Nondestructive Testing for Archaeology and Cultural Heritage: A Practical Guide and New Perspectives 9783030018986, 9783030018993, 3030018989

Table of contents :
Preface
Acknowledgements
Contents
1 Introduction
2 Principles of Mathematics Used in NDT Methods
2.1 Initial Considerations
2.2 NDT Geophysical Data Digitalization
2.3 Spectral Analysis
2.4 A Few Definitions to Remember
Reference
3 Nondestructive Testing Technologies for Cultural Heritage: Overview
3.1 NDT Methods in Cultural Built Heritage and Archaeology: State of the Art
3.2 NDT Geophysical Methods
3.2.1 The Ground-Penetrating Radar Method
3.2.2 The Electrical-Resistivity Active Method
3.2.3 The Induced-Polarization Method
3.2.4 The Self-potential Method
3.2.5 Seismic Method
References
4 NDT Geophysical Instrumentation and Data Acquisition and Processing Enhancement
4.1 GPR Instrumentation Enhancement: Reconfigurable Stepped-Frequency Georadar
4.2 The GPR Data Acquisition
4.2.1 The GPR Frequency of Antenna and Depth of Penetration
4.2.2 The GPR Frequency of Antenna and Resolution
4.2.3 The Sampling Interval of Data Acquisition
4.2.4 The Two-Way Time Window Set
4.2.5 Sampling Interval
4.2.6 Sample Spatial Interval
4.2.7 Survey Profiles Spacing and Orientation
4.3 GPR Data Processing Methodology
4.4 GPR Data Visualization: Time Slices
4.5 GPR Data Visualization: Amplitude ISO-Surfaces
4.6 Electrical-Resistivity Tomography Field Measurements
4.6.1 ERT Survey-Instrument Parameters
4.6.2 Choice of the Best Array
4.6.3 ERT Survey Procedures
4.6.4 ERT Data Inversion
4.7 Induced-Polarization Data Acquisition and Inversion
4.8 Self-potential Data Acquisition and Inversion
4.9 Seismic Sonic and Ultrasonic Data Acquisition and Inversion
References
5 NDT Geophysical Data Interpretation
5.1 GPR Data Interpretation
5.2 ERT Data Interpretation
5.3 IP Data Interpretation
5.4 SP Data Interpretation
5.5 Interpretation of Seismic and Ultrasonic Data
References
6 Site Application: The Archaeological Site of Pompeii (Italy)
6.1 Site History
6.2 Site Natural Hazard
6.3 NDT Geophysical Surveys
6.3.1 Area 1: GPR, ERT and SP Data Interpretation
6.3.2 Area 2: GPR, ERT and SP Data Interpretation
6.3.3 Area 3: GPR, ERT, and SP Data Interpretation
6.3.4 The NDT Geophysical Survey of Tomb D
6.3.5 2D ERT Data Analysis and Interpretation
6.3.6 ERT Data Analysis and Interpretation of the Wall of the Studied Tomb
6.3.7 Seismic Tomography Data Analysis and Interpretation of the Wall of the Studied Tomb
6.3.8 2D GPR Data Analysis and Interpretation
6.3.9 3D GPR Data Analysis and Interpretation
6.4 GPR Data Acquisition and Analysis on the Columns
References
7 Site Application: The Archaeological Site of Sagalassos (Turkey)
7.1 Site Description
7.2 NDT Geophysical Data Acquisition, Processing and Interpretation
7.2.1 Area 1
7.3 The Roman Bath Stability Study
7.3.1 Zone 1
7.3.2 Zone 2
7.3.3 Analysis of the Probability of Long-Term Collapse
7.4 Area 2
References
8 Conclusions
Appendix MATLAB Codes for NDT Geophysical Data Analysis
A.1 Abstract
A.2 Short Description of MATLAB
A.3 Some Basic MATLAB Operations for NDT Geophysics
A.4 Conclusion
A.5 Suggested Readings
Index

Citation preview

Giovanni Leucci

Nondestructive Testing for Archaeology and Cultural Heritage A Practical Guide and New Perspectives

Nondestructive Testing for Archaeology and Cultural Heritage

Giovanni Leucci

Nondestructive Testing for Archaeology and Cultural Heritage A Practical Guide and New Perspectives

123

Giovanni Leucci Institute for Archaeological and Monumental Heritage National Research Council Lecce, Italy

ISBN 978-3-030-01898-6 ISBN 978-3-030-01899-3 https://doi.org/10.1007/978-3-030-01899-3

(eBook)

Library of Congress Control Number: 2018958488 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover illustration: The roman amphitheatre of Catania: Reconstructive hypothesis with the various entrances to the monument. The research undertaken by IBAM-CNR between 2014 and 2015 aimed towards obtaining a three-dimensional reconstruction of the monument by combining diverse methods (virtual archaeology, digital archaeology, NDT integrated technologies) of data acquisition and processing. This made it possible to acquire important data for the creation of an exact reproduction of the parts of the monument that are still hidden and provide a faithful reconstruction of the entire architectural structure. The virtual reconstruction was performed by the Information Technologies Laboratory (ITLab) of the IBAM-CNR (itlab.ibam.cnr.it) (with kind permission of Arch Francesco Gabellone scientific director of ITLab_IBAM-CNR). This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

In the field of archaeological research and the restoration of monumental heritage, nondestructive testing (NDT) survey techniques have already gained widely acknowledged importance. The possibility to understand the extent of the archaeological deposits or the state of preservation of the artifacts without resorting to disruptive activities is extremely useful in identifying unknown or presumed emergencies in order to better understand a site and to target it in a targeted manner, for example, concerning both excavation and restoration operations. The purpose of this volume is therefore to provide a general introduction to the most important NDT techniques related to geophysical and micro-geophysical exploration methods. Their application to archaeology and monumental heritage is highlighted here. The book covers the physical principles, methodology, interpretational procedures, and fields of application of the various survey methods. It introduces new instrumentation with new algorithms for data acquisition and processing and represents a useful guide for all those who approach these methods for the first time since the text widely demonstrates that there is no need for extensive math skills for a general understanding of NDT methods. While writing the book for such a wide possible readership, it was inevitable that problems arose concerning the level of mathematical treatment to be adopted. The physical basis of the discussed methods is a highly mathematical subject so this necessitated more attention in order to show that no great mathematical expertise is necessary for a broad understanding of NDT surveying. But, it is important also to underline that, in order to understand the more advanced data processing and interpretation methodologies in depth, reasonable mathematical ability is required. So, the approach used in this book employs mathematics as simple as possible and reduces mathematical analysis to transparent cases. However, the user employing that approach to NDT methods should have knowledge about the more advanced techniques of analyzing and interpreting NDT data because they can greatly increase the amount of useful information obtained from the data. Therefore, the approach used in the book will enable the reader to assess the scope and v

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importance of the advanced techniques of analysis without entering into the details of their implementation. Examples are taken from measurement campaigns made on sites of significant historical–archaeological importance, at both national and international levels. Through the use of these examples, the reader can understand how to design and perform an NDT survey. The reader is guided to the choice of the most suitable method related to a particular type of problem which arises and is guided to the type of data acquisition and processing that best enables the best possible result. The most innovative data acquisition and processing systems are described that enable rapid reconnaissance of the surface sub-levels of the earth, even over areas of considerable extension, yielding highly detailed evidence, even in very challenging cases. It is hoped that the book will serve as a text for students in archaeology, geophysics, architecture, and engineering disciplines, and can also be a useful guide for specialists who want to increase their knowledge of this fantastic discipline. Lecce, Italy

Giovanni Leucci

Acknowledgements

The author thanks Dr. Lara De Giorgi for her precious collaboration during data acquisition, as well as experts of the international committee of the Pompeii Sustainable Preservation Project. Finally, the author warmly thanks Prof. Jeroen Poblom, Director of the Belgian archaeological mission in Sagalassos, for the opportunity to perform geophysical measurements and for his valuable help during the surveys.

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Principles of Mathematics Used in NDT Methods . 2.1 Initial Considerations . . . . . . . . . . . . . . . . . . . 2.2 NDT Geophysical Data Digitalization . . . . . . . 2.3 Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . 2.4 A Few Definitions to Remember . . . . . . . . . . . Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Nondestructive Testing Technologies for Cultural Heritage: Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 NDT Methods in Cultural Built Heritage and Archaeology: State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 NDT Geophysical Methods . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The Ground-Penetrating Radar Method . . . . . . . . . . 3.2.2 The Electrical-Resistivity Active Method . . . . . . . . 3.2.3 The Induced-Polarization Method . . . . . . . . . . . . . . 3.2.4 The Self-potential Method . . . . . . . . . . . . . . . . . . . 3.2.5 Seismic Method . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 NDT Geophysical Instrumentation and Data Acquisition and Processing Enhancement . . . . . . . . . . . . . . . . . . . . . . 4.1 GPR Instrumentation Enhancement: Reconfigurable Stepped-Frequency Georadar . . . . . . . . . . . . . . . . . . . . 4.2 The GPR Data Acquisition . . . . . . . . . . . . . . . . . . . . . 4.2.1 The GPR Frequency of Antenna and Depth of Penetration . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 The GPR Frequency of Antenna and Resolution 4.2.3 The Sampling Interval of Data Acquisition . . . . 4.2.4 The Two-Way Time Window Set . . . . . . . . . . .

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4.2.5 Sampling Interval . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Sample Spatial Interval . . . . . . . . . . . . . . . . . . 4.2.7 Survey Profiles Spacing and Orientation . . . . . . 4.3 GPR Data Processing Methodology . . . . . . . . . . . . . . . 4.4 GPR Data Visualization: Time Slices . . . . . . . . . . . . . . 4.5 GPR Data Visualization: Amplitude ISO-Surfaces . . . . 4.6 Electrical-Resistivity Tomography Field Measurements . 4.6.1 ERT Survey-Instrument Parameters . . . . . . . . . . 4.6.2 Choice of the Best Array . . . . . . . . . . . . . . . . . 4.6.3 ERT Survey Procedures . . . . . . . . . . . . . . . . . . 4.6.4 ERT Data Inversion . . . . . . . . . . . . . . . . . . . . . 4.7 Induced-Polarization Data Acquisition and Inversion . . 4.8 Self-potential Data Acquisition and Inversion . . . . . . . . 4.9 Seismic Sonic and Ultrasonic Data Acquisition and Inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Application: The Archaeological Site of Pompeii (Italy) . . . . Site History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Site Natural Hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NDT Geophysical Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Area 1: GPR, ERT and SP Data Interpretation . . . . . . 6.3.2 Area 2: GPR, ERT and SP Data Interpretation . . . . . . 6.3.3 Area 3: GPR, ERT, and SP Data Interpretation . . . . . . 6.3.4 The NDT Geophysical Survey of Tomb D . . . . . . . . . 6.3.5 2D ERT Data Analysis and Interpretation . . . . . . . . . . 6.3.6 ERT Data Analysis and Interpretation of the Wall of the Studied Tomb . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.7 Seismic Tomography Data Analysis and Interpretation of the Wall of the Studied Tomb . . . . . . . . . . . . . . . . 6.3.8 2D GPR Data Analysis and Interpretation . . . . . . . . . . 6.3.9 3D GPR Data Analysis and Interpretation . . . . . . . . . . 6.4 GPR Data Acquisition and Analysis on the Columns . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 NDT Geophysical Data Interpretation . . . . . . . . 5.1 GPR Data Interpretation . . . . . . . . . . . . . . . . 5.2 ERT Data Interpretation . . . . . . . . . . . . . . . . 5.3 IP Data Interpretation . . . . . . . . . . . . . . . . . . 5.4 SP Data Interpretation . . . . . . . . . . . . . . . . . . 5.5 Interpretation of Seismic and Ultrasonic Data . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Site 6.1 6.2 6.3

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7 Site Application: The Archaeological Site of Sagalassos (Turkey) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Site Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 NDT Geophysical Data Acquisition, Processing and Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Area 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 The Roman Bath Stability Study . . . . . . . . . . . . . . . . . . . 7.3.1 Zone 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Zone 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Analysis of the Probability of Long-Term Collapse 7.4 Area 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Appendix: MATLAB Codes for NDT Geophysical Data Analysis . . . . . . 221 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

Chapter 1

Introduction

Abstract A correct planning of the archaeological investigation and restoration interventions of the discover archaeological structures and monuments requires a detailed study of building techniques and materials, the mapping of decay patterns, the localization of damages and the identification of their causes. In particular, the detection and mapping of voids and cracks in the masonry structures and plaster detachments and alterations, are crucial both to verify the stability of load bearing structures, and evaluate the state of conservation of architectural and painting surfaces, respectively. Damage of historical buildings, monuments, works of art and other cultural properties is reported from all over the world. One of the greatest dangers for the historical monuments is weathering, caused by climatic changes and air pollution. Building stones are susceptible to various atmospheric factors causing their destruction, especially in Mediterranean basin, where the marine salts are a permanent cause of natural pollution, not only on the coast but also inland. Weathering effects on the physical and mechanical properties of natural stones of monuments. These properties can be studied using the non destructive micro-geophysics methods that includes all the methodologies derived from geophysics with more or less miniaturized instrumentations. The book provide the main characteristics from theoretical and new application point of view of these methods.

In the first half of the nineteenth century, Joseph Henry (American scientist) and Michael Faraday (English scientist) independently made a discovery that had to change the history of humanity: “the phenomenon of electromagnetic induction”. When a magnetic field changes over time, an electromotive force can be induced in a closed circuit, thus generating a current passage in the circuit. This discovery made it possible to understand that it was possible to convert mechanical energy into electrical energy and vice versa. The great physicist Richard Phillips Feynman (Nobel Prize in Physics 1965), remark that: “At the same time that an understanding of the facts of electromagnetism developed, technical possibilities appeared that challenged the imagination of previous generations: it became possible to send signals over long distances to telegraph; talk to other people who are miles away without an intermediate connec© Springer Nature Switzerland AG 2019 G. Leucci, Nondestructive Testing for Archaeology and Cultural Heritage, https://doi.org/10.1007/978-3-030-01899-3_1

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1 Introduction

tion; to run power grids of enormous power: […]; all this works because we know the laws of electromagnetism”. These discoveries also laid the foundations on which James Clerk Maxwell erected his own electromagnetic theory, which connected light with other forms of radiation (radio waves) in a single family, namely, electromagnetic radiation. Maxwell published his research in 1865 with the work “A dynamical theory of the electromagnetic field” in the journal Philosophical Transactions of the Royal Society of London. The work of Maxwell found its definitive confirmation in 1887 when Heinrich Hertz succeeded in providing an experimental confirmation of the existence of electromagnetic waves. Perhaps not even Maxwell imagined that his brilliant work could one day serve to pursue the faint submerged traces of the past and to contribute to the understanding of a typically historical and archaeological problem that spans more than several hundred-thousand years. At the end of the nineteenth century, physicists believed that there was a substance called “ether” that permeated all space. Thanks to ether forces such as gravitational, electrical, and magnetic, they could transmit signals and act at a distance. Indeed, that a scientific discipline such as physics could serve in various fields has been known to scientists for a long time. It has a very important function within problems that are apparently of a completely different nature, such as those of archeology and cultural heritage. In fact, nondestructive testing (NDT) is related to the study of several physical parameter used to investigate, testing the subsoil or evaluating materials, and to obtain information about buried archaeological features or evidences of discontinuities, or differences in characteristics related to the degree of conservation of investigated monuments without destroying the serviceability of the surveyed part. For some years already, more nondestructive tests are closely related to geophysical methods. Geophysics is the application of the principles of physics to the study of the Earth. As is known, the purpose of pure geophysics is to deduce the physical properties of the Earth and its internal constitution from the physical phenomena associated with it: for example, the geomagnetic field, the distribution of heat flows, the propagation of seismic waves, the gravitational field, etc. On the other hand, the objective of applied geophysics is to investigate, with a very high resolution and a relatively smaller scale, more superficial features present in the earth’s crust. Typically, the investigation of these characteristics provides an important contribution to practical problems, such as oil exploration, the identification of water resources, mining exploration, pollutant research, bridge and road construction, and civil engineering. The goal of geophysics is similar to that encountered in the medical sciences, where ultrasound and tomographic techniques for visualizing the interior of the human body are an essential tool in diagnostic procedures. Analogously to the medical sciences in geophysics, indirect methods of investigation are used: The presence of bodies or structures in the subsoil is highlighted by measuring at the surface variations of some physical parameters in the subsoil itself. Nowadays, however, geophysical prospecting is becoming more and more frequently used in the investigation of archaeological sites and, in general, in the study of problems inherent to cultural heritage, and they now have been included in NDT methodologies. In the case of archeology, the application of

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geophysical methods provides the possibility of obtaining indirect information on the presence and conservation status of buried structures and contributes to the planning of an archaeological excavation. In practice, some measurements of a given physical field, electromagnetic, electrical, or seismic nature, are carried out at the surface of a given archaeological area or monument. If the subsoil were perfectly homogeneous, regardless of the position in which the measurement is carried out, the same value of the measured physical parameter would always be obtained. Assuming, instead, that in a certain position of the subsoil there is a body with different physical properties compared to the surrounding material, when the measuring instrument passes in correspondence with the body, the measured value tends to deviate from the unperturbed value, and the observed physical field assumes a value, defined as anomalous, i.e., a variation with respect to the reference value relative to an homogeneous situation (anomaly). The NDT methods are employed to discover, on the basis of the variations of the physical parameters, and therefore on the observation of the anomaly, the nature and the geometry of the buried bodies. Moreover, it is also meant to achieve as objectives the definition of: 1. Methods and instruments for measuring physical parameters; 2. Mathematical procedures to derive the characteristics of the subsoil structures (the so-called model) based on the observations. There are various physical fields to measure: each of these can provide information on the corresponding physical property that generated it. One of the fundamental problems is precisely that of understanding, for the particular problem under examination, which parameter to measure and to optimize the characterization of buried structures. Each physical parameter is linked to a particular NDT method, and each method has its own characteristics that can help to solve specific problems. The NDT methods can therefore be classified according to the physical quantities involved in the measurement. The most-used NDT methods in the field of archaeology and monumental heritage are the following geophysical methods: (i) electrical (active and passive), electromagnetic methods, among which the georadar or Ground Penetrating Radar (GPR), and seismic sonic and ultrasonic (refraction, reflection, and tomography). Each of them measures particular physical quantities (current intensity and electrical potential, travel time and amplitude of electromagnetic and seismic waves, etc.). Since each geophysical method is sensitive to the contrast of particular physical parameters (electrical resistivity, self-potential, induced polarization, relative dielectrical constant, elastic constants, etc.) of the object under investigation with respect to the surrounding environment, it is understandable that the greater or lesser effectiveness of the one with respect to the other depends on the extent of the contrast of the corresponding physical parameters. Therefore, the choice of the most suitable geophysical prospecting methods and techniques for a particular problem is strongly dependent on the objective and is essentially guided by the identification of the physical parameters of the object to be identified that present the greatest contrast with the host environment, and therefore they allow greater ease of detection, as well as considerations of an economic and logistical nature. A summary of the

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Table 1.1 NDT methods used in archaeology and monumental heritage Methods Measurable physical quantity Esteemed physical parameters Electrically Electrical current, I (mA) active Electrical potential, V (mV)

Resistivity, ρ ( m) Induced polarization, IP (mV and/or msec)

Measured techniques V.E.S. (Schlumberger array) 2D and 3D tomography

Electrically Self-potential passive

Self-potential (mV)

2D and 3D measurements

GroundElectromagnetic two-way travel Penetrating time, t (ns) Radar Electromagnetic wave amplitude attenuation, A (dB) Frequency, f (MHz)

Electromagnetic wave velocity, v(ε, σ, μ) Electromagnetic wave attenuation coefficient, α(ε, σ, μ, f)

Continuous profile

Seismic

Seismic wave travel times, t (ms) Seismic wave velocity, Seismic wave attenuation, A (dB) VP (λ, μ, δ) eVS (μ, δ) Seismic wave attenuation coefficient, α

WARR e CMP Tomography Refraction Reflection Tomography

characteristics of some geophysical methods and their main applications in archeology is provided in Table 1.1. Classically, the most widely used NDT geophysical methods in archaeological and monumental heritage research are resistivity, ground penetrating radar and seismic methods: under favorable conditions (i.e., in the case of strong contrasts of resistivity, relative dielectrical constant, and elastic parameters), these methods enable the fast generation of the maps whose interpretation provides indications of the planimetric position of possible archaeological structures. The geophysical investigations evidence the presence of anomalous bodies or structures in the subsoil and/or in the investigated materials through the measurement, performed at the surface, of the variations of some physical properties in the investigated materials and/or in the subsoil itself. The analysis of these measures can highlight physical parameters varying both vertically and laterally. Working at various scales, geophysics can be applied to a wide range of investigations that span from the study of archaeology to applications to structures, such as new and/or old buildings (monumental heritage). In regard to the geophysical NDT methods discussed in this book, measurements within “geographically restricted” areas and on some important monumental heritage are used to determine the distribution of physical properties at depths that reflect the local geology of the subsoil and the conservation state of the monuments. Geophysical NDT surveys are sometimes limited by greater ambiguities or uncertainties in interpretation but, at the same time, offer a relatively rapid means of deriving arealtype information with an excellent cost-benefit ratio. The importance of geophysical NDT exploration as a means of getting information on the subsoil is so great that the basic principles, the purpose of the methods, and their main applications should be appreciated by every practicing earth scientist.

1 Introduction

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There is a distinct division between those NDT geophysical methods that make use of the natural fields of the Earth and those that require the introduction (in the medium to be investigated) of energy, so-called “artificial sources”. The first set can give information on the properties of the Earth at significantly deeper depths, and these are logistically simpler to carry out. The second set, composed of those that are described in this book, are able to give more detailed information and consequently provide an image of the investigated materials and/or the subsoil at a higher resolution. As already mentioned (see also Table 1.1), there is a wide range of NDT geophysical surveying methods for each of which there is an “operative” physical property for which the method is sensitive. The type of physical property to which a method responds clearly determines its range of applications. Thus, for example, seismic sonic and ultrasonic methods can be used for the physical, mechanical characterization of studied materials because they are sensitive to mechanical defects, such as low compressive mechanical strength that could be related to a low seismic wave velocity of propagation; electrical methods can be used for the location of the degradation related to the humidity because the water saturated rock can be distinguished from the dry rock by its higher conductivity. Other considerations also determine the types of methods used in a NDT geophysical exploration program. For example, the inapplicability of an abovementioned method due to the requirement for physical contact with the investigated materials (such as a frescoes). In this case, a GPR method that use antennas not needing direct contact with the materials is preferable. NDT geophysical methods are often used in combination. Thus, for example, the search for archaeological deposits takes place at an early stage with the use of GPR and electrical methods. In fact, in the interpretation phase, the ambiguities resulting from the results of a single method can often be removed by considering the results obtained by using a second method. For example, the reflections in a GPR survey due to the presence of a wall and/or a tomb could be similar. By integrating the GPR survey with an electrical survey, this ambiguity can be solved considering that relatively high resistivity values could be associated with the wall, while relatively low resistivity value could be associated to the earth-filled tomb. Table 1.2 shows the main fields of application of NDT geophysical methods, together with an indication of the most appropriate methods for each application. In NDT geophysical surveys, local variations of the physical parameters measured with respect to the so-called normal values are of primary importance. This variation is attributable to localized areas that have physical properties distinct from the surrounding medium and that could indicate important archaeological characteristics and/or a defect of the investigated material. A local variation of this type is known as an “anomaly”. It is important to stress that, although an interpretation of the results of the here described NDT geophysical methods require relatively advanced mathematical treatments, initial information, as will be shown in the book, can be obtained from the simple observation of the detected data.

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Table 1.2 Main field of application of NDT geophysical methods in order of importance Field of application More appropriate geophysical methods Monumental heritage

(1) Seismic sonic and ultrasonic (2) Ground penetrating radar (3) Electrical resistivity tomography (4) Self-potential

Archaeological

(1) Ground-penetrating radar (2) Electrical resistivity tomography (resistivity and induced polarization) (3) Seismic refraction tomography (4) Self-potential

However, if a degree of uncertainty in geophysical interpretation can often be considerably reduced to an acceptable level by considering the opportunity to perform further measures (even using different methods), the problem of the ambiguity of the measures cannot be circumvented. The general problem is that significant differences related to the actual situation of the investigated medium can give rise to insignificant, or incommensurably small, differences in the physical parameters actually measured during a geophysical survey. In this way, ambiguities arise due to the interpretation of the data and therefore to the reproduction of the investigated medium. It should also be noted that the experimentally derived quantities are never exactly determined because the experimental error that becomes a further degree of uncertainty must be considered. Despite this, NDT geophysical surveying, as will be shown in this text, is a valuable tool for the investigation of the subsoil and assumes a key role in the programs of exploration of archaeological resources and monumental heritage conservations.

Chapter 2

Principles of Mathematics Used in NDT Methods

Abstract NDT geophysical data analysis requires considerable knowledge of mathematical concepts. As underline in the book—for a broad understanding—the more advanced NDT geophysical data analysis and interpretational techniques require a reasonable level of mathematical ability. In this chapter, some basic mathematical concepts are presented as simply as possible. The approach employed enables readers to appreciate their scope and importance, without needing to go into the details of their implementation.

2.1 Initial Considerations NDT geophysical surveys make possible the measurement of the variations of some physical parameters according to the spatial position and/or time. The physical parameter can, for example, be the value of the resistivity along a profile acquired as function of the distance from the electrodes. It can be the electromagnetic-reflection events according to the time due to the passage of an electromagnetic wave. In any case, the simplest way to represent the data is shown in Fig. 2.1, which graphs the variation in the quantity measured with respect to distance or time. On the graph, one can see the waveforms that reflect the variations of the investigated physical parameters. More or less precisely, the shape of the wave may be uncertain because of the difficulties encountered in interpolating the curves relative to measurement stations placed at great distances (Fig. 2.1a). The objective of the NDT geophysical data interpretation is then to separate the useful signal from the noise and to interpret the signal in terms of structures present in the subsoil. Waveform analysis is an essential aspect of the processing of NDT geophysical data and its subsequent interpretation, and this analysis has its foundations in physics and mathematics that may be more complex. This chapter presents a brief overview of the fundamental principles on which the various methods of data analysis are based. There will also be a short dissertation on digital data-analysis techniques that are routinely used by geophysicists. Waveforms will be considered as functions of time, but all the principles that will be discussed can equally be applied to waveforms © Springer Nature Switzerland AG 2019 G. Leucci, Nondestructive Testing for Archaeology and Cultural Heritage, https://doi.org/10.1007/978-3-030-01899-3_2

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Fig. 2.1 a Changes in electrical resistivity along the measured profile; b a typical GPR trace showing the electromagnetic amplitude variation as a function of the two-way travel time measured in nanoseconds (ns)

as functions of distance. In the latter case, the frequency (number of cycles per unit of time of the waveform) is replaced by the spatial frequency or wave number (the number of cycles per unit of distance of the waveform).

2.2 NDT Geophysical Data Digitalization Waveforms of geophysical interest are generally continuous functions of time or distance (analog). In order to obtain a signal readable from a computer, an analogue to digital conversion is needed. In this case, an analogue signal is converted into a digital signal which can then be stored in a computer for further processing. In order for them to be stored and manipulated by a computer, signals must be converted into a discrete digital form using A/D conversion. Consider the signal shown in Fig. 2.2, which is an analogue signal (Fig. 2.2a), since it is continuously changing with time. The object of A/D conversion is to convert this signal into a digital representation, and this is done by sampling the signal (Fig. 2.2b). A digital signal is a sampled signal obtained by sampling the analogue signal at discrete points in time. These points are usually evenly spaced in time, with the intervening time referred to as the sampling interval. The extent to which digital values faithfully represent the original waveform depend on the accuracy with which measurements are made and the value of the sampling interval that is chosen. These two parameters of a digitization system are typically the sampling precision (dynamic range) and the sampling rate.

2.2 NDT Geophysical Data Digitalization

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Fig. 2.2 a Analog representation of a sinusoidal function; b digital representation of the same function

The dynamic range is defined as the ratio between the minimum value Amin and the maximum Amax of the amplitude of a measurable quantity. The higher the dynamic range, the more faithful the digitization of the variations in the amplitude of the analog waveform will be. The dynamic range is expressed on a decibel (dB) scale used to define the electric power ratios. The ratio between two power values P1 and P2 is given by 10log10 (P1 /P2 ) dB. Since the power is proportional to the square of the amplitude A of the signal. In this case, the dynamic range can be write as 20log10 (A1 /A2 ) dB. So, if a digital sampling scheme measures amplitudes over a range of 1 to 1024 amplitude units, the dynamic range is given by 20log10 (A1 /A2 )  20log10 (1024)  60 dB. The sampling frequency is the measure expressed in hertz of the number of times per second in which an analogue signal is measured and stored in digital form. In other words, the sampling frequency is the parameter that is used which “translates” a natural phenomenon that is comprehensible to the human being into a numerical representation that is “understandable” or, in other words, usable for a computer and for other machines whose operation is based on the bit. There will not be any significant loss of information content until the sampling rate is much higher than the highest frequency component of the sampled function. In fact, it is possible to demonstrate, mathematically, that, if the waveform is sampled every millisecond (sampling interval), the sampling rate is 1000 samples per second (1000 Hz). By sampling at this interval, we preserve all frequencies above 500 Hz in the sampled function. This frequency value, equal to half the sampling frequency, is known as the “Nyquist frequency (fN )” and the Nyquist interval is the frequency

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range from zero to fN . Therefore, fN  1/(2t) where t is the sampling interval. If the frequency is above the Nyquist frequency, it will result in a serious form of distortion, known as “aliasing”, in which the higher frequency components are “folded back” within the Nyquist interval.

2.3 Spectral Analysis Spectral analysis consists of signal processing that can be considered as the science that enables modification of the acquired time-series data in order to analyzes or enhance the same data. In NDT geophysical data analysis, the signals are related to seismic waves, electromagnetic waves, electrical signal, etc. Data analysis is related to the idea of a signal and its spectrum. A good example is the case of a person who plays one note on a musical instrument that could be a piano. If the note is perceived by a microphone, it is transformed into an electrical signal that can be displayed on an oscilloscope. On the oscilloscope, you will see the variation of the electrical signal as a function of time E(t) that is periodic. The reciprocal of the period is the frequency. It is clear that the waveform is not a pure sinusoid (Fig. 2.3) but contains harmonics multiples of the fundamental frequency with various amplitudes and phases (Fig. 2.4) or the same phases (Fig. 2.5). The waveform can be analyzed to find the amplitudes and phase of the waveform itself, and a list can be made of the amplitudes and phases of the sinusoids which it comprises. Alternatively, a graph F(f) can be plotted (the waveform-spectrum) of the amplitudes and phases as a function of the frequency (Fig. 2.6). F(f) is the Fourier transform of A(t).

Fig. 2.3 The complex time-domain signal

2.3 Spectral Analysis Fig. 2.4 Sum of two sinusoid: the higher frequency component has twice the width of the lower frequency component and is shifted by π/2

Fig. 2.5 Sum of two sinusoidal waves: the two sinusoidal components have the same amplitude and phase

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Fig. 2.6 Representation in the frequency domain Fig. 2.7 Jean Baptiste Joseph Fourier, 1768–1830, a French mathematician and physicist

Therefore, Fourier (Fig. 2.7) theory makes possible the decomposition of any time-domain phenomenon into one or more sine waves of appropriate frequency, amplitude, and phase.

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In other words, it is possible to transform a time-domain signal into its frequencydomain equivalent. Measurements in the frequency domain enable knowing how much energy is present at each particular frequency. Some measurements require to preserve all information related to the measured signal frequency, amplitude, and phase. However, more measurements are made without knowing the phase relationships between the sinusoidal components. This type of analysis of the signal is known as spectrum analysis. A spectrum is a collection of sine waves that, when combined properly, produce the time-domain signal under examination. This analysis is important in NDT geophysical data analysis. In fact, the waveforms of geophysical interest are a combination of useful signal and noise. The signal is that part of the waveform linked to the structures of interest present in the investigated medium, which can be geological, archaeological, etc. The noise comprises all other components of the waveform. The noise can be further divided into two components that are, respectively, random noise and consistent noise. Random noise is what is statistically foreign and therefore not connected to the geophysical survey. The coherent noise is composed of components of the waveform generated by the geophysical experiment but that are of no direct interest for the interpretation of the results. For example, in an electromagnetic survey, the signal may be the physical pulse that arrives at the receiver antenna after being reflected by a surface of electromagnetic discontinuity placed at a certain depth in the investigated medium. Random noise may be the background vibration induced by a signal transmitted in the bandwidth of the receiver antenna (for example, by a radio station or cellular antennas). The coherent noise could be the surface wave generated by the transmitter antenna that also travels towards the transmitter and receiver in the shallow subsurface and can obscure the desired signal. In favorable circumstances, the signal-to-noise ratio (SNR) is high, and in this case the signal is easily identified to be subsequently analyzed. Often SNR is low and necessitates a special treatment to increase the useful information contained in the waveforms. Different approaches are needed to remove the effect of different types of noise. Random noise can often be suppressed by repeating the measurements and making the comparison between them. The coherent noise can be filtered by first identifying the characteristics of this noise and then applying an ocular filter to remove it. However, the remaining signal may be distorted due to the effects of the recording system, and again, if the type of recording system is accurately known, one can think of applying, also in this case, an ocular filter to eliminate this type of distortion. Digital filtering is widely used in the processing of NDT geophysical data to increase the SNR or otherwise improve the useful characteristics of the signal. All filters are related to the above described Fourier spectral analysis. For more on this, refer to Alessio (2016).

