencies for increasing particle size.

' / S m

We investigated two sets of samples (Table 1). In both sets, the biochar was obtained from pine woodchips by slow pyrolysis at 400 °C. Biochar of various particle diameter (d) and mass fractions (ξ) was added to a well-sorted sand. All samples were flushed with 4 mM NaCl solution.

F.-H.Haegel J.A.Huisman

d)

0.0015 0.0010 0.0005 0.0000 -3 -2 -1 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 frequency (Hz)

Figure 2. Frequency-dependent complex electrical conductivity of sand-biochar mixtures. a) and b) show σ’(ω) and σ”(ω) of sand mixed with 1 %, 2 %, 3 %, 4 % of mass fraction of biochar with particle size of 0.5 - 1 mm. c) and d) show σ’(ω) and σ”(ω) of sand mixed with 2 % biochar with different particle size (0.25 - 0.5 mm, 0.5 - 1 mm and 1 - 2mm). Modeling Results We used the model of Wong (1979) to model the data. Figure 3 shows the measured SIP spectra (dotted lines) and the best fitting results (green continuous lines). In general, the fitting was better for low mass fractions, as expected. Wong (1979) suggested that this model is suitable for the case that the volume fraction of the electronic conductor in the mixture is less than 16 % so that the conductor is well dispersed. Because of the low grain density of the measured biochar, the volume fraction is 3.5 - 4.5 times the mass fraction of biochar. So the volume fraction might be out of the limit given by Wong for ξ = 3 % and 4 %.

CONCLUSIONS We investigated the SIP response of sand-biochar mixtures with varying particle sizes and different amounts of biochar. The results show that biochar in sand shows significant polarization and a characteristic SIP response. The particle size and fraction of biochar have an influence on the characteristics of the SIP signal. The reasonable modelling results show that the electrochemical SIP model has some potential to characterize the SIP signal in the presence of electronic conductors such as biochar. Next, we will extend the model to elliptical particles rather than spherical particles to improve the accuracy of the model for the visibly nonspherical biochar particles.

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SIP on biochar

Z.Gao

ACKNOWLEDGMENTS This research was supported by the China Scholarship Council (CSC). REFERENCES Chan, K. Y., Van Zwieten, L., Meszaros, I., Downie, A., and Joseph, S., 2007, Agronomic values of greenwaste biochar as a soil amendment: Australian Journal of Soil Research, 45, 629-634. Chan, K. Y., Van Zwieten, L., Meszaros, I., Downie, A., and Joseph, S., 2008, Using poultry litter biochars as soil amendments: Australian Journal of Soil Research, 46, 437444. Cheng, C. H., Lin, T. P., Lehmann, J., Fang, L. J., Yang, Y. W., Menyailo, O. V., Chang, K. H., and Lai, J. S., 2014, Sorption properties for black carbon (wood char) after long term exposure in soils: Organic Geochemistry, 70, 53-61.

F.-H.Haegel J.A.Huisman

H.Vereecken

and bio-oil sources: International Journal of Hydrogen Energy, 31, 613-620. Gurin, G., Tarasov, A., Ilyin, Y., and Titov, K., 2013, Time domain spectral induced polarization of disseminated electronic conductors: Laboratory data analysis through the Debye decomposition approach: Journal of Applied Geophysics, 98, 44-53. Hunt, J., DuPonte, M., Sato, D., and Kawabata, A., 2010, The basics of biochar: A natural soil amendment: Soil and Crop Management, 30, 1-6. Sohi, S., Lopez-Capel, E., Krull, E., and Bol, R., 2009, Biochar, climate change and soil: A review to guide future research, CSIRO Land and Water Science Report 05/09. Wong, J., 1979, An electrochemical model of the inducedpolarization phenomenon in disseminated sulfide ores: Geophysics, 44, 1245-1265.

Demirbas, A., Pehlivan, E., and Altun, T., 2006, Potential evolution of Turkish agricultural residues as bio-gas, bio-char

Figure 3. Measured SIP spectra (dotted lines) and best fitting results for the electrochemical SIP model (green continuous lines).

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Numerical correction of phase errors due to leakage currents in wideband EIT measurements E. Zimmermann

J. A. Huisman

A. Mester

S. van Waasen

Central Institute for Engineering, Electronics and Analytics, Electronic Systems (ZEA-2) Forschungszentrum Jülich GmbH, Germany [email protected]

Institute of Bio- and Geosciences, Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, Germany [email protected]

Central Institute for Engineering, Electronics and Analytics, Electronic Systems (ZEA-2) Forschungszentrum Jülich GmbH, Germany [email protected]

Central Institute for Engineering, Electronics and Analytics, Electronic Systems (ZEA-2) Forschungszentrum Jülich GmbH, Germany [email protected]

SUMMARY Advanced model-based data correction methods are needed in order to determine the small phase response of low-polarizable soils and rocks in the higher frequency range up to 10 kHz. Methods have been developed to correct several system-dependent errors, such as amplification errors, signal drift, current measurement errors, potential measurement errors due to high electrode impedances, propagation delay of the signal due to the long cables, and phase errors introduced by inductive coupling between the electrode cables. However, measurements at test sites with high resistivity have shown a new dominating phase error, which was found to be related to capacitive leakage currents between system ground and the soil. In order to correct this error, we enhanced the FEM modelling used for the reconstruction of the electrical conductivity distribution. Using this new formulation of the FEM forward model, this source of error was reduced by a factor of five or more. This enables an electrical conductivity reconstruction for frequencies up to 10 kHz. In future work, it will be investigated whether the capacitive leakage currents can be reduced by optimization of the cable layout. In any case, it is helpful to use the leakage current as a proxy for data error during data filtering, and it can also be used to decide if the enhanced FEM model presented here should be used. Key words: electrical impedance tomography, leakage current, capacitive coupling, inductive coupling.

INTRODUCTION Impedance measurements on low-polarizable soils and rocks in the mHz to kHz range require advanced data correction methods and a sophisticated EIT measurement system to achieve the necessary phase accuracy. For data acquisition, a prototype spectral EIT system optimized for measurements with high phase accuracy has been developed. In addition to the system design, model-based numerical correction methods are used to remove several errors introduced by amplification errors, signal drift, current measurement errors, potential measurement errors due to high electrode impedances, the propagation delay of the signal due to the long cables, phase IP2016 – 6-8 June, Aarhus, Denmark

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errors introduced by inductive coupling between the electrode cables and other system or cable dependent sources (Zimmermann et al. 2008, Kelter et al. 2015, Zhao et al. 2015). The use of model-based corrections enables accurate impedance measurements for frequencies up to some kHz. However, at test sites with high resistivity the correction methods were not sufficient to provide accurate measurements, which is a clear indication that an additional phase error not yet considered in our corrections is affecting measurement accuracy. Close inspection of the errors showed that the remaining errors are related to capacitive leakage currents between system ground and the soil. In this paper, we will present a new correction method based on an enhanced FEM model, and verify the efficiency of the new model-based correction using impedance measurements at resistive and conductive test sites for frequencies up to 10 kHz.

METHOD AND RESULTS Impedance measurements were made using 30 surface electrodes with an electrode separation of 1 m at one conductive and one resistive field site in the vicinity of Milano, Italy. A simple fan-shaped cable layout was used to connect the electrodes to the measurement system. This allows a relatively straightforward calculation of the inductive coupling between the cables, and a subsequent correction following the methods outlined in Zhao et al. (2015). At the conductive test site, previously developed model-based phase corrections worked well. However, the corrections were not sufficient at the more resistive test site. After analysis of the measured data, we found that there was a strong correlation between the capacitive leakage currents between system ground and soil and the phase response of the measured transfer impedances. In a first attempt to correct this error, we developed a correction method based on a simple electrical model. However, this method did not work well due to the inhomogeneous electrical conductivity of the soil and the unknown and variable potential distribution at the surface for different electrode configurations. Therefore, it became necessary to enhance the forward FEM model to directly consider leakage currents during the inversion of the data. Our starting point was the following enhanced FEM model that uses an additional admittance matrix YA to

Abbreviated title

eg: Author1, Author2 and Author3

consider the capacity between the cable shield and the surface of the soil (Y + YA) U = I

(1)

where Y is the admittance matrix of the soil, U is the potential distribution at the nodes of the used mesh, and I the current source (Zimmerman 2011, Zhao et al. 2013). The total capacity between system ground potential, which is also the shield potential of the cable, and the soil is measured with the EIT system. At the resistive test site, it was found to be 10.5 nF. This capacity is considered in the admittance matrix YA by assuming that the capacity is equally distributed along all cable paths. In order to consider the effect of leakage current, we modify the source term of the FEM model: I = IS + IL

(2)

where the vector IS represents a symmetric current injection (normal case) and the vector IL represents leakage currents. Using this modified FEM model, we calculate the transfer impedance according to:

CONCLUSIONS In this study, we could show that the new model-based correction that relies on FEM modelling enables the correction of measured impedances of resistive test sites where leakage currents cause a strong phase error in the data. This correction is important for wideband spectral EIT measurements. However, it requires the measurement of the leakage current and the total parasitic capacity between system ground and the soil in addition to a well-defined cable layout. Based on our current understanding, it is likely that the cable layout can be optimized to reduce errors in measurements of the phase of the impedance. However, the optimal lay-out will depend on the dominating error source (inductive coupling or capacitive leaking currents). In addition, capacitive leaking currents increase with increasing contact impedance of the electrodes, which thus need to be as low as possible in order to minimize phase errors in the impedance measurements. In any case, it is helpful to use the leakage current as a proxy for data error during data filtering, and it can also be used to decide if the enhanced FEM model presented here should be used.

ACKNOWLEDGMENTS Z = ZS + ZL

(3)

where ZS is the impedance for symmetric current injection (normal case), and the impedance ZL for excitation with the leakage current. The leakage current is calculated from the measured current at the two used current electrodes for all configurations. The modified forward FEM model is included in the inversion in order to reconstruct the complex soil conductivity using a 3D mesh for the forward model and a 2D mesh for the inversion. After inversion, we calculated the corrected impedance ZC using ZC = ZM – ZL

(4)

in order to verify the effect of the model-based correction on the imaginary part of the measured impedance Z M. Figure 1 shows the impedance spectra for different correction steps. It can be seen that the correction for inductive coupling has the biggest effect at the conductive site, whereas the correction for capacitive leakage currents has the biggest effect at the resistive site. After correction, the imaginary part of the impedance is consistently negative as expected, and the spread of the impedance values at high frequencies is minimized. As illustrated in Figure 2, the additional modelbased correction developed in this study allows the reconstruction of the soil conductivity for frequencies up to 10 kHz for both conductive and resistive test sites.

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We are grateful to Silvia Inzoli and Mauro Guidici for support during the field measurements. REFERENCES M. Kelter M., Huisman, J.A., Zimmermann, E. Kemna, A. Vereecken, H., 2015, Quantitative imaging of spectral electrical properties of variably saturated soil columns, Journal of Applied Geophysics, 123, 333 - 344. Zhao, Y., Zimmermann, E., Huisman, J.A., Treichel, A., Wolters, B., van Waasen, S., Kemna, A., 2013. Broadband EIT borehole measurements with high phase accuracy using numerical corrections of electromagnetic coupling effects. Meas. Sci. Technol. 24 (8), 085005. Zhao, Y., Zimmermann, E., Huisman, J.A., Treichel, A., Wolters, B., van Waasen, S., Kemna, A., 2015. Phase correction of electromagnetic coupling effects in crossborehole EIT measurements. Meas. Sci. Technol. 26 (1), 015801. Zimmermann, E., Kemna, A., Berwix, J., Glaas, W., Vereecken, H., 2008. EIT measurement system with high phase accuracy for the imaging of spectral induced polarization properties of soils and sediments. Meas. Sci. Technol. 19. (2008) Zimmermann, E., 2011, Phasengenaue Impedanzspektroskopie und –tomographie für geophysikalische Anwendungen (Ph.D. thesis), University of Bonn, Germany (in German).

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Figure 1. Impedance spectra of the measured and corrected transfer impedances of a more resistive (a … e) and a more conductive (g … j) test site with the real (a, f) and imaginary part (b, g) of the uncorrected data, the imaginary part (c, h) after correction for inductive coupling, the imaginary part after additional correction due to the capacitive leakage current (d, i) and after additional removal of impedances with a ratio IL/IS > 10%. It should be noted that the scale can change from step to step.

Figure 2. Magnitude (a, c, e, g) and phase image (b, d, f, h) of the reconstructed conductivity distribution of the more resistive (a … d) and the more conductive (e … h) test site in Milan at the frequencies 164 Hz and 10 kHz.