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2.4 A Few Definitions to Remember Desired signal: a signal that is not corrupted by noise. Signal sampling: the process of obtaining a sequence of instantaneous values of a particular signal characteristic, usually at regular time intervals. Sampling frequency: the frequency at which the analogic–digital conversion samples the analogue signal [usually the number of samples per second (Hz)]. Sampling period: the reciprocal of the sampling frequency, i.e., the interval between corresponding points on two successive sampling pulses of the sampling signal. Sampling range: the range between the minimal and maximal values at which the signal is sampled. Nyquist interval: the maximum time interval between equally spaced samples of a signal that will enable the signal waveform to be completely determined. The Nyquist interval is equal to the reciprocal of twice the highest frequency component of the sampled signal. In practice, when analogue signals are sampled for the purpose of digital transmission or other processing, the sampling rate must be more frequent than that defined by Nyquist theorem because of the quantization error introduced by the digitizing process. The required sampling rate is determined by the accuracy of the digitizing process. Nyquist Sampling rate: the value of the sampling frequency equal to twice the maximal frequency of the signal we are acquiring.

Reference Alessio SM (2016) Digital signal processing and spectral analysis for scientists: concepts and applications. Springer, Heidelberg

Chapter 3

Nondestructive Testing Technologies for Cultural Heritage: Overview

Abstract In this chapter, the most used NDT geophysical technologies applied in the field of preventive archaeology and in the analysis of monumental heritage will be considered. Starting from the current state of the art, we will examine: Ground-Penetrating Radar (GPR), electrical active (Electrical Resistivity Tomography—ERT; induced polarization—IP) and passive (Self-Potential—SP), and seismic sonic an ultrasonic methods. Here some important theoretical aspect will be explained as simply as possible, also using practical examples.

3.1 NDT Methods in Cultural Built Heritage and Archaeology: State of the Art There are numerous types of tests for the identification archaeological deposits or to study the conservation state of monumental heritage. What are the most reliable ones? What methods lower the risk in decisions involving the excavation and/or restoration work? Do one or more ideal methods exist for a given limited budget? These questions are answered in the scientific research to study the methods for estimating the reliability of Nondestructive Testing (NDT) in their application in the field of preventive archaeology and the restoration of monumental heritage. Generally, NDT methods can be classified into six principal categories: (i) Visualoptical; (ii) Penetrating radiation; (iii) Magnetic-electrical; (iv) Mechanical vibration; (v) Thermal; and (vi) Penetrating gas or liquid. The objective of these methods is to obtain information about more physical parameters that enable gathering evidence of the invisible anomalies related to: (i) discontinuities and separations (cracks, voids, inclusions, etc.); (ii) archaeological features (walls, tombs, etc.); (iii) structure or defects (thickness, diameter, gap size, discontinuity size, etc.); (iv) physical (electrical, magnetic, thermal), mechanical, and surface properties (reflectivity, conductivity, elastic modulus, sonic velocity, etc.); (v) stress and dynamic response (residual stress, crack growth, wear, vibration, etc.); signature analysis (image content, frequency spectrum, field configuration, etc.).

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The various methods are divided into methods that inspect shallow surfaces only, the shallow subsurface, and the entire volume. The meaning of shallow surface is that the method is able to inspect a volume partially or in-full for thin components, but that the penetration depth is limited. Different (than those for shallow subsurface inspection) are those that enable inspection of volume in more depth. In the field of preventive archaeology and safeguarding of monumental heritage, NDT methods taken from geophysical science have increasingly taken hold. In fact, they now are known as NDT geophysical methods. The past century has seen a rapid development of NDT geophysical-prospection methods and instruments, permitting ever more efficient and reliable measurements and increased sample density. The main driving force behind the evolution of NDT geophysical prospection in Europe, as it is around the world, has been the incentive of exploration and mining businesses to increase the extraction of natural resources and to image ore bodies, subsurface hydrocarbon reservoirs, and minerals in ever-greater detail (Dobrin and Savit 1988; Telford et al. 1990; Keary and Brooks 1991). As a consequence, a toolbox of refined NDT geophysical methods and instruments has become available, permitting their application to other areas, such as, for example, geological research, geotechnical investigations, nondestructive testing of constructions and materials, groundwater investigations, the search for buried hazardous materials, and the investigation of the shallow subsurface in search of manmade structures and artifacts of historical and pre-historical people and societies (Leucci and De Giorgi 2010; Delle Rose and Leucci 2010). British, French, German, Italian and North-American geophysicists have promoted an increasing specialization in survey techniques, data processing, and interpretation that has resulted in a well-defined discipline called “Archaeological Geophysics”. But in the last ten years, the capabilities of the sensors used have been subject to an increased quality, resolution, and speed (and decreased application costs), a factor with significant impact. Geophysics has, over the past five decades, been successfully employed in the investigation of numerous archaeological sites in Europe and beyond (e.g., Aitken 1961; Scollar et al. 1990; Becker 1995; Conyers and Goodman 1997; Neubauer 2001; Leckebusch 2003; Linford 2006; Campana and Piro 2008; Gaffney 2008; Leucci et al. 2007, 2011, 2012a, b, c; Calia et al. 2012; Cataldo et al. 2009; Nuzzo et al. 2009; Leucci and Negri 2006; De Domenico et al. 2006; Leucci 2006; Carrozzo et al. 2003). The driving force behind the development of archaeological geophysical prospection in many other countries has often been linked to development schemes and national ancient-monument protection laws. These laws state that the developer is responsible for investigating whether any archaeological sites or historic environments will be affected by the development, and, in such cases, also for bearing the costs of any subsequent archaeological investigations. However, the preinvestigation of such an area of archaeological interest is most often performed using traditional archaeological test trenching, and little or no provision has been given to the use of geophysical prospection methods. This is the case of Italy. The reasons for this underdevelopment are manifold: the prevalent geological, pedological, and geomorphological conditions; the character and expression of common archaeological sites and features, archaeological tradition in research and exploration archaeology;

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disappointing initial experiences with geophysical archaeological prospection trials; and possibly also the lack of technical adaptation among some archaeologists that have to be taken into account. Geophysical survey in archaeology most often refers to ground-based subsurface mapping using a number of various sensing technologies. Most commonly applied to archaeology are magnetometers, electrical-resistivity meters, ground-penetrating radar (GPR), and seismic and electromagnetic (EM) conductivity. These methods provide excellent resolution of many types of archaeological features and are capable of high sample-density surveys of very large areas and of operating under a wide range of conditions. Other established and emerging technologies are also finding use in monumental heritage applications (Gerardi et al. 2014; Masini et al. 2017; Leucci and De Giorgi 2015, 2017; Leucci and Quarta 2016). NDT geophysical surveys in monumental buildings is an important issue because it is able to provide both historical and structural information about the monument at hand (Binda et al. 2003, 2004; Ranalli et al. 2004; Pieraccini et al. 2004; Bavusi et al. 2008; Barone et al. 2010; Kadioglu and Kadioglu 2010; Utsi 2010; Leucci et al. 2010). In particular, some issues of structural interest are the possible presence of fractures, voids, infiltrations of humidity or metallic bars due to previous restoration works, possibly dating back to centuries ago (Sambuelli et al. 2010) and not adequately documented. These investigations are well-advised especially if new restoration works are scheduled. In particular, the nondestructive investigations can provide information for addressing the restorations properly and enable one to check the success of the restoration works by means of post-intervention monitoring. Some issues of historical interest are the presence of tombs, walled rooms, and hidden pictures, mosaic and floors (Grasso et al. 2011; Pieraccini et al. 2006). In particular, the changes that a building has undergone through the centuries have not been documented in many cases, or in other cases the documents have been lost. In some cases, the significance of a retrieved buried target can be both historical and structural, as, for example, in the case of a hidden crypt under a church. NDT geophysical surveying has long been a standard tool of archaeology in Europe. With increasing numbers of skilled practitioners and the development of methodologies suited for European sites, highly successful surveys are becoming the norm. No NDT geophysical method can be applied indiscriminately with any expectation of success. Soils, geology, surface conditions, vegetation and terrain, feature type, size, composition, depth, modern impacts, and many other factors must be considered in determining feasibility, appropriate instrumentation, and survey design. Although mathematical models may be applied to survey design problems, field conditions are difficult to quantify. In spite of ongoing progress in this field, assessment is largely qualitative and empirical. Issues related to interpretation are similar, and experience is critical in understanding how the archaeological record is expressed geophysically. Use of multiple methods is good practice in most geophysical survey applications. Not only does this increase the likelihood of success with at least one method, but it can also greatly enhance interpretability. Because each geophysical method responds to different properties, multiple data sets are complementary rather than redundant. For example, a resistance high might correlate with a magnetic dipole, identifying (depending on the cultural context) a possible hearth,

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whereas either anomaly by itself would be ambiguous. The general procedure followed to perform most ground-based surveys is to divide the survey area into a series of square or rectangular survey “grids” (terminology can vary). Each grid is surveyed by taking readings at regular intervals along regularly spaced transects. Successive transects are surveyed in a zigzag pattern until the grid is completed. The value and position of each data point is recorded, generally in digital format. Occasionally, these instruments are also used for less formally “scanning” areas of interest. In Europe, there occurs a huge number of archaeological objects of various age, origin, and size. This link to applications of various geophysical methods is armed by modern interpretation technology. The geophysical investigations at archaeological sites in Europe could be tentatively divided on three stages: (1) past, (2) present, and (3) future. The past stage with very limited application of geophysical methods was replaced by the present stage with the violent employment of numerous geophysical techniques. It is supposed that the future stage will be characterized by extensive development of multidiscipline, physical archaeological databases, employment of all possible indicators for 4-D monitoring of monumental heritage and ancient sites reconstruction, as well as application of combined geophysical multilevel surveys using remotely operated aerial vehicles at low altitudes. In 1921, Colonel William Hawley relocated a circular distribution of buried pits, invisible on the surface since the observations of slight depressions by the antiquarian John Aubrey in 1666, surrounding the familiar ring of raised sarsens (Cleal et al. 1995). Hawley’s method was simple: merely probing the ground by inserting an iron bar and noting the maximum depth of penetration. Given the thin layer of soil developed over the underlying chalk, the presence of a buried pit, cut into the bedrock, was easily distinguished by the more readily yielding sediment that they contain. Indeed, it is unlikely that this was even the first application of geophysical prospecting for archaeology as the pioneering archaeologist: Lieutenant-General Augustus Pitt Rivers reported the successful use of ‘bowsing’ (striking the ground with a pick and listening for any change in the timbre of the impact) during his excavations at Handley Down, Dorset in 1893–1895 (Clark 1990). Interest in this area of research grew rapidly with the development of aerial photography that reveals a rich tapestry of hidden archaeological sites, often appearing only very briefly during fortuitous combinations of climatic conditions, cropping regimes, and aircraft movements. The physical contrasts creating the anomalies recorded by aerial photographs are numerous and vary from visible soil stains found within the thin soils developed over down-land chalk to stress marks within susceptible crops above a near-surface buried wall, depriving the topsoil of essential moisture reserves. Despite the continued success of aerial photography, with new discoveries regularly coming to light, a desire to obtain a less remote, ground-based means of prospecting led to the development of modern methods of geophysical survey. The first use of modern geophysical methodology applied in Europe would appear to have been conducted in 1946 by Atkinson in Britain during which he undertook an earth-resistance survey over the site of a Neolithic henge monument near Dorchester-on-Thames (Linford 2006). An account of this survey was published in the second edition of Atkinson’s influential text on field archaeology (Atkinson 1953) that brought geophysical methodology to the attention

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of a wide range of practitioners eager to test this new means of discovery. Rapid development occurred with the availability of purpose-built instrumentation and the investigation of new methodologies, often spurred by significant developments in apparently unrelated fields. For example, the principle of proton free precession in the Earth’s magnetic field led to the development of field magnetometers including one such device constructed by Edward Hall and Martin Aitken at the Research Laboratory for Archaeology and the History of Art at Oxford University. In March 1958, the first known magnetic survey for archaeological remains was conducted. The pace of development then quickened with the availability of transistorized electronics and the growing sophistication of digital computers. Key developments were the introduction of practical field earth-resistance meters (e.g., Clark 1957), fluxgate gradiometers (e.g., Alldred 1964), high-sensitivity alkali vapor magnetometers (e.g., Ralph et al. 1968), rapid-acquisition wheeled resistivity arrays (e.g., Hesse 1981), research into electromagnetic methods (e.g., Colani 1966), ground-penetrating radar (e.g., Bevan and Kenyon 1975), and algorithms for data processing and display (e.g., Scollar and Kruckeberg 1966). The important growth in teams of European researchers able to apply this new instrumentation and methodology should also not be overlooked. Archaeologists could now consult and commission geophysical survey from a growing body of researchers, some based in university departments, research center, others as dedicated commercial contractors. Nowhere, perhaps, was this more apparent than in the Europe where an exponential rise in the application of geophysical survey in the last 20 years. The need to consider the impact of development on the whole environment, including potential archaeological resources, led to an enormous demand for geophysical techniques to locate, map, and classify significant remains ahead of construction. One area that should not be ignored is the important influence that the availability of affordable digital computing has had on archaeological prospection. This is, of course, true for nearly every area of physical science, but archaeological geophysicists are somewhat unique as they demanded an almost impossible combination of powerful microprocessors, portability for field use, and a low cost to fit slender archaeological budgets. In many respects, the availability of suitable computing power imposed a limiting factor on the early application of geophysical methodology. Although today’s students have inherited a mature discipline, a resurgence in many areas of research has led to new discoveries and the reevaluation of previously discounted methodologies. For example, Ground-Penetrating Radar (GPR) suffered a rather checkered history in archaeological geophysics with many early successes (e.g., Vaughan 1986) outweighed by the frustration of overenthusiastic interpretation of a single profile of data (e.g., Stove and Addyman 1989) and the expense of employing the technique. More systematic research has now begun to define the limitations of the technique, greatly assisted by advances in data processing and visualization, and few archaeologists can fail to be convinced by the detail revealed by GPR survey over a suitable site (e.g., Conyers and Goodman 1997; Leckebusch 2003). Important advances in GPR systems were obtained by an Italian research group inside the Institute for Archaeological and Monumental Heritage (CNR). They designed and realized a GPR, reconfigurable, stepped-frequency system for detection and localization of underground targets. The

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system is able to change the length of the transmitting and receiving antennas by means of the switches that can connect or detach adjacent pieces of the arms versus the frequency. In this way, we have three equivalent couples of antennas that cover a comprehensive band ranging from 50 to 1000 MHz. The system can also modulate versus the frequency the transmitted power and the integration times of each radiated harmonic signal, so that the band of each of couple of equivalent antennas can still be enlarged, and above all narrow-band interference can be rejected in an effective way, i.e., without a strong increasing of the overall required measurement time. The European Convention on the Protection of the Archaeological Heritage, known as Valletta Convention (Trotzig 1993; http://conventions.coe.int/Treaty/EN/ Treaties/Html/143.htm) requires from each signatory “to ensure that archaeological excavations and prospecting are undertaken in a scientific manner” and that “nondestructive methods of investigation are applied wherever possible”. It is hoped that future developments will lead to a stringent implementation of the Valletta Convention and a greater acceptance of geophysical archaeological prospection in European archaeology. Its routine application for the investigation and protection of endangered cultural heritage will benefit current and future generations. The future of archaeological geophysical prospection in Europe is today highly dependent on changing attitudes among professional European archaeologists. To convince archaeologists of the benefits of using archaeological geophysics, it is necessary to combine highquality geophysical surveys with solid archaeological interpretations concerning the collected data. If this approach is combined with educational campaigns aimed at policy makers and professional archaeologists to show the pitfalls and possibilities of the geophysical methods available, it would probably be possible to increase and advance the use of the methods further. Furthermore, an improved integration of geophysical prospection techniques within academic archaeology courses would enable students to achieve a better understanding of how these methods can be implemented as an integrated tool in professional European archaeology. High-resolution geophysical archaeological prospection has the potential to make archaeological excavations more efficient, both in regard to costs and time. It also has a possibility to aid researchers in obtaining information on sensitive archaeological sites that may not be suitable for investigations using traditional invasive archaeological methods. While currently geophysical archaeological prospection in Europe is often still regarded as an extra cost, the method’s main advantages are: (i) their entirely nondestructive character; (ii) their potential to efficiently pinpoint areas of interest within large sites; (iii) their potential to enable targeted excavations, or to abstain entirely from invasive excavations; (iv) their potential to provide complementary information about archaeological structures beyond the limits of excavation trenches; and (v) their potential to image archaeological structures in the ground that otherwise would remain undetected. The implementation of a centralized national database containing information and results of archaeological geophysical prospection surveys performed in Europe would furthermore enable the archaeologists interested in archaeological geophysics to evaluate the quality of data and data interpretation from different sites and surveyors. The geophysical toolbox for archaeological prospection will evolve further in the future and developments towards faster, more efficient survey solutions,

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new data analysis and interpretation algorithms, and integrative interpretations and visualizations in 3D GIS environments are currently being pursued. The amount of data collected will increase rapidly, demanding new routines for data handling and storage. The future will also see the use of highly efficient motorized magnetometer and GPR systems with very dense measurement spacing, guiding and supplementing both research and exploration archaeology. Geophysical prospection data will be integrated with high-resolution digital terrain models and other geospatial data making possible much improved scientific analysis and presentations of the results to the public. In this regard, the 2010 foundation of the Austrian Ludwig Boltzmann Institute for Archaeological Prospection and Virtual Archaeology (LBI), together with its international partner (such as IBAM–CNR Italy) organizations dedicated to the development of new techniques and methodological concepts for remote sensing, geophysical archaeological prospection, and archaeological interpretation and virtual archaeology, will break new ground in Europe. The LBI, Birmingham University (The Visual and Spatial Technology Centre), the Roemisch-Germanisches Zentralmuseum in Mainz, Germany, and IBAM in Italy are now the major accredited institutions for large-scale archaeological prospection (Fig. 3.1). The restrictions of satellite optical imagery for the detection of archaeological features are well overcome by Airborne Laser Scanning (ALS), also referred to as LiDAR (Light Detection and Ranging), which provides direct range measurements mapped into 3D point clouds between a laser scanner and earth’s topography. ASL can penetrate vegetation canopies making possible for the underlying terrain elevation to be accurately modelled. Therefore, it is a powerful tool for recognizing and investigating archaeological heritage in wooded areas, usually well preserved due to the vegetation cover which protects the sites from erosion and from possible damage by mechanical ploughing.

3.2 NDT Geophysical Methods This part of the book presents the background theory of the most commonly applied NDT geophysical methods: ground-penetrating radar (GPR), active and passive electrical (electrical-resistivity tomography—ERT, induced polarization—IP, and selfpotential—SP), and seismic sonic and ultrasonic tomography. Like all these methods, those described are nondestructive and useful for describing both the subsurface conditions and monumental-heritage conditions without requiring test excavation or core sampling.

3.2.1 The Ground-Penetrating Radar Method Ground-Penetrating Radar (GPR) is one of the most recent techniques developed in the field of nondestructive geophysics (in relation to other techniques, such as seis-

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Fig. 3.1 Detection of archaeological features by using various geophysical methods

mic, electrical, etc.), even if the idea to use electromagnetic waves to see through the subsoil dates back to the beginning of the century. The GPR technique is among the most used by the scientific community, thanks to the potential applications offered in various fields, such as civil engineering, hydrogeology, geology, monumental heritage, archeology, and the environment. In many cases (especially in the second half of the eighties), this technique was considered because the resolution of many geophysical problems could not be dealt with by other methodologies. Only in recent years has a more rational approach taken place, aimed at developing a systematic experimentation for identifying its real potential and its limits. GPR could be consid-

3.2 NDT Geophysical Methods

23

ered as one of the more complex methods because it involves the collection of large amounts of data that producing massive 3D databases. A correct use of this technique requires knowledge, in general terms, of the problems related to this methodology, which will be discussed below. GPR methodology consists of the identification of the electromagnetic discontinuities present in the subsoil and/or in the investigated materials due to isolated layers or bodies, having different dielectric characteristics with respect to the surrounding environment. The discontinuities that generate electromagnetic-wave reflections are linked to changes in the dielectric characteristics of the terrain matrix present in the subsoil or, in general, in the material used for the monumental heritage construction, which may be due to lithological changes, to variations in the water content, or to empty spaces present in the ground, such as burials, tombs, tunnels, and fractures. Depth of penetration and the resolution of a GPR survey depend on several factors related to the type of soil and/or material, the chemical composition, the clay content, the moisture content, etc. This is a nondestructive technique that uses short pulses (ranging between 1 and 10 ns) at high frequency (ranging from 10 MHz to some GHz), emitted and received by one or more antennas. Monostatic is the word used to indicate that a single antenna works as a transmitter (Tx) and receiver (Rx). Bistatic is the word used in the case of two antennas working in a separate mode as Tx and Rx, respectively. Clearly the choice of the antennas to be used is determined by the target of the GPR investigation and therefore by the depth of investigation and the size of the anomalous bodies to be investigated. In the two configurations, the acquisition technique normally used is the “continuous profile” (Fig. 3.2). As can be understood from the term “continuous mode”, this acquisition technique consists of moving the antenna (or pair of antennas) continuously along a defined profile, trying to keep the dragging speed constant. The acquisition technique “by points” is instead used in situations of particular condition that determine an impediment in moving the antenna, (presence of obstacle such as walls, pebbles, and trees). In this case, one or both the antennas are moved at discrete spatial intervals. The result of a GPR survey is a radar profile or radar section, in which the set of traces acquired is displayed while the antenna moves on the ground; in these two-dimensional sections, one of the dimensions represents the line along which the antenna was moved and the other the two-way travel time of the electromagnetic wave reflection events. The two-way travel time, once defined the velocity of propagation of the electromagnetic wave within the investigated material, can be transformed in depth. The radar sections can be displayed in wiggle-trace mode (Fig. 3.2c) or in linescan color (Fig. 3.2b) where the different color tones depend on the intensity of the electromagnetic signal amplitude. The amplitudes of the reflected electromagnetic waves are related to the changes in the physical and chemical properties of various

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Fig. 3.2 a Example of data acquisition with the continuous profile mode; radar sections in line-scan color representation (b); and wiggle trace (c)

materials in the ground, and therefore it is important to enhance them in the radar sections using appropriate filter and data amplification techniques. The electromagnetic waves that propagate in the ground and/or in general in the investigated material are a form of electromagnetic energy composed of oscillating electrical and magnetic fields. The phenomena of propagation of the electromagnetic field within homogeneous and isotropic materials are governed by Maxwell’s (Fig. 3.3a) equations, which in an electrically neutral medium (ρ  0 where ρ indicates the charge density), are: ∇ ·E0

(3.1)

∇ ·H0 ∂H ∂B  −μ ∇ ×E− ∂t ∂t ∂D ∂E ∇ ×HJ+  σE + ε ∂t ∂t

(3.2) (3.3) (3.4)

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25

Fig. 3.3 a James Clerk Maxwell, Scottish physicist and mathematician (born in Edinburg, 13 June 1831 and died in Cambridge, 5 November 1879); b Jean Le Rond d’Alembert, French mathematician, philosopher, and writer (born November 17, 1717, Paris, and died 29 October 1783, Paris)

where E is the electric field vector, B is the magnetic induction vector, D is the electric displacement vector, H is the magnetic field intensity vector, and J is the conduction current density. Maxwell’s equations are accompanied by constitutive relations: D  εE B  μH J  σE

(3.5)

where σ, ε, and μ are respectively conductivity (S/m), electrical permittivity (F/m), and magnetic permeability (H/m); these parameters, in a homogeneous and isotropic medium, are constant quantities. Calculating the rotor of both members of Eqs. (3.3) and (3.4), after appropriate substitutions, the D’Alembert (Fig. 3.3b) equations are obtained ∂ 2H ∂H 0 − σμ 2 ∂t ∂t ∂ 2E ∂E 0 ∇ 2 E − εμ 2 − σ μ ∂t ∂t

∇ 2 H − εμ

(3.6a) (3.6b)

These are vector equations, which means that each of the components of the vectors E and H satisfies a scalar equation of the type ∇ 2  − εμ

∂ 2 ∂ 0 − σμ ∂t2 ∂t

(3.7)

whose simplest (but not the most general) solution is that of the plane-wave type in which  is only a function of time t and one of the spatial coordinates, for example, z:

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(z, t)  0 eiωt−γ z Replacing in Eq. (3.7), the following equation is obtained  σ γ 2  iωσ μ − ω2 εμ  −ω2 μ ε − i ω Since γ is a complex number, we can always write it in the form γ  α + iβ and therefore γ2  α2 −β2 +2iαβ. By comparing the two expressions of γ2 , the following equation is obtained α2 − β2 + 2iαβ  −ω2 εμ + iωσμ from which it is possible to derive α and β:   1/2  σ 2 1 1+ −1 α  ±ω εμ 2 ωε   1/2  σ 2 1 √ β  ±ω εμ 1+ +1 2 ωε √

(3.8a)

(3.8b)

where α is called absorption constant and β is called the phase constant. The values of the constants in Eqs. (3.8a) and (3.8b) are: μ  μ0 μr  (4π) × 10−7 H/m (μr  1) ε  ε0 εr  8.85 × 10−2 εr  εr /(36π × 109 ) F/m ω  2πf The value of the dielectric constant εr for various rocks can be obtained from the literature or from measurements on small samples in the laboratory. Using the complex expression of γ, we can write (z, t)  0 eiωt−γz  0 eiωt−(α+iβ)z  0 e−αz e−i(βz−ωt)

(3.9)

which represents a plane wave that propagates along the z direction, with phase velocity vF  ω/ β and which is attenuated by an exp factor (−αz). Note that if the medium is not conductive (perfect dielectric), σ  0, then α  0, √ and then β  ±ω εμ In this case, Eq. (3.9) represents a plane wave that propagates, without attenuation, with velocity: vF 

ω c 1 ω  √ √ √ β ω εμ εμ εr μr

The ratio n  c/v  (εr μr )1/2 is the index of refraction of the medium.

3.2 NDT Geophysical Methods

27

By applying the solution found to the vectors, E and H, it is possible to obtain E  E0 eiωt−γ z and H  H0 eiωt−γ z . Since E  E (z, t) and H  H (z, t), all the partial derivatives of the components of E and H with respect to x and y axes are null, so substituting in the Maxwell equations, the components along the z-axis of the electric and magnetic fields, i.e., Ez and Hz, are null. Therefore, these fields are orthogonal to each other and orthogonal to the direction of propagation of the plane wave. The plane wave is therefore “transverse”: H

1 k×E Z

where k is a versor associated with the propagation direction. Moreover, the vector fields E and H are linked to each other by the relation involving the quantity Z called “wave impedance”: 

1  Ey Ex jσ − 2 ωμ μ  1− − Z ± Ey Ex ωε − jσ ε ωε

(3.10)

 In the empty space σ  0 e Z 0  με00 ∼  376.6 (ohm). The amplitude I of a wave that propagates within a supposed dispersive medium (with σ  0 and Z complex) undergoes an attenuation which, in differential terms, is equal to: dI  −αdz I By integrating both members, for a homogeneous and isotropic medium, we obtain I(z)  I0 e−αz the distance z at which the amplitude decreases to 1/e of the original value (= 0.368  36.8%) is called the skin depth and is: δ  1/α

(3.11)

For the reflection and refraction of plane waves in dissipative media, it is possible define the reflection coefficient R as the ratio between the amplitude of the reflected wave and incident wave, and the transmission coefficient T as the ratio between the amplitude of the transmitted wave and the incident wave. In the case of normal incidence, these coefficients can be written according to the characteristic impedances of the two means (considered semi-infinite) as: R

Z2 − Z1 Z2 + Z1

(3.12)

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T

2Z 2 Z2 + Z1

(3.13)

From the expression (3.10), we see that Z is expressed in terms of the parameters that describe the electromagnetic properties of the material, and this gives the opportunity to express the R and T coefficients according to these parameters and to distinguish four different situations depending on the quantity σ/ωε. 1. In the case of dielectric medium (low conductivity σ), we have √ √ ε1 − ε2 R √ √ ε1 + ε2

(3.14)

2. In the case of first dielectric medium (low σ) and second conductive medium (high σ),    √ σ2 ε1 − ε2 1 − j ωε 2 R (3.15)    √ σ2 ε1 + ε2 1 − j ωε2 3. The third case provides the first conducting medium and the second dielectric, then analogous to the previous one with inversion of the subscripts; 4. In the case of both conductive medium: √ √ σ1 − σ2 R √ (3.16) √ σ1 + σ2 There are two important observations to make: the first is that we considered the case of non-magnetic materials, as are generally the geological ones, in which we assumed μ1  μ2  μ0, where μ0 is the magnetic permeability in the vacuum; The second is that of the four cases mentioned, only the first two are interested in the exploration of GPR (Hara and Sakayama 1984) because, when the upper layer is conductive, the attenuation factor is high. The electromagnetic wave velocity of propagation v and the attenuation α depend substantially on the dielectric and conductive (ε and σ) properties of the materials. The dependence on magnetic permeability μ is, however, negligible (Lazaro-Mancilla and Gomez-Treviño 1996) because geological materials are generally non-magnetic, so it is possible to assume μ ≈ μ0 . When the medium crossed by the electromagnetic wave has a high conductivity, the energy will be attenuated in a very fast mode. Extremely conductive media are salt water, clay (especially if wet), and soils and sediments that contain dissolved salts or electrolytes. The most important physical property that influences the propagation of electromagnetic waves through a medium is the “relative dielectric permittivity εr ”; it can be considered an index of the capacity of a material to acquire a degree

3.2 NDT Geophysical Methods

29

of polarization when it is placed in an electromagnetic field. The relative dielectric permittivity is given by the ratio between the electrical permittivity of the material ε and the vacuum ε0 , and varies with the composition, the water content, the density, the porosity, the physical structure, and the temperature of the material; it also depends on the frequency of the irradiated electromagnetic wave. In general, the higher the εr of the material, the lower is the velocity of propagation of the electromagnetic wave. Moreover, the greater the difference in εr between the materials of the subsoil, the greater will be the amplitude of the generated electromagnetic-wave reflections. To generate significant reflection, the variation of εr between two materials must occur at short distances; a gradual change generates only weak reflections or even no reflection. The permittivity εr can be defined in a complex way by the relation (Von Hippel 1954)

σs   (3.17) εr  εr + i εr + ωε0 where εr is the real part, σs is the conductivity in continuous, i.e., linked to the static field conditions, εr is the permittivity associated with molecular relaxation phenomena, due to the fact that the application of an alternate electric field does not follow an instantaneous biasing process (this delay is the relaxation), and ω is the frequency of the incident wave. At the radar frequencies (10–1000 MHz), the dielectric properties dominate the conductive ones. In this interval, the speeds do not seem influenced by the frequency (Fig. 3.4).

Fig. 3.4 Electromagnetic-wave velocity of propagation trend as a function of frequency (Davis and Annan 1989 (modified))

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For conductivity lower than 100 mS/m, the velocity remains substantially constant in the radar frequency range and can be expressed as a function of the real part of the relative dielectric constant: c v εr

(3.18)

Davis and Annan (1989) published a table that summarizes the values of relative dielectric constant, electromagnetic wave velocity, conductivity, and electromagnetic wave attenuation related to several soil materials (Table 3.1). It can be seen that the real part of the dielectric constant of water is 80, while the dielectric constant of many dry geological materials is in the range of 4–8: this great difference explains why the electromagnetic-wave velocity is strongly dependent on the water content in the traversed materials. Very important in GPR surveys is the choice of the antenna to use to obtain the best result: the ability to resolve buried bodies and the depth to be achieved are, in fact, mainly determined by the frequency and therefore by the length of the transmitted wave. The factors that must be considered are the dimensions and the depth of the object to be highlighted, and furthermore it is necessary to carefully examine the survey area to identify the presence of obstructions or impediments on the surface, electrical power lines, radios FM and cellular repeaters, etc., that can limit the use of some antennas. GPR systems generally use dipole antennas that have a bandwidth of two octaves, i.e. frequencies vary between 1/2 and 2 times the center-band frequency.

Table 3.1 Values of the relative dielectric constant εr , electrical conductivity σ, electromagneticwave velocity, and attenuation in some geophysical materials (Davis and Annan 1989) Materials εr  ε/ε0 σ (mS/m) V (m/ns) α (dB/m) Air

1

0

0.30

0

Distilled water Fresh water

80 80

0.01 0.5

0.033 0.033

2 × 10−3 0.1

Salt water Dry sands

80 3–5

3 × 104 0.01

0.01 0.15

103 0.01

Saturated sands limestone Shale Silt clay

20–30 4–8 5–15 5–30 5–40

0.1–1 0.5–2 1–100 1–100 2–1000

0.06 0.12 0.09 0.07 0.06

0.03–0.3 0.4–1 1–100 1–100 1–300

Granite Dry salt

4–6 5–6

0.01–1 0.01–1

0.13 0.13

0.01–1 0.01–1

3.2 NDT Geophysical Methods

31

High-frequency antennas (>500 MHz) provide high spatial resolutions, but limited depth of penetration, so they are suitable for investigating only small thicknesses. In contrast, low-frequency antennas enable greater penetration depth, but lower spatial resolution. The frequency band, normally used by GPR systems, ranges from about 10 MHz to about 2 GHz (the depth of penetration, in this last case, is drastically reduced to a few cm). In addition, the low-frequency antennas are wider, heavier, and less manageable than higher-frequency antennas. The depth of penetration and resolution also depend on many site-specific factors, such as soil composition, its porosity, and retained moisture. The resolution, for impulsive type radar, is defined by the duration of the transmitted pulse Tp. In fact, the minimum distance L that must exist between two targets in order to be resolved is linked to Tp by the relationship: Tp
(2Lmax /c)  tmax

(3.20)

where Lmax is the unambiguous maximum distance and tmax is the time necessary for the impulse to return to the receiver after being reflected by a target placed at a distance Lmax . The following Table 3.2 is given. The electromagnetic waves transmitted by a standard antenna are irradiated through the ground in a generally elongated elliptical cone. The radiation lobe is generated by a horizontal dipole antenna, to which some protection elements are added (often metallic foils) which reduce the emitted radiation upwards (shielding). When a dipole antenna is placed in the air, the path of the radiation is approximately perpendicular to the antenna axis. When instead it is placed in contact or near the ground and/or the surface of the investigated materials, there is a change in the shape of the radiation lobes due to the coupling with the ground. Variation of both the shape and the lobe directivity also occurs at the variation of h/λ, where h is the height from the ground of the antenna and λ is the wavelength Table 3.2 Wavelength values λ as a function of the frequency at several electromagnetic-wave velocities of propagation (Leucci 2015) Freq. (MHz) P (ns) λ (m) at v  c λ (m) at v  (1/3)c λ (m) at v  (1/6)c 1 10 30 100 300 500 1000 2000 3000

1000 100 33 10 3.3 2 1 0.5 0.33

300 30 10 3 10 0.6 0.3 0.15 0.1

100 10 3.3 1 3.3 0.2 0.1 0.05 0.03

50 5 1.65 0.5 1.65 0.1 0.05 0.025 0.015

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33

Fig. 3.6 Radiation diagram of a dipole antenna placed on the air–ground interface

of the pulse in the first medium (air). For example, if h/λ ∼  0.1, there is a good reduction of the posterior lobe and a not excessive enlargement of the lobes in the ground (Fig. 3.6). The radiation cone (related to the first zone of Fresnel) that intercepts a horizontal flat surface illuminates an ellipse-shaped area with the major axis parallel to the antenna’s trailing direction (Annan et al. 1991). The radiation lobe in the subsoil enables “looking” not only directly under the antenna but also in front, back, and sides as the antenna travels along the ground. This is known as horizontal resolution. If there are long and narrow targets in the subsoil, the best way to highlight them is to intersect them with orthogonal profiles to their elongation direction. The estimation of the radiation lobe is especially important when designing the spacing between the lines of a grid, so as to highlight all the targets of a certain importance in the subsoil. In general, the angle of the cone is defined by the relative dielectric constant of the material traversed by the electromagnetic waves and by the frequency of the transmitter antenna. An equation that can be used to estimate the width of the transmission beam at various depths (the footprint) is (Conyers and Goodman 1997): A

D λ +√ 4 εr + 1

(3.21)

where A is the approximate dimensions of the radius of the footprint, λ is the wavelength of the electromagnetic impulse, D is the depth at which the reflecting object is located, and εr is the relative dielectric constant of the crossed medium (Fig. 3.7). Equation (3.21) can only be used as a rough approximation of the real case because the dielectric permittivity of the medium in which the energy propagates was considered constant. Once the frequency to be used in the GPR survey is chosen and the propagation velocity in the medium that enables us to estimate the depth (D) of the reflections, the relationships written as Eqs. (3.18: λ  v/ f0 ) and (3.21) make it possible obtain the wavelength, the dielectric constant, and the radius of the footprint, and consequently the vertical and horizontal resolution power of the GPR investigation. It is evident that, considering a constant value for the electromagnetic-wave velocity v, the vertical and horizontal resolution power increases with increasing of the frequency. But it is also known that, as the frequency increases, the absorption power of the medium increases and therefore the depth of penetration decreases (Davis and

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Fig. 3.7 Elliptical cone of GPR penetration into the ground (Leucci 2015)

Annan 1989). Therefore, the first problems arise at the air-ground interface, where the first refraction of the propagating wave occurs. The higher the dielectric constant εr of the material of which the subsoil is constituted, the lower is the velocity of the transmitted electromagnetic wave, with the consequence that the foot print is more focused in the transmission through the ground. If the εr decreases, the cone expands with consequent energy dispersion. The expansion of the energy cone under the antenna enables “seeing” a target not only when the antenna actually passes over it, but also before and immediately after, generating the classic “hyperboles” that are often noticed in the radar traces (Fig. 3.8). Some antennas are not shielded and radiate in all directions. Unshielded antennas can record reflections generated by the same operator that drags the radar equipment along the profile, or from some nearby objects, such as a tree or a car, houses, and power lines (Fig. 3.9). These reflections obviously make data analysis more difficult. Buried surfaces that contain dips or ridges can focus or scatter radar energy, depending on their orientation to the surface antenna. If, for example, a surface has an upward convexity, much of the radar energy will be reflected away from the antenna, and no significant reflection will be recorded. This is the so-called “radar scattering”. If instead the buried surface has a concavity upwards, then the energy will be focused towards the antenna, and a very intense reflection will be recorded (Fig. 3.10). Moreover, since there are no losses by absorption in the vacuum, a fair amount of energy can be trapped inside a cavity and the wave can “bounce” more than once from

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35

Fig. 3.8 Forward model: two homogeneous layers with a dielectric constant of 16 and 9 were modelled for the calcarenite and hard bedrock, respectively. In the bedrock, a void space with dielectric constant of one, represents the aqueduct. A soil-filled karst feature, with dielectric constant of 20, was placed at the contact between the two hypothesized layers. It is possible to discern a classical-hyperbolas reflection event (Leucci et al. 2016)

one wall to another, generating reflections every time, which on the radar section are identified as “multiple reflections” (Fig. 3.10). The first contribution to electromagnetic wave attenuation comes from the geometric effect which, in a homogeneous and isotropic medium, provides a decrease of the energy per unit of area that results proportional to 1/r2 . Where “r” represent the distance from the source of electromagnetic wave. When EM waves propagate in the ground and/or in a material, the center-band frequency shifts below the nominal frequency, due to the increased absorption of high-frequency energy. The new propagation frequency will depend on the dielectric properties of the soil. It is important to be aware of this shift of the center-band frequency towards the low frequencies because it will influence all the parameters of the propagation of electromagnetic waves in the ground (velocity of propagation, shape of the radiation lobe, depth of penetration of the signal, resolution, etc.). Moreover, the attenuation suffered by the EM signal in the propagation is mainly caused by the absorption due to the conductivity (Fig. 3.11).

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Fig. 3.9 Scheme of spurious diffractions or reflections coming from objects located above the walking plan that are visible as reflection events labelled D1 and D2 in the GPR sections (200-MHz antenna) (Leucci and Negri 2006)

The attenuation of electromagnetic energy increases as the water content in the soil increases and also varies with the amount and type of salts present in the medium. A high degree of signal attenuation can also be caused by high concentrations of dissolved carbonates in surface soils (Batey 1987). Generally, materials with low electrical conductivity (high resistivity) enable better propagation of the electromagnetic wave and have a low εr . Materials that have a high electrical conductivity and a high εr , such as saturated clays, prevent the propagation of the electromagnetic wave. This phenomenon is expressed by the absorption coefficient α which is found in the relationship that expresses the intensity E of the electric field as a function of the propagation distance

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37

Fig. 3.10 Forward model: two homogeneous layers with a dielectric constant of 20 and 16 were modelled. It is possible to note the a radar scattering; b radar focusing; c expect result on radar section

Ex  E0 exp(−αx)

(3.22)

It is often convenient to express attenuation by absorption in dB per foot, and, indicating by A the logarithmic decrease, it is possible to obtain (Leucci 1999): A  20(0.305/2.301)α  2.65α

(3.23)

and expressing A in dB/m, as 1 ft  30.48 cm, it is possible to obtain: A  8.69 α dB/m where α is calculated, in the MKS system, by (3.8a).

(3.24)

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Fig. 3.11 Example of change of shape of the electromagnetic-wave spectrum in the propagation through the ground

The relationship (3.23) is obtained starting from (3.22). In fact, applying the logarithm in base 10 to both members of (3.22), it is possible to derive: log10 E x  log10 E 0 + log10 e−αx i.e. log10 E x − log10 E 0  −αx log10 e knowing that log10 e  0.434 (its inverse is 2.301) and 1 ft  0.305 m is possible to have: log10

x E0  α Ex 2.301

setting x equal to one foot (i.e., 0.305) and remembering the definition of decibel is obtained:

3.2 NDT Geophysical Methods

20 log10

E0  Ex

 20

39

0.305  α that is Eq. (3.23). 2.301

In less dispersive medium, an approximate relationship can be used for attenuation α (Annan and Davis 1989): α

1.69 × 103 σ dB/m εr

(3.25)

where σ is the electrical conductivity of the investigated medium. The most delicate phase of the GPR survey is the estimation of the average electromagnetic-wave velocity with which the electromagnetic pulse propagates within the surveyed medium. A good knowledge of this very important parameter enables the operator to establish approximately the depth at which the objects responsible for the reflection events observed in the radar sections are located. The values of electromagnetic-wave velocity of propagation in GPR prospections ranging between 30 cm/ns in the air and about 1 cm/ns for salt water. Data acquisition techniques for electromagnetic-wave velocity measurements are essentially two: WARR (wide angle reflection and refraction) and CMP or CDP (common midpoint or common depth point). Both require the use of two antennas (Fig. 3.12). WARR acquisition technique requires that an antenna, generally the transmitter, is kept fixed while the other moves along the chosen profile at a very low and constant speed. In CDP, the antennas must be moved an equal distance, from the opposite side to a common fixed point. Both methods require the reflection surface to be identified preliminarily by the analysis of the radar profiles previously acquired on the site. Several methods are available in order to estimate the velocity of propagation of electromagnetic waves. Each of these has some advantages and disadvantages in practical applications and limits in accuracy. (1) Location of objects at known depth: The two-way travel time is the time that an electromagnetic wave takes to travel through the ground, from the transmitting antenna to the object and back to the receiving antenna. Denoting the depth of the known object with a zknown and the velocity of the electromagnetic wave with v, the two-way travel time for a monostatic configuration of the antenna is given by: t

2zknown v

(3.26)

Since the depth of the object is known, you can take the double travel time from a radar section and express the velocity of the electromagnetic wave using Eq. 3.26 (Fig. 3.13). (2) Reflection from a source point: This is a fast method for estimating speed and is based on the phenomenon that a small object, for example, the cross section of a tube, reflects radar waves in almost all directions (Fig. 3.14).

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Fig. 3.12 a WARR and CMP scheme of acquisition; velocity analysis on selected b WARR and c CMP

Fig. 3.13 Electromagnetic-wave velocity measurements: a the known pipe depth (0.3 m); b the two-way travel time related to reflection event by pipe (6 ns). The calculated electromagnetic-wave velocity will be v  2zknown /t  0.6/6  0.1 m/ns

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41

Fig. 3.14 a Geometry of the reflector point; b Velocity analysis with the diffraction-hyperbolas method

Denoting the depth of the object with z and the lateral distance of the monostatic antenna from the object with x, the length w of the wave path can be simply expressed by: w2  4(x2 + z2 ) and therefore the function of the two-way travel time with: √ w 2 x2 + z2 t(x)   v v

(3.27)

(3.28)

Denoting with t0 the two-way travel time, on the vertical to the object, one has t0 

2z v

(3.29)

4x2 2 + t0 v2

(3.30)

Therefore:  t(x) 

which is the formula for the so-called “ diffraction hyperbola”. Since we know, from the radar section, for each x position, the corresponding double travel time t(x), the velocity can be calculated by inverting Eq. (3.30). The shape of the hyperbola is governed by the velocity of the wave through the ground and by the geometry of the buried object (Fruhwirth and Schmoller 1996) (Fig. 3.14b). (3) Registration of a simple CDP: In a CDP measurement transmitter and receiver are moved away from each other in equidistant steps (Fig. 3.15a), and, at each position, a trace is measured. This way, the reflected signal can be measured using a number of different angles. The resulting radargram displays the travel time as a function of the antenna separation (Fig. 3.15b). Since air and groundwaves travel directly between the transmitting and receiving antenna, there is

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Fig. 3.15 EM-wave velocity measurements: a CDP acquisition scheme; b CDP radargram

a linear relationship between the travel time t of each wave and the antenna separation a with the constant of proportionality 1/v: t  a/v, with v  c for the air wave and v  c/(εr )1/2 for the ground wave. Due to their different velocities, the slopes of both direct waves in the travel-time diagram are different. Consequently, the propagation velocity v of the electromagnetic wave through the soil can be determined directly from the radargram by estimating the slope of the ground wave. Since the ground wave travels near the soil-air interface, it covers that soil section which is, for example, important for plant growth. The airwave travel time is usually applied during data processing as a reference for calculating absolute travel times. From a CDP measurement, one can determine the reflector depth below the midpoint between the transmitting and the receiving antenna. From the reflection hyperbolas displayed in the travel-time diagram,

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Fig. 3.16 EM-wave velocity measurements in the field

the relative permittivity and reflector depth can be determined independently. Plotting the measured data in a t2 -a2 -diagram leads to a linear relationship between t and a: t2 

a 2 4h 2 + 2 v2 v

(3.31)

The propagation velocity of the electromagnetic wave can now be directly determined from the slope of line. The depth of the reflector can be directly inferred from the intersection of the line with the y-axis. An example of CDP data acquired in the field is shown in Fig. 3.16. From the quantitative point of view, the velocity analysis shows a trend of electromagnetic wave velocities slightly decreasing with depth (from surface 10.5–9.0 cm/ns at a 40 ns time depth). The Dix analysis (1955) seem to characterize a sequence of alternating layers in agreement with observations. (4) Use of standard electromagnetic wave velocity: This method is based on the knowledge of the relative dielectric constant of the materials constituting the subsoil of the area under study. In many cases, it is sufficient to approximate the velocity v with the well-known relationship: v  c/(εr )1/2

(3.32)

The assumptions are: – an isotropic medium, therefore magnetic permeability, conductivity, and permittivity are independent of direction; – an homogeneous medium, conductivity, magnetic permeability, and permittivity are independent of position and time; – the charge density in the medium is considered null; – the vehicle has no magnetic properties.

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3.2.2 The Electrical-Resistivity Active Method Electrical-resistivity active techniques are based on the response of the investigated medium to an injected flow of electrical current. In this method, an electrical current is injected through the medium through two electrode called “current electrodes”, and a resultant potential difference is measured at two electrodes called “potential electrodes”. This enables estimation of the electrical resistivity of the studied medium. The electrical resistivity is therefore a function of the ratio of potential to current and the geometry of the electrode array. To understand the active resistivity method, it is important to consider Ohm’s law, which describes the electrical properties of any medium. Ohm’s law affirms that the electrical potential difference V is related to the electrical current I by the relationship V  IR, where R is the electrical resistance. This relationship holds for earth materials, as well as simple circuits. However, electrical resistance is not a material constant, while electrical resistivity is an intrinsic property of the medium describing the resistance of the medium to the flow of electric current. Considering Fig. 3.17 in which a cylindrical rock sample, of length l and section S, the electrical resistance R between the extreme faces is expressed by: Rρ

l S

where ρ is a constant called electrical resistivity of the sample and it is measured in ohm-m, and is the reciprocal of the conductivity of the material. Table 3.3 displays some typical Earth materials resistivities. Earth resistivities can range over nine orders of magnitude. Looking at Table 3.3, it is possible to note that the resistivity ranges of various earth materials overlap. Thus, resistivity measurements can be directly related to the type of soil or rock in the subsurface only if other information are available to the interpreter. This information could be obtained, for example, using other geophysical methods. The resistivity changes in the materials are controlled mainly by the porosity due to electricity flows in the near surface connected to ions transport through pore space in the materials. Electrical resistivity values are controlled also by other factors: (i) the porosity (amount of pore space); (ii) the permeability (connectivity of pores); (iii) the water

Fig. 3.17 Ohm’s law for a cylindrical conductor

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45

Table 3.3 Resistivity and conductivity values for some types of rocks (Loke 2001) Material Resistivity ( ·m) Conductivity (S/m) Igneous and metamorphic rocks Granite

5 × 103 –106

10−6 –2 × 10−4

Basalt

103 –106

10−6 –10−3

Slate

6 × 102 –4 × 107

Marble

102 –2.5

Quaitzite

102 –2 × 108

5 × 10−9 –10−2

Sandstone

8–4 × 103

2.5 × 10−4 –0.125

Shale

20–2 × 103

5 × 10−4 –0.05

Limestone Soils and waters Clay

50–4 ×

2.5 × 10−3 –0.02

1–100

0.01–1

Alluvium Groundwater (fresh)

10–800 10–100

1.25 × 10−3 –0.1 0.01–0.1

Sea water Chemicals

0.2

5

Iron 0.01 M potassium chloride

9.074 × 10−8 0.708

1.102 × 107 1.413

0.01 M sodium chloride 0.01 M acetic acid

0.843 6.13

1.185 0.163

Xylene

6.998 × 1016

1.429 × 10−17

×

108

2.5 × 10−8 –1.7 × 10−3 4 × 10−9 –10−2

Sedimentary rocks

102

(or other fluid) content of the pores; and (iv) the presence of salts. Another important factor that produces large resistive anomalies is air-filled subsurface voids. In resistivity methods, the potential field measurements are performed on the surface of the medium. The potential field is clearly due to the distribution of the current passing through the investigated medium. This potential is a solution to Poisson’s equation: ∇ 2 V  0, where ∇ 2 is a second derivative operator and V is the potential. A solution of Poisson’s equation for the potential P at a distance r from the current source I (an infinite half space below) is:

Iρ 1 . V 2π r If C indicates the current electrode and P1 and P2 indicates the two potential electrodes, the value of the potential found in P1 is due to the current injected into C (Fig. 3.18).

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Fig. 3.18 Scheme of the distribution of the current I through a C electrode in a homogeneousresistivity subsoil ρ

V1 

Iρ , 2πC P1

V2 

Iρ . 2πC P2

while in P2, the potential is

Thus, a current electrode C produces a potential difference between P1 and P2 of

Iρ 1 1

V  − . 2π C P1 C P2 If two current electrodes C1 and C2 (which respectively input current +I and −I) are considered, the potential difference V between P1 and P2, calculated using the overlapping principle, is equal to:

1 Iρ 1 1 1 ,

V  − − + 2π C1P1 C1P2 C2P1 C2P2 and therefore:

V · 2π ρ I

 1 C1P1

where k is the geometrical factor.

−

1 C1P2

1 −

 1 C2P1

+

1 C2P2



V k I

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Fig. 3.19 Arrangement of electrodes on the investigated material surface: a 2D and b 3D multielectrode geoelectrical investigations

In recent decades, resistivity measurements are made using a system consisting of a large number of electrodes. This technique, by the name of electrical resistivity tomography (ERT), is particularly suitable for investigations on the ground in areas of geological, mining, hydrogeological, engineering, and archaeological interest. But it can also be used on the surface of objects of monumental heritage to obtain information about the conservation degree. ERT can be 2D or 3D. In the first case, the electrodes are arranged on the ground and/or on the surface of the monumental heritage—all aligned and equispaced, while, in the second case, they are always arranged on the surface of the material—but on the nodes of a square grid. Figure 3.19 illustrates the two ways in which the electrodes can be arranged. In the case of multielectrodes, a series of equispaced electrodes, connected through a multi-channel cable to an instrument able to manage the current input and the measurement of the potential difference from the four electrodes each time affected by the measurement, is used. The various electrode devices are characterized by a series of parameters, on which the investigation will depend. The operator will decide, based on the purposes of the survey, on the characteristics of the region affected by the measurement, the available time, and the amount of memory available on the computer, which is the most suitable for the measurements, case by case. In the following, the three most-often used arrays are described. The Wenner array: The Wenner array, as can be seen from Fig. 3.20a, b and c, can be of three types, α, β, and γ, depending on the reciprocal positions of the four electrodes. The Wenner α device will be treated first because it is the most frequently used. It is characterized by the pairs of electrodes that are all equally spaced, i.e., a single parameter (a) is enough to define the entire device. “A” represents the distance between each pair of electrodes. For this array, the geometric factor k is:

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Fig. 3.20 Electrode arrays and corresponding geometric factors (Loke 2001)

k  2πa 

2 πL, 3

(3.33)

where L indicates the length of the quadripolar array. In measurements, the “a” can assume a value equal to ms, where s is the spacing between the electrodes and m is an integer ranging from 1 to the integer part of (N − 1)/3. The number of measures that can be obtained for each value of m (and therefore of a) is (N − 3 m). Proceed as follows: the first measurements will be made with a  s, starting from the first four electrodes on the left and then moving to the right. The total number of these measurements will be N − 3 (if N indicates the total number of electrodes of the entire array). The measurements are then repeated with a  2s. Their number will be N − 3*2. Continue in this way until the maximum value of “a” is reached for the number of electrodes available. To clarify the concept, a numerical example follows. Suppose that 24 electrodes are available. Figure 3.21a shows the sequence of measurements that can be made with 24 electrodes, while in Fig. 3.21b the same measurements are represented in a vertical section, as would be done by placing the 24 electrodes at an interelectrode distance of 1 m. On the horizontal axis of this section is indicated the distance,

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Fig. 3.21 Wenner array: a Measurement sequence; b Distribution of measurements in the ground according to the depth of investigation

expressed in m, while on the vertical axis is indicated the depth of investigation, which is related to the concept of level of data points: in the case of the Wenner array, the data measured with a  1s are related to the first level, while those with a  2s to the second level and so on. Dipole–Dipole array: The dipole–dipole array is characterized by the parameter “a”, which represents the distance both between the two current electrodes and between the two potential electrodes, but also by a value “n”, which represents the ratio between the distance C1-P1 and “a”. For this device, the geometric factor is:

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k  πn(n + 1)(n + 2)a  πn(n + 1)L,

(3.34)

where L indicates the length of the quadripolar array. From an operational point of view, for each “a” and for each “n”, measurements are taken along the entire profile. In practice, a value of “a” is set and, therefore, a value of “n”. If for a is set value of a  ms, with m  1, …, M, where M is the integer part of (N − 1)/3, for each value of m, n can vary between 1 and [(N − 1)/ m] − 2. In the field measurements, for this type of array, it is advisable to take n ≤ 6, because, for higher n values, the measured signal due to the current injected into the ground can become comparable with the background noise. Returning to the example with 24 electrodes, in Fig. 3.22 all the measures that can be made are shown with values of a  1, 2, and 3s and with values of n integers and not greater than 6. The total number of measurements is equal to 231. The number of measures for this type of array is greater than the Wenner array. The Wenner-Schlumberger array: This type of array is a hybrid between the Wenner α and Schlumberger array. The fundamental parameters for this array are “a” the distance between the potential electrodes and “n” the ratio between the distance C1-P1 and “a”. The geometric factor of the Wenner-Schlumberger array is: k  πn(n + 1)a  πn(n + 1)L/(2n + 1).

(3.35)

where L indicates the length of the quadripolar array. In Fig. 3.23, all the measurements that can be obtained with 24 electrodes using the Wenner-Schlumberger array are shown. They are performed with values of n ranging from 1 to 6 for a  1s, with n from 1 to 5 for a  2s and n from 1 to 3 for a  3s. The total number of measures is 173, but they can be increased by adding other levels of “a” and “n”. Resistivity measurements are associated with varying depths depending on the distance between the current and potential electrodes. Two dimensional images of the subsurface resistivity variation are called pseudosections. A pseudosection is an easy representation of an electrical-resistivity distribution in the investigated material (Fig. 3.24). The depth of investigation is a survey parameter of fundamental importance. Knowing at least approximately the depth, the dimensions, and the shape of the target of the survey enables choosing the better array and the better electrode spacing (Roy and Apparao 1971). It is important not to confuse the depth of investigation with the penetration of the electrical signal. In fact, the depth of penetration of the electrical signal depends only on the position of the current electrodes, while the depth of penetration depends on the position of the potential electrodes.

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Fig. 3.22 Dipole–Dipole array: a Measurement sequence; b Distribution of measurements in the ground according to the depth of investigation

The values of average depth, for the other array, are shown in Table 3.4 (Loke 1999). It is important to emphasize that these values have been calculated for the ideal case of an homogeneous medium. In real cases, an increase or decrease of the penetration depth could be observed due to the noise related to the particular condition of the investigated material.

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Fig. 3.23 Wenner-Schlumberger array: a Measurement sequence; b Distribution of measurements in the ground according to the depth of investigation

Topography is an element of great importance in the study of the electrical characteristics of the sub-soil. Systematic studies of anomalies of resistivity in the subsoil in the presence of particular topographic elements (ridges, valleys, and inclined surfaces) were carried out by Fox et al. (1980). Figure 3.25 illustrates the general effects of topography on current lines and equipotential surfaces, in a homogeneous medium in the presence of a current source located at a hypothetically infinite distance.

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Fig. 3.24 Pseudosection visualization on a computer during ERT data acquisition

It is possible to see that the current lines diverge under a hill and converge under a valley. The equipotential surfaces, which are normal to the current lines, also diverge under a hill, producing lower potential differences than an approximately flat topography and therefore low resistivity values, while converging under a valley, producing high resistivity values.

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Table 3.4 Depth of investigation of the various electrode arrays (Loke 1999) Electrodes array Zmean /a Zmean /L Wenner alfa Wenner beta Wenner gamma

0.519 0.416 0.594

0.173 0.139 0.198

n1

0.416

0.139

n2 n3 n4 n5 n6 Wenner-Schlumberger n  1

0.697 0.962 1.22 1.476 1.73 0.52

0.174 0.192 0.203 0.211 0.216 0.173

0.93 1.32 1.71 2.09 2.48

0.186 0.189 0.19 0.19 0.19

Dipole-dipole

n2 n3 n4 n5 n6

Fig. 3.25 Effect of topography on equipotential surfaces and current lines (Fox et al. 1980)

3.2.3 The Induced-Polarization Method By the term of induced polarization (IP) is meant a set of transitory phenomena occurring in the medium when it is subjected to an electric field applied through a classical quadripolar array C1C2 P1P2, where C1 and C2 are the electrodes of current and P1 and P2 are potential electrodes. When the medium is energized with a constant intensity of current I through the electrodes C1 and C2 for a certain time T, the equilibrium potential Ve between the electrodes P1 and P2 is not instantaneously achieved, but according to an asymptotic pattern. In a completely similar manner, the difference between potentials P1 and P2 does not instantaneously fall to zero when the energizing current is interrupted, but it takes some time to discharge, with an asymptotic fall to zero (Fig. 3.26). The duration of this phenomenon can vary

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Fig. 3.26 Induced polarization and discharge curve

from a few seconds to a few minutes and depends on the degree of polarization of the medium. Although it is a complex phenomenon, it is possible to approximate the behavior of the medium by the phenomena of charge and discharge of capacitors. The main factors that determine the IP are: the mineralogical composition; weaving; the percentage of water (natural moisture); and the chemical composition of interstitial water (electrolyte). Two polarization types are considered to explain the origin of the IP: membrane polarization and electrode polarization. The membrane polarization, also called electrolytic, takes place if in the medium is present silicate mineral particles, which overlook the walls of the pores, in the presence of interstitial fluid. These minerals, negatively charged in the surface, attract cations, forming a widespread electrical double layer (due to the Van der Waals forces). The tubular clay particles (phyllosilicates) are the minerals in which this situation is best achieved since they are present on the surface in contact with the electrolyte and the oxygens of their tetrahedral elementary structure, which, negatively charged, attract the cations present in the fluid. There is therefore a thickening of electrolyte ions which causes a partial obstruction of the pores, thus preventing the passage of current. In fact, when the soil is energized through the electrodes C1 and C2, the positive ions pass easily through the cationic cloud, while the negative ones are attracted to it and stop: the cloud therefore functions as a “selective ion membrane” (Fig. 3.27). Thus, zones with different ionic concentration are formed, and it is this very different mobility of ions that determines the polarization. When the external current ceases, the return of the ions in the equilibrium distribution constitutes a residual current that prevents the potential to cancel immediately, thus giving rise to the effect of IP. The electrode polarization, also known as metallic or electronic, occurs when conductive metallic or mineral particles, such as sulfides (pyrite, chalcopyrite, galena), oxides (magnetite, ilmenite, cassiterite), and graphite are present in the medium, not in a massive mode but disseminated throughout the matrix of the medium. Also in the case of the metal particle, an electrical double layer is created at the interface between the metallic mineral and the solution, which is the equivalent of an effective electric

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Fig. 3.27 Mechanism of membrane polarization

Fig. 3.28 Mechanism of electrode polarization

dipole. When the current passes through, the ions accumulate at the interface of the conducting granule and obstruct the flow, thus generating an additional polarization (Fig. 3.28). When the current flow is interrupted, the blocked ions are diffused to restore the original equilibrium situation, thus generating a residual current and the phenomenon of the IP. IP measurements can be performed in the time domain or in the frequency domain. The measurements in the time domain are performed by injecting direct-current pulses into the subsoil with a duration equal to a time T (Fig. 3.26). For the study of the phenomenon, we analyze the soil response to the interruption of the current, i.e., we precisely study the discharge curve as a function of time. The remaining voltage (measured in mV) after a time t from the interruption of the current (Fig. 3.26) is the IP. The measurement of the IP is often expressed by the ratio (mV/V), where the equilibrium tension is reached after a certain soil-energization time (measured in V); this quantity is called apparent polarization. Another measure used to measure IP is the “apparent load chargeability”, defined as: 1 M Ve

t2 V (t)dt t1

(3.36)

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57

in which t1 and t2 e (t2 > t1 ) are two times after the energy interruption. Chargeability will be expressed in milliseconds. The charging time T and the integration time are generally on the order of magnitude of seconds and hundredths of a second, respectively. With regard to time domain measurements, these can be performed with the same instrumentation used for resistivity measurements. Chargeability and resistivity data sets are then analyzed in a similar manner. Tables 3.5 and 3.6 show the chargeability typical values for mineral and rock respectively. In many situations, given the non-uniqueness of the solution of the inverse problem and the complexity inherent in the interpretation of the results, the geoelectrical survey should be flanked by other surveys, such as GPR or seismic, to obtain complementary information or confirmation for the characterization of the investigated medium. One of the fields of investigation in which the resistivity method has been used with considerable success is that aimed at identifying pollutants present in the subsoil. For example, materials containing waters polluted by fertilizers or pesticides used in agriculture have lower resistivity values than those containing uncontaminated water, as the conductivity of water increases in the presence of such substances (Christensen and Soresen 1994; Leucci et al. 2003). Resistivity methods have also been used to delimit geothermal fields, exploiting the fact that geothermal waters perform better than normal due to the higher content of dissolved salts. Being also sensitive to the difference in the moisture content of the materials, this method may be suitable for differentiating parts of land that have been reworked from those not reworked and for mapping karst environments and geological structures (Leucci et al. 2003, 2004). It is also frequently used in archaeological studies (Carrozzo et al. 2002). In archeology or engineering, exten-

Table 3.5 Typical values of chargeability for some types of minerals Mineral Chargeability (ms) Mineral

Chargeability (ms)

Pyrite

13.4

Erubescite

6.3

Chalcocite Copper

13.2 12.3

Galena Magnetite

3.7 2.2

Graphite

11.2

Malachite

0.2

9.2

Hematite

0.2

Chalcopyrite

Table 3.6 Typical values of chargeability for some types of rocks Rock Chargeability (ms) Rock

Chargeability (ms)

Aquifer

0

Schist

5–20

Alluvion Gravel

1–4 3–9

Sandstone Argilite

3–12 3–10

Volcanic

8–20

Quartzite

5–12

Gneiss

6–30

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sive use of these methods has been to delineate buried foundations or stone walls characterized by different resistivity values compared to the surrounding sediment. Adequately supported by other geophysical methods, the use of resistivity methods becomes increasingly frequent for the identification of the degree of fracturing of a rock formation (Leucci 2003); in fact, the lower or higher degree of fracturing of the rock, as well as the different type of material used to fill the fractures (air, red earth, water or other), affects the resistivity values of the investigated medium. As for the induced polarization method, it gives good results in many types of applications, especially in sites where clays or some types of metals are present. A combination of the resistivity and induced polarization methods certainly provides more accurate results than those obtained using a single method. In fact, some substances may have the same resistivity values but different chargeability values. This is the case, for example, of some clays and some types of groundwater with high salt content (Roy and Elliott 1980): with the resistivity method, it would be impossible to distinguish the clay layer from the water stratum; the induced polarization, on the contrary, can give good results since the water does not suffer the effects of induced polarization, while the clay has high values of chargeability.