Comparison of Cole-Cole and Constant Phase Angle modeling in time-domain induced polarization Myriam Lajaunie

Pradip Kumar Maurya

Gianluca Fiandaca

EOST Ecole et Observatoire des Sciences de la Terre Université de Strasbourg (France) [email protected]

HydroGeophysics Group Department of Geoscience Aarhus University (Denmark) [email protected]

HydroGeophysics Group, Department of Geoscience Aarhus University (Denmark) [email protected]

SUMMARY The Cole-Cole model and the constant phase angle (CPA) model are two prevailing phenomenological descriptions of the induced polarization (IP), used for both frequency domain (FD) and time domain (TD) modeling. The former one is a 4-parameter description, while the latest one involves only two parameters. Choosing between a ColeCole description and a CPA one to invert a specific frequency domain data set is easy, since a look at the data is enough to estimate their spectral content. This is, however, not the case with TDIP data. This work aims at understanding how the spectral content is reflected in TDIP data, and therefore, at identifying (1) if and when it is possible to distinguish, in time domain, between a ColeCole description and a CPA one, and (2) if features of time domain data exist in order to know, from a simple data inspection, which model will be the most adapted to the data. Synthetic forward responses were computed for homogeneous Cole-Cole models, varying both time range of the modeled IP data and Cole-Cole parameters. Subsequently, CPA inversions were carried out on the Cole-Cole data. The inversion results show that it is generally possible to distinguish CPA and Cole-Cole models in time domain, except when the Cole-Cole frequency exponent is small (below 0.1) or for specific combinations of the Cole-Cole parameters. The distinctness increases with the time range of the IP data, but usually two decades in time are sufficient to distinguish the two models. Furthermore, forward modeling of quadrupolar sequences on 1D and 2D heterogeneous CPA models shows that the CPA decays differ among each other only by a multiplication factor. Consequently, the inspection of field data in log-log plots gives insight on the modeling needed for fitting them: the CPA inversion cannot reproduce the shape variability of the IP decays. Field examples of this latter result are presented. Keywords: Cole-Cole, CPA, time-domain, spectral inversion

METHOD AND RESULTS The Cole-Cole and CPA models are the two principal phenomenological models used to describe the induced polarization of rocks and soils. The complex resistivity ζCole-Cole of the Cole-Cole model takes the form:

𝜁𝐶𝑜𝑙𝑒−𝐶𝑜𝑙𝑒 = 𝜌 (1 − 𝑚0 (1 −

1 )) 1 + (𝑖𝜔𝜏)𝐶

The Induced Polarization of rocks and soils can be described with a frequency-dependent complex resistivity. Several models are used to describe the induced polarization of geomaterials, but the most used are the Cole-Cole model presented by Pelton et al. (1978) and the constant phase angle model (CPA), as described for instance in Van Voorhis et al. (1972). The CPA model is suitable if no or negligible variation of the phase shift is observed in the complex resistivity data. Thus, the

1

(1)

where ρ is the direct current resistivity, m0 is the intrinsic chargeability, τ is the time constant, C is the frequency exponent and i is the imaginary unit. The CPA model is much simpler, and describes the complex resistivity using only two parameters:

𝜁𝐶𝑃𝐴 = 𝐾(𝑖𝜔)−𝑏

(2) 𝜋

where b is a positive fraction, 𝜑 = − 2 𝑏 represents the phase shift and completely defines the IP response, K is a constant and i is the imaginary unit. In the CPA model the DC resistivity cannot be defined, because the complex resistivity increases indefinitely at low frequencies. For this reason Van Voorhis et al. (1973) introduced the Drake model:

𝜁𝐷𝑟𝑎𝑘𝑒 = 𝐾(𝑖𝜔 + 𝜔𝐿 )−𝑏

INTRODUCTION

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choice of using the Constant Phase Angle (CPA) model instead of the Cole-Cole model to describe a specific set of frequency domain IP data is straightforward. This is, however, not the case with time domain IP data. Being able to understand how the Cole-Cole description differs from the CPA description in time domain will allow us to judge more easily, which description will manage best to describe the induced polarization of a specific studied area. TDIP forward responses of homogeneous half-spaces have been computed, using the Cole-Cole modeling and varying the acquisition time ranges. Each synthetic decay has then been inverted using the CPA modeling, in order to test to what extent the CPA inversion is able to fit Cole-Cole data. Finally, a field data set has been inverted using both models, to assess in a real 2D situation their ability to explain data.

(3)

where in comparison with the CPA model a low frequency pole 𝜔𝐿 is introduced and the DC resistivity can be defined as 𝜌 = 𝐾𝜔𝐿 −𝑏 . In our implementation of the time-domain forward response, we used the Drake model of equation (3) with a fixed value for the low frequency pole 𝜔𝐿 = 10−5 Hz. In this way, the inversion is set up in terms of the model parameters 𝜌 and 𝜑. We computed synthetic time domain data using the Cole-Cole description of the induced polarization, and tested for different types of acquisition to what extent the CPA inversion was able

to fit the synthetic data. We chose to simulate data from homogeneous half-spaces, to be able to interpret the results of the tests easily. The computations of forward responses and inversions have been realized using the algorithm presented in Fiandaca et al. (2012). We simulated different data, changing the Cole-Cole model parameters C and τ, at fixed m0 and ρ values. In particular, we chose as synthetic models every possible combination of the following parameters: ρ = 100 Ωm, m0 = 40 mV/V, C = [0.1, 0.3, 0.5], τ = [0.001, 0.01, 0.1, 1, 10] s. Different acquisition ranges have been investigated, starting from a reference acquisition with 40 log-increasing gates ranging from 1 millisecond to 10 seconds. The reference acquisition range has been reduced by (Figure 1): decreasing the Ton=Toff values (Ton and Toff being the current on-time and off-time, respectively), and consequently the time of the last gate (range-type 1); increasing the delay after the current turnoff mdly, and consequently by increasing the time of the first gate (range-type 2);increasing mdly and decreasing Ton at the same time (range-type 3).

along the y axis. Practically, the shape of the CPA decays in log-log scale is univocally defined by the current waveform (in terms of current on-time Ton, current off-time Toff and stack size). For specific combinations of τ and C parameters (e.g. τ=1 s and C=0.3) the CPA and Cole-Cole decays are really similar, but in general the decays differ significantly.

Figure 2. CPA fits of Cole-Cole decays (5% error bars) when varying models and range-types, but keeping constant the number of gates (10 gates).

Figure 1. Definition of the three acquisition range-types. Range-type 1: the time length of the decay is increased by adding gates at the end of the acquisition time, keeping mdly = 1 ms (red lines). Range-type 2: the time length of the decay is increased by adding gates at early times and keeping Ton=Toff = 10 s (blue lines). Range-type 3: the length of the decays is increased by adding gates both at the late and at the early times (yellow lines). Figure 2 shows exemplary fits of Cole-Cole decays with CPA modeling when only 10 gates (one decade in time) are used in the acquisition range for all the three different range-types. The CPA inversion manages to explain the 10 gates-long curves for any C values, and it is not possible to distinguish CPA and ColeCole modeling. Figure 3 presents the CPA fits of three different 40-gates Cole-Cole decays, for different τ values (0.01 and 1 seconds) and C values (0.3 and 0.5). The shape of the Cole-Cole forward responses changes significantly when varying τ and C, while the shape of the CPA modeling in log-log scale remains practically unchanged, the only difference being a translation

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Figure 3. Exemplary CPA fits of Cole-Cole decays (5% error bars, 40 gates) when varying Cole-Cole parameters.

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Figure 4. Complete results of the synthetic tests in terms of inversion residuals (χ values, 5% error bars). The results have been sorted according to the acquisition range-type (row), the frequency exponent (column) and the time constant (line color). For each case, the inversion residuals are displayed as a function of the number of gates in the synthetic data.

modeling are almost always distinguishable, except for specific models when less than two decades are used in the acquisition time range. In particular, it is more difficult to distinguish the CPA and Cole-Cole models for high τ values and range-type 1 when too few gates are used (i.e. when we miss the late times). With range-type 2 the CPA and Cole-Cole models are more difficult to distinguish with low τ values. The results with C=0.3 are similar to the results with C=0.5, except that the inversion misfits is smaller. Interestingly, with τ=1 s the CPA and ColeCole models are more difficult to differentiate, and the CPA inversion often fits the Cole-Cole data within 5% also with 40 gates. Finally, Figure 5 shows the comparison of CPA and Cole-Cole modeling of field data, inverted in 2D following Fiandaca et al. (2013). The field data were acquired at Grindsted, Denmark, with a Terrameter LS (ABEM Instrument). We used an on-time and an off-time of 8 s both, and 10 gates per decade (re-gating the full-waveform data and applying the de-noising scheme described by Olsson et. al (2016)). The data quality was generally good, and after processing, most of the decay curves had still ~ 30 gates. As for the synthetic modeling for homogeneous halfspace, the shape of the CPA forward responses does not change in log-log plots. Consequently, the CPA description cannot explain the variety of shapes present in the data. On the contrary, the Cole-Cole modeling is able to retrieve the shape of the field decays. Figure 5. Examples of field decays, along with their ColeCole and CPA fits obtained through a 2D inversion. Figure 4 shows the inversion residuals (χ values, 5% error bars) of the CPA inversions carried out on Cole-Cole forward decays, when varying model, range-type and number of gates. All the models with C=0.1 present misfit below/equal to one, regardless of the number of gates. This is easily understood considering that the Cole-Cole model tends to the CPA model when C goes to zero. On the other hand, with C=0.5 the two IP2016 – 6-8 June, Aarhus, Denmark

CONCLUSIONS The synthetic results show that it is generally possible to distinguish CPA and Cole-Cole models in time domain, except when the Cole-Cole frequency exponent is small (below/equal to 0.1) or for specific combinations of the Cole-Cole parameters. The distinctness increases with the time range of the IP data, but usually two decades in time are sufficient to distinguish the two models. Furthermore, the shape of the CPA forward responses in log-log plots is univocally defined by the current waveform, also for 2D modeling. Consequently, the

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inspection of field data in log-log plots gives insight on the modeling needed for fitting them: the CPA inversion cannot reproduce shape variability of the IP decays, as verified on field examples. ACKNOWLEDGMENTS Support was provided by the research project GEOCON, Advancing GEOlogical, geophysical and CONtaminant monitoring technologies for contaminated site investigation (contract 1305-00004B). The funding for GEOCON is provided by The Danish Council for Strategic Research under the Programme commision on sustainable energy and environment. REFERENCES Cole K.S., Cole R.H., 1941. Dispersion and absorption in dielectrics I. Alternating current characteristics. J. Chem. Phys. 9 (4), 341. Fiandaca G., Auken E., Christiansen A.V. & Gazoty A., 2012. Time-domain-induced polarization: Full-decay forward modeling and 1D laterally constrained inversion of Cole-Cole

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parameters, Geophysics, 77, E213-E225. 10.1190/geo20110217.1. Fiandaca G., Ramm J., Binley A., Gazoty A., Christiansen A.V., Auken E., 2013. Resolving spectral information from time domain induced polarization data through 2-D inversion. Geophys. J. Int. 192 (2), 631–646. Olsson P.I., Fiandaca G., Larsen J.J., Dahlin T., Auken E., 2016. Doubling the spectrum of time-domain induced polarization: removal of non-linear self-potential drift, harmonic noise and spikes, tapered gating, and uncertainty estimation. 4th IP Workshop, 6-8 June 2016, Aarhus, Denmark. Pelton W.H., Ward S.H., Hallof P.G., Sill W.R., Nelson P.H., 1978. Mineral discrimination and removal of inductive coupling with multifrequency IP. Geophysics 43 (3), 588–609. Van Voorhis G.D., Nelson P.H., Drake T.L., 1973. Complex resistivity spectra of porphyry copper mineralization. Geophysics 38 (1), 49–60

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Airborne IP for Kimberlite Exploration Douglas W. Oldenburg

Seogi Kang

University of British Columbia University of British Columbia 6339 Stores Rd., Vancouver, Canada 6339 Stores Rd., Vancouver, Canada [email protected] [email protected]

contamination. The possibility exists however, that the chargeability is reflective of the kimberlite and it is therefore “signal” that we want to interpret.

SUMMARY Negative transients in coincident loop airborne time domain electro-magnetic (ATEM) data have often been observed when exploring for kimberlite deposits. It is usually supposed that the negative transients arise from chargeable material such as surficial clays or ice in permafrost. As such, this EM signal is generally regarded as a “problem” in mineral exploration because it distorts the EM signals from the conductive kimberlites, and if not corrected for, results in an incorrect conductivity. However, chargeability could be reflective of the kimberlite, hence the induced polarization (IP) effects can be valuable “signal”. The ATEM surveys at the Tli Kwi Cho (TKC) kimberlite complex have been a testbed for illustrating the existence of negative transients and we focus on that region. The two pipes that constitute TKC have been extensively drilled and the resultant geologic models can be used to validate our inversion results. In addition, the complex impedance of TKC core samples have been measured in the laboratory and the results showed that the kimberlites can be chargeable and that different kimberlite units have different IP characteristics. In this paper, we first address the important issue about depth of resolution of buried chargeable bodies relevant to kimberlite exploration. After showing its potential we remove the EM effects from the IP data and invert them to recover 3D distributions of pseudo-chargeability at multiple time channels. The recovered pseudo-chargeability at different times provides meaningful information about the diamondiferous portion of the pipe and distinguishes it from other kimberlitic rocks. Key words: airborne EM, Kimberlite, and 3D inversion

Induced

polarization,

Figure 1. (a) General structure of kimberlite pipe. (b) Physical properties of geological units in the kimberlite pipe. The Tli Kwi Cho (TKC) kimberlite complex is located approximately 360 km northeast of Yellowknife, NWT, Canada within the Archean Slave craton. The complex is part of the larger Lac de Gras kimberlite field. The TKC kimberlites are composed of two main pipes called DO-18 and DO-27, and they are respectively located at northern and southern part of the region as shown in Figure 2(a). There are four rock units of importance: XVK (Xenolithic kimberlite), VK (volcaniclastic kimberlite), HK (hypabyssal kimberlite) and PK (pyroclastic kimberlite). DO-18 pipe is mostly XVK and DO-27 is a combination of PK and HK. The PK unit is the sought diamondiferous portion of the pipe. An east-west geological section at DO-27, generated from drilling results (Harder et al., 2006) is shown in Figure 2(b). Petrophysical data including density, susceptibility, Koenigsberger, complex conductivity have been measured from core samples at both pipes. Figure 3 shows the measured complex impedance from TKC core samples corresponding to PK (green), HK (red), and XVK (purple) units.

INTRODUCTION Figure 1(a) shows a typical geologic model of a kimberlite composed of three different parts: crater, diatreme, and hypabyssal facies. Physical properties of those three facies are shown in Figure 1(b). Kimberlite exploration has focused on looking for high magnetic susceptibility, low density and high conductivity (Power and Hildes, 2007). The high conductivity is often associated with lake bottom sediments as well as the pyroclastic units at depth. The conductivity of the kimberlites is usually found using airborne EM (AEM) surveys, and in particular airborne time domain EM (ATEM) systems. Often however, negative transients observed (Jansen and Witherly, 2004) indicating there is chargeable material (Weidelt, 1982). Ice and near surface clays are known to be chargeable (Smith and Klein, 1996), and these materials distort the AEM signals and impede ability to extract good information about the conductivity. As such, the existence of chargeable materials is usually considered to be a “problem” and it is referred to as IP IP2016 – 6-8 June, Aarhus, Denmark

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Figure 2. Geological background of Tli Kwi Cho (TKC) Kimberlites. (a) Plan maps of TKC with kimberlite units: PK, HK, VK, and XVK. (b) East-west geological section of DO-27 pipe. The map showing PK is at a shallower depth than the map showing HK. The impedance plots indicate that the kimberlites are chargeable, and analysis shows that the estimated time constants are different; PK has a much slower decay than HK and XVK. This raises two important questions: a) Can we invert ATEM data for chargeability? and b) Can this provide some meaningful information about the kimberlite?

AIP for Kimberlite Exploration

Douglas W. Oldenburg and Seogi Kang

A major challenge for extracting IP information from airborne data arises from the 1/r3 decay of signal away from the source and the fact that the top few tens meters often include permafrost and clay (Macnae, 2015). AIP is thus often thought of as a ‘clay mapper’. Investigation of the depth resolution on AIP is therefore crucial. We will use the geometry of TKC pipes to address this question and then carry through an analysis to extract geologic information from the AIP data. To investigate depth resolution for AIP data we generate synthetic AIP data sets with a chargeable target at different depths and apply a 3D IP inversion to them. To proceed, we briefly outline essential definitions and procedures. Detailed information can be found in Kang and Oldenburg (2016).