3.2.4 The Self-potential Method The self-potential (SP) measurements are performed using a non-polarizable electrodes. Several charge-polarization mechanisms were proposed to explain SP anomalies (Reynolds 2011). They are associated with electrokinetic, electrochemical, thermoelectric, redox, and piezoelectric effects. The general equation for coupled flows can be written (Overbeek 1956):  Li j Fj (3.37) Ji  j

where the fluxes Ji (of charges, matter, heat, etc.) are related to the various forces Fj (gradients of electrical potential, pressure, temperature, etc.) through the coupling coefficients Lij (“phenomenological coefficients” or “conductivities”) (Sill 1983; de Groot and Mazur 1983). The Lij can be considered as a symmetric matrix. In this matrix, each flow is related to any combination of forces and the diagonal elements are typical conductivities, such as those in Ohm’s or Darcy’s laws (Reynolds 2011). The total electric-current density generated through coupling with one other phenomena in the Earth can be write in the simplest case as: J  −L11 ∇F1 −L1k ∇Fk  −σ∇ϕ − L1k ∇Fk That represent a simplification of Eq. 3.37 (Reynolds 2011).

(3.38)

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The term (−σ∇ϕ) is the conduction-current density that flows throughout the Earth (σ represent the electrical conductivity); the term (−L1k ∇Fk ) is a source-current density related to the coupling process. If the external sources of electric current are absent, the application of conservation equation (Reynolds 2011) enables affirmation that the total current density is divergence-free (i.e., ∇ · J  0) and therefore: −∇ · σ∇ϕ  ∇L · ∇F + L∇ 2 F

(3.39)

The second term of Eq. (3.39) is related to the primary forcing process. It provides a source term for the self-potential signal (Sill 1983; Revil 2002) and is the main cause of the measured electric potential field in the ground surface. To solve Eq. (3.39), typical boundary conditions require that φ → 0 as the distance from the source region becomes larger, and the normal component of the electric current density is zero at the Earth’s surface, i.e., n · σ∇φ  0 (Dey and Morrison 1979).

3.2.5 Seismic Method Historic buildings, no matter whether they are famous monuments or so called “minor” or even vernacular, architecture represent an important part of our cultural heritage. This patrimony, which is the living memory of the country’s history and development, must be preserved as much as possible as an historic document of our past. Unfortunately, wars and other dramatic events (earthquakes, floods, slides, fires, etc.), but also abandonment and lack of maintenance, are constant menaces to the cultural heritage in every country in the world. Difficulties exist when is necessary to evaluate the degree of the degradation process within the building heritage. The degradation processes affects as much the structural level (cracks, fissures, detachments, displacements…) as the aesthetic level (dirt, crusts, efflorescence, etc.) of historical buildings. The knowledge of this reality will be important for the valuation of stability conditions and also for the restoration planning process. The main pathologies that can result in the breakdown of historical buildings are: humidity damage caused by capillarity ascent, breeze, or high humidity environments; successive freeze–thaw cycles that result in crystallization, broken mortar joints, loss of the most exposed material; and finally erosion damage caused by lack of vegetation. Centering on structural pathologies (cracks, fissures, etc.), the detection and characterization of the above mentioned problems is important to estimate the state and to plan possible repairs. This chapter describes the possible applications of a nondestructive testing (NDT) methods related to the study of the propagation of sonic and ultrasonic waves to analyze the conservation state of building heritage. Some examples of masonry investigations and the conditions for applicability are here reported. They provide necessary information and decision criteria for the planned application of the methods to historic masonry buildings. The chapter comprises a short summary of the technical

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basic principles of the method and describe the required equipment, the measurement setup, the application and relevant limits and site conditions, the data analysis and interpretation, and the required safety cautions. In seismic surveys, waves are emitted by a controlled source and propagate through the subsurface. Several waves will backscattered at the surface due to refraction or reflection at boundaries within the surveyed materials. Receivers distributed along the surface detect the motion caused by these returning waves and measure the arrival times of the waves at various distances from the source. The travel times are then converted into velocities, and the spatial distribution of velocities can be systematically mapped. Sources suitable for seismic surveying usually emit pulses that are associated with a wide range of frequencies (Reynolds 2011). With the only exception of the areas near the source, the strains associated with the passage of a seismic pulse are very low and may be assumed to be elastic. Based on this assumption, the propagation velocities are determined by the elastic moduli and densities of the materials. The elastic waves can be classified in two groups, i.e., body waves and surface waves. Body waves can propagate through the interior of an elastic solid and can be of two types. Compressional waves (the longitudinal, primary, or P-waves) propagate by compressive and expansive uniaxial strains in the direction of wave travel (Fig. 3.29a). Shear waves (the transverse, secondary, or S-waves) propagate by pure shear strain in a direction perpendicular to the direction of wave travel (Fig. 3.29b). Body waves are non-dispersive; this means that all frequency components in a wave train or pulse propagate through any material at the same velocity, which is determined only by the elastic moduli and density of the material. Surface waves can propagate along the boundary of the solid. Rayleigh waves are seismic surface wave causing the ground to shake in an elliptical motion, with no transverse, or perpendicular, motion (Fig. 3.30a). Love waves are surface waves having a horizontal motion that is transverse (or perpendicular) to the direction the wave is traveling (Fig. 3.30b). A seismic pulse propagates at a velocity determined by the physical properties of the surrounding materials. If the pulse travels through a homogeneous material, all the waves will travel at the same velocity and accordingly the wave-front, defined as the locus of all points that the pulse has reached at a particular time, will be a sphere. For sonic and ultrasonic standard surveys, only the body waves P and S are considered. The travel time and the sonic pulse velocity provide basic information about the quality and conservation state of the medium element under investigation. The sonic pulse-velocity test is very similar to the ultrasonic pulse-velocity test for what concerns basic theories, the purpose of the tests, and application of the method. The difference between the two methods regards the frequency of the emitted wave, as described previously. The commonly used sonic methods are: sonic transmission method; sonic/seismic tomography; sonic/seismic reflection method; and the ultrasonic reflection method. The sonic transmission method involves the propagation f a sonic wave through the thickness of the wall (or the structure) under investigation. Emission of the wave

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Fig. 3.29 Elastic deformations and ground particle motions associated with the passage of body waves: a P-wave; b S-wave

Fig. 3.30 Elastic deformations and ground-particle motions associated with the passage of surface waves: a Rayleigh wave; b Love wave

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3 Nondestructive Testing Technologies for Cultural Heritage …

Fig. 3.31 Transmission modes for sonic wave tests: a direct; b semidirect; c indirect

is performed on one side of the structure by the impact of the force hammer or pulsed generator; an accelerometer, positioned directly opposite the force hammer, receives the transmitted signal on the other side of the wall (Fig. 3.31a). The resulting wave velocity is an average of the local velocity along the path, and it is not possible to evaluate the position and the extent of any possible inhomogeneity. The velocity variations may be plotted on a contour map, with grid points as X and Y coordinates and the pulse velocity as the Z co-ordinate. This format makes possible a simple evaluation of the status of the masonry or concrete walls of the structure or an evaluation of the internal conditions of a structure. It has generally been recognized that the direct-transmission arrangement is a simple technique to apply in the analysis of structures since it provides a defined path length through the structure. Furthermore, since the arrival time of the first wave is of primary concern, no attempt to distinguish complex wave frequencies and reflections is required for the analysis. This method has been successfully used to evaluate material uniformity, detect the presence of voids, estimate the depth of surface crack, and calculate an average compressive strength for the structure or the material. The detection of flaws is possible due to the fact that sonic waves cannot transmit across an air gap, which could be due to a crack, void, or delamination at the interface between brick or stone and mortar. A propagating wave must find a path around the void, resulting in attenuation and an increase in the transit time of the signal. Figures 3.31b and c illustrate indirect transmission modes used mainly for tomographic surveys. Sonic tomography represents an improvement in the sonic-transmission test method because tests are performed not only in the direct mode but also along paths that are not perpendicular to the wall surfaces. The wall of the structure or the masonry section is thus traversed by a dense network of ray-paths, each of them defining a specific travel time between the sonic source and receiver. These values of travel time are processed in order to achieve a 3D reconstruction of the velocity distribution across the structure or selected cross-section; in this way, local variations of the velocity can be identified and correlated to zones of weakness or flaws in the internal fabric of the structure (Fig. 3.32).

3.2 NDT Geophysical Methods

63

Fig. 3.32 Typical ray path in a tomography acquisition (S: sources, A: receivers)

It is usual to assume a homogeneous structural response in the application of the tomographic method. This is because the response is measured by transducers far from the location of the impact, where inhomogeneous behavior may arise. Therefore, any variation from the expected travel time is attributed to inhomogeneity in the structure or damage has occurred. To increase the accuracy of the measurements, it is necessary to maximize the amount of experimental data included in any calculation used by ensuring that all areas of the proposed tomographic section have adequate ray-path coverage. A number of inversion algorithms are available commercially for tomographic reconstruction (Cheeke 2002). In the sonic reflection method, the emitters and receivers are on the same side of the masonry; thus, the stress wave recorded is the direct stress wave reflected from any internal flaw or the rear face of the structure being investigated. The value of velocity calculated from the rear wall or face of a structure is a measure of the local velocities along the path. The problems that reflection methods may be used for in the investigation of retaining walls are: (i) internal dimensions and shape; (ii) type and properties of fill; (iii) voiding within the fill material; and (iv) cracks and voids within the internal fabric of the structure. Seismic reflection techniques is not a method currently recommended since the resolution achievable with the low-frequency energy is poor, and it is often difficult to distinguish reflections from surface waves and refracted arrivals.

64

3 Nondestructive Testing Technologies for Cultural Heritage …

Ultrasonic waves, which are generated by a piezoelectric transducer at frequencies above 20 kHz, propagate with a wavelength of around 50–100 mm (as a function of the wave-velocity propagation). This form of testing is used successfully for the detection of flaws in metal castings and was the first nondestructive technique that was developed for the testing of concrete. However, it is much less practical in concrete and masonry, which have much higher attenuation characteristics, and hence lower-frequency signals are required to obtain a reasonable penetration. At present, the method is not commonly used for these purposes, due to a number of technical difficulties. In the case of ultrasonic signals, the main factors to overcome are the need for good coupling of the transducer to the surface, which is often rough, and the scattering of the waves due to material heterogeneity. The need for effective coupling requires the use of a coupling agent, such as grease or petroleum jelly, to temporarily adhere the transmitter and receiver to the surface. This makes the process of moving the points of measurement quite slow, and it is often difficult to achieve adequate coupling on some uneven surfaces. Scattering of the signal limits the propagation through the material and also leads to a complicated series of return signals. This makes it difficult to identify defects amid the noise. In addition, surface waves, which travel more slowly than the compression waves, may arrive at the receiver within the same time interval and confuse interpretation. Further developments of the ultrasonic technique, for example, improvements in signal generation, detection, and data processing, are underway and may lead to a practical tool if the aforementioned problems can be overcome. Seismic resolution is a measure of how large an object need to be seen by seismic methods. The vertical resolution is derived from the length of the soundwave, and layers can be discerned when their thickness is below 1/4 wavelength. Still, it is possible to detect layers down to 1/32 wavelength. When referring to vertical resolution, it is normally at 1/4 wavelength. The wavelength is calculated by (Reynolds 2011): λ  V/F The vertical seismic resolution is calculated by λ/4, where λ is the wavelength, F is the seismic frequency, and V is the seismic velocity. The seismic wave is sent out from the source move in 3D and spreads out over a larger area the further away it gets from the source. The horizontal resolution is derived from the Fresnel zone, the part of a reflector covered by the seismic signal at a certain depth. On a buried horizon, all features with a lateral extent exceeding the Fresnel zone will be visible. The radius of this zone is often taken as the horizontal resolution for unmigrated seismic data. As with the wavelength, the Fresnel-zone size also increases rapidly with depth (Reynolds 2011). Fresnel zone  V(D/F)0.5 where F is the seismic frequency, V is the seismic velocity, and D is the depth in time.

3.2 NDT Geophysical Methods Table 3.7 Target of sonic and ultrasonic measurements Target

65

Acquisition type

Detection of inhomogeneities (e.g., variation of material texture, repair interventions, presence of different materials…)

DT, T

Detection of multiple leaves and measurement of the thickness of each leaf Detection of detached external leaves

T DT, T

Detection of voids or chimney flues

DT, T

Evaluation of effectiveness of repair interventions (e.g., grout injections, repointing, etc.…)

DT, T, ST

Detection of damaged portions of structure or of crack patterns

DT, IT, T

Sonic (S) and ultrasonic (US) can be used on built heritage with direct tomography (DT), semi-direct tomography (ST), indirect tomography (IT) transmission method, or with tomographic (T) mode, depending on the objective of the investigation. Problems that can be analyzed are listed in Table 3.7, with an indication of the most appropriate acquisition mode. The successful application S and US methods depends on the appropriate application of the method, but there also exist unfavorable conditions where the application to some of these problems might fail. Sonic pulses do not undergo significant signal attenuation. The execution of the tests is thus generally successful. On the other hand, these methods are characterized by low resolution, which cannot be sufficient for the detection of small voids or small inclusions or when dealing with the detection of multiple leaves, detached external leaves, cracks, etc. Higher frequencies and smaller wavelengths are needed to improve the resolution, and this entails the use of US waves. The resolution of S and US tomographies depends also on the dimension of the grid used to transmit/acquire the sonic waves. However, very dense grids, if not accompanied by the use of higher-frequency stress waves, may not lead to improved resolution. As the presence of moisture produces an apparent S and US pulse-velocity increase, the application of the method to very moist masonry should be carefully evaluated. If metal elements (ties or anchorages) exist within the investigated structure, it is possible to observe an apparent S and US pulse-velocity increase. This is due to the faster propagation of the wave through the metal element; thus, the tests should be carried out at a certain distance from the position were the ties are placed. Particular care is needed when the hammer/accelerometer must be used on a precious surface decorated with frescos or plasters; in these cases, a good practice consists of protecting the surface (when hitting/receiving) from contact with a simple piece of clean paper. Table 3.8 shows some values of Vp and Vs for a wide variety of materials (Zanzi 2004).

66 Table 3.8 P- and S-wave velocities in various types of geological materials (Zanzi 2004)

3 Nondestructive Testing Technologies for Cultural Heritage … Material

vP (m/s)

vS (m/s)

Air Dry sands

330 400–1200

– 100–500

Saturated sands Clay

1500–4000 1100–2500

400–1200 200–800

Marne Arenarie Limestone gypsum

2000–3000 3000–4500 3500–6000 2300–2600

750–1500 1200–2800 2000–3000 1100–1300

Shale dolomite water Granite Basalt Coal Ice

4500–5500 3500–6500 1450 4500–6000 5000–6000 2200–2700 3400–3800

2000–3100 1900–3600 – 2500–3300 2800–3400 1000–1400 1000–1900

When a seismic pulse propagates, the original energy E, which is transmitted outside from the source, begins to be distributed on a spherical shell of expanding radius. If the radius of the shell is r, the amount of energy contained within the shell per unit of area is E/4πr2 . Therefore, along the beam path, the energy decreases as 1/r2 due to the geometrical dispersion of the energy (Fig. 3.33). The amplitude of the wave, in a homogeneous medium, is proportional to the square root of the wave energy, and decreases as 1/r. A further cause of energy dispersion along the path of a beam is due to the imperfect elasticity of the medium and by the consequent response to the passage of the seismic waves. The elastic energy is gradually absorbed in the medium by the internal friction, which causes the total disappearance of the seismic perturbation.

Fig. 3.33 Energy lost (expressed in dB) due to geometrical spreading as a function of distance (Burger 1997)

3.2 NDT Geophysical Methods

67

The “absorption coefficient (α)” expresses the portion of energy lost during the seismic wave transmission through a distance equivalent to the wavelength λ. In general, the propagation of a seismic wave in the z-direction is described by the relationship: A(z, t)  A0 exp(−αz) exp[jω(t − z/v)]

(3.40a)

where A (z, t) is the amplitude of the wave at the point z (that is the distance from the source) at time t; v is the phase velocity; and A0 is the amplitude of the wave in z  0 at time t  0 (on the source). This propagation can essentially be described by two parameters: • the merit factor Q; • phase velocity (Turner and Siggins 1994). The merit factor is defined in a way that the ratio ω/Q is equal to the ratio between the energy lost per unit of time (Toraldo di Francia 1988). Since is possible to write: ω dU dt  − Q U

(3.40b)

where U is the total energy stored and dU is the energy dissipated over the time dt. By integrating both members of this relationship: ω

U(t)  U(0) · e− Q t

(3.40c)

Comparing the exponential part that appears in Eq. (3.40c) with the exponential part that appears in Eq. (3.40a) (and considering the fact that the energy is proportional to the square of amplitude), it is possible to write: ω

e−2αz  e− Q t

(3.40d)

From which is possible to derive 2αz  (ω/Q) t; that is Q

ω 2αv

(3.40f)

For seismic waves, this parameter is independent of frequency (for a wide range of frequencies). This behavior is the result of the large number of attenuation mechanisms present in the investigated materials, each of which has some frequency dependence, but together produce a quasi-linear attenuation form the frequency (Turner and Siggins 1994). Values of attenuation for common soil materials vary from 0.25 to 0.75 dB λ−1 . Considering the simple medium shown in Fig. 3.34, which involves two homogeneous layers of seismic velocities V1 and V2 separated by a horizontal interface at a depth z, the velocity of the P wave is higher in the lower layer (V2 > V1 ). From a source S close to the surface, there are three types of possible paths through which

68

3 Nondestructive Testing Technologies for Cultural Heritage …

Fig. 3.34 Direct, reflected, and refracted wave paths

energy can reach the surface and be detected by a sensor placed at a horizontal distance x from the source. The direct wave travels along a straight line across the top of the material from S to D at velocity V1 . The reflected wave is obliquely incident on the interface and is reflected by the second layer towards the surface. The refracted wave travels in the layer with velocity V1 and is refracted (at the critical angle) with velocity V2 . The travel time of the direct wave is simply given by: TDIR  x/V1 That, in the x-t plane, defines a straight line passing through the origin of the axes with slope 1/V1 . The travel time of the reflected beam is given by:

TRFL

x 2 + 4z 2  v1

1/2

That, in the x-t plane, defines a hyperbola. The travel time of the refracted wave is given by: TRFR

1/2

2z v22 − v21 x  + v2 v1 v2

which, in the x-t plane, is the equation of a straight line that has slope 1/V2 and meets the time axis in the point t0 which does not have a physical meaning because in x  0 there is no refraction. These curves, known as “dromocrones” are shown in Fig. 3.35.

References

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Fig. 3.35 Time-distance curves (dromocrones) for the arrival of direct, reflected, and refracted waves

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Carrozzo MT, Leucci G, Negri S, Nuzzo L (2002) Applicazione di metodi elettrici, magnetici ed elettromagnetici per prospezioni archeologiche in area urbana: il caso di Muro Leccese (Lecce). Atti del 21° Convegno Nazionale GNGTS, Roma, 6–9 novembre 2002 Carrozzo MT, Leucci G, Negri S, Nuzzo L (2003) GPR survey to understand the stratigraphy at the Roman ships archaeological site (Pisa, Italy). Archaeol Prospect 10(1):57–72 Cataldo R, Leucci G, Siviero S, Pagiotti R, Angelici P (2009) Analysis of deterioration in the crypt of the Abbey of Montecorona with integrated methods. J Geophys Eng 6:205–220. https://doi. org/10.1088/1742-2132/6/3/001 Cheeke D (2002) Fundamentals and applications of ultrasonic waves. CRC Press, pp 504 Christensen NB, Sorensen KI (1994) Integrated use of electromagnetic methods for hydrogeological investigations. In: Proceedings of the symposium on the application of geophysics to engineering and environmental problems, Boston, Massachusetts, pp 163–176 Clark AJ (1957) The transistor as the archaeologist’s latest tool. Illustrated London News 230:900–901 Clark AJC (1990) Seeing beneath the soil. Batsford, London Cleal RMJ, Walker KE, Montague R (1995) Stonehenge in its landscape: Twentieth century excavations. English Heritage, London Colani C (1966) A new type of locating device—I. The instruments. Archaeometry 9:3–8 Conyers LB, Goodman D (1997) Ground penetrating radar: an introduction for archaeologists. AltaMira Press, Walnut Creek Davis JL, Annan AP (1989) Ground-penetrating radar for high resolution mapping of soil and rock stratigraphy. Geophys Prospect 37(5):531–551 de Groot SR, Mazur P (1983) Non-equilibrium thermodynamics. Dover Pubblications, New York De Domenico D, Giannino F, Leucci G, Bottari C (2006) Integrated geophysical surveys at the archaeological site of Tindari (Sicily, Italy). J Archaeol Sci 33:961–970 Delle Rose M, Leucci G (2010) Towards an integrated approach for characterisation of sinkhole hazards in urban environments: the unstable coast site of Casalabate, (Lecce, Italy). J Geophys Eng 7:143–154 Dey A, Morrison HF (1979) Resistivity modeling for arbitrarily shaped three-dimensional structures. Geophysics 44(4):753–780 Dobrin MB, Savit CH (1988) Introduction to geophysical prospecting. McGraw Hill Fox RC, Hohmann GW, Killpack TJ, Rijo L (1980) Topographic effects in resistivity and inducedpolarization surveys. Geophysics 45(1):75–93 Fruhwirth RK, Schmoller R (1996) Some aspects on the estimation of electromagnetic wave velocities. In: Proceedings 6th international conference on ground penetrating radar (GPR’96), Sendai, Japan, 30 Sept–3 Oct, pp 135–138 Gaffney C (2008) Detecting trends in the prediction of the buried past: a review of geophysical techniques in archaeology. Archaeometry 50:313–336 Gerardi E, Leucci G, Masini N, Persico R (2014) On-site non invasive diagnostics and monitoring for the study, conservation and restoration of historical built heritage. In: Malfitana D (ed) A decade for centuries, pp 127–130 Grasso F, Leucci G, Masini N, Persico R (2011) GPR prospecting in Renaissance and Baroque monuments in Lecce (Southern Italy). In: Proceeding 6th international workshop on advanced ground penetrating radar IWAGPR, Aachen, Germany, June, pp 22–4 Hara T, Sakayama T (1984) The applicability of ground probing radar to site investigations, OYO technical note, 38 pp Hesse A (1981) Realisation et experimentation d’un resistivimetre autotracte enregistreur ‘RATE’ (en Collaboration avec A Jolivet). Compte rendu de fin d’etudes d’une recherche finance par la DGRST, d’ecision d’aide no. 78 7 0247 AC Les Sciences de la Terre et les problemes d’Amenagements d’Urbanisme et de Construction 14-3-1981 Kadioglu S, Kadioglu YK (2010) Picturing internal fractures of historical statues using ground penetrating radar method. Adv Geosci 24:23–34

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Keary P, Brooks M (1991) An introduction to geophysical exploration. Blackwell Scientific Publications, Oxford Lázaro-Mancilla O, Gómez-Treviño E (1996) Synthetic radargrams from electrical conductivity and magnetic permeability variations. J Appl Geophys 34:283–290 Leckebusch J (2003) Ground-penetrating radar: a modern three-dimensional prospection method. Archaeol Prospect 10:213–241 Leucci G (1999) Prospezioni elettromagnetica e di sismica a riflessione: studio dell’influenza dei parametri strumentali sul rapporto segnale/rumore. Tesi di laurea in Fisica, Università degli Studi di Lecce Leucci G (2003) I metodi elettromagnetico impulsivo, elettrico e sismico tomografico a rifrazione per la risoluzione di problematiche ambientali: sviluppi metodologici e applicazioni. Tesi di Dottorato di Ricerca in Geofisica per l’Ambiente e il Territorio, Università degli Studi di Messina Leucci G (2006) Contribution of ground-penetrating radar and electrical resistivity tomography to identify the cavity and fractures under the main church in Botrugno (Lecce, Italy). J Archaeol Sci 33(9):1194–1204. https://doi.org/10.1016/j.jas.2005.12.009 Leucci G (2007) Ground Penetrating Radar: un introduzione per gli archeology. Aracne Editrice, Roma Leucci G (2015) Geofisica Applicata all’Archeologia e ai Beni Monumentali. Palermo, Dario Flaccovio Editore, p 368 Leucci G, De Giorgi L (2010) Microgravimetric and ground penetrating radar geophysical methods to map the shallow karstic cavities network in a coastal area (Marina di Capilungo, Lecce, Italy). Explor Geophys 41:178–188 Leucci G, De Giorgi L (2015) 2D and 3D seismic measurements to evaluate the collapse risk of cave in soft carbonate rock. Cent Eur J Geosci 7(1):84–94. https://doi.org/10.1515/geo-2015-0006 Leucci G, De Giorgi L (2017) Il molino coratelli: indagini micro-geofisiche per la diagnostica strutturale. In I molini e l’industria molitoria in puglia. P 61–68 Leucci G, Negri S (2006) Use of ground penetrating radar to subsurface archaeological features in an urban area. J Archaeol Sci 33:502–512. https://doi.org/10.1016/j.jas.2005.09.006 Leucci G, Quarta G (2016) The Cathedral of SS Annunziata in Castro (Lecce, southern Italy): Structural-Diagnostic surveys. Int J Innovative Sci Eng Technol 3(2):7–14 Leucci G, Margiotta S, Negri S, Nuzzo L, Sansò P, Varola A (2003) Integrated geophysical, geological and geomorphological investigations for study the impact of agricultural activities on a complex karstic area. In: Proceedings del SAGEEP 2003 della Environmental and Engineering Geophysical Society, S Antonio, Texas, USA, 6–10 Apr 2003 Leucci G, Margiotta S, Negri S (2004) Geological and geophysical investigations in karstic environment (Salice Salentino, Lecce, Italy). J Environ Eng Geophys (JEEG) 9:25–34 Leucci G, Greco F, De Giorgi L, Mauceri R (2007) 3D sesimic refraction tomography and electrical resistivity tomography survey in the Castle of Occhiolà (Sicily, Italy). J Archaeol Sci 34:233–242. https://doi.org/10.1016/j.jas.2006.04.010 Leucci G, Persico R, Quarta G (2010) GPR time lapse to quantify the subsidence degree in an urban area. In: Joint SIG workshop: urban-3D-radar-thermal remote sensing and developing countries, Ghent, Belgium, 22–24 Sept 2010 Leucci G, Masini N, Persico R, Soldovieri F (2011) GPR and sonic tomography for structural restoration: the case of the Cathedral of Tricarico. J Geophys Eng 8:76–92. https://doi.org/10. 1088/1742-2132/8/3/S08 Leucci G, Masini N, Persico R, Quarta G, Dolce C (2012a) A multidisciplinary analysis of the Crypt of the Holy Spirit in Monopoli (Southern Italy). Near Surf Geophys 10:1–8. https://doi. org/10.3997/1873-0604.2011032 Leucci G, D’Agostino D, Cataldo R (2012b) 3D high resolution GPR survey yields insights into the history of the ancient town of Lecce (south of Italy). Archaeol Prospect 19(3):157–165. https:// doi.org/10.1002/arp.1423

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Leucci G, Masini N, Persico R (2012c) Time–frequency analysis of GPR data to investigate the damage of monumental buildings. J Geophys Eng 9:S81–S91. https://doi.org/10.1088/1742-2132/ 9/4/S81 Leucci G, Parise M, Sammarco M, Scardozzi G (2016) The use of geophysical prospections to map ancient hydraulic works: the Triglio underground aqueduct (Apulia, southern Italy). Archaeol Prospect 23(3):195–211. https://doi.org/10.1002/arp.1541 Linford N (2006) The application of geophysical methods to archaeological prospection. Rep Prog Phys 69:2205–2257 Loke MH (1999) Time–lapse resistivity imaging inversion. In: Proceedings of the 5th meeting of the Environmental and Engineering Geophysical Society European Section, Em 1 Loke MH (2001) Electrical imaging surveys for environmental and engineering studies. A practical guide to 2-D and 3-D surveys. RES2DINV Manual. IRIS Instruments. www.iris-instruments.com Masini N, Sileo M, Leucci G, Soldovieri F, D’Antonia A, De Giorgi L, Pecci A, Scavone M (2017) Integrated in situ investigations for the restoration: the case of regio VIII in Pompeii. In: Masini N, Soldovieri F (eds) Sensing the past: from artifact to historical site. Springer, pp 557–586. https://doi.org/10.1007/978-3-31950518-3 Neubauer W (2001) Magnetische Prospektion in der Archaologie. Verlag der Osterreichischen Akademie der Wissenschaften, Wien Nuzzo L, Leucci G, Negri S (2009) GPR, ERT and magnetic investigations inside the Martyrium of St. Philip, Hierapolis, Turkey. Archaeol Prospect 16:1–16. https://doi.org/10.1002/arp.364 Overbeek J (1956) The Donnan equilibrium. Prog Biophys Biophys Chem 6:57–84 Pettinelli E (1993) Il georadar: teoria ed applicazioni. Tesi di dottorato di ricerca in Geofisica Applicata Università degli Studi La Sapienza di Roma. 361 Pieraccini M, Luzi G, Noferini L, Mecatti D, Atzeni C (2004) Joint time frequency analysis of layered masonry structures using penetrating radar. IEEE Trans Geosci Remote Sens 42:309–317 Pieraccini M, Noferini L, Mecatti D, Atzeni C, Persico R, Soldovieri F (2006) Advanced processing techniques for step-frequency continuous-wave penetrating radar: the case study of ‘Palazzo Vecchio’ walls (Firenze, Italy) Res. Nondestruct Eval 17:71–83 Ralph EK, Morrison F, O’Brien D (1968) Archaeological surveying utilizing a high-sensitivity difference. Magnetometer Geoexplor 6:109–122 Ranalli D, Scozzafava M, Tallini M (2004) Ground penetrating radar investigations for restoration of historical building: the case study of Collemaggio Basilicata (L’Aquila, Italy). J Cult Heritage 5:91–99 Revil A (2002) Self-potential signals associated with variations of the hydraulic head during an infiltration experiment. Geophys Res Letters 29:7 Reynolds JM (2011) An introduction to applied and environmental geophysics. Wiley, Chichester Roy A, Apparao A (1971) Depth of investigation in direct current methods. Geophysics 36:943–959 Roy K, Elliott M (1980) Resistivity and IP survey for delineating saline water and freshwater zones. Geoexploration 18:145–162 Sambuelli L, Calzoni C, Stocco S, Rege R (2010) Geophysical measurements on the occasion of the moving of an ancient Egyptian sculpture. In: Proceedings of GNGTS conference, Trieste, Italy, 16–19 Nov, pp 595–9 Scollar I, Kruckeberg F (1966) Computer treatment of magnetic measurements from archaeological sites. Archaeometry 9:61–71 Scollar I, Tabbagh A, Hesse A, Herzog I (1990) Archaeological prospecting and remote sensing. Cambridge University Press, New York Sill WR (1983) Self-potential modeling from primary flows. Geophysics 48(1):76–86 Stove GC, Addyman PV (1989) Ground probing impulse radar: an experiment in archaeological remote sensing at York. Antiquity 63:337–342 Telford WM, Geldart LP, Sheriff RE (1990) Applied geophysics. Cambridge University Press Toraldo di Francia G (1988) Onde elettromagnetiche, Zanichelli Editore, p 705; Turner G (1994) Constant Q attenuation of subsurface radar. Geophysics 59:1192–1200

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Chapter 4

NDT Geophysical Instrumentation and Data Acquisition and Processing Enhancement

Abstract Scientists who work in the field of NDT geophysical methods for archaeology and monumental heritage seek to address today’s demands to detect, characterize, and discriminate buried archaeological features and to obtain useful information about the conservation degree of an important monument for remediation and restoration disposal. They increasingly rely on high-resolution NDT geophysical methods to provide accurate and efficient results. In comparison with other direct procedures, NDT geophysical methods are especially well-suited for this application because they minimize time and cost factors and maximize the amount of data, information, and knowledge obtained. This chapter introduces a new mode to acquire, process, and interpret NDT geophysical data that could be define as “not standard”. This mode is intended to provide a framework for viewing the basic problem, the appropriate solving data processing and the relationship between the data, the information, and the knowledge throughout this process. In addition, this mode provides a conceptual organizing structure for identifying the means by which data, information, and knowledge can be enhanced for both site and monument characterization. Lastly, a look at how advanced visualization techniques can help address classical problems will be taken. This latter process can help in distinguishing materials that have different physical property characteristics.

4.1 GPR Instrumentation Enhancement: Reconfigurable Stepped-Frequency Georadar A brief description of the reconfigurable stepped frequency georadar system is proposed. Figure 4.1 is a photo of such a system. This instrument was developed in 2010–2011 thanks to acollaboration between the Institute for Archaeological and Monumental Heritage, the Florence Engineering and the Ingegneria dei Sistemi (IDS) Corporation. It is documented under Italian patent number 0001395231. The system offers the capability of changing the length of the antenna (reconfiguration) in order to change the central band frequency (Persico and Prisco 2008) © Springer Nature Switzerland AG 2019 G. Leucci, Nondestructive Testing for Archaeology and Cultural Heritage, https://doi.org/10.1007/978-3-030-01899-3_4

75

76

4 NDT Geophysical Instrumentation and Data Acquisition …

Fig. 4.1 The reconfigurable stepped-frequency georadar system

(Fig. 4.2). It is possible also to change the radiated power at each frequency and the integration time of each harmonic tone (Persico and Prisco 2008). The reconfiguration of the radiated power is achieved by the attenuation selectively chosen via the frequencies. The reconfiguration of the length of the arms of

Fig. 4.2 Scheme for reconfigurable antennas: the antennas are “short” if all the switches are off; they are “medium” if the internal switches are on and the external ones are off; they are “long” if all the switches are on (Persico et al. 2014)

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the antennas (essentially, two bow-ties) is achieved by making use of two series of switches implemented with PIN diodes (Persico et al. 2016). This makes possible implementing three pairs of equivalent antennas just by making the arms of a unique couple of antennas longer or shorter, which, of course, minimizes space compared to the case of three physically distinct pairs of antennas (Persico et al. 2014; Matera et al. 2015). This is important because the depth of the target and the material characteristics in many cases are unknown a-prior; consequently, the optimal frequency band for the survey are also unknown, and so the capability to simultaneously gather more Bscans with different bands can be helpful (Matera et al. 2016; Persico and Leucci 2016). Several commercial georadar systems contain a double pair of antennas, but, to the best of our knowledge, none contain three pairs of antennas together. The central frequencies of the three equivalent antennas in the reconfigurable georadar system are calibrated at about 120, 250, and 550 MHz, with some site-dependent variation, and the band of each equivalent antenna is of the same order as its central frequency. The system is able to sweep the band 50–1000 MHz (or part of it), with the option to set the frequency step to 2.5 or 5 MHz (Persico and Leucci 2016). In a commercial georadar, a pulsed signal is transmitted that is the sum of all harmonic components of the signal at the same time. For the stepped-frequency transmitted signal, the harmonic components of the spectrum are transmitted one at a time in sequence. Actually this discourse is not rigorous because each sinusoidal component should, strictly speaking, last an infinite time (and start at an infinitely small time), so that it is physically impossible to transmit them in sequence. However, if the transmitted sine waveforms contain many cycles of each sine wave, the approximation related to the transmission of the entire sine wave is acceptable. The signal received from the stepped frequency is, in practice, a sequence of sine-wave segments, and it can be converted by software into an equivalent pulsed signal by summing the sine wave pieces arriving in sequence. The discourse is actually more extensive and complex, but here we can consider this summary to be sufficient; for broader and more detailed discussions related to the theoretical, technological, and performance differences obtainable with the two types of system, reference is made to the scientific literature (Noon 1996; Persico 2014). Here, it is of interest to establish the sampling step necessary to correctly collect the measurements, which, in the case of a stepped-frequency system, translates into the problem of establishing a correct “pitch” in frequency and a correct spatial step. In fact, a stepped-frequency system transmits the spectrum of an equivalent pulsed signal and receives the spectrum of an equivalent synthetic signal over time, frequency by frequency. A stepped-frequency system samples the spectrum of the signal of interest instead of sampling the signal itself over the time. Finally, as stated, the system can reconfigure the integration time of the harmonic tones selectively, i.e., frequency by frequency. The integration time of the harmonic tones constitutes the parameter of interest because it enables removal of any unwanted signal already in the data-

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Fig. 4.3 Radar sections recorded with the antennas at 200 MHz of the pulse system (a) and with the medium-frequency antennas of the reconfigurable system (b)

acquisition phase. In particular, the possibility of selectively extending the integration times educes the problem of how to perform this extension in a proper way. In order to understand some differences between a reconfigurable stepped frequency and a pulsed georadar, a comparison between two homologous processed radar sections is shown in Fig. 4.3. The dashed yellow rectangle indicates the presence of some anomalies at 45 ns (1.6 m in depth) and at 60 ns. These anomalies can be ascribed to the hypogeal tomb (probably to the ceiling and to the floor, respectively). The two GPRs detect the same anomalies and also appear to be in good agreement with respect to the estimated time depth of the main anomalies. It is also possible that the reflection events are slightly better evidenced by the stepped-frequency georadar (Fig. 4.3b). This observation is better demonstrated by the 3D data analysis (Fig. 4.4). Here, the GPR slices related to the two georadar systems are in satisfactory agreement; they clearly indicate that the anomalies related to the archaeological features are slightly better revealed in the stepped-frequency georadar (Fig. 4.4b).

4.2 The GPR Data Acquisition The expression of the properties of the materials is the relative dielectric constant εr, which cannot be controlled for in a GPR survey. On the contrary, there are numerous other parameters instead that can be varied in order to obtain the maximum for depth of investigation and for resolution. These parameters are obviously: (i) antenna frequency; (ii) sample interval; (iii) two-way time window; (iv) samples per trace; and (v) transect spacing and orientation.

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Fig. 4.4 Comparison of the 3D results obtained with the two GPR systems

4.2.1 The GPR Frequency of Antenna and Depth of Penetration In Chap. 3, the ability of the electromagnetic waves to effectively penetrate the ground and/or any medium to a particular depth was addressed. It is primarily dependent on: (i) the frequency of the chose antenna; and (ii) the characteristics of the material (Conyers 2004). But is also depends on the electronic characteristic of the GPR instrumentation (Leucci 2008). The wave frequency can be controlled for, choosing the correct antenna frequency for a GPR survey. As is known, lower-frequency antennas provide the deepest penetration and lowest resolution, whereas high-frequency antennas are only able to image shallow features and have higher resolution (Conyers 2004; Leucci 2015). It is important to emphasize that the maximum penetration depth of GPR in the subsoil and/or in the any material is commonly unknown among GPR users. The electrical conductivity of the materials traversed by the electromagnetic waves introduces significant absorptive losses, which limit the penetration depth into earth formations, and so it is primarily dependent on the water content and mineralization present. Few studies describe efficient GPR techniques for determining the radarenergy attenuation, the relative dielectric permittivity, and the electrical conductivity (Cook 1975; Godio and Guo 1998; Leucci 1999; Reppert et al. 2000). Several studies, instead, describe efficient laboratory techniques for determining these parameters (Topp et al. 1980; Sen et al. 1981; Feng and Sen 1985; Olhoeft and Capron 1993). In the following, the theory elaborated to determine the radar-energy attenuation and the maximum penetration depth related to the antenna frequency is described. It is important to outline that the effectiveness of GPR is limited in many problems by its maximum effective range or probing distance (PD) in the medium of interest. This is determined both by radar system limitations and by propagation loss in the material to be investigated. The combined effect of the radar-system parameters and

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the absorption parameters of the medium provide the following conventional radar equation (Di Franco and Rubin 1968): PF ≥ total propagation loss  spreading loss + absorption loss

(4.1)

where PF (in dB) is the “performance figure” defined as  PF  (radiated peak power) (minimum detectable received signal power) (4.2) which represents the radar-system limitations. The TPL (in dB) is done by following relationship (Cook 1975):    TPL  10 log10 8(PD)3 c a4 f(εr )1/2 + 2(PD)A

(4.3)

where a  antenna aperture; c  3 × 108 m/s (velocity of electromagnetic waves in vacuum); f  radar signal frequency; PD  maximum probe depth; and A  the absorption loss in decibels per meter  8.69 α dB/m. For more details, the interested reader is addressed to Leucci (1999). Once the value of the radar energy and instrumentation attenuation has been established, it is possible to characterize, from the point of view of the maximum penetration depth, the materials object of the investigations. Starting from Eq. (4.3) and considering PF ≥ TPL, it is possible to appreciate the relationship between maximum penetration depth and frequency antenna. The performance figure is a characteristic related to the GPR instrumentation. In Eq. (4.3): • PF has been furnished by the manufacturer, and generally the value is 160 dB in air; • f represents the frequency of the center band of the used antenna; • PD is the depth of penetration (unknown); • a2 is the real area of the antenna (unknown); • L is the constant of attenuation (L  8.96 α/f) (Cook 1975). For the calculation of the TPL, the better conditions TPL  PF (in air) were considered. In this case, the radar energy-attenuation term through the ground in Eq. (4.3) is equal to zero. Unfortunately, Eq. (4.3) has two unknown terms, PD and a2 . To estimate PD, it is possible to consider the relationship that expresses the maximum penetration depth of the radar energy in air:    2(PD) c  tmax

(4.4)

where tmax is the maximum time range applicable. From Eq. (4.4), it is possible to derive:  (PD)  c tmax 2

(4.5)

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Once PD has been determined, it is possible to calculate a2 by utilizing Eq. (4.3). Once the value a2 has been established, depending on the chose antenna, it is possible to determine TPL in the medium if the attenuation coefficient α is known. Using the radar energy-attenuation value estimated in (4.3), it is possible to create Table 4.1. Using both the attenuation coefficient value and the TPL values, it is possible to graph Fig. 4.5, which represents TPL versus antennas frequency. It is important to note that, as can be seen, TPL decreases with increased frequency. Using the attenuation-coefficient value (for example, 1.34 m−1 ), it is possible to obtain the graph that represent TPL as a function of depth penetration (PD) in the range of depth (0–1 m) for antennas with an elevated value of the center band that is usually used for investigating small thickness (Fig. 4.6). A general graph for all antennas used in the field surveys is presented in Fig. 4.7. The figure underlines the limits (for the penetration depth) associated with both instrumentation and the attenuation coefficient. At this point, it is important to emphasize how to determine the attenuation coefficient. It is possible to use Table 2.1 that displays the values of α for several common geological materials. Another way to determine α is directly from the acquired GPR data (Leucci 2008). Consider a simple measurement of electromagnetic wave velocity performed in the field using the CDP or WARR method. In this latter case, the data shown in Fig. 4.8 are obtained. In Fig. 4.8a, several waves are visible: the direct-air wave, the ground wave, and the reflected wave. The ground wave can be used for wave-velocity determination, as its propagation path and the transmitter–receiver spacing are known. In the case of Fig. 4.8, the ground-wave velocity was estimated as 0.1 m/ns. The amplitude of the ground wave decays faster (as 1/r2 : geometrical spreading) with distance from the source.

Table 4.1 Antenna parameters, determined in experimental mode, based on the values of attenuation calculated in the field survey Antenna frequency Antenna time range a (m) TPL (dB) (MHz) (ns) 1000

20

2.84 × 10−4

82.7

1000

15

2.29 × 10−4

82.4

8 100 300 150 500 250 500 1000

1.43 × 10−4

81.7 74.8 63.1 62.1 53.8 53 54.9 54

1000 500 200 200 100 100 35 35

0.0011 0.0032 0.0019 0.0056 0.0034 0.0073 0.0123

82 Fig. 4.5 Experimental graph of the TPL versus antenna frequency

Fig. 4.6 Experimental graph of the TPL versus penetration depth using the value of α  1.34 m−1

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Fig. 4.7 Experimental graph of the TPL against penetration depth, obtained using the value of α  1.34 m−1

Fig. 4.8 WARR data processing in order to calculate radar-energy attenuation: a raw radar section (100 MHz antenna); b remove gain section; c section corrected for geometrical spreading

The first step is the “ungain” (Fig. 4.8b) and correcting for the geometrical spreading (Fig. 4.8c). In order to remove the gain factor from the GPR data, the following gain function must be considered (Leucci 1999): A0 (n)  Ai (n) 10g(n)/20

(4.6)

where n (n  1, N, and N is the total samples number) represents the index of the generic sample that varies as we move along the axes of time of the radar section. In any step, the output amplitude will be: A0 (n)  Ai(n) 10g(n)/20

(4.7)

In order to remove the applied gain from the radar traces (4.7), it must be multiplied by 10−g(n)/20 .

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The wave amplitude at the time t is given by: A(t)  G(t) A0 exp(−αvt)

(4.8)

where A0 is the value of the initial amplitude at the time t  0, and the factor of geometrical spreading is G(t)  [1/(vt)2 ]. The correction for the geometrical spreading is done by multiplying the unamplified radar traces by 1/G(t). The radar-energy attenuation can be determined comparing the values of the ground-wave amplitude in the red crosses with the value of the air-wave amplitude (first black cross). In fact, all these points represent the radar energy that has travelled though the ground and been received at the receiving antenna. So, the radar-energy attenuation is α  1.34 m−1 .

4.2.2 The GPR Frequency of Antenna and Resolution The ability to resolve (the resolution) the dimension of the hidden features, as affirmed in Chap. 3, is “in part” affected by the antenna wavelength (which is directly related to antenna frequency). As already see (in Chap. 3), higher-frequency antennas provide higher resolution than lower-frequency antenna (Conyers and Goodman 1997; Conyers 2004; Reynolds 2011; Conyers 2013; Leucci 2015). This is due to the fact that the shorter wavelengths related to higher frequencies produce a close cone of transmission of electromagnetic waves below the antenna (lower footprint), which can focus on smaller areas and thereby resolve smaller features. Wider wavelengths related to lower frequencies produce higher footprints that cause more spread-out transmission cones (Conyers 2004). The center-frequency wavelength of an antenna is: λ

c √ f εr

(4.9)

The maximum horizontal resolution is equivalent to the area of the energy footprint (or area of illumination), which varies with frequency and depth (Conyers and Goodman 1997): A

D λ +√ 4 εr + 1

(4.10)

where A is the long dimension of the elliptical footprint; λ is the center frequency; (f) wavelength of the antenna (in m); D is the depth below the surface (in m); εr is the average relative dielectric constant from the surface to depth D; and c is the electromagnetic-wave velocity in the vacuum. Since the maximum resolvable horizontal target is equivalent to A, an important rule to determine the appropriate fre-

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quency is that the smallest object that can be resolved is approximately λ/4 (Conyers 2004; Leucci 2015). Maximum resolution of vertical features is related to Eq. (4.9) rewritten as f  v

(4.11)

where v is the electromagnetic-wave velocity in the medium. Neubauer (2002) underlined that the vertical resolution is λ/2.

4.2.3 The Sampling Interval of Data Acquisition This acquisition parameter refers to the number of samples needed to construct a single reflection trace. As seen in Chap. 2, this parameter influences the resolution of the reflected waveform. The minimum number of samples collected per trace in most GPR surveys is 512; other common values could be 1024 and 2048 samples per trace. The number of samples per trace varies with the time window and sampling interval as described by the equation:  SW t where S is the samples per trace, W is the time window (in ns), and t is the sampling interval (in ns). Figure 4.9 shows an example in which a GPR trace had been conducted with 512 samples per trace (Fig. 4.9a), 256 samples per trace (Fig. 4.9b), and 128 samples per trace (Fig. 4.9c). It is important to note the differences in trace reconstruction. In fact in the trace acquired with 128 samples, some information was lost.

4.2.4 The Two-Way Time Window Set This parameter is the amount of time for which the receiving antenna will record two-way travel time data. The two-way time window can be calculated using the equation (Conyers 2004):    W  1.3 2D v where W is the length of the time window (in ns), d is the maximum depth to be resolved (in m), and v is the minimum electromagnetic-wave velocity in the surveyed material (in m/ns).

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Fig. 4.9 GPR trace: 512 samples per trace (a), 256 samples per trace (b), and 128 samples per trace (c)

4.2.5 Sampling Interval This parameter is related to the time between points collected for each recorded waveform. It can be estimated using the following equation  t  1000 6f where t is the sampling interval (in ns) and f is the center frequency of the antenna (in MHz) (Sensors & Software 1999). It is standard that the sampling interval does not exceed half of the period of the highest frequency, taken to be 1.5 times the center frequency of the antenna.

4.2.6 Sample Spatial Interval This parameter represents the spatial interval in which a radar section is acquired in the field, for example, one trace every 0.03 m. Clearly, as is shown in Fig. 4.10, the smaller the size of the spatial sample interval, the higher will be the resolution of the data collected.

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Fig. 4.10 a Radar section acquired with a spatial sample interval of 0.034 m with a zoom (b); c radar section acquired with a spatial sample interval of 0.3 m with a zoom (d)

4.2.7 Survey Profiles Spacing and Orientation This parameter is related to the 3D resolution of the anomalies connected to the buried objects inside the investigated materials. Generally, profiles should be separated by less than the long dimension of the footprint. This is based on the Nyquist rule (see Chap. 2). For the frequency antenna ranging from 400 to 600 MHz, which are the frequencies commonly used in archaeological target survey, the recommended standard profiles spacing ranges from 0.25 to 0.5 m (Leckebusch 2003). For high frequency antennas, the spacing ranging from 0.05 to 0.15 m (Leucci 2015). The orientation of the profiles also plays an important role in the 3D resolution of the buried features. Generally, to obtain a best resolution in a single direction survey,

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Fig. 4.11 Depth slices related to GPR profiles acquired in the a x direction, b y direction, and c x and y direction

assure that the profiles are collected perpendicular to the anomalies direction. But, in more and more cases, the orientation of the anomalies is unknown, and therefore it is appropriate to acquire combined data in both x and y directions (Conyers 2004, 2013; Leucci 2015). Figure 4.11 shows the results related to GPR data acquired inside the Saint Sebastian Church located in Lecce (south Italy). Data were acquired along parallel profiles spaced 0.4 m, using the Ris Hi-mod GPR system with 600-MHz central frequency antenna, in the x direction (Fig. 4.11a), y direction (Fig. 4.11b), and xy direction (Fig. 4.11c). It is possible to note that the shallow subsurface archaeological features perpendicular to the x axes are well evidenced in the profiles acquired in the x direction (Fig. 4.11a), while they are lost in the profiles acquired in the y direction (Fig. 4.11b). The shallow and deeper archaeological features are clearly resolved in the data related to the profiles acquired in both x and y directions.

4.3 GPR Data Processing Methodology One of the advantages of the GPR method is that the acquired raw data are easily viewed in real time on a computer screen.

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Frequently, only simple steps of data processing are required for an initial interpretation, with most of the effort directed towards data visualization. On the other hand, depending on the application and target of interest, it may be necessary to perform sophisticated data processing, and many practitioners find that techniques common to seismic reflection, such as migration, can be applied. The outcome of processing is a cross section of the subsurface electromagnetic properties, displayed in terms of the two-way travel time. The amount of processing undertaken can range from basic, which allows rapid data output, to the more time-consuming application of algorithms designed for use on seismic dataset (Yilmaz 1987), which produce highquality output (Daniels et al. 1988; Conyers and Goodman 1997). The processing steps usually developed for GPR raw data are done below: Zero-time adjust (static shift): During a GPR survey, the first waveform to arrive at the receiver is the air wave. There is a delay in the time of arrival of the first break of the air wave on the radar section due to the length of the cable connecting the antennae and the control unit. Therefore, one needs to associate zero-time with zero-depth, so any time offset due to instrument recording must be removed before interpretation of the radar image (Fig. 4.12). Background removal filter BGF (subtract average trace to remove banding): Background noise is a repetitive signal created by slight ringing in the antennae, which produces a coherent banding effect, parallel to the surface wave, across the section (Conyers and Goodman 1997). The filter is a simple arithmetic process that sums all the amplitudes of reflections that were recorded at the same time along a profile and divides by the number of traces. This makes up the resulting composite digital wave, which is an average of all background noise that is then subtracted from the data set (Fig. 4.13). If it is supposed that the averaging is performed on 2N + 1 traces, starting from the Nth traces before the current one and ending at Nth traces after the current one, and s is the spatial step of the measurements, one obtains the following equation: E bg f (x, t)  E(x, t) −

N  1 E(x − ns, t) 2N + 1 n−N

in the domain of time, and

Fig. 4.12 a GPR raw data; b GPR time-zero correction data

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Fig. 4.13 a Radar section with a coherent banding effect (ringing), the ringing is related to undesired reflection of the currents within the arms of antenna; b radar section with BGF

E bg f (x, ω)  E(x, ω) −

N  1 E(x − ns, ω) 2N + 1 n−N

in the domain of frequency. Care must be taken in this process not to remove real linear events in the profile. The time window in which the filter operates must be specified so that the filter is not applied until after the surface wave passes. Horizontal (distance) stretch to get constant trace separation (horizontal normalization): This correction need to remove the effects of non-constant motion along the profile. Data are collected continuously, and they will not be represented correctly in the image if steps are not taken to correct for the variable horizontal data coverage. Gain function: Gain is used to compensate for amplitude variations in the GPR image; early signal arrival times have greater amplitude than later times because these early signals have not travelled as far. The loss of signal amplitude is related to geometric spreading, as well as intrinsic attenuation. Various time-variable gain functions may be applied in an effort to equalize the amplitudes of the recorded signals. The most commonly applied is an automatic gain control (AGC) that is a time varying gain which runs a window of chosen length along each trace, point by point, finding the average amplitude over the length of the window about each point. A gain function is then applied such that the average at each point is made constant along the trace. Topographic corrections: Surveyed elevation data are used to apply topography to the GPR survey profiles. Firstly, trace windowing is applied to the data to remove all artefacts in the survey that arrived before the time zero arrivals. The actual elevation

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recorded along the GPR line are then entered into the data-processing package, and the time-zero arrivals are hung from the topographic profile by applying a time shift to each individual trace (Fig. 4.14). Frequency filtering: Although GPR data are collected with source and receiver antennae of specified dominant frequency, the recorded signals include a band of frequencies around the dominant frequency component. Frequency filtering is a way of removing unwanted high and/or low frequencies to produce a more interpretable GPR image. High-pass filtering maintains the high frequencies in the signal but removes the low-frequency components. Low-pass filtering does just the opposite, removing high frequencies and retaining the low-frequency components. A combination of these two effects can be achieved with a band-pass filter, where the filter retains all frequencies in the pass band, but removes the high and low frequencies outside the pass band (Fig. 4.15). Migration: Migration is a processing technique that attempts to correct for the fact that energy in the GPR profile image is not necessarily correctly associated with depths below the 2-D survey line. Migration can be seen as an inverse processing step that attempts to correct the geometry of the subsurface in the GPR image with respect to the survey geometry. For example, a subsurface scattering point would show up in a GPR image as a hyperbolic-shaped feature. Migration would associate all the energy in the wavelets making up the hyperbolic feature with the point of diffraction, and imaging of the actual earth structure (the heterogeneity represented by the point diffractor) would recorded more clearly. Migration operators require a good estimate of subsurface electromagnetic- wave velocity to apply the correct adjustments to the GPR image (Fig. 4.16). For more, see Persico (2014).

Fig. 4.14 GPR data acquired in the archaeological site of Ventarron-Lambayeque (Perù), a radar section without topographical correction; b radar section with topographical correction

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Fig. 4.15 a GPR raw data; b effect of band pass filter on both the spectrum and single trace; c GPR band-pass filtered data

Fig. 4.16 a Scheme related to the hyperbolic shape obtained in a GPR profile; b GPR raw date; c GPR migrated data

F-K filter: It is well-known that a dipping line in the x-t domain maps to a line passing through the origin and with an orientation normal to the original line in the f-k amplitude spectrum. In other words, a line of apparent constant velocity corresponds to a line of constant slope in the f-k domain. In particular, horizontal lines map to the vertical direction, along the f-axis. Dipping events that overlap in the x-t domain can be separated in the f-k domain by their dips. This makes possible the elimination of certain types of unwanted energy from the data, representing linear coherent noise. Regardless of their location, lines with the same dip (parallel lines) map to the same radial line in the f-k amplitude spectrum, so that f-k filters could be effective for removing, at the same time, all undesired lines with the same slope, but impractical if one wants to remove only some of them instead of the whole family. F-k filters are generally used for dip filtering. In these cases, the amplitude spectrum of the input is multiplied by a suitable function, the amplitude response of the filter consisting of ones in a fan-shaped zone and zeros elsewhere, to obtain the amplitude spectrum of

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the output, whereas the phase spectrum is left unchanged. Finally, the filtered signal is obtained by a 2-D inverse Fourier transform (Fig. 4.17). The Wavelet Transform: It is possible to decompose the radar signal into various scales where signal and certain noises may be effectively separated/isolated (multiresolution analysis). Subsequent muting of the noise is easily achieved in the Wavelet Transform (WT) domain operating only on the scales where the offending noise appears. An example of the multi-resolution analysis is show in Fig. 4.18. GPR data show a hyperbolic-shape reflection obtained from the presence of a tree in surface (Fig. 4.18a). Using multi-resolution analysis, it is possible to isolate hyperbolic-shape reflection (Fig. 4.18b) and to remove it from the radar section (Fig. 4.18c).

Fig. 4.17 F-K filter applied to remove signal (noise) originating from objects placed on the surface: a GPR raw data; b GPR filtered data

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Fig. 4.18 a GPR raw data with a noise related to the hyperbolic shape reflection; b multiresolution analysis; c GPR filtered data

4.4 GPR Data Visualization: Time Slices GPR surveying in archaeology and monumental-heritage analysis possesses the capability to easily scan (suitable for archaeologists and restorers) and to map, thus to identify the shape, size, depth, and location of buried anomalies that could be related to archaeological features or to the conservation degree of monumental heritage. In this way, it is possible to plan an excavation or a restoration intervention. With GPR data acquired using closed spaced profiles, it is possible to map the stratigraphy of investigated medium by identifying important reflection events present in 2D data. This could be done by the amplitude slice map analysis that creates maps of differences between reflected-wave amplitudes, both spatially and with depth in a grid (Conyers and Goodman 1997) (Fig. 4.19). As is known, the amplitude of the reflected events is directly correlatable with the contrast between the dielectrical characteristics of the objects present in the investigated medium; therefore, the 3D visualization, by amplitude intervals, of the distribution of the reflected events makes possible the spatial localization of the structures that determine the reflections themselves. Obviously, each time slice corresponds to a layer of the investigated medium, whose depth and thickness depend on the velocity of propagation of the electromagnetic waves in the medium. The result of amplitude mapping can be a series of maps and other images that illustrate in three dimensions the location of reflection anomalies (Fig. 4.20). The choice of two-way time interval dt is related to the used frequency antenna. Generally, it is of the order of the dominant period (Nuzzo et al. 2002) (Fig. 4.21).

4.5 GPR Data Visualization: Amplitude ISO-Surfaces An approach for visualizing 3D radar data was proposed by Zanzi and Valle (1999) for automatic mine detection. In the first case, after an appropriate processing of radar data, a 3D image of the sought diffracting or reflecting object could be easily obtained

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Fig. 4.19 Schematization of the construction of a time slice. The acquisition on parallel profiles enables spatially correlating the signals present on each section using the analysis of the amplitude of the reflected events within assigned time intervals

by: (i) extraction of a particular complex-signal attribute (trace envelope); (ii) thresholding; and (iii) 3D contouring by means of iso-amplitude surface. Whereas this was effective in the case of a laboratory experiment, the low signal–noise ratio observed in a real case induced the authors to propose an alternative approach consisting of: (i) extraction of the most promising complex-signal attributes (trace energy and envelope); (ii) three stacks separately performed along each coordinate axis, providing separate 2D results: stacking of the energy along the depth or z axis, in order to obtain a plan view of the high-energy suspected zones; stacking of the trace envelope along x; stacking of the envelope along y; (iii) thresholding; (iv) 3D rendering of the presumed target by projection in 3D space of the automatically selected thresholded data (Fig. 4.22). As pointed out by the authors, in both cases, the threshold calibration is a very delicate task. In Fig. 4.23, examples of an application of the last visualization procedure in an archaeological context are given.

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Fig. 4.20 An example of time slices overlapped to the orthophotos of the surveyed site at several depths

4.6 Electrical-Resistivity Tomography Field Measurements This part of the book presents the “best practices” for the collection and analysis of electrical-resistivity tomography (ERT) data. As underlined in Chap. 3, the advances over the previous decade in ERT hardware technology and software represented a rapid evolution of the state of the art related to data acquisition and analysis. Expert utilizers of ERT methods in data acquisition and analysis have benefited from numerous additional choices in selecting acquisition and inversion parameters, some of which clearly can affect the results in a substantial way. As a result, it is now possible for them to know: (i) how to design robust survey geometries; (ii) how select the acquisition and inversion parameters; and (iii) how it is possible to obtain good images of the investigated medium in order to facilitate the interpretation of the results.

4.6.1 ERT Survey-Instrument Parameters Until the early 1990s, ERT data were collected using a fixed set of geometries (e.g., Wenner, Schlumberger, or dipole-dipole arrays) because scientists moved the two current and two potential electrodes by hand, and they used simple geometries where analytic methods could be used to estimate the subsurface resistivity without complex inversion (Parasnis 1997). Such work was highly labor intensive and timeconsuming. The development of multichannel instrumentation with the possibility

4.6 Electrical-Resistivity Tomography Field Measurements

97

Fig. 4.21 Schematic example related to the choice of the two-way time interval dt in the construction of the time slices

Fig. 4.22 a GPR raw data; b traces envelope; c thresholding; d 3D rendering

to have a higher number of electrodes enables much faster data collection. Furthermore, modern inversion software is capable of processing ERT data in minutes on a low-end PC, and, as will be seen, does not require that the electrode arrangement correspond to any of the traditional, standard array types (e.g., Schlumberger, Wenner, dipole-dipole).

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Fig. 4.23 The 3D visualization of GPR data by amplitude iso-surfaces

The following discussion will treat some important aspects of ERT measurements. The first one is related to the fact that most multichannel instruments have the ability to adapt their input range in order to accommodate the resistance values intrinsic to the investigated medium. The instruments have the electronic capability to apply a gain factor to the difference of potentials that lies across the two potential electrodes before the actual values are measured (Schmidt 2013) because an improved match between the supplied voltage and the electronic of the instruments is obtained. This gain factor is automatically adjusted in several commercial instruments. In fact, the applied gain is related to the measured contact resistance values between the electrodes and the surface of the investigated medium. In this case, resistance checks should be run on the electrodes prior to data collection to assure that contact resistances are not too large. In surface arrays, it is possible to add saltwater around the electrodes to decrease the contact resistance. Generally, values on the order of 20 k or less are acceptable. Higher values may indicate that limited current can be injected for that electrode pair. Contact/resistance values can provide a basis for editing data associated with particular electrodes that are malfunctioning or in poor contact with the surface of investigated medium. Another important parameter is related to the possibility to collect each quadrupole several times and average the results. This procedure is referred to as “stacking.” Stacking is important in the improvement of the signal-to-noise ratio. In fact, in this way random noise can be averaged out. Furthermore, the stacking error of the measurements that are repeated (known as standard deviation) allow both to quantify the error that affects the measured data and define data weights for inversion. Generally, a values ranging from three (minimum stack) to six (maximum stack) are used (Leucci 2015). This constitutes a good compromise between “data quality” and time of acquisition.

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In more multichannel instruments, a reciprocal measurement option is implemented. It involves swapping current and voltage electrode pairs. In other words, the current electrodes are swapped with potential electrodes, while the geometrical factor K remains the same. Clearly this option does not influence the measured apparent-resistivity values. The error related to the reciprocal measurements provides a measure of instrument error. It is greater than the stacking error, and it provides a better quantification of noise than stacking errors (Leucci 2015). This option tends to slow down the ERT data collection and increase the time of acquisition compared with the stacking option. The duration of the current injection can be selected by the user. It is related to the physical parameter that must be acquired. Only for resistivity, the acquisition pulse duration could be set to 250 ms. Generally, in rho-mode acquisition, the current is injected into the investigated medium, as a succession of alternative positive and negative current pulses (Fig. 4.24). For resistivity and data acquisition for induced polarization, the current duration can be selected to be several seconds. In this case, the current is injected alternatively in the surveyed medium with a succession of positive and negative current pulses but also with a cut-off between each of them. This enables injection of a current between the current electrodes to measure the potential between the potential electrodes and to estimate both the electrical resistivity and the induced polarization or chargeability (Fig. 4.25).