Figure 3. Complex impedance measured from core samples from PK (green), HK (red), and XVK (purple) units. Left and right panel shows real and imaginary parts of the impedance.

COMPLEX CONDUCTIVITY

often expected that the resolution is only a few tens of meters for a compact target at the surface and about 90 m for chargeable layers (Macnae, 2015). We systematically treat this issue in the context of kimberlite exploration. We consider a circular-shaped chargeable target, which is moderately conductive and embedded in a resistive background. This could correspond to a PK unit or a crater facies (Figure 1a). Depth resolution of the AIP data includes two important items: detection and delineation. For the first item, using an ATEM survey geometry shown in Figure 1(a), we perform forward modelling and compute db z/dt (Figure 1b) using the EMTDIP code (Marchant et al., 2014). The half-space earth (10-4 S/m) includes a conductive and chargeable cylinder and Cole-Cole parameters of the chargeable unit are =10-1 S/m, =0.1, 3 c=0.5 and =10 micro-s. With fixed thickness (75 m) and radius (100 m) of the cylinder, we alter the depth from the surface as 0, 75, and 150 m. Although the amplitude of the observation decreases with increasing depth, the time at which the negative value appears is almost constant (~700 micro-s) for all three depths. Assuming a noise level of 10-3 pV/A-m2, the detectability level is about 150 m. The cylinders at depths of 75 or 100 meters have numerous time channels of negative values that are well about this threshold. The main difference of the responses at the three depths is just an amplitude factor so it is not likely that depth information can be obtained from a single sounding. In practice, however, we obtain ATEM data from a number of sounding locations.

Complex conductivity in the frequency domain can be expressed as (1) is conductivity at infinite frequency, and  is where angular frequency (rad/s). Different descriptive models exist but, following Smith et al. (1988), we use the Cole-Cole model from Pelton et al. (1978): , (2) where  is intrinsic chargeability,  is time constant, and c is frequency dependency.

LINEAR FORM OF IP RESPONSE An ATEM observation, dobs, includes both EM and IP effects and can be expressed as , (3) , which does where the fundamental response is not include any IP effects, and dIP is the IP response. Here F [] indicates Maxwell’s operator which takes conductivity and computes a TEM response. The IP datum can be expressed as , (4) This procedure can be considered as EM-decoupling because we are removing EM induction effects from the observations. The IP responses can be written in a linear form: ,

(5)

is the pseudowhere G is the sensitivity function and chargeability. Note that this pseudo-chargeability is timedependent, but the intrinsic chargeability is not. This linear form will be the forward function that we use to invert IP data.

Figure 4. (a) Geometry of an ATEM system, and a chargeable cylinder embedded in the half-space earth. (b) Observed vertical magnetic fields (dbz/dt) with varying depths for the chargeable unit. Solid and dotted lines respectively indicate positive and negative data. We perform two forward modellings: F [] (observation) and F [ ] (fundamental) at 210 sounding locations. Then, using Eq. (4), we evaluate the IP data at 1300 micro-s as shown in Figure 5. As the depth increases, the IP responses get broader and smoother due to the geometric effects. Although not shown here, the spatial variation of the IP data hardly changes in time, hence, this is similar to potential field data. Similar to the inversion of magnetic data we apply a depth weighting to compensate for the (1/r3) decay. In the following we carry out 3D IP inversions with, and without, the depth weighting applied to IP data sets where the models had different depths (z = 0, 75, and 150 m). Forming the sensitivity function requires a 3D conductivity model, and we used the true conductivity model for each case. Figure 6 shows the recovered pseudo-chargeability models. Based upon these results, resolving depth information looks possible and the depth weighting seems to be advantageous, but not crucial.

DEPTH INFORMATION IN AIP The depth resolution of AIP data is limited because of the geometric decay of the IP signal from a chargeable target. It is IP2016 – 6-8 June, Aarhus, Denmark

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AIP for Kimberlite Exploration

Douglas W. Oldenburg and Seogi Kang

Figure 5. True IP responses computed by subtraction using Eq. (4). Depth of the chargeable cylinder varies: a) 0m, b) 75 m, and c) 150-m depth. Dots indicate horizontal locations of soundings.

Figure 7. TKC VTEM data. Maps of VTEM responses at (a) 90 micro-s and (b) 680 micro-s. Easting profile line data near (c) DO-18 and (d) DO-27. 3D ATEM and IP inversions Our approach to invert AIP data is based upon Kang and Oldenburg (2016). The first step is to invert ATEM data to recover the conductivity. To exclude IP effects in the observations, we only use the first 6 time channels of the VTEM data (90-190 micro-s) near DO-27. This cannot be done for VTEM data near DO-18 since even the earliest channel is negative. Fortunately, DIGHEM data covers the entire TKC area and we assume it is not significantly affected by IP, so we cooperatively invert VTEM and DIGHEM data. The recovered 3D conductivity model is shown in Figure 8. At B-B’ section, we overlay the boundaries of different kimberlite units obtained from drilling results (Figure 2b). The two conductive pipes are imaged at depth. The pipe for DO-27 extends deeper depth than one for DO-18. The location of recovered conductive pipe at DO-27 matches well with the PK unit.

Figure 6. Sections of recovered pseudo-chargeability at different depths. (a) Without depth weighting and (b) with depth weighting. Top, middle, and bottom panel correspondingly indicate a chargeable target at 0, 75, and 150 mdepth.

FIELD EXAMPLE: TKC TKC ATEM data Airborne EM surveys flown over TKC include DIGHEM, AeroTEM, and VTEM systems We focus on the VTEM data set because it illustrates the challenges we can encounter when handling AIP data. As shown in Figure 7(a), even at the earliest time (90 micro-s), VTEM data have negative values (dotted contours) over DO-18 and between DO-18 and DO-27. DO-27 shows a positive anomaly (solid contour) at this time, but data become negative at 680 micro-s as shown in Figure 7b. Easting profile lines over DO-18 and DO-27, respectively shown in Figure 7(c) and (d), show the transition.

IP2016 – 6-8 June, Aarhus, Denmark

Figure 8. Recovered 3D conductivity model. Left panel shows plan view at 65.5 mbsf. Middle and right panels show section views at Northing 713445m and 7133595m. Based upon the recovered conductivity, est, we proceed with EM-decoupling: , (6) is raw IP data, F [est] is estimated fundamental where data. Figure 9 shows the observed, estimated fundamental response, and raw IP data at 130 and 410 micro-s where both EM and IP effects are substantial. Our EM-decoupling effectively removes EM induction effects due to the conductive pipe at DO-27 at both of the times evaluated here.

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AIP for Kimberlite Exploration

dobs

F [σest ]

Douglas W. Oldenburg and Seogi Kang

P dIr aw

130 micro-s

410 micro-s

Figure 9. Plan maps of observed (left panel), estimated fundamental (middle panel) and raw IP (right panel) data at 130 (top panel) and 410 (bottom panel) micro-s. We separately invert each time channel of raw IP data and recover 3D pseudo-chargeability at multiple times. Figure 10. shows recovered pseudo-chargeability at 130 and 410 micro-s. Four chargeable anomalies, A1-A4, are imaged. A1-A3 are imaged at 130 micro-s, whereas A4 is not imaged at that time but is apparent at 410 micro-s. This reflects the different time decays associated with the AIP signals, and it is consistent with the complex impedance measurements shown in Figure 3 if the A4 anomaly is a PK unit and the other anomalies, A1-A3 are associated with the other kimberlitic rocks. Through a comparison of Figure 10 and Figure 2(a), which was obtained from drilling, it appears that A1, A2, A3, and A4 might respectively be connected to XVK, VK, HK, and PK units. Recalling that PK is the most diamondiferous unit, the recovered pseudo-chargeability at the two different times shows that the PK unit is distinct from three other units: XVK, VK, and HK in 3D space. In particular, at the B-B’ section through DO-27 we have overlaid the pseudo-chargeabilty with the geological boundaries. (see right panel of Figure 10.) Comparisons of the boundaries and pseudo-chargeability at 130 and 410 micro-s suggests we are delineating between the PK from HK units.

In this paper, we investigated the feasibility of the AIP technique for kimberlite exploration and used the TKC kimberlite region as an example. The area has been extensively drilled and four types of kimberlitic rocks have been found. Lab measurements on core samples showed TKC kimberlites are chargeable and that they have different IP parameters. This promoted two important questions: a) Can we invert ATEM data for chargeability at depth? and b) Can the results provide meaningful information about the kimberlite? Through the use of a synthetic model that emulates a TKC pipe, we analyzed the depth resolution issue and found that targets buried 75-100 meters might still be detectable and that inversion that included a depth weighting was beneficial, but might not be crucial. We applied a 3D ATEM-IP inversion workflow to TKC VTEM data. To recover conductivity, we inverted early time channels of VTEM data (presumed to have insignificant IPcontamination) cooperatively with DIGHEM data. The details for that result will be published in a separate paper. The recovered conductivity includes two moderately conductive pipes near DO-18 and DO-27. The conductivity was used to estimate the fundamental EM response which was subtracted from the data to generate raw IP data at multiple time channels. 3D IP inversions were carried out and the pseudochargeabilities at multiple times were obtained. Four chargeable anomalies are imaged at depths (~70 m): A1-A4 possibly correspond to four different kimberlites: XVK, VK, HK and PK. These correspondences can be inferred by comparing the recovered chargeability with geologic logging in boreholes. The recovered pseudo-chargeability at different times suggests a distinction between the PK unit and the other three kimberlite units. Moreover, the outline of the inferred PK unit matches well with the boundaries of the PK unit obtained from drilling, but some of this is likely attributed to the conductivity model and the fact that IP sensitivities are enhanced in regions of higher conductivity. From a geologic perspective, the two main results might be the differentiation of rocks associated with the two pipes. The XVK unit comprising DO-18 is substantially different from the dominant PK unit at DO-27. On a smaller scale, we appear to be able to differentiate between the PK and HK units at DO-27. This is potentially important since PK is strongly diamondiferous and HK has minimal diamond showings. This discrimination might be further enhanced through the use of ground IP using either galvanic or inductive sources. Overall, our study of AIP shows the potential benefits in kimberlite exploration, and hence motivates further research and application in other geoscience problems.

ACKNOWLEDGEMENTS

Figure 10. Recovered 3D pseudo-chargeability model at 130 (top row) and 410 (bottom row) micro-s. Left panel shows plan view at 65.5 mbsf. Middle and right panels show section views at Northing 713445m and 7133595m.

CONCLUSIONS

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We thank Ken Witherly and Joel Jansen who provided the motivation and ATEM data to carry out this research, and Brook Clements and Jennifer Pell of Peregrine for providing data and cores for lab measurements. We thank Dom Fournier and Mike McMillan for their contribution to the development of the conductivity model, and Randy Enkin of Gelogical Survey of Cananda, Thibaut Astic, Devin Cowan and others at UBC-GIF for participating in lab measurements and in extensive discussions about TKC.

REFERENCES Jansen, J., and K. Witherly, 2004, The Tli Kwi Cho kimber- lite complex, Northwest Territories, Canada: A geophysical case study: SEG Technical Program Expanded Abstracts, 1147– 1150.

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Kang, S., and D. W. Oldenburg, 2016, On recovering distributed IP information from inductive source time domain electromagnetic data (in revision): Geophysical Journal International. Macnae, J., 2015, Quantifying Airborne Induced Polarization effects in helicopter time domain electromagnetics: Journal of Applied Geophysics. Marchant, D., E. Haber, and D. Oldenburg, 2014, Threedimensional modeling of IP effects in time-domain electromagnetic data: Geophysics, 79, E303–E314. Power, M., and D. Hildes, 2007, Geophysical strategies for kimberlite exploration in northern Canada: Proceedings of

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Douglas W. Oldenburg and Seogi Kang

Exploration ’07: Fifth Decennial International Conference on Mineral Exploration, 1025–1031. Smith, R. S., and J. Klein, 1996, A special circumstance of airborne induced polarization measurements: Geophysics, 61, 66–73. Smith, R. S., P. Walker, B. Polzer, and G. F. West, 1988, The time-domain electromagnetic response of polarizable bod- ies: an approximate convolution algorithm: Geophysical Prospecting, 36, 772–785. Weidelt, P., 1982, Response characteristics of coincident loop transient electromagnetic systems: 47, 1325–1330.

5

Geometrical constraints for membrane polarization Andreas Hördt

Katharina Bairlein

Hermann Stebner

TU Braunschweig Mendelssohnstr. 3 38106 Braunschweig [email protected]

TU Braunschweig Mendelssohnstr. 3 38106 Braunschweig [email protected]

TU Braunschweig Mendelssohnstr. 3 38106 Braunschweig [email protected]

SUMMARY We investigate under which conditions membrane polarization might be relevant for realistic pore space geometries. We review some basic properties of the theoretical model and illustrate general constraints by modelling studies. We focus on geometrical parameters of the model, e.g. radii r and lengths L of two cylindrical pores. In principle, a wide range of spectra can be generated, covering orders of magnitude in both maximum phase shift and characteristic time scales. One ingredient to obtain large phase shift is a small radius of the narrow pore in the range of tens of nm. Time scales are mainly controlled by pore lengths. Generating large time scales and phase shifts at the same time in principle requires large ratios between pore lengths and radii. However, within the four-dimensional parameter space, which exhibits regimes of different behaviour, examples can be found where moderate L/r ratios (10:1) can produce time scales in the range of seconds with phase shifts of a few mrad. The results encourage further attempts to combine impedances of 2-pore systems to approach the simulation of real rock systems.

connect several such 2-type systems to a complex network (Stebner et al., 2016). However, since the model has many parameters and allows a huge number of parameter combinations, it is also essential to understand the model behavoir. Therefore, we review the properties of the model with a particular emphasis on the geometrical parameters, i.e. two pore lengths and pore radii. We investigate which range of parameters is necessary to obtain spectra that are typically obtained with laboratory data, and discuss whether these geometries are realistic to occur in real rocks.

THE MODEL The model suggested by Bücker and Hördt (2013a) consists of an infinite sequence of wide and narrow pores, the geometry of which is described by the pore length and pore radii (figure 1).

Key words: membrane polarization, characteristic time, phase shift, pore space. Figure 1. Basic model used to parameterize the pore space, consisting of a sequence of two cylindrical pore types defined by radius and length.

INTRODUCTION In order to estimate hydraulic parameters of sediments from frequency-dependent electrical properties, theoretical models to simulate the electrical impedance depending on the geometrical properties of the material at the pore scale may be useful. Existing models are either based on the sedimentary grains (e.g. Leroy et al., 2008) or on the properties of the pore space (e.g. Titov et al., 2002). Here, we focus on a class of the pore-space models, describing a process called membrane polarization. Recently, Bücker and Hördt (2013a) extended the 1-D theory suggested by Marshall and Madden (1959) to two-dimensional pores. The model had some success in reproducing qualitatively some features that are commonly observed with laboratory data, such as the temperature dependence (Bairlein et al., 2016), or the increase of imaginary conductivity with increasing fluid salinity, followed by a decrease at extreme salinities (Hördt et al. 2016). So far, the model is limited to a relatively simple sequence of two types of wide and narrow cylindrical pores. In order to simulate more realistic pore geometries, one possibility is to IP2016 – 6-8 June, Aarhus, Denmark

1

In addition to the purely geometrical parameters, the membrane polarization depends on the ion concentration in the free fluid, ion mobility, and the properties of the electrical triple layer that builds up at the mineral surface. The triple layer is characterised by the Zeta potential and the partition coefficient that determines the distribution of the surplus charge between the Stern layer and the diffusive layer. Some of those parameters also depend on temperature and pH, as described in detail in Hördt et al. (2016). A total number of 10 parameters define the model. The basic set that is used for the study in this work, and from which variations are being carried out, is given in table 1.

Geometrical constraints for membrane polarization

Property

Symbol

Value

Length of pore 1

L1

500 μm

Length of pore 2

L2

5 μm

Radius of pore 1

r1

200 μm

Radius of pore 2

r2

20 μm

Ion concentration

c0

1 mol/m3

pH

pH

6

Mobility of all ions

μp1= μp2=

510-8m2/(Vs)

μn1= μn2 Zeta-potential

Ϛ

-75mV

Partition coefficient

fQ

0,2

Temperature

T

293 K

Figure 2 illustrates that a wide range of spectra may be obtained by just varying geometrical parameters. Relatively large phase shifts of several tens of mrad with the maximum at low frequencies (in this case 0,01 Hz, curve 1), corresponding to long relaxation times., intermediate phase shifts and intermediate relaxation times (curve 3), and large phase shifts combined with small relaxation times (curve 2). These curves are just a few examples, a much wider range can actually be obtained by further variations. The phase spectra in these images are relatively sharp, i.e. there is a well-defined maximum. This is a typical feature of the model, but broader spectra may of course be obtained by combining several impedances in a network.

Hördt, Bairlein, Stebner

MODEL STUDIES Pore radii First, we investigate for which pore radii we obtain realistic phase shifts, typically in the range between at least 1 mrad up to several tens of mrad. Figure 3 shows the maximum phase shift, colour coded on a logarithmic scale vs. the radii of the two pores. There is a finite size zone where phase shofts are above 1 mrad. The radius of the small pore (r2) is in the tens of nm range. It is constrained by the diffusive layer thickness, defined by the Debye length (e.g. Bücker and Hördt, 2013a). If the pore is large compared to the Debye length, the relative transport of anions and cations is approximately equal, and no membrane effect exists. The radius of the second pore is roughly 10 times larger. The optimum ratio between pore radii is related to the length ratio (in this case 100:1) by a square root relationship, consistent with findings of Bücker and Hördt (2013a). The Debye length depends on several parameters, and the partition factor might also become important, such that general rules are difficult to derive. However, small pore radii in the range below 0.1 μm can be considered typical to generate measurable phase shifts.

Figure 3: Maximum phase shift extracted from the frequency-dependent spectra, colour coded vs. the radii of the two pores. The pore lengths are L1=5 μm, L2=0,05 μm, all other paramters as given in table 1.

Figure 2. Simulated phase spectra for the following parameters: 1: As given in table 1. 2: L1=5 μm, L2=0,05 μm, r1 =200nm. 3: L1=50 μm, L2=0,5 μm, r1 =1000nm. In prinicple, almost any type of reasonable spectrum might possibly be simulated theoretically. In the following, we explore the parameter space to assess which geometrical parameters required to fit data are realistic and might represent real rock conditions. IP2016 – 6-8 June, Aarhus, Denmark

Whether or not submicron pores are relevant in real rock is not trivial to decide from independent measurements. CT images hardly have a resolution below 1 μm. Mercury injection measurements provide data down to a few nm. Weller et al. (2011) show examples of different sandstones where pore radii below 100 nm constitute more than 20% of the pore volume. Recently, Weller et al. (2015) found that they obtained better correlation between imaginary conductivity and specific internal surface area (Spor) if they use a wet-state methylene blue (MB) method instead of the conventional BET to determine Spor. The reason is that the MB method is also sensitive to the small pores in Clay minerals and thus provides higher Spor values. We take this as further evidence that pores in the range 0,1 μm and smaller, are indeed relevant in real rock.

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Geometrical constraints for membrane polarization

Pore lengths The pore lengths have a strong influence on the characteristic times, calculated here from the frequency fmax at which the maximum phase shift occurs: τmax=1/(2π fmax)

Hördt, Bairlein, Stebner

Which L/r ratios are realistic in real rock is even more difficult to assess than for the radii alone, as independent methods tend to determine the radii rather than the pore length. Certainly, determinations from images will require careful definitions of L and r, and simple assumptions, for example that the radius is roughly the same scale as the length, will not be useful in the context of membrane polarization.

The relationship is illustrated in figure 4. In general the characteristic time increases with the pore length. Two regimes can clearly be separated where τmax is either controlled by the length of the narrow or the wide pore. The regimes were defined more generally by Bücker and Hördt (2013b) and named “long narrow pore (LNP)” (top left in fig. 4) and “short narrow pore (SNP)” (bottom right) regime depending on the geometrical parameters.

Figure 4: Characteristic time, colour coded vs. the length of the two pores. The radius of the large pore r1 was fixed to 500 nm, the radius of the small pore r2 was fixed to 50 nm. Figure 4 shows that by varying pore lengths, it is possible to obtain characteristic times that are usually obtained with real rocks, in the range between 0,001 s and 100s (e.g. Kruschwitz et al., 2010). However, to cover the upper end in the range around 10s, relatively long pores up to a mm seem to be necessary.

Length-to-radius ratios We now have established that small pores are required to generate a sufficient phase shift, whereas long pores generally cause large characteristic times. This implies that in order to fulfil both criteria, large ratios between pore length and pore radius will be required. In figure 5, we investigate this relationship in detail for one particular example. Note that the figure was generated by fixing L1 and r2, and varying L2 and r1, which is one possibility to cut a plane out of the 4D parameter space, but not the only way, of course. The figure shows that it is possible to obtain both large characteristic times and large phase shifts with moderate L/r ratios in the range of 10:1 (bottom left corner of the figure). This may be a particular situation, but at least the figure illustrates that large L/r ratios are not mandatory.

IP2016 – 6-8 June, Aarhus, Denmark

Figure 5: Top panel: Maximum phase shift, colour coded vs. the length-to-radius ratio of the two pores. The radius of the small pore r2 was fixed to 50 nm, and the length of the large pore L1 was fixed to 500 μm; r1 and L2 were varied to obtain the corresponding ratios. Bottom panel: same as top panel, for characteristic times.

CONCLUSIONS We have carried out a model study to illustrate which geometrical parameters are required to obtain phase shifts and relaxation times in the range typically measured with natural sandstones. We fcous on geometrical parameters and fix those describing the electrical double layer, but even then the parameter space is 4-dimensional and not trivial to explore. As general guidelines, a small (tens of nm) minimum pore radius in the range of the Debye length is required to obtain significant phase shifts. There is evidence, however, that these exist and are relevant in real rock. Relatively long pores are required if large characteristic times in the range of seconds need to be explained. Although these two conditions appear to

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Geometrical constraints for membrane polarization

require large L/r ratios, parameter combinations exist where moderate ratios around 10:1 are sufficient. Our results also show that speculations, membrane polarization might be particularly important at long characteristic time scales, which can sometimes be found in literature (e.g. Leroy and Revil, 2009) are not consistent with the conceptual model underlying the theory used here, as it coversa wide range of relaxation times. When attempting to match geometrical parameters typically found in real rock, it seems challenging to produce long time scales rather than short ones.

Hördt, Bairlein, Stebner

Bücker, M., and Hördt, A., 2013b. Long and short narrow pore models for membrane polarization: Geophysics, 78, E299-E314. Kruschwitz, S., Binley, A., Lesmes, D. and Elshenawy, A. 2010. Textural controls on low-frequency electrical spectra of porous media: Geophysics 75, WA113-WA123. Leroy, P., Revil, A., Kemna, A., Cosenza, A. and Ghorbani, A. 2008. Complex conductivity of water-saturated packs of glas beads: J. of Colloid and Interface Science 321, 103-117.

The considerations here are intended to provide a general understanding of membrane polarization. Another aim is to provide guidelines for combinining impedances in networks, to get one step further towards the description of real rock geometries (Stebner et al. 2016).

Leroy, P. & Revil, A. 2009. A mechanistic model for the spectral induced polarization of clay materials: J. Geoph. Res., 114, B10202.

ACKNOWLEDGMENTS

Stebner, H. and Hördt, A., 1016. Simulation of membrane polarization for 2D and 3D pore networks. this issue.

The work is sponsored by the German Science foundation (Project Ho1506/23-1). REFERENCES Bairlein, K., Bücker, M., Hördt, A., Hinze, B. and Nordsiek, S., 2016. Temperature dependence of spectral induced polarization data: experimental data and membrane polarization theory: Geoph. J. Int., accepted. Bücker, M., and Hördt, A., 2013a. Analytical modelling of membrane polarization with explicit parameterization of pore radii and the electrical double layer: Geoph. J. Int., doi: 10.1093/gji/ggt136.

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Marshall, D. J. and Madden T. R., 1959. Induced polarization: A study of its causes: Geophysics 24, 780-816.

Titov, K., Komarov, V. Tarasov, V. and Levitski, A. 2002. Theoretical and experimental study of time domain-induced polarization in water-saturated sands: Journal of Applied Geophysics 50, 417-433. Weller, A., Slater, L., Huismann, J.A., Esser, O., and Haegel, F.-H. 2015. On the specific polarizability of sands and sandclay mixtures: Geophysics 76, F315-F327. Weller, A., Breede, K., Slater, L. and Nordsiek, S., 2011. Effect of changing water salinity on complex conductivity spectra of sandstones: Geophysics 76, F315-F327.

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Abstracts from poster session B

New technology for delineation of resistive and polarizable kimberlite fissures using TEM method in South Africa V. Hallbauer-Zadorozhnaya Council for Geoscience 280 Pretoria Rd., Pretoria, South Africa [email protected]

SUMMARY TEM sounding have been carried out in the Limpopo province, South Africa. The aim of the research is to delineate a kimberlite fissure in some portion of diamond fields. The edge of kimberlite fissure is located at the depth about 20-25 m. Rocks composed the fissure, are quite resistive, polarizable and have low susceptibility. TEM survey had been performed along 10 profiles, all of then crosses the fissure but delineation of fissure had to be done with very high accuracy (about 2-3 meters in lateral). Using TEM FAST 48 we observed that the fissure should be seen at least twice when both sides of square loop locates above the fissure. Using instrument Tsickl 5 and horisontal magnetic dipole we obtained more stronger signals related to the fissure. This phenomenon relates to the theory of electromagnetic field proporation on ingemoginated media. Mathematical modeling of dipped/vertical S plane overlapped by horizontal S plane (both can be polarizable) for both components dBz/dt and dBy/dt have been calculated. The result shows that the preferable TEM configuration for searching quasi vertical objects is large transmitter loop and horizontal magnetic dipole. We are proud to tell that following drillings of seven boreholes opened the fissure in all proposed points. Key words: TEM, chargeability, resistivity, kimberlite fissure, modelling.

INTRODUCTION The aim of the research is to delineate a kimberlite fissure in Mokopane site, Limpopo province, South Africa. This fissure is very long and extends for more than 100 km. However the thickness of the fissure is very narrow (about 3 – 7 m) and edge depth of fissure is 20-30 m. Most of the fissures in South Africa are quite resistive (about 100 Ohmm) and surrounded by host rocks (dolerites and granites) with very high resistivity (between 500-1000 Ohmm and more). Laboratory measurements showed that polarization of fresh kimberlites are high. Susceptibility of many South African fissures is quite low and methods of magnetometry are not enough effective. Many electrical and electromagnetic methods have been used in the Mokopane sites. Results did not satisfy the client and it creates the preconditions for using TEM for seach of kimberlite fisssure.

METHOD AND RESULTS IP2016 – 6-8 June, Aarhus, Denmark

1

The time-domain EM method has been used in investigated area. The instrument TEM-FAST 48 has been used. This instrument iincludes a generator of uni-polar rectangular pulses (transmitter or Tx), a measuring block that provides the registration of the signals (receiver or Rx), a control block (controller), a power supply (battery). All devices are assembled in a single case. Portative PC serves for selection of parameters and registration of the signals and its visualization. A complete set include instrument, antennas (cables), battery and PC, fits in such small case and weights 5 kg is presented in the figure 1.