Fig. 4.24 Current waveform in rho-mode acquisition

Fig. 4.25 Current waveform in rho- and IP-mode acquisition

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4.6.2 Choice of the Best Array In Chap. 3, some types of electrode arrays were studied in detail. Now, the question is which of them is most suitable for archaeological prospection and which for monumental-heritage diagnosis. In order to answer this important question, we must define the: (i) spatial resolution; (ii) strength of response; and (iii) depth of distinction. The spatial resolution is related to the dimension of the buried features. The rule should be that the spatial extent of the resistivity anomalies should not be larger than the features that cause them (Schmidt 2013). The strength of response is related to the resistivity contrast between the features of interest and the hosting medium. Anomalies related to feature with weak-resistivity contrast should be enhanced in order to be as strong as possible. The depth of distinction describes how well features can be distinguished when they are buried at various depths (Schmidt 2013). The Wenner array is technically the Wenner alpha array. This type of array is sensitive to vertical changes in the resistivity of the investigated medium (Loke 2001; Leucci 2015). However, it is less sensitive to horizontal changes in the resistivity within the investigated medium. Therefore, the Wenner array is a good one to resolve vertical changes and therefore horizontal structures, and it is not considered for detection of horizontal changes (vertical structures). As seen in Chap. 3, the depth of investigation for the Wenner array is approximately 0.5a, where a is the spacing between the electrodes pairs. The array has a strong signal strength, and this is important in surveys where the investigated medium presents high background noise. A disadvantage is the relatively poor horizontal coverage (Figs. 4.26 and 4.27). As evident in Figs. 4.26 and 4.27, increasing the number of levels (n) increases the depth of investigation but decreases the horizontal coverage. The dipole-dipole array is most sensitive to horizontal changes in resistivity but relatively insensitive to vertical changes in resistivity (Loke 2001; Leucci 2015). Therefore, it is good to map vertical structures. As seen in Chap. 3, the depth of

Fig. 4.26 Wenner array for a dispositive of 48 electrodes spaced 2 m (a = 2 m) and 9 level (n  9)

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Fig. 4.27 Wenner array for a dispositive of 48 electrodes spaced 2 m (a = 2 m) and 15 level (n  15)

investigation depends on a and n factors. Compared to the Wenner array, the dipoledipole array has a shallower depth of investigation, but has greater horizontal coverage (Figs. 4.28 and 4.29). This advantage in horizontal coverage is important in cases in which the number of nodes available with a multichannel system is small. A disadvantage of this array is the low signal strength for high values of n factor. In fact, to use this array the multichannel instrument should have high sensitivity and very good noise-rejection circuit, and furthermore it needs a very good resistance contact between the electrodes and the investigated medium surface. The Wenner-Schlumberger array is a hybrid between the Wenner and Schlumberger arrays (Loke 2001; Leucci 2015). This array is moderately sensitive to both horizontal and vertical structures, and therefore this array is a good compromise between the Wenner and dipole–dipole array (Figs. 4.30 and 4.31).

Fig. 4.28 Dipole–dipole array for a dispositive of 48 electrodes spaced 2 m (a = 2 m) and 9 level (n  9)

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Fig. 4.29 Dipole–dipole array for a dispositive of 48 electrodes spaced 2 m (a = 2 m) and 15 levels (n  15)

Fig. 4.30 Wenner-Schlumberger array for a dispositive of 48 electrodes spaced 2 m (a = 2 m) and 9 levels (n  9)

Fig. 4.31 Wenner-Schlumberger array for a dispositive of 48 electrodes spaced 2 m (a = 2 m) and 15 levels (n  15)

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The signal strength of this array is lower than the Wenner array but higher than the dipole-dipole array. It has slightly better horizontal coverage than the Wenner array but a slightly worse horizontal coverage than the dipole–dipole array (Figs. 4.30 and 4.31). The spatial vertical and horizontal resolution of these arrays is related to the sensitivity function of a single array. To improve the data quality and therefore the resolution, it is possible to use the overlapping data levels with various combinations of “a” and “n” values for the Wenner, Wenner-Schlumberger, and dipole–dipole arrays. As an example, consider a Wenner-Schlumberger array with electrodes spacing of 1 m along the survey line. Start with the “a” spacing (which is the distance between the potential electrodes) equal to 1 m, and repeat the measurements with “n” values of 1, 2, 3, and 4 (Fig. 4.32). Increasing the “a” spacing to 2 m leave “n” equals to 1, 2, 3 and 4 (Fig. 4.33). This process is repeated for all possible values of the “a” spacing (Fig. 4.34).

Fig. 4.32 Wenner-Schlumberger array for a dispositive of 48 electrodes spaced 1 m (a = 1 m) and 4 levels (n  4)

Fig. 4.33 Wenner-Schlumberger array for a dispositive of 48 electrodes spaced 1 m (a = 2 m) and 4 levels (n  4)

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Fig. 4.34 Wenner-Schlumberger array for a dispositive of 48 electrodes spaced 1 m (a = 3 m) and 4 levels (n  4)

It is possible to note in this example that the overlapped level contribute to having an increment of the spatial resolution and, naturally, the depth of investigation. Similar considerations can be done with the dipole–dipole array (Fig. 4.35). Some disadvantages could be related to the fact that increasing both the a spacing and n level increase the number of measurements and therefore the required memory in the georesistivimetry control unit. Furthermore, measurements with the higher n values over four would encounter higher noise levels. However, by having such redundant measurements using the overlapping data levels, the effect of the more noisy data points will be reduced (Edwards 1977).

4.6.3 ERT Survey Procedures The fundamental considerations about ERT field measurements are related to survey strategies in regard to the aims of the survey. The 2D ERT surveys are usually carried out using a large number of electrodes connected to a multi-core cable (Griffiths and Barker 1993). The necessary field equipment is commercially available from a number of international companies. Figure 4.36 shows the typical setup for a 2D survey with a number of electrodes along a straight line attached to a multi-core cable. Normally, a constant spacing between adjacent electrodes is used. The sequence of measurements to take, e.g., with a Wenner array, involves several steps. The first step is to make all the possible measurements with an electrode spacing of “1a”. For the first measurement, electrodes number 1, 2, 3 and 4 are used (Fig. 4.36). Electrode 1 is used as the first current electrode C1, electrode 2 as the first potential electrode P1, electrode 3 as the second potential electrode P2, and electrode 4 as the second current electrode C2. For the second measurement, electrodes number 2, 3, 4 and 5 are used for C1, P1, P2, and C2, respectively. This is repeated down the line of electrodes until electrodes 21, 22, 23, and 24 are used for the last measurement with

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Fig. 4.35 Dipole–dipole array for a dispositive of 48 electrodes spaced 1 m: a a = 1 m, n  4; b a = 3 m, n  4

Fig. 4.36 The arrangement of electrodes for a 2D ERT survey and the sequence of measurements

“1a” spacing. After completing the sequence of measurements with “1a” spacing, the next sequence of measurements with “2a” electrode spacing is made. First electrodes 1, 3, 5, and 7 are used for the first measurement. The electrodes are chosen so that

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the spacing between adjacent electrodes is “2a”. The same process is repeated for measurements with “3a”, “4a”, “5a”, and “6a” spacings. In order to extend horizontally the area covered by the survey, for a system with a limited number of electrodes, the roll-along method is used (Fig. 4.37). After completing the sequence of measurements, the cable is moved past one end of the line by several unit electrode spacings. All the measurements that involve the electrodes on part of the cable that do not overlap the original end of the survey line are repeated. The results of the 2D ERT survey is the pseudo-section that shows the resistivity distribution in the investigated medium (Fig. 4.38). Considering that the buried structures are 3D, a fully 3D resistivity survey should in theory give the most accurate results. Generally, 3D data sets are constructed from a number of parallel 2D survey lines. Ideally, there should be a set of survey lines with measurements in the x direction, followed by another series of lines in the y-direction (Fig. 4.39). The use of measurements in two perpendicular directions helps to reduce any directional bias in the data. In order to better understand this, synthetic data were created assuming that a number of 24 2D lines parallel to the x axis and 24 2D lines parallel to the y axis using a dipole–dipole array. The interline and interelectrode spacing was 1 m, while the maximum number of the recorded depth layers was set equal to seven. Three-dimensional rectangular-feature shaped models, which mainly appear in the archaeological sites, were considered (Fig. 4.39a). The hypothetical structures were given with resistivity value of 1000 m, inside background resistivity value of 100 m; successively with resistivity value of 100m, inside background resistivity value of 1000 m. They were considered to be at a depth of 0.75–2.20 m (Fig. 4.39b).

Fig. 4.37 Scheme of the roll-along method

Fig. 4.38 2D ERT pseudo-section that shows the resistivity distribution in the subsoil. “W” indicates the high-resistivity values object (likely a wall) and the bedrock with lower resistivity values

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Fig. 4.39 a Arrangement of hypothetical 576 electrodes in a 24 two-dimensional lines parallel to the x axis and 24 two-dimensional lines parallel to the y axis; b 2D model with the location of the archaeological feature

These resistivity values are typical for calcarenite material present in the Salento peninsula (Leucci et al. 2004). Each resistivity tomography, along x and y axes, was processed and inverted using the Res3Dinv software (Loke 2001). In the case in which the structure with resistivity of 1,000 m and the background resistivity value of 100 m (Fig. 4.40), the depth slices show that the 3D feature was fully reconstructed. In the case in which the features with resistivity of 100 m in the background resistivity of 1000 m (Fig. 4.41) the depth slices show that the three-dimensional feature was fully reconstructed. Both cases show more substantial differences if x, y, or xy data are considered. Grid-orientation effects can distort the feature image. This effect is clearly evidenced in the depth slices that represented the 3D inversion results along x and y direction. The distortion is due to the fact that an anomaly of very low resistivity was considered in a high-resistivity background that influenced the sensitivity function. The sensitivity function (Frechét derivative) of the array varies in relation to the variation in ground resistivity. When profiling across a highly resistive band at the surface, a negative anomaly will result when the two electrodes are placed on each side of the zone, due to the negative sensitivity function between the electrodes. Thus, the distortion in the data image acquired along x axes and y axes is an effect of the nearby surface area with higher resistivity. The feature was well reconstructed using both x and y data sets. In conclusion, it is necessary to conduct the survey along both the x and y axes to ensure that no feature details will be missed. There are field situations in which a typical grid of electrode lines is limited by physical conditions (the presence of obstacle or the necessity to investigate the foundation’s conservation degree of a monumental heritage. In this case, it is possible

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Fig. 4.40 Synthetic data: 3D resistivity model; the features were given with resistivity of 1000 m, where the background resistivity was 100 m

to use a “non-conventional” array that consists of multiple L-shaped arrays for a grid of electrodes by surrounding an area with a square of electrode lines. Initially, a 2D survey is conducted along each perpendicular line or transect. In the next step, the current electrodes remain at the end of one line, while the potentials are moved along the line. Then the current electrodes are moved one electrode position, and the potential electrodes are moved as previously described. The process is repeated until the current and potential electrodes cover the L geometry. This sequence of observations produces a series of resistivity towards and beneath the central portion of the array. The colored circles in Fig. 4.42 represent the attribution points, where the apparent resistivities are measured for the performed ERT array. This process is discussed in detail by Tejero-Andrade et al. (2015). Several L-arrays can be combined to surround a structure to build a 3D matrix of observations. Figure 4.43 depicts the results obtained using a series of L lines acquired in Pompeii (south Italy). As is possible to see in Fig. 4.43, some alignments (dark dashed lines) with relatively high resistivity values are visible. Furthermore, it is possible to use a non-conventional array that incorporates a random disposition of the electrodes on the surface of the investigated medium (Fig. 4.44).

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Fig. 4.41 Synthetic data: three-dimensional resistivity model; the features were given first ones resistivity of 100 m, where the background resistivity was 1000 m

Fig. 4.42 The apparent resistivity measured points in a non-conventional array

To achieve the goal of revealing the buried part of a Roman Amphitheatre, ERT profiles surround the buildings with a random distribution of electrodes. The results show the buried part of the amphitheatre (Fig. 4.45).

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Fig. 4.43 ERT depth slices at a depth of 6.0 m and a photo of the excavation

Fig. 4.44 Non-conventional ERT profiles acquired in Catania (south Italy)

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Fig. 4.45 3D model of resistivity distribution: a depth of 1 m; b depth of 4 m; c depth of 6 m; d resistivity distribution model at a depth of 6 m overlapped by a photo of the investigated area; e 3D visualization through the iso-resistivity surfaces

4.6.4 ERT Data Inversion After the acquisition the ERT data, they must be inverted to make electrical-resistivity images. A variety of commercially codes are available for this purpose. Most codes follow the same inversion approaches, which are based on quasi-Newton algorithms. On the basis of the selection of a starting model and inversion parameters, these codes should produce similar results; default values differ greatly, however, and it is not always clear how parameters are used within the inversion. The selection of the inversion parameters is somewhat subjective and guided by the operator’s intuition and/or the a priori information about the investigated medium or the nature of the targets. In order to obtain reproducible results, it is critical to: (i) report all parameter selections and default values; (ii) document the algorithm used by the software; and (iii) archive a copy of the software code or executable. It is also important to underline that there is not enough information to find a unique solution for a data inversion, and calculating the true distribution of resistivity in the medium is a highly nonlinear problem because the current paths through the medium are dependent on the resistivity structure (Day-Lewis et al. 2005; Singha and Moysey 2006; Leucci 2015). In NDT geophysical tomographics, these problems are solved with an excess number of model parameters and use regularization to create a mathematically stable solution (Constable et al. 1987) because this problem is solved using iterative inversion (Tripp et al. 1984). The solution to the inverse problem results in a 2D or 3D map that visu-

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alizes the 2D or 3D distribution of the electrical resistivity values. To a great degree, this is based on the cases of nonlinear, least-squares minimization of a two-part objective function. The misfit between the predicted and measured resistance values is the first part of this function. It minimizes the discrepancy between field experimental data and the computed data based on Poisson’s Equation (∇ 2 V  0). The term that minimizes the roughness of the field measured electrical resistivity is the second part of this function, and tt allows for well-posedness of the inverse problem. An example of the possible results that should be obtained using Res2Dinv software (by Geotomo software http://www.geotomosoft.com/) is show in Fig. 4.46. In this case, the inversion routine used by the program is based on the smoothness-constrained least-squares method (deGroot-Hedlin and Constable 1990; Sasaki 1992). In order to prevent overfitting or underfitting, data should be weighted by their measurement errors. In fact, the inversions will match the data within the expected measurement errors starting from the errors measured in the field-data acquisition. Constable et al. (1987) described the Occam inversion, which is the approach used in the ERT data inversion that set the tradeoff between the data match and the complexity (roughness) of the inverted resistivity tomograms. Table 4.2 summarizes some commercial software commonly used for 2D and 3D ERT data inversion.

Fig. 4.46 The 2D ERT inversion results using the Res2Dinv software

4.7 Induced-Polarization Data Acquisition and Inversion Table 4.2 Software programs commonly used in ERT data inversion ERT software Producer Algorithm

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Produced images

Res2Dinv

Geotomo software

Based on the smoothness-constrained least-squares method

2D

Res3Dinv

Geotomo software

Based on the smoothness-constrained least-squares method

3D

ERTLab

Geostudi Astier srl

Based on tetrahedral finite-elements forward modeling. Smoothness constrained least squares inversion. Robust inversion with data reweighting algorithm

3D

TomoLab

Geostudi Astier srl

Based on finite-element modeling

2D

AGI EarthImager 2D

AGI Advanced Geosciences Inc.

AGI EarthImager 3D

AGI Advanced Geosciences Inc.

Uses a model-stabilizing 2D function; is based on the assumption of exponential distribution of data errors; and minimizes the sum of the square-weighted data errors Uses a model-stabilizing 3D function; is based on the assumption of exponential distribution of data errors; and minimizes the sum of the square-weighted data errors

4.7 Induced-Polarization Data Acquisition and Inversion The Induced Polarization (IP) measurements are performed using the same instrumentation used for electrical-resistivity measurements. It can be considered an extension of the resistivity method by exploiting the georesistivimetry to make an additional measurement of the ability of the ground to store electrical charge. In this case, the current injection waveform shown in Fig. 4.25 must be used. It is necessary also to increase the time of acquisition to at least 2 s (Leucci 2015). Originally developed for mineral exploration (Madden and Cantwell 1967), it is currently being employed also in the fields of environmental and engineering geophysics (Ogilvy 1972; Roy and Elliott 1980). IP instruments measure both the conductive and capacitive properties of the investigated medium using either time-domain or frequencydomain techniques. The low frequency capacitance of rocks and soils is primarily a

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function of the surface chemical properties of the sample. In non-metallic samples, the IP response is an indicator of surface area and charge density of the material. IP measurements are therefore sensitive to clay content, as well as to mineralogy and pore–fluid composition. IP methods have been used to estimate the hydraulic properties of rocks and soils, as well as to map subsurface contamination (Slater et al. 2000). The method is also sensitive to subsurface metals (Reynolds 2011). And it has also been used for archaeological surveying (Aspinall and Lynam 1968, 1970; Schleifer et al. 2002; De Domenico et al. 2006; Florsch et al. 2011; Schleifer et al. 2002; Weller et al. 2000; Florsch et al. 2012). The IP can be measured either in the time or frequency domain using standard arrays already illustrated in the case of resistivity measurements. Therefore, steel and non-polarizing current and potential electrodes can be used. Time-domain measurements are performed by applying a wave signal, as evidenced in Fig. 4.25, to the current electrodes and recording the decay of any induced polarization voltage over a period of time shortly after the applied field has been removed. When the current is applied, the measured voltage will rapidly rise to within a few percentage points higher/lower than the maximum voltage, and then it approaches (but, theoretically, never reaches) this maximum asymptotically. Similarly, when the current is removed, the measured voltage will fall to the same induced polarization voltage just above zero before decaying over a time period of up to 1 s or more (Reynolds 2011; Leucci 2015). The first step in the data processing consists of obtaining a pseudo-section by plotting the apparent IP versus the depth for each midpoint of a given electrode configuration. The inversion of the data is carried out in a similar way to that already explained in the section on ERT data inversion. It is an iterative process that aims at minimizing the difference between the measured pseudo-section and the calculated pseudo-section based on a starting model (Fig. 4.47).

Fig. 4.47 The 2D IP inversion results using the Res2Dinv software

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This model is updated after each iteration until it reaches acceptable agreement between measured and calculated data or until no further improvements are possible. For 3D IP, measurements are valid with the same considerations made in the case of 3D resistivity measurements and processing. The same commercial software can be used. Figure 4.48 shows the results related to an important application of the 3D IP method in an important archaeological site, a Roman ship in Pisa (Leucci et al. 2014). Here the resistivity data were insensitive to the buried structure (i.e., resistivity values related to the Roman ship were similar to the host medium), but use of IP method yielded good results. In this case, the ErtLab software was used to automatically invert the IP acquired data and to yield a 3D-IP model. Overlaying the excavation plan with the IP depth slices, it is possible to see the position of other buried ships near the pier.

Fig. 4.48 The IP depth slices (respectively 1.5- and 2.5-m depths) overlaid in transparence on the excavation plan (Leucci et al. 2014)

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4.8 Self-potential Data Acquisition and Inversion Simple equipment is required to acquire SP data, i.e., non-polarizing electrodes (typically Pb-PbCl2 ). They consist of a metal conductor in a saturated solution of its own salt that allows gradual leakage from the electrode and contact with the ground (Fig. 4.49). The electrodes are connected by wire to a digital multi-meter with highinput impedance capable of a reading accuracy of ±0.0001 V. Schematically, the method of conventional SP data acquisition is showed in Fig. 4.50. One electrode represents the base station. The wire is unreeled to station 1 where the roving electrode is placed in a shallow hole (~10 cm deep) in the ground. The voltage between the base-station electrode and the roving electrode is recorded with the defined sign convention. The base pot is always attached to the negative lead of the voltmeter. After making the voltage measurement, the roving electrode is picked up and moved to station 2 as more wire is unreeled. The roving electrode is again placed in the ground, and another voltage measurement is made. This process is repeated until the survey is complete. The spacing between two successive measurement stations depends on the size of the anomalies expected. The value of the electrical resistance is also measured before each SP measurement to check the electrical contact between the electrodes. A new reference station is established every time the end of the cable is reached or before (depending on the field conditions). The measurements are generally performed in a loop (closed profiles or profiles connected at both extremities to other profiles) to evaluate and correct the drift undergone during the acquisition of the data. This process requires two corrections of the raw SP data, the reference correction and closure correction (or loop correction). In a graph, SP data is represented as a function of the distance. However, there is also another method of measurements called dipole configuration (gradient configuration). It involves recording a measurement and then moving the electrodes along a survey line, maintaining fixed spacing. The trailing electrode becomes the leading electrode as the electrodes are leap-frogged along the line. The positive voltmeter lead is always connected to the leading electrode to maintain proper polarity. The current measurement method is slow and bulky and requires a trained technician to gather reliable data. Therefore, an innovative system capable of performing multi-automatic SP measurements has been built. The Syscal-kid multi-channel resistivity-meter was modified in order to acquire SP in an automatic mode. In this case, the internal circuits were modified to obtain a reconfigurable instrumentation that enables the measurements of the electrical resistivity, induced polarization, and self-potential. First, the input impedance is increased to better assure a low contact resistance between soil and electrodes. Higher input impedances are desirable due also to the impedance reduction of air moisture. To switch the instrumentation from resistivity to a SP-measurements circuit, a simple switch was added. The first idea for an electrode array capable of making SP measurements was to call for automating the rotation using solid-state switches.

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Fig. 4.49 Self-potential data-acquisition electrode

Electrode-array designs in the form of rectangular grid were considered. The connections between electrodes are controlled by PC via a USB interface. To assure a good switch and SP measurements, an analog-device cross-point switch was chosen because of its high density and simple programming interface. As a cross-point switch, it can connect any of its 12 inputs to any of its 8 outputs, making an electrode array with 100 or more electrodes feasible (Fig. 4.51). The device has a 300 MHz bandwidth and is capable of handling a 3 V input swing relative to its analog ground. The classical SP inverse problem consists of determining position and magnitude of SP sources. The first step in data processing is the reference correction. This correction is made to join the various parts with the same SP profile, correcting the various changes of reference electrode. The second step of SP data correction is the closure correction. In the case of a closed profile, the first point is identical to the last one, so the SP value measured should theoretically be the same. This would be true if no environmental perturbation occurred between the moments when the first and the last measurements were made. However, during the survey, the measurement conditions can change (e.g., due to soil moisture, soil temperature, or instrumental error), and a drift will be observed. The drift increases regularly from the first point to the last one, and it accumulates during the whole acquisition time. This drift is considered as parasitic and it must be corrected.

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Fig. 4.50 Self-potential field-data acquisition scheme

The estimation of the SP sources “s” could be done successfully via the inverse problem. Obviously, it involves the calculation of s from a set of measured potentials. There are two principal difficulties that are addressed during the inversion. The first one involves the large variation in sensitivity of the data to various model parameters. The sensitivity is typically greatest near the measurement locations, though it is also a function of the resistivity structure. Sensitivity scaling is therefore applied by calculating the cumulative sensitivity of each model parameter to all the measured data. The second one is the non-unique solution, which is compounded by the limited set of available measurements. To address this non-uniqueness, a class of source solutions that have a desired spatial compactness could be selected. This choice amounts to the addition of prior knowledge about the properties of s, which may be dependent on the particular problem of interest. Starting from Eq. (4.12). ∇ · σ ∇ϕ  s

(4.12)

and introducing the matrix K  ∇ · σ ∇, it is possible to write Kϕ  s

(4.13)

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Fig. 4.51 The self-potential acquisition-circuit scheme

Therefore, K−1 s  ϕ

(4.14)

Equation (4.14) states the basic inverse problem. The sources s could be estimated “theoretically”, if ϕ (the electrical potential) is known. In practice, ϕ is sampled at a limited subset of locations that are often restricted to the surface of the Earth. Therefore, it is possible to consider the N measured potential ϕd that is related to the sources through a subset of the K−1 matrix. This new operator O is a selector matrix N × M that consists of a single 1 on each row in the column that corresponds to the measurement location. Therefore, Eq. (4.14) can be written as: O K−1 s  ϕd

(4.15)

Each row of K−1 contains the Green’s function that multiplies the source vector and results in SP measurements. The solution that minimizes the squared difference between the predicted and observed SP is given in Eq. (4.16): 

 K−1 OT O K−1 s  K−1 OT ϕd

(4.16)

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To estimate the depth of a buried structure from the SP data, it is possible to use a least-squares analysis method (Abdelazeem and Gobashy 2006) based on normalizing the residual SP anomaly using three characteristic points and their corresponding distances on the anomaly profile; then, the depth for each horizontal position of the buried structure is determined using the least-squares method. The computed depths are plotted against the assumed horizontal positions on a graph. The solution for the depth and the horizontal position of the buried structure is read at the common intersection of the curves. Knowing the depth and the horizontal position and applying the least-squares method, the shape factor is determined using a simple linear equation. Procedures are also formulated to estimate the polarization angle and the electric-dipole moment. The method is semi-automatic, and it can be applied to short or long residual SP anomaly profiles.

4.9 Seismic Sonic and Ultrasonic Data Acquisition and Inversion The equipment required to carry out sonic and ultrasonic-pulse velocity tests consists of several components. The stress wave is generated by means of an impulse force hammer or by a pulse #generator, equipped with a piezoelectric sensor to record the impulse force. The frequency and energy content of the impulse force are dictated by the characteristics of the source. The hammer-tip hardness determines the amplitude and duration of the impulse force: harder tips generate higher-amplitude, shorterduration signals. The mass of the hammer determines the initial energy content of the input stress wave. The hammer can be replaced with a calibrated impactor. The small vibrations of the material are measured by means of accelerometers, which can be fixed to the surface by means of steel angles or plates glued with epoxy or screwed to the wall, or simply leaned against the wall and hand-supported for a fully nondestructive test procedure. The signals of both the impact hammer and the accelerometer pass through a power amplifier and an analog to digital converter and are subsequently displayed and/or recorded by means of an external device, such as an oscilloscope or digital-waveform recorder. Figure 4.52 shows a typical instrumentation for both S and US pulse velocity measurements. The sensitivity of the acceleration transducers may vary between 100 and 1000 mV/g, which is sufficient for the scope of the signal acquisition. The sampling rate is an important issue concerning the accuracy of the acquired data. In fact, the use of digital-computer technology means that the analogue signal must be sampled at regular intervals in time in order to be processed. Figure 4.53 shows a signal sampled at two different intervals. The top slide shows that a good representation of the 20-Hz signal can be made by samples taken every 25 ms (marked by the dark stars). In the bottom slide, samples are taken every 75 ms. If an insufficient number of samples is taken, the higher frequency information is “lost” or aliased. The original 20-Hz blue curve appears as a 6.7-Hz red dotted curve. The highest

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Fig. 4.52 Experimental set-up for sonic and ultrasonic measurements

Fig. 4.53 Example of a sample rate

frequency F, which can be sampled by interval d, is 1/2d. This is called the Nyquist frequency. Higher frequencies than this are said to be temporally aliased because they will appear as if they are lower frequencies. Typical sampling intervals are 10, 20, 40, and 80 ms with aliasing occurring above 5000, 2500, 1250, and 625 Hz, respectively. Before the data are sampled, the higher frequencies which would be aliased, should be cut-off by an analogue filter in the recording system.

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The design of the seismic sonic and ultrasonic survey should take into account the aims of the survey and the on-site conditions. Clearly, the plan for the seismic campaign should be done by experts, in cooperation with experts in built heritage structures. The latter should define the aims of the tests and the relevant areas to be tested. An on-site preliminary inspection of the multidisciplinary expert-team, is very useful to select the optimal measurement arrays. It is then necessary to take into account several factors, such as, e.g., the geometry and morphology of the structures to be tested and access to the experiment location. The typology of the S and/or US test to be performed (DT, ST, IT or T) has to be chosen according to the aim of the investigation, in agreement with the potential targets’ testing problems, the cost effectiveness of the specific investigation, the required depth of investigation, and the accessibility of the site. To acquire significant data, a minimum distance from transmitter to receiver, related to the texture and unit dimension, must be considered. Lower distances are indicative of limited portions of structures and lead to local results. As already stated, the accuracy of the data recorded depends on the sampling rate of the acquiring instrument and on the average velocity of the seismic wave within the investigated medium (i.e., acquiring at 100,000 samples per s corresponds to a sampling time of 10 ms or to frequency sampling of 100 kHz), and, considering an average velocity of 1500 m/s, the accuracy in terms of distance is ±1.5 cm, corresponding to an error of 10%, if the distance between source and receiver is 15 cm. The tomographic approach is more effective on pillars and columns since a reliable tomographic reconstruction requires good coverage of the surveyed medium. The goal in designing the acquisition scheme is to ensure that any region of the medium is traversed by a number of transmitter–receiver (TX–RX) ray paths arriving from any possible direction. As a result, for a pillar, TX and RX positions should be designed to collect transmission data from every accessible side towards any other side (not only towards the opposite side). The distance between subsequent TX and RX positions along each side of the tomographic section should be calibrated according to the expected resolution. The survey preparation depends on the type of experiment (DT, ST, IT, or T), being in any case quite similar for the various testing typologies. The test preparation starts with the survey of the area to be tested. If the test crosses the structure section, it is necessary to mark a reference point on the various sides of the structure. Since, in many cases to reach the two sides of a structure it is necessary to make a long detour, the reference point must be chosen with the help of meters or distance meters and levels. Subsequently, the complete acquisition grid has to be marked on the surface/s of the area to be measured. When the structure surface cannot be directly marked or when the surface is delicate (frescos, bas-reliefs, etc.), pre-marked paper should be placed over the experiment area. It is advisable that the rows and/or columns chosen for the data acquisition have a regular, prefixed spacing. If, for any reason, a point of the line/grid has to be shifted, the changed position must be immediately reported on the drawings of the structural elements.

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Once the marking work has been done, the exact position of the measurements must be reported with respect to the selected reference points. The most common testing arrangement consists of drawing a rectangular/square grid on the masonry wall to be tested and the corresponding grid on the other side of the wall. The numeration must be unequivocal and correspond from one side to the other. The minimum number of rows and columns depends on the aims of the investigation. A similar arrangement has to be considered for the indirect sonic test, on one side of the structure. It is necessary to set the acquisition grid to have several horizontal and vertical paths, considered meaningful distances, where the test is performed. Figures 4.54a, b show a typical geometry of acquisition of seismic S and US tomography data. In the case of tomography, performed on two or more sides of a structure (wall/pillar), the most common testing arrangement considers a cross section (horizontal or vertical) of the structure to be tested. The source transmits the signal that is received on all of the positions chosen on the other side/sides (Fig. 4.54a). A good strategy to ensure a proper recording is to take pictures of the experiment areas after the marking work; pictures of the marked profiles with a measuring tape that shows the distance from the reference points of the area are also a good practice. Pictures taken from a point distant enough to include the whole area of an experiment will be very useful to prepare the final report by superimposing the sonic results on the exact position of the investigation. In principle, the final criterion in producing the field documentation is that this documentation must be sufficient to repeat the experiments exactly in the same positions and in the same way at a later time. Any evidence of metal elements observed on the surface of the experiments (tie-rods, nails, hooks, etc.), just as for other evident different material inclusions within the masonry-wall portion tested, should be reported (e.g., with pictures or drawings) to facilitate the final interpretation of the results. Seismic S and US instruments need a cross-check of the source and receiving devices, with their connection cables, by verifying of the signal input in the power amplifier and the corresponding visualization of the signal on the display. A proper setup of the acquisition parameters is extremely important to ensure a successful investigation, and the acquisition system may have various parameters to be checked. The factors that are usually set are the sampling rate and the signal gain. If possible, it is recommended to calibrate the acquisition system on some masonry samples, or brick/stone units, whose geometry and morphology are directly observable. It is good practice to report the final parameters that have been selected for the experiment in the field documents (Fig. 4.55). Data acquisitions should be performed according to the investigation design. An unambiguous naming convention must be chosen for the data files, and this convention must be indicated in the drawings. Any variation with respect to the design or to the naming convention must be properly reported on the field documents. Similarly, any variation of the setup parameters must be monitored. Since it is necessary to have a clean signal record, it is recommended to choose a firm position where to hit the instrumented hammer or to position the acceleration transducer. If the chosen point of the grid has been located on an unsteady masonry unit or deteriorated mortar joint, it would be better to shift the point of few centimeters to select a more suitable

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Fig. 4.54 Example of acquisition geometry for a T and b IT

position. To get more accurate results, it is advisable to have more than one record file per each ray path. Three record files per acquisition point would be convenient. Data processing must be performed by an expert in sonic-test processing using dedicated software products. This entails evaluating the pulse transit time by measuring the elapsed time of the recorded waveforms, that is to say, by picking, on the amplitude-versus-time diagram the starting point of the hammer pulse and the first arrival recorded by the accelerometer. In the case that the time selection has been performed with automated procedures, by using a threshold value to find the wave onset, the reliability of the procedure and appropriateness of the threshold value should be checked. After evaluating the transit time, the pulse velocity is calculated as follow: v  l/t where v is the pulse velocity, [m/s]; l is the distance between transducer, [m]; and t is the transit time, [s]. This simple procedure should be followed for S- and US-pulse velocity tests with direct, semi-direct, or indirect transmission methods. Data processing for tomography requires specific software codes. The tomographic inversion is a challenging problem, and the performances and the flexibility of tomographic programs can vary significantly. The standard procedure in a tomo-

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Fig. 4.55 Example of instrument setup

graphic reconstruction consists of first picking the travel times of the direct wave traveling from TX to RX positions through the masonry section. The transit times are then inverted by the tomographic software to obtain a velocity map. The problem is typically nonlinear, and the final solution is the result of several iterations where ray-paths are iteratively updated by using a ray-tracing module. The critical issues in this procedure are the design of the inversion grid and the control of the stability and reliability of the inversion. The grid size should be defined with special care, considering the expected resolution of the experiment and the spacing between acquisition points. Pillars with complex geometries may create data where the direct wave partially or totally travels in air. These data should be removed before the inversion stage to prevent artifacts in the final velocity map. The processing flow used in the method is shown in Fig. 4.56. The first step in the tomography survey consists of measuring the travel times of first arrivals of sonic waves related to source-receiver distances located along the profile (Fig. 4.57). These travel times should be picked manually on a PC. To determine the velocity distribution, the travel times of each source and each receiver must be combined to achieve an initial velocity model, by assuming a homogeneous medium. The model is represented by N × M cells (Fig. 4.58). Rays are traced through this model to give calculated travel times. A misfit function, consisting of the squared differences between the observed and computed travel times, is calculated. The model is adjusted until the misfit is minimized. The iterations are stopped when the root-mean-square (RMS) travel time residual (difference between the calculated travel times for the initial model and the observed ones) is less than the average pick error of the travel times.