Figure 1. TEMFAST-48 Usually, the primary pulses EM field is generated by a transmitter loop. In TEM-FAST 48 the transmitter loop is also utilized as a receiver loop. There are some advantage and disadvantage using TEM-FAST 48. Portability, excellent software written especially for TEM-Fast 48 instrument data is allowing interprete signals distorted by induced polarization and superparamagnetic effects (SPME). However due to using coaxial loops namely SPME presents nearly in all TEM signals significantly complicating interpretation TEM survey has been carried out along the ten profiles with spacing 5 m. Size of transmitter/receiver loop was 25 x 25 m. Each profile crosses the fissure. The interpretation has been curried out using the software TEM RESEARCHER (www.aemr.net). As example the fissure observed in the profile 5 is very clear identified in the (stations #20 and #25.) We have to note that the coordinates of TEM station had been taking at the left Usually 2 or 3 layers or rocks are deliniated in each section. There are are soil, high weatherd and less weatherd granites and dolerites (diabases) and underlayed by a non-weathered rocks (basdement). Resistivity

V. Hallbauer-Zadorozhnaya

and chargeability of all three layers along the profile 5 is shown the figures 3 and 4. Resistivities of the overboden decreases better indicate to pesence of a fissure. Owever the chargeability of rocks relating to weatherd fissure considerably increases approching to the fissure. However the resistivity undelayered halfspace is much low (130-150 Ohmm) and obcerved twice along the profile (# 20 and # 25) it meand exactly 25 m, length of square loop size (Figuire 2). Chargeability of portion of the section benith the soil string indicated to presence of an inhomoginatiy (again obcerved twice.) (Figure 4). We are proud that following drilling of all 7 boreholes in different profiles crossing the fissure were completely proved our prediction.

less. Than I decided that instead of moving transmitter/ receiver loop every 5 m I can use a large transmitter loop (as example 50 x 50 m) and portable mobile sensor. More over, the portable receiver loop can be turned in the space and records two and three components of electromagnetic field: dBz/dt, dBy/dt and dBz/dt. For experiment the instrument Tsicl 5 manufactured by ELTA-Geo. Ltd, Novosibirsk, Russia has been used. Specification parameters of this instrument are similar as modern TEM instruments manufacturing in the world. Receiver loop with size 80 x 80 cm is shown in the figure 5. This loop was moving along the profile with separation 1 m. Recording time of one stacked signal is about 1 second for one component. Than 30 m of profile (usually with length of +/- 100 m can be recorder in 5 minutes.

P r o f ile 5

R e s is tiv ity , O h m m

400

300

Fissure

200

100

0 5

10

15

20

25

T E M n u m b e rs S o il, 1 .5 - 2 .2 m

Figure 5. Receiver loop used with Tsickl 5. Author Dr. Zakharkin A.K.

S e c o n d la y e r T h ir d la y e r

Figure 3. Resistivity of soil, weathered (secondary layer) and fresh (third layer) rocks. P r o f ile 5 1 .0

0 .6

Signal dBz/dt at 0.0686 s 16

0 .4

14 0 .2

0 .0 5

10

15

20

25

T E M n u m b e rs F is s u r e

Figure 4. Chargeability of soil, weathered (secondary layer) and fresh (third layer/half space) rocks.

Amplitude V/A

C h a r g e a b ility

0 .8

As we know that the kimberlite fissures in South Africa are mostly vertical. It means for its delineation the best components is dBy/dt (we accept that the dike orients on x direction). It is known that the dBy/dt does not exist in the horizontal uniform media whereas this component of EM field always present in inhomogeneous media. Thus if horizontal magnetic dipole (HMD, vertically positioned loop) is orientated in the same direction as the vertical fissure we can expected an anomaly signals.

12 10 8 6 4

Fissure

2 0 0

In spite of success with results obtained using TEM FAST 48 with coaxial loop we realized that time of field work is considerably increasing if step between stations is 5 m and IP2016 – 6-8 June, Aarhus, Denmark

10

20

30

Distance, m

2

V. Hallbauer-Zadorozhnaya

Figure 6. dBz/dt signals at the time 0.086 s. Part of the profile 7.

Amplitude, V/A

Signals dBy/dt at 0.069 s 10 9 8 7 6 5 4 3 2 1 0

more complicated: overlayed S plane is to be added as well as polarization components. All mentioned above models contained dBz/dt only. However we have to make our model even more complicated: we rotating the S plane S 1 at arbitrary angle α (keeping S2=0): it is our desired model. Calculations for both components have been done and show that using the HMD is more effective for searching for quasi vertical polarizable and relatively high resistive objects.

Fissure 0

10

20

30

Distance, m Figure 7. dBy/dt signals at the time 0.069 s. Part of the profile 7 Comparison of obtained data shows that the dBy/dt amplitude much larger than traditionally measured dBz/dt (Figures 6 and 7). Drilling was carried out within the identified anomalies in the fissure was opened at a depth of about 25 m. Eventually the fissure has been traced along the profile (Figure 8). To reinforce our success, we decided to conduct mathematical modelling of different EM components arising in the dipped/ vertical dyke overlapped by soil and thin layers of weathered rocks. Roughly the section consists of two thin layers which can be regarded as S planes. The first person who describes “the flowing S plane” was W.R. Smythe (1950). He showed that vector-potential of S plane can be written as an integral: t  A    f 0 t

  r ,  , 

z 

2

,S,t  

S

 d  , 

(1 )

where r and  are polar coordinates, S is conductivity of S plane,  is magnetic permeability, t is a time. The advantage of using S planes models is relatively simplicity of mathematical solutions and construction of numerical algorithms. A solution for induction part of process can be presented in analytical forms. Conductivity of polarization S plane can be given as:

S (t )   S 0

where

S0

 exp



1  

  t



 , 

(2)

is conductivity of non-polarized S plane, η is it

chargeability and τ is decay constant. The problem is slowed sing the method of successive approximation (Zadorozhnaya and Lepyoshkin, 1998) and induction and polarization terms of EM field can be calculated and analyzed separately. The initial model is shown in the figure 9. It consists of two connected S planes with conductivity S1 and S2. In special case S2 can be equal to zero (model contains half-S plane only). Than we have added to our calculation a polarization term. Further model becomes IP2016 – 6-8 June, Aarhus, Denmark

Figure 9. Initial model containing two contacted S planes (S1 and S2) and imaginary sources J 0' , J 1' , J 2' .

CONCLUSIONS TEM sounding have been carried out in the Limpopo province, South Africa. The aim of the research is to delineate a kimberlite fissure in some portion of diamond fields. The edge of kimberlite fissure is located at the depth about 20-25 m. Rocks composed the fissure, are quite resistive, polarizable and have low susceptibility. TEM survey had been performed along 10 profiles, all of then crosses the fissure but delineation of fissure had to be done with very high accuracy (about 2-3 meters in lateral). Using TEM FAST 48 we observed that the fissure should be seen at least twice when both sides of square loop locates above the fissure. Using instrument Tsickl 5 and horisontal magnetic dipole we obtained more stronger signals related to the fissure. This phenomenon relates to the theory of electromagnetic field proporation on ingemoginated media. Mathematical modeling of dipped/vertical S plane overlapped by horizontal S plane (both can be polarizable) for both components dBz/dt and dBy/dt have been calculated. The result shows that the preferable TEM configuration for searching quasi vertical objects is large transmitter lop and horizontal magnetic dipole. We are proud to tell that following drillings of seven boreholes opened the fissure in all proposed points.

ACKNOWLEDGMENTS The author acknowledges Dr. Leonie Maré for her contribution of study physical properties of rocks and staff of Vutomi Diamond Fields (Pty) .Ltd for helping me with field work which eventually became the trigger for developing both a new technology for searching for kimberlite fissures and mathematical consideration of this geoelectrical problem. REFERENCES Smythe W.R., 1950. Static and Dynamic Electrisity. McGrawHill Book Company In.

3

V. Hallbauer-Zadorozhnaya

Zadorozhnaya V.Yu., and Lepyoshkin V.P., 1998. Induced Polarization Effect on the Inductive Sounding of Multilayered Sections: Izvestiya Physics of the Solid Earth, 34, 4, 314-320.

Figure 2 Resistivity along the profile 5. Recommend drilling at the station #25. Depth of the anomalies is about 20-22 m. m. Very strong signals are recorded. The black arrow indicates a “fouls anomaly” and white arrow indicates proposed location of the fissure.

Figure 5. Delineated fissure in diamond fields area. Green squares indicate the TEM loops locations, purple squares indicates points where anomaly had been recorded (twice or more along each profile). Black lines indicate a proposed location of the fissure using TEM data.

IP2016 – 6-8 June, Aarhus, Denmark

4

Different kinds of IP effects and laboratory measurements samples V. Hallbauer-Zadorozhnaya

G Santarato

L. Maré

Consulting Box 1153 Silverton 0127v Pretoria South Africa [email protected]

University of Ferrara Via Saragat, 1, Ferrara FE, Italys [email protected]

Council for Geoscience 280 Pretoria Rd, Pretoria, South Africas [email protected]

SUMMARY Several kinds of Induced Polarization (IP) effects occur and will be reviewed in the present paper, namely electrosmosis effect, membrane polarization, MaxwellWagner effect and electrolytical polarization. All effects are based on different physical phenomena. The electrosmosis processes occur in all rocks/sediments. However the amount of double electric layer plays the major role. This phenomenon is described by HelmholtzSmoluhowsky equation and is linear. Decay constant of electrosmosis process is usually in range 10-6-10-2 s and can be mostly observed on Transient Electro-Magnetic (TEM) signals. The membrane polarization is based on constrictivity of pore. When an electrical current flows through rocks containing channels and pores with different sizes, an excess/loss of ions accumulates at the boundaries. The homogeneous diffusion equation, with specified (nonlinear) boundary conditions, has been used for solving this problem. This type of polarization is non-linear, depends on applied current and may depend on current pulse length (in TEM method). Duration of membrane polarization can reach 10 s and more. Maxwell-Wagner model consists of isolated pores. The homogeneous diffusion equation also has been used for solving the problem of ions distribution in the pores. However the boundary conditions are linear. The ions move in the pores with constant velocity and accumulated the neighbour of the pore ends. Duration of process of redistribution is comparable with duration of the electro osmosis process. The pores with unallocated ions may be represented by an equivalent electrical circuit (a capacitor). The Cole-Cole or capacitor discharging formula can be used to describe the effect. Numerous laboratory measurements of different types of rocks and minerals and some field TEM data demonstrate different kinds of IP effects. Key words: electroosmosis polarization, membrane polarization, Maxwell-Wagner effect, sample

INTRODUCTION It was shown that there are several types of Induced Polarization effect which affect electrical and electromagnetic data. There are named are electrosmosis effect, membrane polarization, Maxwell-Wagner effect and electrolytical polarization. All effects are based on different physical phenomena.-what is why the study and interpretation of the signals distorted by IP effects cannot be treated with the same

IP2016 – 6-8 June, Aarhus, Denmark

1

yardstick. Traditional use of the Cole-Cole formula no longer satisfies the requirements of exploration geophysics especially for membrane IP effect. This work is the summary of research conducted by the authors in the last ten years. We solved mathematical problems for electrosmosis and membrane polarization and Maxwell-Wagner effect using equations with specified boundary conditions. Numerous samples have been measured to study these different kinds of IP effects. The aim of this research is to show different mechanisms of IP effect, and their influence on the results of laboratory and field measurements.

DIFFERENT KINDS OF INDUCED POLARIZATION EFFECTS The electroosmosis (EO) phenomenon is based on HelmholtzSmoluhowsky equation. The EO polarization arises as a result of the transport of the electrolyte through the sediments when a gradient in the electrical field is applied. This will move some of the cations from the diffusion part of the electrical double layer (DEL) into free solution, (relative to the solid medium). An electric field is generated which in its turn produces a gradient of fluid pressure. After the field returns to zero (time-off) that pressure gradient moves the pore fluid in the opposite direction, and this process generates an electroosmosis potential. It was shown (Hallbauer-Zadorozhnaya and Stettler, 2006) that the chargeability of electrosmosis effect η is the ration of the surplus electrical conductance of DEL to the conductance of pore fluid. Decay constant τ depends on pore radii (in square). The decay constant of electrosmosis is in the range 10-6-10-2 s. It means that the EO effect mostly affected TEM signals. However EO effect could be observed at frequency 100th kHz-1MHz (Kamenetsky and Hallbauer-Zadorozhnaya, 2002). This type of polarization is linear and arises if electrical current or voltage is applied. Membrane polarization is based on constrictivity of pores. It was shown (Marshall and Madden, 1959) that when electrical current flows through a rocks containing channels and pores with different radii (transfer numbers), an excess/loss of ions accumulates at the boundaries. The basic theory of this effect is as follows. If a pore space contains many parallel and negatively charged capillaries then the counter ions will be cations and ions will be anions. The cations moving to the cathode will pass the boundary between narrow and large capillary, enter at the anode side of large capillary and move further. It was shown (Kobranova, 1986) that if the surface areas of a large pore I and narrow capillary II are different then transfer numbers of cations and anions in pore and capillary are different: in narrow pores they are larger than in large pores .

 m k  m I k  m II

 m a  m I a  m II

k

a



q Fz



( n II

(1 )

k

q Fz

 n I k )  0,

k

( n II

a

 n I a )  0,

(2)

no difference. (Hallbauer-Zadorozhnaya and Maré, 2012). We improved our measuring technique using both electrical current and voltage as sources. This allows us to calculate the “real resistivity”, i.e. resistivity free of IP effect.

A

m k  m a ,

where ∆m is a difference mass of cations and anions which enter into the volume ∆V in large pore close to the border with a narrow capillary and left this volume in the other side of pore, q is the amount of charge (in Coulomb) that passes through the boundary II - I, F is the Faraday constant, zk is the valence of cations, nIIk and nIk are transfer numbers in narrow capillary and large pore. Subscripts k and a indicate the cations and anions, respectively. The equations (1) and (2) show that at the boundary II and I, the salinity of cations and anions increases, while at in the boundary I and II the salinity of cations and anions decreases (i.e. it depends on sense; Kobranova, 1986). It means that at the boundary of pores with different radii a concentration difference occurs, that cannot be represented by electrical diagrams (each pore as a capacitor). Hence salinity distribution agrees with the diffusion process: this problem must be regarded as a homogeneous diffusion equation with specified specific initial and boundary conditions. In this case the boundary conditions are non-linear (Hallbauer-Zadorozhnaya and Maré, 2012).

Figure 1. Holder containing a sample of rock and silicone electrodes. The claystone, graphitic black schists as well as sandstone samples demonstrate the presence of membrane polarization: decay signals, resistivity and chargeability strongly depends on applied electrical current and voltage (Figures 2 and 3). C 1 4 3 0 5 C la y s to n e , g r a p h y tic b la c k s c h is ts 1000 C u rre n t

The model of electrolytic (electrode) polarization is well known and has been described many times since at least 60th of past century (as an example: Keller and Frischknecht, 1966). This model describes metal particles blocking pore channels. Most researchers present this model as an universal model of IP, which is not correct.

R e s is tiv ity , O h m - m

V o lta g e

Maxwell-Wagner effect model consists of isolated pores. The homogeneous diffusion equation also has been used for solving the problem of ions distribution in the pores. However the boundary conditions are linear. It was shown that the ions move in the pores with constant velocity and accumulated at vicinity of the pore ends. The thickness of the layer containing ions is about 1-3 molecules. Time of the ions distribution in pores is in the range from microseconds to several milliseconds. It means that the decay constant will compares with the decay constant of IP electrosmosis process. The pores with unallocated ions may be represented by an equivalent electrical circuit (a capacitor). The Cole-Cole or capacitor discharging formula can be used.

100

10 1 e -7

1 e -6

1 e -5

1 e -4

1 e -3

C u r r e n t, A

Figure 2. Resistivity of claystone, graphitic schists vs electrical current. C 1 4 3 0 5 C la y s to n e , g r a p h y tic b la c k s c h is ts 0 .7 C u rre n t 0 .6

V o lta g e

LABORATORY MEASUREMENTS AND FIELD DATA The rock samples have been collected along several profiles in Rwanda where Council for Geoscience of South Africa (CGS) carried out several geophysical surveys. Measurements of physical properties have been carried out in the laboratory at CGS. The instrument used was GDD Core IP tester (Canada). The sample holder is shown (Figure 1). The sample of rock is located between the electrodes. At time-on both electrodes serve as transmitter electrodes, at time-off – as receiver electrodes. Conductive silicon electrodes were used instead of traditional saline sponges, gels or electrolytic fluids. The electrodes were carefully tested and comparison with copper electrodes shows

C h a r g e a b ility

0 .5 0 .4 0 .3 0 .2 0 .1 0 .0

1 e -7

1 e -6

1 e -5

1 e -4

1 e -3

C u r r e n t, A

Figure 3. Chargeability of claystone, graphitic schists vs electrical current. The same we can tell about non-conductive hematite vein

(Figure 4 and 5).

C 1 4 3 0 2 F e r r ig e n o u s v e in

C 1 4 3 0 1 3 H e a m a tite v e in C u rre n t 0 .6

10000

V o lta g e

C h a r g e a b ility

C u rre n t

R e s is tiv ity , O h m - m

V o lta g e

1000

0 .4

0 .2

100

0 .0 1 e -7

1 e -6

10

1 e -5

1 e -4

C u r r e n t, A

1 e -7

1 e -6

1 e -5

1 e -4

1 e -3

C u r r e n t, A

Figure 7. Chargeability of ferrigenous vein vs current.

Figure 4. Resistivity of hematite vein vs current.

The small IP effect of vein ores was registered quite often and indicates that the rare inclusion of conductive pores cannot produce significant IP effect. Only if ore grains will be grind in dust, then the IP effect will be observed (M. Chouteau, private conversations).

C 1 4 3 0 1 3 H e a m a tite v e in C u rre n t

C h a r g e a b ility

0 .6

V o lta g e

Another two more figures (8 and 9) present resistivity and chargeability of a quartz vein with very few hematite/tungstein mineralization.

0 .4

C 1 4 3 0 6 Q u a r tz v e in w ith v e r y f e w h e a m a titic /tu n g s te in m in e r a liz a tio n

0 .2

10000 C u rre n t

0 .0

V o lta g e

1 e -6

1 e -5

1 e -4

R e s is tiv ity , O h m - m

1 e -7

1 e -3

C u r r e n t, A

Figure 5. Chargeability of hematite vein vs current. Some part of collected samples contains metal particles. In the figures 6 and 7 we clearly see that the resistivity of these rocks does not change vs. current. The different behaviour of different rock samples further proves the reliability and efficiency to use two-electrodes holder.

1000 1 e -7

1 e -6

1 e -5

C u r r e n t, A

Figure 8. Resistivity of quartz vein with very few hematite/tungstein mineralization vs current.

C 1 4 3 0 2 F e r r ig e n o u s v e in 10000 C u rre n t

C 1 4 3 0 6 Q u a r tz v e in w ith v e r y f e w h e a m a titic /tu n g s te in m in e r a liz a tio n

1000

0 .6

C h a r g e a b ility

R e s is tiv ity , O h m - m

V o lta g e

100 1 e -7

1 e -6

1 e -5

1 e -4

0 .4

0 .2

C u r r e n t, A

C u rre n t

Figure 6. Resistivity of ferrigenous vein vs current

V o lta g e 0 .0

The measurements demonstrate the high resistivity (about 1000 -1100 Ohmm) and quite low chargeability (about 0.1). It means that these rocks contain very narrow capillaries through which current flows, i.e. a practical absence of pores with radii larger than radii of capillary.

1 e -7

.

1 e -6

1 e -5

1 e -4

C u r r e n t, A

Figure 9. Chargeability of quartz vein with very few hematite/tungstein mineralization vs current.

Resistivities obtained by applied current and voltage are different. It is definitely against Ohm’s law. We propose that the difference can be explained by presence of MaxwellWagner effect occurring only in isolated pores. When the current flows through the pores and capillaries the resistivity of the sample is much lower than if voltage is applied and the membrane effect occurs. This case the Maxwell-Wagner effect cannot be observed (Fig. 8). However when voltage is applied, then positive and negative ions concentrated close to the opposite charged electrodes. Chargeability due to membrane (current) and MaxwellWagner (voltage) are completely different Combinations of IP effect. In 2012 Prof. G. Santarato and Dr. N. Abu-Zeid (University of Ferrara, Italy) and Dr. M. Goldman (the Geophysical Institute of Israel) simultaneously recorded a new type of TEM signals. The relaxation curves were affected by the typical IP distortion, but their shape depends on current pulse length. To our knowledge, nobody reported similar data or even discussed this specific anomalous behaviour, so that it can be considered as a “new” phenomenon, to be related to non-linearity of the IP effects. We supposed that there are two overlapping IP effects: electroosmosis and membrane (Hallbauer-Zadorozhnaya et al., 2015). The algorithm for interpretation has been developed and visualization of interpretation using one geological model for all used frequencies is presented in the Figure 10.

The membrane polarization is based on constrictivity of pores. When electrical current flows through a rocks containing channels and pores with different size an excess/loss of ions accumulates at the boundaries. The homogeneous diffusion equation with specific (non-linear) boundary condition has been used for solving this problem. This type of polarization is non-linear, depends on applied current and may depend on current pulse length (in TEM method). Duration of the membrane polarization can reach 10 s. The Maxwell-Wagner effect model consists of isolated pores. The homogeneous diffusion equation also has been used for solving the problem of ions distribution in the pores. However the boundary conditions are linear. The ions move in the pores with constant velocity and accumulate at vicinity of the pore ends. Duration of process of redistribution is comparable with duration of the electrosmosis process. The pores with unallocated ions may be represented by an equivalent electrical circuit (a capacitor). The Cole-Cole or capacitor discharging formula can be used. Numerous laboratory measurements of different types of rocks and minerals and some field TEM data demonstrate different kinds of IP effects. ACKNOWLEDGMENTS The authors acknowledge the staff of Beak (Pty).Ltd (Germany) for helping us with field work and collection the samples. The authors also acknowledge Dr. N. Abu Zeid and Dr. S. Bignardi (both from University of Ferrara, Italy) for their contribution to study the complex IP effects occurring on the TEM soundings collected at a site in Italy. REFERENCES Hallbauer-Zadorozhnaya V., Santarato G. and Abu Zeid N., 2015, Non-linear behaviour of electrical parameters in porous,water-saturated rocks: a model to predict pore size distribution. Geophysical Journal International., 202, 2, 883897. Hallbauer-Zadorozhnaya,V and Stettler, E.H., 2006, The detection of hydrocarbon contaminated of groundwater by using the IP effect in TDEM soundings: South African Journal of Geology. 109, 4, 529-540.

Figure 10. Data and best-fitting 1D model of TEM 3. CONCLUSIONS Several kinds of effects have been the subjects of this work, namely electrosmosis effect, membrane polarization, MaxwellWagner effect and electrolytical polarization. All effects are based on different physical phenomena. The electrosmosis processes occur in all rocks/sediments. However the amount of double electric layer plays the major role. This phenomenon is linear and described by Helmholtz-Smoluhowsky equation. Decay constant τ of electrosmosis process is usually in range 10-6-10-2 and can be mostly observed on TEM signals.

Kamenetsky F.M., Hallbauer-Zadorozhnaya V.Yu and, Schmidbauer E., 2002, Laboratory measurements of frequency dispersion of sedimentary rocks electric properties as applied to ground water hydrocarbon contamination: The 16th Workshop on Electromagnetic Induction in the Earth, SantaFe, USA, Abstract, EM1-2. Keller G.V. and Frischknecht F.C., 1966, Electrical Methods in Geophysicsl Prospecting: Pergamon Press. Kobranova V.N., 1986, Petrophysics, Handbook: Nedra. Moscow (in Russian) Marshal, D.J., and Madden, T.R., 1959, Induced Polarization, a Study of its cases: Geophysics, 24, 4, 790-816..

Relationship between Cole-Cole model parameters and spectral decomposition parameters derived from SIP data Maximilian Weigand

Andreas Kemna

Department of Geophysics Steinmann Institute Meckenheimer Allee 176 53115 Bonn, Germany [email protected]

Department of Geophysics Steinmann Institute Meckenheimer Allee 176 53115 Bonn, Germany [email protected]

SUMMARY Spectral induced polarization (SIP) signatures are analyzed using different phenomenological model descriptions. One approach uses the Cole-Cole (CC) model, or variants of it, to describe one or several distinct polarization peaks. The other approach yields a relaxation time distribution (RTD) by using a decomposition procedure which describes SIP data by a superposition of a large number of polarization terms. Based on this RTD, integral spectral parameters similar to CC model parameters can be derived. We here compare chargeability and relaxation time parameters, obtained with Debye and Warburg decomposition approaches, with the original CC parameters used to generate synthetic SIP data. Understanding the relationship between CC decomposition parameters helps to prevent interpretation errors when results from both approaches are combined. We identified potential underestimations of the CC chargeability by up to 80% and deviations of 𝜏𝑚𝑒𝑎𝑛 from the CC relaxation time by up to three orders of magnitude. These results highlight the importance of consistent SIP data analysis procedures. Key words: SIP; Debye decomposition; Cole-Cole model

INTRODUCTION

where Cole-Cole model parameters are estimated by means of decomposition approaches. We here present results from numerical studies in which the Cole-Cole model was used to generate single-peak SIP signatures, which were subsequently analyzed with different decomposition schemes. Obtained chargeability and relaxation time estimates were assessed in dependence of the input Cole-Cole relaxation time and the input dispersion parameter.

METHOD AND RESULTS Spectral complex resistivity signatures, 𝜌̂(𝜔), were created with the Cole-Cole model 𝜌̂(𝜔) = 𝜌0 [1 − 𝑚 (1 −

1 1+(𝑗 𝜔𝜏)𝑐

with ω the angular frequency, 𝜌0 the low-frequency resistivity, m the chargeability, j the imaginary unit, τ the relaxation time, and c the frequency dispersion parameter. The relaxation time was varied between 1.59 ⋅ 10−5s and 159.15 s and the parameter c between 0.05 and 1.0. Relaxation time limits were computed using the inverse relationship to the position of the frequency peak of 𝜌′′: 𝜏=

1 2 𝜋𝑓𝑚𝑎𝑥

(1)

.

Subsequently, the Cole-Cole model based signatures were analyzed with a Cole-Cole decomposition scheme, in which the Cole-Cole model was used as the kernel function: 𝑁

The Cole-Cole model is commonly used to analyze the characteristics of SIP data. Recently, decomposition approaches, which describe a given SIP signature by a superposition of a large number of polarization terms (e.g., Lesmes and Morgan, 2001; Nordsiek and Weller, 2008; Weigand and Kemna, 2016), have been widely adopted. These polarization terms are Cole-Cole terms with fixed relaxation time and frequency dispersion. While relaxation times are distributed over a large time bandwidth (inversely related to the data frequency domain), the frequency dispersion is kept fixed for a given decomposition. Notable instances are the Debye and the Warburg decompositions (e.g., Florsch et al., 2014). In light of the large number of phenomenological models used to describe SIP signatures, there is a common trend to merge results of different studies to improve data coverage of certain relationships or processes and thus improve the interpretation of SIP data. Even though uncertainties of various analysis approaches have been examined and quantified (e.g., Ghorbani et al., 2007; Keery et al., 2012), we are not aware of any studies investigating possible interpretation errors in the case IP2016 – 6-8 June, Aarhus, Denmark

1

)],

𝜌̂(𝜔) = 𝜌𝐶𝐶𝐷,0 [1 − ∑ 𝑚𝑘 (1 − 𝑘=1

1 )], 1 + (𝑗 𝜔𝜏𝑘 )𝑐̃

with 𝜌𝐶𝐶𝐷,0 the low-frequency resistivity, N the number of considered relaxation times, and 𝑚𝑘 the relative weight corresponding to the k-th relaxation time 𝜏𝑘 . The parameter 𝑐̃ is kept fixed and controls the frequency dispersion. We refer to this decomposition as Cole-Cole decomposition (CCD), which includes all choices of 𝑐̃ . The distribution of relative weights 𝑚𝑘 (𝜏𝑘 ) is called the relaxation time distribution (RTD), based on which the following parameters are calculated: -

The parameter 𝑚𝑡𝑜𝑡 = ∑𝑖 𝑚𝑖 sums up the chargeabilities of the polarization terms and serves as a proxy for the total polarization reflected by the SIP signature (e.g., Nordsiek and Weller, 2008).

Fidelity of spectral decomposition parameters

-

The

mean

relaxation

∑𝑁 𝑘=1 𝑚𝑘 log(𝜏𝑘 )

𝑒𝑥𝑝 (

∑𝑁 𝑘=1 𝑚𝑘

time

Weigand and Kemna

𝜏𝑚𝑒𝑎𝑛 =

) is the chargeability-weighted

logarithmic mean value of the RTD (e.g., Nordsiek and Weller, 2008).

Results

the CCD scheme has only limited coverage in these regions. Correspondingly, if CC signatures with small c values are analyzed with CCD schemes with 𝑐̃ ≥ 𝑐, chargeability will be underestimated because of missing polarization contributions outside the data frequency range. Similarly, the CC parameter τ is determined solely by the polarization peak, whereas the CCD parameter 𝜏𝑚𝑒𝑎𝑛 is computed from the RTD by averaging. This causes large estimation errors if τ is close to the relaxation time limits.

CONCLUSIONS In this study spectral parameters, as recovered from a decomposition using different kernel functions, were compared to the original Cole-Cole parameters used to generate synthetic signatures. Chargeability is underestimated by up to 80% and relaxation time differs by up to three orders of magnitude, depending on the relaxation time and frequency dispersion. These results highlight the importance of a consistent SIP data analysis procedure, especially if results from different studies are to be quantitatively compared. Figure 1. Deviation of CCD-derived 𝒎𝒕𝒐𝒕 from original CC m. Different CC kernels with 𝒄̃ = 1.0, 0.5 and 0.3 were used. Signatures were generated with 𝒎 = 𝟎. 𝟓. The CCD derived total polarization parameter 𝑚𝑡𝑜𝑡 increasingly underestimates the original CC based m parameter with decreasing c value and with τ approaching the relaxation time limits (Fig. 1). This behavior can be observed for different CC kernels and is compressed within the range 𝑐 ≤ 𝑐̃ .