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Fig. 4.56 The seismic-tomography, data-inversion scheme

Fig. 4.57 a Picked seismogram; b first-arrival travel-time curves

Fig. 4.58 Principle of ray tracing

The results of data processing may be visualized in the form of 2D or 3D contour maps in grey or color scales, or other (Figs. 4.58 and 4.59).

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Fig. 4.59 The velocity distribution visible as 2D depth slices

Tomographic results can be presented as velocity maps or color images where the color is associated with a given velocity (Fig. 4.59 and 4.60). This visualization enables direct evaluation of the internal composition of a surveyed material structure, such visualizations being, in general, areas with higher/lower velocities representing changes in terms of material, the presence of flaws/voids, or diffuse crack patterns. Whatever the representation is, it is essential to include a drawing of the structural element (wall, pillar, etc.) with an accurate indication of the location of the experiment. An effective method to facilitate the location of the results is to superimpose the images on the drawings or on the pictures of the structure (Fig. 4.61). For easier visualization and for the correct interpretation of the tests results, it is also necessary to use the same color scale throughout the entire testing report, even if the values of S-pulse velocity are very different (e.g., if the quality of different structural elements vary a lot, the same test is carried out before and after injection, etc.). This may need a recalibration of the color scale after all the tests are finished and the data processed.

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Fig. 4.60 The velocity distribution shown as 3D volumes

Fig. 4.61 The velocity distribution superimposed on the surveyed wall

References Abdelazeem M, Gobashy M (2006) Self potential inversion using genetic algorithm. J King Abdulaziz Univ Earth Sci (JKAU) 17:83–101 Aspinall A, Lynam JT (1968) Induced polarization as a technique for archaeological surveying. Prospezioni Archeol 3:91–93 Aspinall A, Lynam J (1970) An induced polarization instrument for the detection of near-surface features. Prospezioni Archeologiche 5:67–75 Constable SC, Parker RL, Constable CG (1987) Occam’s inversion: a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics 52:289–300 Conyers LB (2004) Ground-penetrating radar for archaeology. Alta Mira Press, Walnut Creek Conyers LB (2013) Ground-penetrating radar for archaeology, 3rd edn. Alta Mira Press, 258 pp Conyers LB, Goodman D (1997) Ground penetrating radar: an introduction for archaeologists. AltaMira Press, Walnut Creek

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Cook JC (1975) Radar transparencies of mine and tunnel rocks. Geophysics 40(5):865–885 Daniels D, Gunton DJ, Scott HF (1988) Introduction to subsurface radar. Proc Inst Electr Eng 135(F4):278–320 Day-Lewis FD, Singha K, Binley AM (2005) Applying petrophysical models to radar travel time and electrical resistivity tomograms: resolution-dependent limitations, J Geophys Res 110:B08206, https://doi.org/10.1029/2004JB003569 De Domenico D, Giannino F, Leucci G, Bottari C (2006) Integrated geophysical surveys at the archaeological site of Tindari (Sicily, Italy). J Archaeol Sci 33:961–970 de Groot-Hedlin C, Constable S (1990) Occam’s inversion to generate smooth, two dimensional models from magnetotelluric data. Geophysics 55(12):1613–1624 Di Franco JV, Rubin WL (1968) Radar detection. Artech House, Dedham Edwards LS (1977) A modified pseudosection for resistivity and induced-polarization. Geophysics 42:1020–1036 Feng S, Sen PN (1985) Geometrical model of conductive and dielectric properties of partially saturated rocks. J Appl Phys 58(8):3236–3243 Florsch N, Llubes M, Tereygeol F, Ghorbani A, Roblet P (2011) Quantification of slag heap volumes and masses through the use of induced polarization: application to the Castel-Minier site. J Archaeol Sci 38(2):438–451 Florsch N, Llubes M, Tereygeol F (2012) Induced polarization 3D tomography of an archaeological direct reduction slag heap. Near Surf Geophys 10:567–574 Godio A, Guo T (1998) Characterisation of sandy soil with georadar measurements. J Tech Environ Geol 4:17–27 Griffiths DH, Barker RD (1993) Two-dimensional resistivity imaging and modeling in areas of complex geology. J Applied Geophys 29:21–26 Leckebusch J (2003) Ground-penetrating radar: a modern three-dimensional prospection method. Archaeol Prospect 10:213–241 Leucci G (1999) Prospezioni elettromagnetica e di sismica a riflessione: studio dell’influenza dei parametri strumentali sul rapporto segnale/rumore. Tesi di laurea in Fisica, Università degli Studi di Lecce Leucci G (2008) Ground penetrating radar: the electromagnetic signal attenuation and maximum penetration depth. Sch Res Exch 2008(926091). https://doi.org/10.3814/2008/926091 Leucci G (2015) Geofisica Applicata all’Archeologia e ai Beni Monumentali. Dario Flaccovio Editore, Palermo, p 368. ISBN 9788857905068 Leucci G, Margiotta S, Negri S (2004) Geological and geophysical investigations in karstic environment (Salice Salentino, Lecce, Italy). J Environ Eng Geophys (JEEG) 9:25–34 Leucci G, De Giorgi L, Scardozzi G (2014) Geophysical prospecting and remote sensing for the study of the San Rossore area in Pisa (Tuscany, Italy). J Archaeol Sci 52:256–276. https://doi. org/10.1016/j.jas.2014.08.028 Loke MH (2001) Electrical imaging surveys for environmental and engineering studies. A practical guide to 2-D and 3-D surveys. RES2DINV Manual, IRIS Instru-ments, www.iris-instruments. com Madden TR, Cantwell T (1967) Induced polarization: a review, Mining Geophysics, II. Society of Exploration Geophysicists, Tulsa, pp 373–400 Matera L, Noviello M, Ciminale M, Persico R (2015) Integration of multisensor data: an experiment in the archaeological park of Egnazia (Apulia, Southern Italy). Near Surf Geophys 13(6):613–621 Matera L, Persico R, Geraldi E, Sileo M, Piro S (2016) GPR and IR tests in a multilevel historical building. Geosci Instrum Data Syst 5:541–550 Neubauer W, Eder-Hinterleitner A, Seren S, Melichar P (2002) Georadar in the Roman civil town Carnuntum, Austria: an approach for archaeological interpretation of GPR data. Arch Prospection 9(3):135–156 Noon DA (1996) Stepped-frequency radar design and signal processing enhances ground penetrating radar performance. Ph.D. thesis, Department of Electrical & Computer Engineering, University of Queensland, Australia

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Nuzzo L, Leucci G, Negri S, Carrozzo MT, Quarta T (2002) Application of 3d visualization techniques in the analysis of GPR data for archaeology. Ann Geophys 45(2):321–337 Ogilvy AA (1972) Hydrogeologic and engineering geologic possibilities for employing the method of induced potentials. Geophysics 37(5):839–850 Olhoeft GR, Capron DE (1993) Laboratory measurements of the radio-frequency electrical and magnetic properties of soils from near Yuma, Arizona. Open-File Report 93–701. USGS, Washington, DC Parasnis DS (1997) Principles of applied geophysics. Springer, Netherlands, p 429 Persico R (2014) Ground penetrating radar inverse scattering and data processing. Wiley, p 368 Persico R, Leucci G (2016) Interference Mitigation achieved with a reconfigurable stepped frequency GPR System. Remote Sens 8:926; https://doi.org/10.3390/rs8110926 Persico R, Prisco G (2008) A reconfigurative approach for SF-GPR prospecting. IEEE Trans Antennas Propag 56(8):2673–2680 Persico R, Ciminale M, Matera L (2014) A new reconfigurable stepped frequency GPR system, possibilities and issues; applications to two different Cultural Heritage Resources. Near Surf Geophys 12(6):793–801. https://doi.org/10.3997/1873-0604.2014035 Persico R, Dei D, Parrini F, Matera L (2016) Mitigation of narrow band interferences by means of a reconfigurable stepped frequency GPR system. Radio Sci 51. https://doi.org/10.1002/ 2016rs005986 Reppert PM, Morgan FD, Toksoz MN (2000) Dielectric constant determination using groundpenetrating radar reflection coefficients. J Appl Geophys 43(2–4):189–197 Reynolds JM (2011) An Introduction to applied and environmental geophysics. Wiley, Chichester Roy K, Elliott M (1980) Resistivity and IP survey for delineating saline water and freshwater zones. Geoexploration 18:145–162 Sasaki Y (1992) Resolution of resistivity tomography inferred from numerical simulation. Geophys Prospect 40:453–464 Schleifer N, Weller A, Schneider S, Junge A (2002) Investigation of a Bronze Age plankway by spectral induced polarization. Archaeol Prospect 9:243–253 Schmidt A (2013) Earth resistance for archaeologists (Series Editors: Conyers LB, Kvamme KL). AltaMira Press, 195 pp. ISBN 978-0-7591-1204-9 Sen PN, Scala C, Cohen MH (1981) A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. Geophysics 46(5):781–795 Sensors & Software (1999) Ground penetrating radar survey design. Sensors & Software, Mississauga Singha K, Moysey S (2006) Accounting for spatially variable resolution in electrical resistivity tomography through field scale rock physics relations. Geophysics 71(4):A25–A28, https://doi. org/10.1190/1.2209753 Slater L, Binley AM, Daily W, Johnson R (2000) Cross-hole electrical imaging of a controlled saline tracer injection. J Appl Geophys 44:85–102 Tejero-Andrade A, Cifuentes G, Chavez RE, Lopez Gonzalez A, Delgado-Solorzano C (2015) “L” and “Corner” arrays for 3D electrical resistivity tomography: an alternative for urban zones. Near Surf Geophys 13:1–13. https://doi.org/10.3997/1873-0604.2015015 Topp GC, Davis JL, Annan AP (1980) Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour Res 16(3):574–582 Tripp AC, Hohmann GW, Swift CM (1984) Two dimensional resistivity inversion. Geophysics 49:708–717 Weller A, Brune S, Hennig T, Kansy A (2000) Spectral induced polarization at a medieval smelting site. In: 6th Meeting of the Environmental and Engineering Geophysical Society (European Section, Bochum) Yilmaz O (1987) Seismic data processing. In: Neitzel EB (ed) Seismic data processing. Society of Exploration Geophysicists, Tulsa Zanzi L, Valle S (1999) Elaborazione di dati GPR 3D per la ricerca di mine antiuomo. In: Atti del 18° Convegno Nazionale del Gruppo Nazionale di Geofisica della Terra Solida, Novembre 1999, Roma, CD-ROM, File 04.12

Chapter 5

NDT Geophysical Data Interpretation

Abstract Structural interpretation of NDT geophysical data sets typically constitutes part of an exploration program. Experts in this field apply their extensive knowledge of the methodologies and associated physical parameters that could be related to the presence of buried structures and/or defects in the construction materials of monumental heritage. Products can include an interpretation of data related also to integration with other data (i.e., archaeological data, structural data; data from one or more NDT techniques).

5.1 GPR Data Interpretation In the past, GPR data interpretation was performed by printing the raw data on paper and analyzing and visualizing the alignment of the reflection events. It is clear that this method of interpretation was at best “crude and inaccurate” (Conyers 2013). Another way to interpret GPR data is the so-called “on-the-fly” method that provides a direct interpretation in the field of the raw data during the data acquisition. These interpretations can lead to incorrect conclusions. It is important to underline that: the GPR raw data should be processed to remove noise; the vertical scale must be corrected to transform two-way time into depth measurements; it should be recognized (if possible) that reflection events (anomalies) may or not of have any meaning regarding the questions being asked. Unfortunately, there are many who have not much expertise approaching data interpretation for the first time and who concentrate on finding and mapping “anomalies” without understanding its meaning. In fact, GPR profiles contain a series of “anomalies” that could be have a precise meaning, but could be related to a change in wave velocity along buried interfaces. Any change in the electromagnetic properties within the surveyed material will produce reflections that are not necessarily anomalies. Therefore, one must be able to understand which of these reflected events can be linked to structures of interest for the preordained purposes of the GPR survey.

© Springer Nature Switzerland AG 2019 G. Leucci, Nondestructive Testing for Archaeology and Cultural Heritage, https://doi.org/10.1007/978-3-030-01899-3_5

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Fig. 5.1 Examples of several different types of ray-paths (R: reflected; T transmitted) from the GPRSim software

The first step in GPR data interpretation could be the creation of “synthetic models” of 2D-GPR profiles. Modeling can provide the interpreter with an idea of how real-world GPR reflection data should done and therefore produce more accurate interpretation of GPR reflection profiles once they have been processed. There are several software programs that produce accurate data-reflection modelling. Among them are: GPRSim (http://www.gpr-survey.com/gprsim.html), GPRmax (http://www.gprmax.com/), and Reflexw (http://www.sandmeier-geo.de/ reflexw.html). In the model construction, it is critical to define: (i) the electrical properties of the materials and boundaries that are to be included in the simulation; and (ii) the shape and dimension of the bodies that simulate a target and their depth. Clearly, a real case can have infinitely variable dielectrics and conductivities located at all locations in the surveyed material (heterogeneity), but the model should contain an idea of the expected reflection events. In the modelling, several paths of propagating electromagnetic energy can be considered (Fig. 5.1). Reflected waves are defined as R, transmit, reflect, and then transmit waves denoted as TRT, while RRR waves undergo multiple reflections. They are reflected at depth, then rise to the surface and reflect off the air–ground interface, then goes back into the ground and reflect again before being recorded. The RR wave in a plane-layer model will never return to the recording antenna and can be ignored. For example, there are several ray-paths involved in the acquisition of GPR data in a church where the presence of a dome can create errors in the interpretation. In fact, examples the GPR data acquired in the Crypt of the Basilica of Saint Nicolas in Bari (Calia et al. 2012) show several reflection events with a typical hyperbola shape (Fig. 5.2). In this case, the anomalies labeled 1, 2 and 3 in Fig. 5.2 could suggest the presence of structures in the subsoil below the crypt. To understand the origin of these reflection events and therefore to better interpret the results, a model that considers GPR-data acquisition below a dome was generated using GPRSim software (Fig. 5.3). This program enables the user to generate a synthetic model of what might be expected using the known properties of the ground and the geometry of underground features (Conyers 2013). A semicircular dome with a 2.5 m high dome and a 3.0 m diameter can generate a reflection which is concave downward. This radar pattern is completely opposite

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Fig. 5.2 GPR data acquired in the Crypt of Saint Nicolas: a photo; b processed 2D-GPR section; c scheme of the crypt

Fig. 5.3 Synthetic model for GPR data acquisition below a dome

of what one might expect. In fact, one expect a reflection with a concave-upward configuration due to an increase of the wave path and therefore of the two-way travel time. This is due to the focusing of returned energy which is dependent on the shape of the dome surface. In fact, considering the 2D radar section of Fig. 5.2b, it is possible to note that the apex of the reflection events involve a 30 ns two-way travel time. This means that, considering that the electromagnetic-wave velocity in the empty space is 0.3 m/ns, the reflection events are generated at a depth of about 4.5 m, which is the height of the apex of the dome. Another important case is related to the presence of voids and/or cavities: that of a 2D-GPR profile acquired to cross the hypothetical cavity related to a Roman

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Fig. 5.4 Synthetic model: two homogeneous layers with a dielectric constant of 16 and 9 were modeled for the calcarenite and hard bedrock, respectively. In the bedrock, a void space with dielectric constant of 1 represents the aqueduct. Soil-filled karst features, with a dielectric constant of 20, were placed at the contact between the two hypothesized layers (Leucci et al. 2016)

aqueduct. In this case, very confused reflection events were obtained (Leucci et al. 2016). To understand the nature of these reflection events, a 2D synthetic model was produced using GPRSim (Goodman 2013). A model of stratified subsoil with the presence of a void related to the aqueducts and a soil-filled karst feature was assumed (Fig. 5.4). Two homogeneous layers with dielectric constants of 16 and 9 were modeled for the calcarenite and hard bedrock, respectively. In the bedrock, a void space, with dielectric constant of 1, represents the aqueduct ceiling. A soil-filled karst feature, with a dielectric constant of 20, was placed at the contact between the two modeled layers. The synthetic reflections demonstrated that the aqueduct-ceiling arch would generate reflection when energy intersected the void space, as was expected. The floor of this feature also generated an upward-bowing reflection from the velocity “pull up” in the void space. Other reflection events were generated at the contact between soils 4 and 7 with lower amplitude reflections produced from the soil-filled karst features. When this model was compared to the reflection profile (Fig. 5.5), all the modeled reflections were visible. Figure 5.5 (600 MHz central-frequency antenna) shows the contact between calcarenites and bedrock, labelled “B”. This reflection event is visible at variable depths between 0.4 and 0.8 m. Numerous reflections between the abscissa 0–12 m and 0.8–2.4 m in depth, labelled “V”, are probably soil-filled karst

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Fig. 5.5 Real 2D-GPR data (600 MHz), in which are highlighted some reflection events that were interpreted as a vertical shaft filled with materials (A1), the ceiling and floor of Triglio aqueduct, the contact between the calcarenite and the bedrock (B), and some soil-filled karst features within the bedrock (V)

features, such as the reflections at the abscissa 18–32 and 0.8–2.8 m in depth. As visible in Fig. 5.5, the reflections visible at the abscissa 16–18 m and depth of about 2.4 m indicate the aqueduct ceiling. The higher frequency energy (600 MHz) was attenuated before it could be transmitted to the floor of the aqueduct, and that feature remains invisible in those data images. It is important to underline that, when radar energy is reflected from a buried interface where the wave velocity decreases, the polarity of the reflected wave will be the same as the direct-wave generated from the transmitting antenna. This is the normal case in most ground conditions, and therefore, most reflections are recorded as normally polarized sine waves (Conyers 2015a, b). However, if a drastic increase in velocity occurs at a boundary, such as a void space where propagating radar waves increase again to the speed of light, a reflection will be generated that is visible in traces as a reversed-polarity sine wave (Conyers 2015a, b). Discontinuities along banded reflections may indicate the presence of joints or fractures. A mottled reflection pattern may indicate fractured bedrock or soil or that gravel fill materials are present that scatter EM energy. In instances where cavities/voids/caves were interpreted as being present, due to the resonance of the EM energy within the void and likely irregular and unknown shape of the bottom of these features, the horizontal extent and depth to the upper interface of bedrock and void were most discernable. Usually, as radar energy moves deeper into the ground, moisture retention increases and EM-wave velocity will decrease. When radar energy is reflected from a buried interface where the EM-wave velocity decreases, the polarity of the reflected wave will be the same as the direct-wave generated from the transmitting antenna (Conyers 2015a, b). This is the normal case in most ground conditions, and therefore, most

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reflections are recorded as normally polarized sine waves. If a drastic increase in velocity occurs at a boundary, it would occur when waves enter a void space and move at the speed of light, and a reflection will be generated that is visible in traces as a reversed-polarity sine wave (Conyers 2015a, b). Figures 5.6a, b show the trace reflections and illustrate the difference between reflections generated from the soil-filled karst feature (Fig. 5.6a) and the ceiling of a cavity (Fig. 5.6b). The change of polarity to a reversed-polarity reflection at this feature is confirmation that this feature is the bedrock-air interface at the aqueduct ceiling. The reflection from the nearby soil-filled karst features exhibits normal polarity (Leucci et al. 2016). A confirmation of polarity changes is visible in the processed GPR section acquired of a series of cavities (Fig. 5.7). An important case is related to study of the conservation state of monumental heritage. In this case, it is important to identify the presence of fractures and/or the volumetric water content. To facilitate the interpretation of GPR data acquired on monumental heritage, the following points were developed: if fractures are sufficiently open and filled with air or water, the high amount of radar energy will be backscattered (Grandjean et al. 1996). Because the fractures will be identified by the properties of their content in terms of nature, air, water, and size, the processing step related to identify the fracture could be: (i) gain function removal; amplitude compensation; in this case, the function g(t) is applied on the radar section. The function g(t) consists of a linear and an exponential part (Sandmeier 2013; Leucci 2003): g(t)  (1 + a · t) · eb·t a a pulse width v bα· 8.69

(5.1) (5.2) (5.3)

with (i) The pulse width is automatically taken from the nominal frequency. The two parameters a (linear gain, not dimensional) and α (exponential in dB/m) are the geometrical spreading and attenuation energy compensation; (ii) Background removal filter; the average trace was subtracted to remove the back ground; (iii) Kirchhoff migration; considering the amount of diffracted signal that could be contained in the data, shown as hyperbolas on the raw data, the migration makes possible concentration of the diffracted energy into bright spots; (iv) Envelopes; due to the amount of diffracted arrivals compared to reflected ones, amplitude envelopes were plotted versus time. Figure 5.8 shows an example of processed data acquired on a fractured medium (Leucci 2003). The fractures are characterized by the presence of small disconti-

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Fig. 5.6 Comparison of reflection traces from waves reflected from soil-filled karst feature (a) and cavity ceiling (b). The usual case for most buried materials produces reflections that are normal polarity (a). In burials that retain void spaces, the reflections are reversed in polarity (b)

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Fig. 5.7 GPR processed section acquired above a series of cavities

Fig. 5.8 GPR processed data acquired on a fractured medium: a raw data; b ungain data; c amplitude compensation; d migrated; e envelop

nuities, representing karstic voids or recrystallized zones, where electromagnetic energy is diffracted. If the fractures are composed of an alignment of these discontinuities, the geometry of the fractures in the space can be restored by picking the succession of bright spots. Figure 5.8e shows the picked lines and the bright spots (dark lines and dark areas respectively). To estimate the volumetric water content eventually related to the conservation degree of the investigated medium, one must take into consideration the relative dielectric. In a porous material, it is highly sensitive to its volumetric water content w because the relative dielectric constant of water (εr,w  80) is several orders of magnitude greater than the dielectric constant of most minerals forming a rock matrix (εr  3 ÷ 5) and of air (εr,a  1). Thus, the knowledge of the variations of the relative

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139

dielectric constant enable the determination of the water-content distribution in the soil. Several models can be found in the literature (e.g., Sen et al. 1981; Shen et al. 1985) that propose a relationship between the dielectric constant and the water content. One of these relationships is known as the Complex Refractive Index Method (CRIM) (Freedman and Vogiatzis 1979). The major problem with the CRIM formula is that it does not take into account the geometrical information on the internal structure of the materials and on microscopic fluid distribution. This has a significant effect on dielectric properties of partially saturated materials (Endrea and Knight 1992). The above restriction may be overcome by using the Hanai–Bruggeman formula. It makes possible determination of: (i) the effective relative dielectric constant of a water-air mixture (εr,w/a ); (ii) the effective relative dielectric constant of the total rock by mixing the mineral grains into the water-air mixture. The main problem with the two previous approaches is that it is not possible to derive both the porosity and the water content from the dielectric constant. Therefore, it is not possible to obtain information about the water content without strong a priori assumptions. For this reason, it is preferable to use the well-known empirical equation derived in Topp et al. (1980) regarding the study of the dielectric response εr of various soil samples (presenting various degrees of saturation), as a function of their net water content w. This formula is given by: w  −5.3 10−2 + 2.92 10−2 εr −5.5 10−4 ε2r + 4.3 10−6 ε3r

(5.4)

since it is important to estimate the relative dielectric constant. As seen in Chap. 3, the relative dielectric constant is related to the electromagnetic-wave velocity. It can be more quickly and easily determined from the reflection profiles acquired in continuous mode, using the characteristic hyperbolic shape of reflection from a point source. Figure 5.9 shows an example of velocity analysis performed with a computer algorithm developed in Reflexw software (Sandmeier 2013). The application of this method points out both vertical (in time) and lateral velocity variations from about 0.05 to 0.09 m/ns. Using the relationship (Eq. 5.4), it is possible to obtain the volumetric water-content variation model (Fig. 5.10). Another important target in GPR-data interpretation are to identify the walls. To achieve this, a synthetic model was created using GPRSim (Fig. 5.11). Model shows two homogeneous layers with dielectric constants of 20 and 9 respectively. A dielectric constant of 20 was associated to the soil and the dielectric constant of 9 was associated to the hard bedrock. In the bedrock, two walls with a dielectric constant of 6 were inserted. Reflection events in the modelled radar section clearly revealed the walls and the bedrock. The modelled result enabled interpretation of the reflection events found in the raw and processed real data as wall (w) (Fig. 5.12) . At this point, it is important underline that 2D data analysis of GPR data has an important role in the interpretation phase.

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Fig. 5.9 a Estimated EM-wave velocity propagation using the hyperbola diffraction method. Nearby to every hyperbole the EM wave velocity value in m/ns unit is visible; b the resulting electromagnetic-wave velocity distribution

Fig. 5.10 Volumetric water-content distribution estimated using the Topp formula

5.2 ERT Data Interpretation Due to the variability in resistivities of materials, interpretation of electricalresistivity tomography data must be handled with caution. As seen in Chap. 3, there are overlaps of the resistivity values of earth materials that, in most cases, are given as ranges of values rather than absolute values. Other factors that affect resistivity changes are temperature, porosity, conductivity, salinity, clay content, saturation, and lithology.

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Fig. 5.11 Synthetic model: Two homogeneous layers with a dielectric constant of 20 and 9 were modeled for the soil and hard bedrock respectively. In the bedrock, two walls with dielectric constant of 6 were inserted

Also, since, in the case of ERT data interpretation, the first step is related to the creation of “synthetic models” of 2D and 3D ERT profiles. Modeling can provide the interpreter with an idea of what to expect from resistivity data related to structures of archaeological interest and/or to the conservation state of monumental heritage, and therefore it enables more accurate interpretation after data has been processed. There are several software programs that enable accurate ERT data modelling. Among them are: RES2Dmod, Res3Dmod (http://www.geotomosoft.com), and ErtLab (http://www.geostudiastier.it). In the model construction, it is important to define: (i) the geoelectrical properties of the materials and boundaries that are to be included in the simulation, and (ii) the shape and dimension of the bodies that simulate a target, their depth, and the associated resistivity values. Furthermore, to obtain a more accurate model the resistivity values, one should assume they may vary in one horizontal direction (usually referred to as the x direction) but are assumed to be constant in the other horizontal (the y) direction. A more realistic model would be a fully 3-D model where the resistivity values are allowed to change in all three directions (Loke 2001). For example, synthetic ERT data were created to take into account the complexity of the subsoil in an archaeological site. These help in interpretation of field data. The synthetic data were created by assuming a 2D resistivity model (Fig. 5.13a) that includes a 800 m surface layer (1.50 m thickness) labelled A and an underlying

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Fig. 5.12 GPR data acquired in the archaeological site of Cavallino in Lecce (south Italy) by Leucci and Negri (2006): a raw; b processed

30 m layer (1.25 m thickness) labelled B. Layer A appears again below layer B. These layers geologically could correspond to a calcarenite bedrock (A) overlying a conductive ground (B) and again the calcarenite bedrock (A). At the 11.5 m abscissa, a rectangular block labelled W with a resistivity of 400 m is modelled. The block is located inside a rectangular conductivity material (30 m). W represents the wall of pebbles, generally used in the Messapian period (Leucci and Negri 2006). To simulate a field survey, an array with 24 electrodes with 1 m spaces was modelled, and a dipole–dipole array was used. Synthetic data were generated with Res2Dmod software (Loke 2001). Model cells with widths of half the unit spacing option was used to provide better resolution of the calculated resistivity distribution. Figure 5.13b shows the resistivity images determined from the resistivity model in Fig. 5.13a. Results indicate that the wall should be very clearly resolved. In Fig. 5.14a, the 2D resistivity model was created in order to simulate the cut inside the calcarenite bedrock without the wall of pebbles. Also in this case, the results show the expected differences in resistivity values (Fig. 5.14b). Subsequently, the 2D ERT field data were compared with the synthetic data. In fact, the 2D-ERT profile indicates the wall of pebbles (Fig. 5.15a) which the archaeologists found after the excavation (Fig. 5.15b and Fig. 5.16). When compared, Fig. 5.13b demonstrates that the anomaly W could be interpreted as a wall. The study of resistivity changes in the presence of fractures is an important tool in analysis of the conservation degree of monumental heritage. This was achieved through the use of simple synthetic models.

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Fig. 5.13 Resistivity model employed for the analysis of field data: a with wall; b result of the inversion with the wall

A model that assumes a homogeneous medium was used. It posited two layers with homogeneous resistivity equal to 100 m and 1000 m (Fig. 5.17a). The resistivity values chosen are typical of monumental construction material used on the Salento peninsula (Leucci 2003). The inversion carried out on the data relative to the starting model (Fig. 5.17a), assuming a dipole–dipole electrode array with an electrode distance of 10 cm, perfectly indicates the two layers (Fig. 5.17b). The homogeneous two-layer model was modified with the addition of four fractures of variable geometry. Different filling materials were associated. In Fig. 5.18a, the new model is shown with, starting from left to right: • a fracture filled with wet watered material (resistivity of about 10 m); • a fracture filled with dry material with pores filled with air and water (resistivity of about 300 m); • a fracture filled with dry material with pores filled with air (resistivity of about 1000 m); • a fracture filled with all three types of listed materials. See Fig. 5.18b for the results of the inversion. Here, the two layers of the model are clearly highlighted, and the resistivity values vary at the fractures, assuming high or low values, depending on the material that fills the fractures. Given the interelectrode distance of 10 cm, the fracture size was not highlighted.

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Fig. 5.14 Resistivity model employed for the analysis of field data: a without wall; b result of the inversion without the wall

Fig. 5.15 a Resistivity distribution in the subsoil; b scheme of the excavation results

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Fig. 5.16 Photo of the excavation results

Fig. 5.17 a Medium model consisting of two homogeneous main layers; b result of the inversion of the synthetic model

In Fig. 5.19, the result of the inversion obtained with an electrode separation of 5 cm is shown. In this case, the smaller distance between the electrodes enabled a better delineation of the geometry of the fractures.

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Fig. 5.18 a Medium model consisting of a series of fractures; b result of the inversion of the synthetic model

Fig. 5.19 Result of the inversion of the synthetic model used an electrode separation of 5 cm

5.3 IP Data Interpretation The instrumentation for electrical imaging surveys was developed to measure the Induced Polarization (IP) in a multi-electrode mode. Therefore, the same considerations for the interpretation of ERT data are applicable for IP data interpretation. First, it is important to know the IP values (in terms of mV/V) for several mineralized rocks and common rocks. This is collected in Table 5.1. As in resistivity, the overlapping IP values of earth materials makes data interpretation very difficult. In this case, modelling is also an important tool to help understand the presence of structures of interest when resistivity does not deliver useful results.