ACKNOWLEDGMENTS Part of this work was conducted in the framework of the SFB TR32 ''Patterns in soil-vegetation-atmosphere systems: monitoring, modelling and data assimilation'' funded by the Deutsche Forschungsgemeinschaft (DFG). REFERENCES Florsch, N., Revil, A., & Camerlynck, C., 2014. Inversion of generalized relaxation time distributions with optimized damping parameter, Journal of Applied Geophysics, 109, 119– 132, doi:10.1016/j.jappgeo.2014.07.013. Keery, J., Binley, A., Elshenawy, A., & Clifford, J., 2012. Markov-chain monte carlo estimation of distributed Debye relaxations in spectral induced polarization, Geophysics, 77(2), E159–E170.

Figure 2. Deviation (log10) of 𝝉𝒎𝒆𝒂𝒏 from original CC τ. Different CC kernels with 𝒄̃ = 𝟏. 𝟎, 𝟎. 𝟓 𝐚𝐧𝐝 𝟎. 𝟑 were used. Signatures were generated with 𝒎 = 𝟎. 𝟓. The deviation between input and recovered relaxation time shows a similar pattern as observed for the chargeability. Deviations of up to three orders of magnitude exist for decreasing c value and τ approaching the relaxation time limits (Fig. 2).

Lesmes, D. & Morgan, F., 2001. Dielectric spectroscopy of sedimentary rocks, Journal of Geophysical Research, 106(B7), 13329–13346. Nordsiek, S. & Weller, A., 2008. A new approach to fitting induced-polarization spectra, Geophysics, 73(6), F235–F245, doi:10.1190/1.2987412. Weigand, M. & Kemna, A., 2016. Debye decomposition of time-lapse spectral induced polarisation data, Computers and Geosciences, pp. 34–45, doi:10.1016/j.cageo.2015.09.021.

DISCUSSION Obtained estimates of the CC parameters m and τ in form of the CCD decomposition parameters 𝑚𝑡𝑜𝑡 and 𝜏𝑚𝑒𝑎𝑛 can be explained by the nature of the decomposition, which is limited to the relaxation time range defined by the data frequency range. While the CC model describes the full frequency domain, including frequencies outside the data frequency range,

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Temperature dependence of complex surface conductivity Katharina Bairlein

Andreas Hördt

Institute of Geophysics and extraterrestrial Physics TU Braunschweig Mendelssohnstr. 3 38106 Braunschweig [email protected]

Institute of Geophysics and extraterrestrial Physics TU Braunschweig Mendelssohnstr. 3 38106 Braunschweig [email protected]

SUMMARY The complex electrical conductivity of water-saturated rocks, measured with induced polarization (IP), is affected by temperature. The main reason for the temperature dependence of fluid conductivity is that the mobility of the ions in the pore fluid is increased with temperature. In addition to the fluid conductivity, surface conductivity is influenced by temperature, but it is not investigated yet, which parameters of the rock surface and the fluid are the dominating factors. We measured the complex electrical conductivity of a sandstone sample at temperatures between 0 and 40 °C and ion concentrations from 1 to 2000 mol/m3. From measurements at high salinities, we are able to separate surface conductivity from the real part of bulk conductivity and to determine its dependence both on temperature and salinity. The experimental results are compared to calculations of a membrane polarization model. We use a Walden exponent as a measure of the strength of the temperature dependence. The Walden exponent of the real part of surface conductivity increases, while the Walden exponent of the imaginary part slightly decreases with increasing salinity. Calculations with the model predict a decrease in both the temperature dependence of the real and imaginary part of conductivity. The measured and calculated surface conductivities show, that temperature dependence in the electrical double layer cannot be attributed to an ion mobility similar to the mobility in the free electrolyte. Key words: temperature; surface conductivity; ion concentration; membrane polarization

INTRODUCTION For spectral induced polarization (SIP) measurements at the field scale, temperature cannot be controlled as in the laboratory. Near-surface temperatures show seasonal variations, which can cause deviations in the prediction of petrophysical or hydrological parameters from complex conductivity, if the influence of temperature is neglected. As hydraulic conductivity can be estimated from IP data in the field (e.g. Börner et al. 1996, Hördt et al. 2007), SIP is also suitable for the exploration of geothermal sites, where temperature may differ several tens of degrees celsius from typical laboratory or near-surface temperatures. Temperature dependence of fluid conductivity has been widely investigated in the past (e.g. Sorensen and Glass 1987, Sen and Goode 1992, Hayley et al. 2007). For surface conductivity only few studies exist, showing that temperature dependence of the IP2016 – 6-8 June, Aarhus, Denmark

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real part of surface conductivity of shaly sandstones is different from that of fluid conductivity (Revil et al. 1998, Hayley et al. 2007). For sandstones, the increase of the imaginary part of conductivity at 1 Hz is similar to that of the real part (Binley et al., 2010), but the increase depends on the frequency (Zisser et al. 2010). Mechanistic models can help to understand the processes occurring in the pore space that are related to temperature. To examine, whether the membrane polarization model accurately describes the temperature dependence of the polarization processes, model results have to be compared to SIPmeasurements.

THEORY Electrical conductivity is strongly influenced by temperature. For a non-conducting rock matrix saturated with an electrolyte, the conductivity consists of an electrolytic part, which depends on the fluid conductivity σf and the geometry of the pore space, described by the formation factor F, and the real and imaginary part of surface conductivity σs:

𝜎=

1 𝜎 + 𝜎′𝑠 + 𝜎′′𝑠 𝐹 𝑓

(1)

The temperature dependence of an electrolyte is well-known and is controlled mainly by the mobility of the ions solved in the water. The ion mobility at a certain temperature µ(T) can be described by the semi-empirical modified Walden product (Sorensen and Glass, 1987)

𝜂(𝑇0 ) 𝛼 𝜇(𝑇) = 𝜇(𝑇0 ) ( ) 𝜂(𝑇)

(2)

with the dynamic viscosity η, the temperature T, a reference temperature T0, and the Walden exponent α. The Walden exponents depend on salinity, pH and type of ions. At low salinities the Walden exponents of Na+- and Cl--Ions are 0.94 and 0.89, respectively (Sorensen and Glass, 1987). Assuming that surface conductivity can be neglected, the temperature dependence of the real part of conductivity can be described by the ion mobility

𝜂(𝑇0 ) 𝛼 𝜎(𝑇) = 𝜎(𝑇0 ) ( ) 𝜂(𝑇)

(3)

Surface conductivity also increases with temperature. Both stronger and weaker temperature dependencies than that of fluid conductivity have been reported (Revil et al. 1998, Hayley et al. 2007).

Abbreviated title Author3

MEASUREMENTS AND RESULTS For the SIP measurements we used a Bunter sandstone sample with a porosity of 0.10, fully saturated with sodium chloride (NaCl) solution of varying ion concentration and pH of approximately 7. For changing the salinity of the saturating fluid, the saturated sample was put into a small container with the fluid of the new ion concentration c0, starting at small ion concentrations and increasing c0. We waited for at least one week for the fluid in the pores to equilibrate. Temperature was varied from 0 °C to 40 °C in steps of 5 °C. The formation factor F was determined from the real part of the conductivity at ion concentrations of 500, 1000, and 2000 mol/m3 and the fluid conductivity at each of these concentrations, assuming that surface conductivity can be neglected. The mean formation factor from the three conductivities is F = 20.0 with a standard deviation of 4.3. The real part of surface conductivity was calculated from the real part of conductivity, the formation factor and the fluid conductivity at each temperature and ion concentration. Both the real and imaginary part of surface conductivity increase with increasing ion concentration, shown in Figure (1) for a temperature of 20 °C. At high salinities, the imaginary part saturates, while the real part increases.

eg: Author1, Author2 and

exponent of the real part of surface conductivity increases relatively strongly with fluid conductivity.

Figure 2. Walden exponents, describing the strength of the temperature dependence, of the real part of the measured bulk conductivity σ’ and the real part of surface conductivity σ’s. The solid line shows the Walden exponents of the sodium chloride solution used as pore fluid. Error bars are the standard errors of fitting equation (3) to the data.

The maximum of the imaginary conductivity increases with temperature and salinity (Figure 3). The increase with temperature is nearly constant with varying ion concentration. Only a small decrease of the temperature dependence is observed. At 1 mol/m3 the imaginary part at 40 °C is 1.96 times the value at 0 °C, whereas at 100 mol/m3 it is 1.76 times σ’’max(0°C). The real and imaginary part of surface conductivity show the opposite temperature-dependent behaviour when salinity is increased: Walden exponents increase with temperature for the real part (figure 2), whereas temperature dependence decreases for the imaginary part (Figure 3). Figure 1. Real σs’ and imaginary part σ’’ of surface conductivity at 1 Hz vs. ion concentration of the sandstone sample at a temperature of 20 °C.

In the following, we use the Walden exponent as a measure of the strength of temperature dependence. Originally, the modified Walden product is valid for electrolytic conductivity only, but since it provides reasonable fits also for the real part of surface conductivity, we consider it useful for comparison and to draw conclusions on conduction mechanisms. For this case, the Walden exponent α not only represents the temperature dependence of the ion mobility, but also other parameters relevant for surface conductivity. As a reference value of the temperature dependence of the pore fluid we also determined the Walden exponents of sodium chloride solution at different ion concentrations from measurements on a waterfilled sample holder. The temperature dependence of the real part of conductivity slightly decreases with increasing salinity (Figure 2). Even at high salinities, where surface conductivity is supposed to be small enough to neglect it, the Walden exponents differ from the values of the sodium chloride solution. The Walden IP2016 – 6-8 June, Aarhus, Denmark

Figure 3. Maximum imaginary part of the measured conductivity vs, temperature for three different ion concentrations.

2

Abbreviated title Author3

eg: Author1, Author2 and

MEMBRANE POLARIZATION MODEL To calculate the temperature dependence with membrane polarization theory, we use the extended membrane polarization model by Bücker and Hördt (2013). It is based on a cylindrical geometry of one wide pore with length L1 and radius r1 and one narrow pore (L2 and r2) in sequence. The pore surface is covered by an electrical double layer, which is characterized by its size and the distribution of ions within the layer. As the model in Bücker and Hördt (2013) results in a 1D admittance, we convert it to an effective conductivity as described in Bairlein et al. (2016). Temperature-dependent parameters of the model are the ion mobility, which is implemented by equation 2, the negative zeta-potential, increasing with temperature, and the Debye length, which decreases with increasing temperature. The effective conductivity increases with both ion concentration and temperature. For each ion concentration the real part of effective conductivity was fitted by equation 3. The temperature dependence becomes weaker when salinity is increased (Figure 4). At high salinities the Walden exponent converges to the Walden exponent of the ion mobility (α ≈ 0.91), where fluid conductivity dominates. At small salinities surface conductivity is dominating the temperature dependence. The Walden exponent of the real part of surface conductivity also decreases with c0, but is always larger than that of σ’eff. The salinity dependence of the imaginary part of the model conductivity has been discussed in Hördt et al. 2016: σ’’ at 1 Hz increases with salinity at small ion concentrations and decreases at high ion concentrations. Here, we focus on the temperature dependence and normalized the imaginary part to its value at 25 °C. The increase of the imaginary part becomes weaker with increasing ion concentration. At 1 mol/m3 the imaginary part increases a hundredfold and at 100 mol/m3 tenfold. This can be attributed mainly to the decrease of the absolute value of the zeta-potential with increasing salinity.

Figure 5. Maximum imaginary part of the effective model conductivity, normalized to the maximum imaginary part at the reference temperature T0 = 25 °C, as a function of temperature for three different ion concentrations. Model parameters are similar to the parameters used in Figure 5.

CONCLUSIONS SIP measurements on a sandstone sample show that surface conductivity increases when the temperature is increased. The temperature dependence is influenced by salinity, resulting in an increase of the temperature dependence for the real part and a slight decrease for the imaginary part of surface conductivity with increasing salinity. However, the model predicts a strong decrease for the temperature dependence of both real and imaginary part. The temperature dependence of the real part of surface conductivity of the measurements and model is stronger than the temperature dependence of the pore fluid, consistent with the results of Revil et al. (1998). The strong temperature dependence allows two possible conclusions. Either, the dependence of the surface conductivity on temperature is not mainly controlled by ion mobility or the temperature dependence of the ions in the electrical double layer differs strongly from the free electrolyte. Our results are based on measurements on only one sample and may be different for other sandstones and rock types. As temperature dependence of the surface conductivity depends on surface properties, rocks with different compositions may vary in the temperature dependence of their complex conductivity.

REFERENCES

Figure 4. Walden exponents of the real part σ’ and the real part of surface conductivity σ’s of the effective model conductivity vs. ion concentration of the free electrolyte. Additionally, the Walden exponent of the ion mobility is shown. Model conductivity was calculated for pH 7 and pore length and radii L1 = 100 µm, L2 = 1 µm, r1 = 10 µm, and r2 = 0.1 µm.

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Bairlein, K., Bücker, M., Hördt, A., Hinze, B. and Nordsiek, S., 2016, Temperature dependence of spectral induced polarization data: experimental results and membrane polarization theory: Geophysical Journal International, accepted. Börner, F., Schopper, J. and Weller, A., 1996, Evaluation of transport and storage properties in the soil and groundwater zone from induced polarization measurements, Geophysical Prospecting, 44(4), 583–601. Bücker, M., and Hördt, A., 2013, Analytical modelling of membrane polarization with explicit parameterization of pore radii and the electrical double layer. Geophysical Journal International, 194(2):804–813.

3

Abbreviated title Author3

Hayley, K., Bentley, L., Gharibi, M. and Nightingale, M., 2007, Low temperature dependence of electrical resistivity: implications for near surface geophysical monitoring, Geophysical Research letters. 34(18). Hördt, A., Blaschek, R., Kemna, A. and Zisser, N., 2007, Hydraulic conductivity estimation from induced polarisation data at the field scale - the Krauthausen case history, Journal of applied Geophysics, 62(1), 33–46. Hördt, A., Bairlein, K., Bielefeld, A., Bücker, M., Kuhn, E., Nordsiek, S., Stebner, H., 2016, The dependence of induced polarization on fluid salinity and pH, studied with an extended model of membrane polarization, Journal of Applied Geophysics, accepted.

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eg: Author1, Author2 and

Revil, A., Cathles, L., Losh, S., and Nunn, J., 1998, Electrical conductivity in shaly sands with geophysical applications. Journal of Geophysical Research: Solid Earth (1978–2012), 103(B10):23925–23936. Sen, P.N. and Goode, P.A., 1992, Influence of temperature on electrical conductivity on shaly sands, Geophysics, 57(1), 89– 96. Sorensen, J. A., and Glass, G. E., 1987, Ion and temperature dependence of electrical conductance for natural waters. Analytical Chemistry, 59(13):1594–1597. Zisser, N., Kemna, A. and Nover, G., 2010, Dependence of spectral-induced polarization response of sandstone on temperature and its relevance to permeability estimation, Journal of geophysical Research, 115(B9).

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Complex Resistivity for Dynamic Imaging of Plant Root Traits and Root – Soil Interactions Yuxin Wu

Susan Hubbard

Baptiste Dafflon

Lawrence Berkeley National Lab 1 Cyclotron Rd, MS 74-316C Berkeley, CA 94720 [email protected]

Lawrence Berkeley National Lab 1 Cyclotron Rd, MS 74-316C Berkeley, CA 94720 [email protected]

Lawrence Berkeley National Lab 1 Cyclotron Rd, MS 74-316C Berkeley, CA 94720 [email protected]

SUMMARY Electrical methods (complex resistivity and ERT) are explored for plant root trait imaging and the study of dynamic root – soil interactions. The links between the moisture dynamics, root architectural and morphological traits and electrical properties of the plant roots and root zone soil are established for a deciduous plant (Acer palmatum) under controlled temperature and soil moisture conditions. Specifically, resistivity – moisture correlation is closely linked with the plant’s seasonal growth cycle and the effects of the roots on soil resistivity are evident. In addition to deploying previously tested configurations under controlled laboratory conditions, we employed novel imaging strategies that utilize root systems as distributed electric transmitters to quantify critical root structural and morphological traits and their responses to variable soil and climatic conditions. The links between root architectural (root distribution, rooting depth) and morphological traits (root mass, effective root area) and root dielectric signals are clearly demonstrated during the different stages of plant growth, indicating the dynamic changes of root activity in response to water and nutrient needs and availability during different stages of plant growth. These results demonstrated the potential of electrical methods for the study of root zone dynamics, which can lead to a new direction in developing much needed, minimally invasive and in-situ root phenotyping tools with broad application in terrestrial carbon cycle, forestry and agricultural studies. Key words: complex resistivity, ERT, root traits, soil

INTRODUCTION Plants play a critical role in shaping the earth’s surface, providing life supporting materials for mankind and regulating critical elemental cycling, especially water, carbon and nitrogen. Plant growth and productivity are strongly affected by changes of edaphic and climatic conditions. While the role and response of aboveground plant traits, such as above ground biomass and tissue chemistry, to environmental changes are widely studied, how the belowground plant traits, such as root structure, root mass and water/nutrient acquisition efficiency, adapt to changing environmental conditions are significantly understudied. Roots make up a significant portion of the total plant biomass and serve the critical function of plant anchorage and water and nutrient uptake. Different plant species have developed a wide range of underground strategies to capture nutrient/water and adapt to changes in environmental conditions, resulting in an extremely IP2016 – 6-8 June, Aarhus, Denmark

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diverse and complex spectrum of root traits. Belowground root traits are very difficult to study due to the inaccessibility of the soil. Typical root phenotyping methods involve direct, and destructive, access to the root systems (e.g. shovelomics, minirhizotrons). It is often impossible to access the whole root system with such methods, primarily because of the break off of the fine roots during excavation or limited view only in vicinity of access tubes. Often, these methods only allow the characterization of the root traits at a specific time of plant life. Here we explore the utilization of complex electrical methods, in junction with other point-scale measurements, for the monitoring of plant root traits and root – soil interactions. Our results demonstrated the promises of using complex electrical signals for in-situ, minimally invasive imaging of dynamic plant root traits and root-soil interaction during plant growth under changing environmental conditions.

BACKGROUND A number of studies have evaluated the utilization of electrical methods for studying root zone dynamics. For example, Jayawickreme et al (2008) monitored root zone moisture variation with resistivity method. Cassiani et al, (2015) conducted electrical resistivity tomography (ERT) monitoring of the moisture content around an orange tree driven by irrigation, precipitation and plant evapotranspiration. Garre et al (2011) conducted 3D ERT monitoring of root zone water dynamics. In addition to soil moisture monitoring, Amato et al (2008) found a fairly good correlation between resistivity of soil and root dry mass. Al Hagrey and Petersen (2011) also confirmed the sensitivity of ERT to root mass and water and soil properties near root zone. In addition to traditional ERT methods, novel approach through current injection into the root system has also been tested for root zone imaging. Aubrecht et al (2006) and Cermak et al (2006) developed the theory behind the electrical method for monitoring the absorption surfaces of tree roots and tested it in the field. Cermak et al (2014) later improved this method and tested it on more tree types and sizes. In addition to pure resistivity measurements, capacitive methods have also been tested for root imaging. Dalton (1995) developed an equivalent circuit model for such an approach, which led to additional interests on this method. For example, Preston et al (2004) found a good correlation between root capacitance and root dry mass on young poplar trees and Cao et al (2011) tested this concept on willow roots in the lab on a broader frequency spectrum.

METHOD AND RESULTS Our research was motivated by both the possibilities illustrated in the previous work as well as by the demonstrated limitations or assumptions made. To better constrain experimental interpretation, our initial experiments were

conducted under controlled conditions where plants are grown in soil packed pots under manipulated temperature, moisture and nutrient conditions. Both complex resistivity spectrum from milli- to kilo- Hertz and ERT were used in combination with auxiliary soil sensors for moisture and temperature monitoring. While conventional ERT methods were mainly used to monitor soil moisture dynamics and their impacts on plant root distribution and transpiration, we employed novel imaging strategies utilizing root systems as distributed electric transmitters to quantify critical root structural and morphological traits and their responses to variable soil and climatic conditions. In this research, our principal hypothesis linking root architectural and morphological traits with electrical signals is based on the pattern of current field distribution under the influence of roots and the dielectric properties across root-soil interfaces. Specifically, we hypothesize that coarse roots with suberized and insulating epidermic cells mainly act as electric conductors with minimal current leakage, while fine roots surface act as a capacitive interface for current exchange between roots and soils. We further hypothesize a direct link between fine root density and current density distribution in the soils closest to the roots. An example of our experimental setup is shown in Figure 1.

Figure 3: Correlation between electrical resistivity (temperature normalized) and moisture content highlighting the effects of the roots which are concentrated on the top layer of the soil. Our initial geophysical root traits monitoring has focused on root architectural and morphologic traits. These include the distribution pattern of roots with depth (Figure 4), the mass of roots and also the effective root area. Our data revealed a concentration of roots near the soil surface at ~ 20 cm below soil surface, as well as a maximal rooting depth in responding to simulated groundwater levels. Further, dynamic imaging of the root system during its seasonal cycle revealed changes of its dielectric behaviour that is closely tied with nutrient and water uptake activities in responding to the need driven by plant transpiration and growth.

Figure 1: Experimental setup for dynamic root trait and root – soil interaction imaging. The dimension of the soil pot is roughly 60 cm ID x 96 cm Depth. Acer palmatum was used for this experiment. Two pots (tree – containing and tree – absent) were setup for comparative studies. Temporal changes of bulk resistivity were useful for quantifying the moisture dynamics of the soil in responding to the plant’s seasonal growth cycles. Results indicated significant moisture uptake at the beginning of spring sprouting with subsequently more intensive transpiration activities, resulting in a significant contrast of the moisture profile between the tree-containing and tree-absent pots (Figure 2). The effects of the presence of root on electrical resistivity of the bulk soil are also evident from the experiments (Figure 3), suggesting the possibility of root imaging based on ERT data alone, as has been shown by other studies mentioned above.

Figure 2: The contrast in resistivity profile between tree – containing and tree –absent pots during to root water uptake and plant transpiration.

Figure 4: Root distribution in the soil based on electrical current field distribution. The arrow on the right figure indicates position of concentrated fine roots at ~ 20cm below soil surface.

CONCLUSIONS Our study has demonstrated the potential of complex electrical methods for monitoring the interactions between root and soil, identification of critical plant root traits and monitoring the dynamic response of plant root traits to plant growth and changes of environmental conditions. These results can lead to a new direction in developing much needed, minimally invasive and in-situ root phenotyping tools under dynamic field conditions with broad application in terrestrial carbon cycle, forestry and agricultural studies. These results will be tested on more plant genotypes and at field conditions for generalization across species with various root phenotypes and validation at more complex field conditions.

ACKNOWLEDGMENTS The work was supported by the genome to watershed scientific focus area (SFA) at Lawrence Berkeley National Lab funded by the subsurface biogeochemical research

program at the U.S. Department of Energy. The authors acknowledge Paul Cook and Justin Erspamer for helping with the experimental setup. We also thank Thomas Gunther (Leibniz Institute for Applied Geophysics, Germany) for providing the BERT code for resistivity data inversion

REFERENCES Al Hagrey, S.A., T. Petersen, 2011, Numerical and experimental mapping of small root zones using optimized surface and borehole resistivity tomography, Geophysics, Vol 76, NO.2 P G25-G35. Amato, M., B. Basso, G. Celano, G. Bitella, G. Morelli, R. Rossi, 2008, In situ detection of tree root distribution and biomass by multi-electrode resistivity imaging, Tree Physiology, Vol 28, P1441-1448 Aubrecht, L., Z. Stanek, J. Koller, 2006, Electrical measurement of the absorption surfaces of tree roots by the earth impedance method: 1. Theory. Cao, Y., T. Repo, R. Silvennoinen, T. Lehto, Paavo, Pelkonen, 2011, Analysis of the willow root system by electrical impedance spectroscopy, Journal of Experimental Botany, Vol 62, P 351-358. Cassiani, G., J. Boaga, D. Vanella, M.T. Perri, S. Consoli, 2015, Monitoring and modelling of soil-plant interactions: the joint use of ERT, sap flow and eddy covariance data to characterize the volume of an orange tree root zone, Hydrology and Earth System Sciences, Vo. 19, P2213-2225 Cermak, J., R. Ulrich, Z, Stanek, J, Koller, L, Aubrecht, 2006, Electrical measurement of the absorption surfaces of tree roots by the earth impedance method: 2. Verification based on allometric relationships and root severing experiments, Plant and Soil Cermak, J., N, Nadezhdina, V. Nadezhdin, Z, Stanek, J. Koller, M. Trcala, M. Amato, P, Kantor, 2014, Absorptive root area and stem resistivity in whole trees of constrasting structure and size – improvement of methods, Tree Physiology, V26, P1113-1121 Dalton, F.N., 1995, In-situ root extent measurements by electrical capacitance methods, Plant and Soil, V173, P 157165. Garre, S. M. Javaux, J. Vanderborght, L. Pages, H. Vereecken, 2011, Three – dimentional electrical resistivity tomography to monitor root zone water dynamics, Vadose Zone Journal, V 10, P412 – 424 Jayawickreme, D.H., R.L. Van Dam, D.W. Hyndman, 2008, Subsurface imaging of vegetation, climate, and root-zone moisture interactions, Geophysical Research Letters, VOL. 35, L18404 Preston, G.M., R.A. McBride, J. Bryan, M. Candido, 2004, Estimating root mass in young hybrid poplar trees using the electrical capacitance method, Agroforestry Systems, Vol, 60, P 305-309.

SIP response of compacted natural and lime-cement-treated loam Carole Kaouane

Michel Chouteau

Philippe Côte

CEREMA-Normandie Centre 10 ch, de la Poudriere 76121 Le-Grand-Quevilly, France [email protected]

Ecole Polytechnique de Montreal C.P. 6079, succ. Centre-Ville Montreal (Qc) H3C 3A7 Canada [email protected]

IFSTTAR - Nantes Route de Bouaye CS 4 44344 Bouguenais Cedex France [email protected]

energy. Results show very distinct complex conductivity features between the two groups.

SUMMARY We investigate the applicability of Spectral Induced Polarization (SIP) to geotechnical engineering for assessing soil compaction. We make two groups of samples at different compaction levels: group N is made from a silty loam and group T is from the same loam treated with 1% lime and 5 % cement. Groups show distinct complex conductivity spectrums. Debye decomposition is applied to the measured data and we extract the relaxation time distribution (RTD). Group-N samples show an increase of total chargeability M with an increase in saturation and no dependence of the mean frequency on saturation, while group-T samples show a decrease of M and an increase of the mean frequency with an increase in saturation. We suggest that the compacted loam possesses a continuous conductive matrix composed of saturated silt aggregates. We cannot derive firm conclusions on group-T samples because of the possible chemical reactions, which transform the porous matrix of the samples. The observation of the RTD could be a practical tool to monitor those reactions. Key words: SIP; loam; lime and cement treated soil; geotechnical engineering; compaction.

INTRODUCTION In the last two decades, the range of SIP applications has been widely extended from mineral and petroleum exploration to environmental monitoring: prediction of the hydraulic permeability, mapping of contaminant plumes, bioremediation (Kemna et al., 2012). Because of its sensitivity to textural parameters of porous media, SIP also shows a high potential to assess the condition of building materials (Kruschwitz et al., 2014) and recent work investigates linkages between geotechnical parameters and the SIP response (Boadu and Owusu-nimo, 2010). Geotechnical engineering is in need for efficient methods to map the in-situ properties of compacted soils. Most of the standardized geotechnical tests are point measurements, destructive, time consuming and may require employing nuclear probes. Moreover, the use of lime and cement treatments to stabilize water-sensitive soils is not always efficient because of the complexity of the lime-cement-fines reactions and how it affects the pore space (Saussaye, 2012). In situ monitoring of the reaction would be of high interest. The present study was designed to (1) observe characteristics features of a natural and treated soil, and to (2) assess the ability of SIP to discriminate between samples compacted near the Optimum Proctor (OP). The OP determines the optimal water content to obtain a maximal dry density after compaction at a given IP2016 – 6-8 June, Aarhus, Denmark

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METHOD AND RESULTS Sample preparation Samples are mechanically compacted cores (5 cm-diameter and 10 cm-long) according to French standards (NF P 94-2301). Samples from group N are made from a silty loam, sieved at 2 mm, composed of 20 % clay (d