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Table 5.1 The IP values for some rocks and minerals Material IP in mV/V Sandstone and siltstone Volcanic stuff Mineralized rock with 8–20% sulfide content Mineralized rock with 2–8% sulfide content Greenstone, trap, dense volcanic rocks

10–50 30–80 100–200 50–100 10–50

Shale Granite and granodiorite

5–10 1–5

Limestone and dolomite

1–5

Fig. 5.20 IP model employed for the analysis of field data: a with wall; b result of the inversion with the wall

The synthetic data were created by assuming a 2D IP model (Fig. 5.20a) that includes a 5 mV/V associated to the soil material and IP values of 10 mV/V associate to the rectangular block (simulate a wall). To simulate the field survey, an array whit 24 electrodes 1 m apart in a dipole–dipole configuration was supposed. Results indicate that the rectangular box was well resolved (Fig. 5.20b). When compared with Fig. 5.20b, field data demonstrate that the anomaly could be interpreted as a wall (Fig. 5.21).

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Fig. 5.21 IP field data

Fig. 5.22 Photo of: a a visible part of a buried column; b ERT test line perpendicular to column position

Generally, IP and ERT data are acquired at the same time to effect a better interpretation of the results. This is so in the following case. At the archaeological site of Tindari (Sicily, south Italy) a test survey was carried out on a line lying above an area where some objects, such as partially buried columns, were visible (Fig. 5.22) (De Domenico et al. 2006). The dipole–dipole array was employed to acquire resistivity and IP imaging of buried objects. A 48-channel, Syscal R1 Resistivity Meter from IRIS Instruments was employed in a multi-electrode configuration using 48 electrodes with 1 m spacing. To improve the data quality, especially at great depth, a “high-resolution” survey technique with overlapping data levels was chosen. As seen in Chap. 3, this technique allows the number of data points to be increased. Also, IP measurements were performed, which is a valuable geophysical tool in subsoil investigations as it provides unique information on structural properties (primarily of clay content). The results of IP and resistivity tomography obtained with the dipole–dipole configuration are shown in Fig. 5.23a and b. The coincidence of the location of high resistivity (ρ > 90 m) and high IP anomalies (C > 2 mV/V) suggests that these anomalous zones, in the first meter of depth, could correspond to remains of an archaeological nature. In fact, the anomaly at about 6 m (in the x direction) corresponds to the partially buried columns visible

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Fig. 5.23 Test survey: a dipole-dipole resistivity model; b dipole–dipole IP model. Arrow indicates position of partially buried column

from the northeastern side of the investigated area. It is important to underline that IP results clearly indicate the column; this could be due to the fact that the buried materials, over the centuries, have become insensitive to variations of resistivity.

5.4 SP Data Interpretation Although the costs of SP instrumentation are low, as seen in Chap. 4, the acquisition data are very time demanding. The interpretation of SP data is no less time consuming and is very difficult compared to the high variability of natural-current flow in the subsoil and in the other medium related to monumental heritage. Based on the experience of SP utilizer and on simple modelling related to buried structures with precise geometrical shape, some consideration can be made concerning the SP data interpretation. For example, take projects related to the bioelectric activity of plants, trees, etc. In this case, the SP has several hundred millivolts and the anomalies are observed with a sharp negative form (Telford et al. 1976). In fact, SP measurements performed at a site with the presence of several trees (Fig. 5.24) show negative self-potential corresponding to trees (Fig. 5.25).

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Fig. 5.24 The SP-surveyed area

Fig. 5.25 The SP map with yellow circles related to the position of the trees

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151

Fig. 5.26 The SP map, dark dashed line, is related to the position of the old water pipe

Clearly, in areas with the presence of plants, trees, etc., SP anomalies that could be related to structures of interest may be lost (Drahor et al. 1996). Also in areas with buried corroded pipelines and metals, the SP records large amplitudes with positive or negative anomalies (Corwin 1990). In fact, Fig. 5.26 is a self-potential map related to the data acquired near an old water pipe. So, it is advisable not to use the SP method in archaeological areas that contain corroded pipelines or metal, plants and bushes. In fact, in archaeological applications, SP anomalies, generally, show low amplitudes (Drahor and Kaya 2000). Also in the SP data, the interpretation could be related to forward modelling. More and more, we see examples in which the total and gradient anomaly curves were calculated for different geometrical bodies, such as point currents, horizontal lines, and spherical, cylindrical and vertical dipole sheets, by means of modelling (Heiland 1940; Rao et al. 1970; Telford et al. 1976; Fitterman 1979; Bhattacharya and Roy 1981; Murty and Haricharan 1985). For example, Fig. 5.27 graphs a SP curve related to both a negative point source and a dipping positive source. Since the archaeological structures are generally found in vertical and horizontal forms in the soil, the sources of such anomalies may be interpreted by assuming an inclined sheet model (Drahor 2004). In the study performed by Drahor (2004), the inclined sheet model was calculated for shallow bodies at various depths. The obtained values demonstrate that the amplitude of the model curves suddenly decreases as the depth of the model increases. The polarization angle is another important parameter by which an SP anomaly is directly affected. It controls the shape of the anomaly. An interpretation of actual SP field-measurements results in an archaeological application is presented next. Measurements are related to the famous archaeo-

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Fig. 5.27 2D model with a synthetic source

logical site of Roman ships in Pisa (northern Italy). Here, SP measurements were needed due to the geological condition of the site. In fact, the presence of shallow groundwater (about 6 m deeper) and conductive sediments makes the application of the GPR methodology useless (Leucci et al. 2014). Furthermore, additional structures, such as the pier and the ships, over the centuries, become insensitive to changes in resistivity values (i.e., they have assumed resistivity values similar to the host medium) (Carrozzo et al. 2003; Leucci et al. 2014). The SP data were acquired at the surface in a set of 864 measured points located along nine parallel lines; the surveyed area (about 35 × 45 m) is located immediately to the west of the excavation area (Fig. 5.28). Each electrode was placed inside a 10 cm hole and filled with a moistened bentonite and gypsum mixture to ensure good contact between the electrode and the ground, and stones were placed above the electrodes (Fig. 5.29). Measurements of the self-potential signals were carried out with a Keithley 2701 multi-channel voltmeter and used non-polarizing Pb/PbCl2 (Petiau) electrodes (Perrier et al. 1997). All the electrodes were scanned during a period of 30 s. SP data were filtered with a low-pass filter in the frequency domain to avoid edge effects of space-domain filters, so that high frequencies were eliminated and low frequencies were preserved (Aubanel and Oldham 1985). A least-squares analysis method to estimate not only the depth and shape but also to determine the horizontal position of a buried structure from the SP anomaly profile was used (Abdelrahman et al. 2006). The method is based on normalizing the residual SP anomaly using three characteristic points and their corresponding distances on the anomaly profile and then determining the depth for each horizontal position of the buried structure using the least-squares method. The computed depths are plotted against the assumed horizontal positions on a graph. The solution for the depth and the horizontal position of the buried structure is read at the common intersection of the curves. With knowledge of the depth and the horizontal position and applying the least-squares method, the shape factor is determined using a simple linear equation. Procedures are also formulated to estimate the polarization angle and the electric-dipole moment. The method is semi-automatic, and it can be applied to short or long residual SP anomaly profiles. These processed data are used to build the SP map shown in Fig. 5.30. Using

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Fig. 5.28 SP-surveyed area

Fig. 5.29 SP electrode

the aforementioned method, the SP anomalies were posed at depths between about 5 and 6 m. Self-potential values vary between −100 and 300 mV. According to Drahor (2004), the high positive SP anomalies were interpreted as due to structures such

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Fig. 5.30 SP map

as buried stones (dark dashed lines). In fact, buried stone foundations with relatively non-porous bodies should interrupt the vertical flow of water and give rise to a positive SP voltage above it (Drahor 2004). The high negative SP anomalies were interpreted as due to buried ships (yellow dashed lines). In fact, the wood structures could be related to loose material with many cracks and a relatively larger downward movement of water, which gives rise to an SP negative on the ground above it. The moderately positive SP values were interpreted as due to a possible palaeo-river bed. Another important application of the SP method is related to monumental heritage. The application to industrial archeology is particularly interesting. Here, ancient industries built in reinforced concrete are taken into consideration. SP methods can evidence the corrosion of reinforcement steel. Under normal conditions, reinforcement steel is protected from corrosion by a thin, passive film of hydrated iron oxide. This passive film decomposes due to the reaction of the concrete with atmospheric carbon dioxide (CO2 ), or by the penetration of substances aggressive to steel, in particular, chlorides from de-icing salt or salt water. At the anode, ferrous ions (Fe++ ) are dissolved, and electrons are set free. These electrons drift through the steel to the cathode, where they form hydroxide (OH− ) with the generally available water

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155

Fig. 5.31 Principle of steel corrosion in concrete

Fig. 5.32 Typical SP curve for moist carbonated concrete

and oxygen. This principle creates a potential difference that can be measured by the half-cell method (Fig. 5.31). The basic idea of the SP measurement is to measure the potentials at the concrete surface to obtain a characteristic picture of the state of corrosion of the steel surface within the concrete. For this purpose, a reference electrode is connected via a highimpedance voltmeter to the steel reinforcement and is moved in a grid over the concrete surface (Fig. 5.32). The reference electrode is a Cu/CuSO4 half-cell. It consists of a copper rod immersed in a saturated copper-sulphate solution, which maintains a constant, known potential. Typical orders of magnitude for the half-cell potential of steel in concrete measured against a Cu/CuSO4 reference electrode are in the following ranges (Leucci and De Giorgi 2017) – – – –

water saturated concrete without O2 : −1000 to −900 mV moist, chloride contaminated concrete: −600 to −400 mV moist, chloride free concrete: −200 to +100 mV moist, carbonated concrete: −400 to +100 mV

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Fig. 5.33 A view of the mill Fig. 5.34 The location of ERT and SP profiles

– dry, carbonated concrete: 0 to +200 mV – dry, non-carbonated concrete: 0 to +200 mV. To confirm this, SP measurements were performed in an abandoned mill, which remained as a monument of industrial archeology. In this case, it was necessary to use methods that allow a high spatial resolution and the ability to highlight the state of conservation of the irons. ERT, together with SP methods, could guarantee a good compromise between resolution and the ability to identify the presence of a high degree of humidity and consequently underline the state of conservation of the investigated structure (Fig. 5.33). Therefore, 24 electrodes with variable interelectrode distance were used in a non-conventional array (Fig. 5.34). The distributions of the parameters’ electrical resistivity and spontaneous potentials were estimated.

5.4 SP Data Interpretation

157

Fig. 5.35 Depth slices: a resistivity distribution at 2 cm depth; b self-potential distribution at 2 cm depth; c self- potential distribution at 8 cm depth

Resistivity and spontaneous potential maps were constructed using ERTLab software and a special algorithm implemented in the Matlab environment (Fig. 5.35). From the resistivity distribution model (Fig. 5.35a), the presence of an heterogeneous structure with resistivity values between 10 and 5000 m is evident. Note the presence an area (blue color) with low resistivity values between 10 and 50 m, where there may be high water content. In the SP distribution maps (Fig. 5.35b and c), there are three points (blue) in which there is a concentration of very high negative potentials (−1000 mV) which indicates the presence of water-saturated concrete. Around these areas (green color), the values of SP increase, reaching values between −600 and −400 mV. These values indicate the presence of CO2 . In the red areas, the values of spontaneous potential increase to a positive range (400–500 mV) indicating the presence of dry concrete. Active corrosion can be expected at points where a negative potential is surrounded by increasingly positive potentials, i.e., points with a positive potential gradient. A potential gradient of about +100 mV, within a measured area of 1 m2 , together with negative potentials, are a clear indication of active corrosion. So, it is likely that, in the blue areas surrounded by the red areas, there is an active corrosion phenomenon. This phenomenon has been confirmed by direct observation (Fig. 5.36).

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Fig. 5.36 Photo of the degraded area

5.5 Interpretation of Seismic and Ultrasonic Data Interpretation of the results is a fundamental and critical step. In many cases, using only S and US tests cannot resolve all the ambiguities, and some additional information or calibrations (from complementary investigations, from local invasive and other non-invasive measurement, from a priori knowledge of the building, from expertise on construction techniques, etc., is required. Macroscopic inclusions (e.g., beams, voids, chimney flues, and the presence of different materials) can be detected by means of direct test and/or tomography. In general, it is not possible to associate the velocity anomalies to the nature of the targets. The nature of the targets can only be inferred from assumptions or other information or directly checked with a local invasive test, whose positioning can be chosen on the basis of the S and/or US test results. If the resolution of sonic tomography is sufficient, it is possible to detect outer leaves and internal filling, which appear as areas with different sonic velocities (Fig. 5.37). The detection of damaged portions of masonry or of crack patterns is in general possible by examining the retrieved low velocity values. Since the dimension of cracks is far smaller than the sonic wavelength, it is not possible to localize them, but only to record a decrement in terms of velocity. The tests permit also evaluation of the effectiveness of repair interventions (e.g., grout injections, repointing) on the basis of the outcomes of the investigation campaign before and after the strengthening intervention. In this case, a ratio between the local/average sonic velocity value before and after the intervention can be considered a quantitative parameter. Variations in moisture levels can be indicated by an apparent increase in the sonic-pulse velocity. For a quantitative calibration, local measurements of moisture level with other methods are needed. Figure 5.37 shows results obtained by the sonic tomography survey performed by Leucci et al. (2011) on a pillar in the Cathedral of Tricarico (south Italy). The core and endoscopic images were captured inside the hole. The core and the endoscopy analysis evidenced the presence of a void and a crossing crack between the right pilaster and the central nucleus where very low elastic waves velocity values were measured.

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Fig. 5.37 Sonic tomogram with the overlaid core. Upper right: zoom A of the core with an endoscopic image that puts into evidence a void and a crack that are the cause of the low-velocity values of the sonic wave (Leucci et al. 2011)

Important consideration about the seismic data interpretation can be made to compare laboratory and field measurements results. Ultrasonic measurement is one of the nondestructive microgeophysical methods commonly used to provide data related to the elasticity, anisotropy, and mechanical and weathering resistance of the stones, porosity, dry density, and water absorption. This method can be applied both in the laboratory and in situ. The study of P- and S-wave velocities has been used in several area of application, such as rock-mass characterization (Boadu 1997; Leucci and De Giorgi 2006; Bery and Saad 2012). There are several studies related to the application of ultrasonic methods to study the damage to historical buildings and monuments (Zezza 1993; Christaras et al. 1997; Christaras 2003; Cosentino et al. 2009; Leucci et al. 2011, 2012; Calia et al. 2013). Some authors have investigated the relationship between seismic-wave velocity and bulk density (Gardner et al. 1974; Miller and Stewart 1991). Also, the effect of water content on the ultrasonic velocities were studied by several authors (Wyllie et al. 1956, 1958; Thill and Bur 1969; Nur and Simmons 1969; Gregory 1976; Carcione 2001). Kahraman (2007) performed P-wave velocity measurements were performed on 41 different rock types, 11 of which were igneous, 15 of which were sedimentary, and 15 of which were metamorphic; he found a strong linear correlation between the dry- and wet-rock P-wave velocities. Although several researchers have investigated both the effect of saturation and the variation of bulk density on elastic-wave velocity of different rocks, none of them has derived empirical equations for the

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Fig. 5.38 Ultrasonic wave velocity versus volumetric water content: a P-wave; b S-wave

relationships between dry- and wet-rock P and S-wave velocities and between P and S wave velocities and bulk density. Furthermore, these studies will be useful in the interpretation of sonic and ultrasonic data. Since the effects of saturation on the elastic wave velocity and the relationship between bulk density, water content, and ultrasonic wave velocity were studied on some of Apulia’s porous calcarenites, such as Leccese stone, the Ostuni stone, and the calcareous “Tufo delle Murge”. The ultrasonic P- and S-wave velocity measurements were performed on cubic samples

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161

Table 5.2 Model for correlation between volumetric water content and ultrasonic P-wave velocity Rock type

Model type

Equation

R2

Pietra leccese

Polynomial

w  6.9 * 10−11 * Vp3 − 1.8*10−8 *Vp2 + 4.07 * 10−4 * Vp − 0.312

0.7792

Pietra Gentile

Polynomial

w  4 * 10−6 * Vp3 − 0.0487 * Vp2 + 184.19 * Vp − 232208

0.8103

Tufo delle Murge

Polynomial

w  5 * 10−5 * Vp3 − 0.2382 * Vp2 + 413.83 * Vp − 239499

0.9243

Table 5.3 Model for correlation between volumetric water content and ultrasonic S-wave velocity Rock type

Model type

Equation

R2

Pietra leccese

Polynomial

0.9072

Pietra Gentile

Polynomial

Tufo delle Murge

Polynomial

w  −5 * 10 − 6 * Vs3 + 0.0121 * Vs2 − 10.881 *Vs + 3367.2 w  6 * 10 − 5 * Vs3 − 0.3969 * Vs2 + 843.21 * Vs − 596978 w  −3 * 10 − 6 * Vs3 + 0.0074 * Vs 2 − 6.5347 *Vs + 1999.9

0.8204 0.8592

under natural conditions (e.g., without applying external pressure on the samples), using the transmission method. Variations of P- and S-wave velocity were related to density, compressive strength, and percentages of water content. Furthermore, the seismic velocity variations as a function of frequency was studied. The correlation between Vp and normalized saturation degree (w) was evaluated using the method of least-squares regression. Linear, polynomial, exponential, and power-curve fitting approximations were tried, and the best approximation equation with highest correlation coefficient (R2 ) was determined for each regression. There is a strong correlation between the Vp and w (Fig. 5.38a). The relation follows a polynomial function. The equation of the lines is summarized in Table 5.2. S-wave velocity plots as a function of normalized saturation degree for the three types of rock are given in Fig. 5.38b. For the pietra gentile, the Vs values increase rapidly with the increase of normalized saturation degree. The S-wave velocity plots as a function of normalized saturation degree for “tufo delle murge” rock the experimental results shows a behavior different than “pietra gentile”. In fact, the Vs values decrease with the increase of normalized saturation degree. As “tufo delle murge” in the “pietra leccese” rock, the S-wave velocity decreases with an increase of the normalized saturation degree. The equation of the lines is summarized in Table 5.3. Bulk densities were determined by the weight-volume method. Statistical analysis procedures were used to examine the relationships between the P and S-wave velocity and density for the three studied rock types. The results obtained are presented in Fig. 5.39. The relationship between density and velocity can be represented by linear

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5 NDT Geophysical Data Interpretation

Fig. 5.39 Pietra gentile: ultrasonic wave velocity versus bulk density: a P-wave; b S-wave; pietra leccese: ultrasonic wave velocity versus bulk density: c P-wave; d S-wave; tufo delle murge: ultrasonic wave velocity versus bulk density; e P-wave; f S-wave

Table 5.4 Model for correlation between bulk density (kg/m3 ) and ultrasonic P-wave velocity (m/s) Rock type

Model type

Equation

R2

Pietra leccese

Linear

Density  0.1997Vp + 1332.7

0.8153

Pietra Gentile

Linear

Density  0.2657Vp + 1030.9

0.7449

Tufo delle Murge

Linear

Density  0.7884Vp + 363.27

0.8955

Table 5.5 Model for correlation between bulk density (kg/m3 ) and ultrasonic S-wave velocity (m/s) Rock type

Model type

Equation

R2

Pietra leccese

Linear

Density  0.2226Vs + 1324.9

0.8726

Pietra Gentile

Linear

Density  0.3581Vs + 1255.4

0.7513

Tufo delle Murge

Linear

Density  0.7068Vs + 1058.8

0.7521

regression models. The coefficients of determination (R2 ) were found to be significant and ranged from 0.74 to 0.89. In all the studied samples, the relationship between ultrasonic velocity and bulk density indicate that the velocity tended to increase as the density of the samples increased. However, when various rock types are considered, the correlations are different, as can be observed in the experimental results (Tables 5.4 and 5.5). Furthermore, an experiment that considers the velocity variations as a function of frequency was carried out using the same samples (dry and saturated), and the

5.5 Interpretation of Seismic and Ultrasonic Data

163

Fig. 5.40 Ultrasonic-wave velocity versus frequency

Fig. 5.41 In-situ acquisition of ultrasonic-wave velocities on a pietra leccese pillar

instrumental package contains additional electronics, including a digital oscilloscope, an impulse generator, and a bandpass filter. The system was controlled by a PC using Labview codes, and average velocities were used. The results (Fig. 5.40) indicate that the velocity variations are confined at frequencies greater of 1 MHz. The NDT ultrasonic test performed in the laboratory are a useful tool in the interpretation of the in situ measurements. Here, these results have provided information on the quality and consistency of masonry structures of the important historic building

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Fig. 5.42 In-situ measurements: 2D distribution of Vp (a); bulk density (b); and volumetric water content (c)

in Lecce (Fig. 5.41). The P-wave velocity distribution is shown in Fig. 5.40a. Vp values ranging from 1500 to 2200 m/s. They were interpreted as follow: Vp < 1800 m/s indicates damaged masonry; 1800 < Vp < 2500 m/s indicates masonry with average damage. This interpretation was related to the laboratory results obtained for the undamaged “pietra leccese” that show Vp variations between 2800 m/s and 3300 m/s. Using the above relationships, water content and density were estimated (Fig. 5.42b and c). The density distribution (Fig. 5.42b) show values ranging from 1520 to 1554 kg/m3 . While the water content distribution (Fig. 5.42c) show values ranging 20–49%. These values were verified by core results that indicate a density values ranging 1500–1540 kg/m3 and values of volumetric water content ranging from 0 to 41%.

References

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References Abdelrahman EM, Essa KS, Abo-Ezz ER, Soliman KS, El-Araby TM (2006) A least-squares depth-horizontal position curves method to interpret residual SP anomaly profiles. J Geophys Eng 3:252–259 Aubanel EE, Oldham KB (1985) Fourier smoothing without the fast Fourier transform. Byte 10(2):207–218 Bery AA, Saad R (2012) Correlation of seismic P-Wave velocities with engineering parameters (N value and rock quality) for tropical environmental study. Int J Geosci 3:749–757 Bhattacharya BB, Roy N (1981) A note on the use of a nomogram for self-potential anomalies. Geophys Prospect 29:102–107 Boadu FK (1997) Fractured rock mass characterization parameters and seismic properties: analytical studies. J Appl Geophys 36(1997):1–19 Calia A, Leucci G, Masini N, Matera L, Persico R, Sileo M (2012) Integrated prospecting in the crypt of the Basilica of Saint Nicholas in Bari, Italy. J Geophys Eng 9:271–281. https://doi.org/ 10.1088/1742-2132/9/3/271 Calia A, Lettieri M, Leucci G, Matera L, Persico R, Sileo M (2013) The mosaic of the crypt of St. Nicholas in Bari (Italy): integrated GPR 1 and laboratory diagnostic study. J Archaeol Sci 40:4162–4169. https://doi.org/10.1016/j.jas.2013.06.005 Carcione JM (2001) Wave fields in real media. Theory and numerical simulation of wave propagation in anisotropic, anelastic and porous media. Pergamon Press Carrozzo MT, Leucci G, Negri S, Nuzzo L (2003) GPR survey to understand the stratigraphy at the Roman ships archaeological site (Pisa, Italy). Archaeol Prospect 10(1):57–72 Christaras B (2003) P-wave velocity and quality of building materials. In: Yuzer E, Ergin H, Tugrul A (eds) Proceedings of the international symposium industrial minerals and building stones, Istanbul, pp 295–300 Christaras B, Mariolakos I, Foundoulis J, Athanasias S, Dimitriou A (1997) Geotechnical input for the protection of some Macedonian Tombs in Northern Greece. In: Proceedings of the 6th international symposium conservation of monuments in the Mediterranean Basin, Rhodes, pp 125–132 Conyers LB (2013) Ground-penetrating radar for archaeology, 3rd edn. Alta Mira Press, p 258 Conyers LB (2015a) Analysis and interpretation of GPR datasets for integrated archaeological mapping. Near Surf Geophys 13:645–651 Conyers LB (2015b) Ground-penetrating radar data analysis for more complete archaeological interpretations Corwin RF (1990) The self-potential for environmental and engineering applications. In: Ward SH (ed) Geotechnical and environmental geophysics. Investigations in geophysics, vol 5. Society of Exploration Geophysicists, Tulsa, USA, pp 127–145 Cosentino PL, Capizzi P, Fiandaca G, Martorana R, Messina P (2009) Advances in microgeophysics for engineering and cultural heritage. J Earth Sci 20(3):626–639 De Domenico D, Giannino F, Leucci G, Bottari C (2006) Integrated geophysical surveys at the archaeological site of Tindari (Sicily, Italy). J Archaeol Sci 33:961–970 Drahor MG (2004) Application of the self-potential method to archaeological prospection: some case histories. Archaeol Prospect 11:77–105 Drahor MG, Kaya A (2000) A large-scale geophysical prospection in Acemhöyük, the site of the Assyrian Trade Colony Period. Turk Acad Sci J Archaeol 3:85–107 Drahor MG, Akyol AL, Dilaver N (1996) An application of the self-potential (SP) method in archaeogeophysical prospection. Archaeol Prospect 3:141–158 Endrea AL, Knight R (1992) A theoretical treatment of the effect of microscopic fluid distribution on the dielectric properties of partially saturated rocks. Geophys Prospect 40:307–324 Fitterman DV (1979) Calculations of self-potential anomalies near vertical contacts. Geophysics 44:195–205

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Freedman R, Vogiatzis JP (1979) Theory of microwave dielectric constant logging, using the electromagnetic propagation method. Geophysics 44:969–986 Gardner GHF, Gardner LW, Gregory AR (1974) Formation velocity and density: the diagnostic basis for stratigraphic. Geophysics 39:770–780 Goodman D (2013) GPR sim manual. http://www.gprsurvey.com/ Accessed on June 2013 Grandjean G, Gourry JC (1996) GPR data processing for 3D fracture mapping in a marble quarry (Thassos, Greece). J Appl Geophys 36:19–30 Gregory AR (1976) Fluid saturation effects on dynamic elastic properties of sedimentary rocks. Geophysics 41(1976):721–895 Heiland CA (1940) Geophysical exploration. Hafner, New York Kahraman S (2007) The correlations between the saturated and dry P-wave velocity of rocks. Ultrasonics 46:341–348 Leucci G (2003) “I metodi elettromagnetico impulsivo, elettrico e sismico tomo-grafico a rifrazione per la risoluzione di problematiche ambientali: sviluppi metodo-logici e applicazioni”, Tesi di Dottorato di Ricerca in Geofisica per l’Ambiente e il Territorio, Università degli Studi di Messina Leucci G, De Giorgi L (2006) Experimental studies on the effects of fracture on the p and s wave velocity propagation in sedimentary rock (“calcarenite del Salento”). Eng Geol 84:130–142. https://doi.org/10.1016/j.enggeo.2005.12.004 Leucci G, De Giorgi L (2017) Il molino coratelli: indagini micro-geofisiche per la diagnostica strutturale. In I molini e l’industria molitoria in puglia. pp 61–68. ISBN-978-88-98773-44-2 Leucci G, Negri S (2006) Use of ground penetrating radar to map subsurface archaeological features in an urban area. J Archaeol Sci 33(4):502–512. https://doi.org/10.1016/j.jas.2005.09.006 Leucci G, Masini N, Persico R, Soldovieri F (2011) GPR and sonic tomography for structural restoration: the case of the cathedral of Tricarico. J Geophys Eng 8:76–92. https://doi.org/10. 1088/1742-2132/8/3/S08 Leucci G, Masini N, Persico R, Quarta G, Dolce C (2012) A multidisciplinary analysis of the crypt of the holy spirit in Monopoli (Southern Italy). Near Surf Geophys 10:1–8. https://doi.org/10. 3997/1873-0604.2011032 Leucci G, De Giorgi L, Scardozzi G (2014) Geophysical prospecting and remote sensing for the study of the San Rossore area in Pisa (Tuscany, Italy). J Archaeol Sci 52:256–276. https://doi. org/10.1016/j.jas.2014.08.028 Leucci G, Parise M, Sammarco M, Scardozzi G (2016) The use of geophysical prospections to map ancient hydraulic works: the Triglio underground aqueduct (Apulia, southern Italy). Archaeol Prospect 23(3):195–211. https://doi.org/10.1002/arp.1541 Loke MH (2001) “Electrical imaging surveys for environmental and engineering studies. A practical guide to 2-D and 3-D surveys. RES2DINV Manual”, IRIS Instru-ments, www.iris-instruments. com Miller SLM, Stewart RR (1991) The relationship between elastic-wave velocities and density in sedimentary rocks: a proposal. CREWES Research Report, Consortium for Res. in Elastic Wave Explor. Seismol., Calgary, Canada. http://www.crewes.org/Reports/1991/1991-17.pdf Murty BVS, Haricharan P (1985) Nomogram for the complete interpretation of spontaneous polarization profiles over sheet-like and cylindrical two-dimensional sources. Geophysics 50:1127–1135 Nur A, Simmons G (1969) The effect of saturation on velocity in low porosity rocks, Earth Planet. Sci Lett 7:183–193 Perrier FE, Petiau G, Clerc G, Bogorodsky V, Erkul E, Jouniaux L, Lesmes D, Macnae J, Meunier JM, Morgan D, Nascimento D, Oettinger G, Schwarz G, Toh H, Valiant MJ, Vozoff K, YaziciCakin O (1997) A one-year systematic study of electrodes for long period measurements of the electric field in geophysical environments. J Geomagn Geoelectr 49(11–12):1677–1696. https:// doi.org/10.5636/jgg.49.1677 Rao BSR, Murthy IVR, Reddy SJ (1970) Interpretation of self-potential anomalies of some simple geometric bodies. Pure appl Geophys 78:66–77 Sandmeier KJ (2013) Reflexw 7.0 manual. Sandmeier Software: Karlsruhe

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Sen PN, Scala C, Cohen MH (1981) A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. Geophysics 46(5):781–795 Shen LC, Savre WC, Price JM, Athavale K (1985) Dielectric properties of reservoir rocks at ultrahigh frequencies. Geophysics 50:692–704 Telford WM, Geldart LP, Sheriff RE, Keys DA (1976) Applied geophysics. Cambridge University Press, Cambridge Thill RE, Bur TR (1969) An automated ultrasonic pulse measurement system. Geophysics 34(1969):101–105 Topp GC, Davis JL, Annan AP (1980) Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resour Res 16(3):574–582 Wyllie MRJ, Gregory AR, Gardner LW (1956) Elastic wave velocities in heterogeneous and porous media. Geophysics 21:41–70 Wyllie MRJ, Gregory AR, Gardner GHF (1958) An experimental investigation of factors affecting elastic wave velocities in porous media. Geophysics 23:459–493 Zezza F (1993) Evaluation criteria of the effectiveness of treatments by non destructive analysis. In: Proceedings of the 2nd Course of CUN University School of Monument Conservation, Heraklion, pp 198–207

Chapter 6

Site Application: The Archaeological Site of Pompeii (Italy)

Abstract The research carried out in the area of the Necropolis of Porta Nocera at Pompeii has led to the creation of an innovative system for the documentation, representation, and preservation of archaeological contexts. The scientific rigor and precision of traditional instrumental mapping, together with the use of NDT geophysical methods, have produced high-definition 3D models of the funerary monuments and necropolis as tools to store and manage scientific information. Conserve and preserve, also through the study and application of avant-garde technologies and methods in the field of restoration, means working not only for present generations, but also, and primarily, for future generations. New technologies and a multidisciplinary approach constitute a capital in which to invest in order to create a more responsible and aware society, capable of understanding how much of its future comes from growing up with respect for one’s historical roots and own distinctive past.

6.1 Site History The Porta Nocera and the via Nucerina necropolis constitute one of the six cemetery areas uncovered during excavations at Pompeii and which almost completely surrounded the ancient city. The two sectors of Porta Nocera and via Nucerina are situated to the south-east of the ancient city. Today, these cemetery sectors are separated by an unexcavated area in correspondence with Piazzale dell’Anfiteatro, one of the modern entrances to the site. Originally, they were part of the same funerary area, which in this sector developed on a south-west/north-east alignment, following the line of an extra-urban road that from the Porta Nocera to the ancient city of the same name (Fig. 6.1). The Porta Nocera necropolis is the westernmost of the two funerary areas. Excavated by Amedeo Mauri between 1954 and 1956 (D’Ambrosio and De Caro 1983), it is the larger of the two areas and offers visitors an evocative example of a “romantic” landscape, thanks to the particular coexistence in the same place of funerary monuments and natural elements (Fig. 6.2a). © Springer Nature Switzerland AG 2019 G. Leucci, Nondestructive Testing for Archaeology and Cultural Heritage, https://doi.org/10.1007/978-3-030-01899-3_6

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6 Site Application: The Archaeological Site of Pompeii (Italy)

Fig. 6.1 The archaeological area of Pompeii (light blue). circled in red, on the right side, are the cemetery areas of the Necropolis of Porta Nocera (the big one, in orange, on the left side) and via Nucerina (the small one, in orange, on the right). The red arrow indicates the entrance to the archaeological site from “Piazzale dell’Anfiteatro”

Fig. 6.2 Pompeii: a Necropolis of Porta Nocera from the south-west; b Via Nucerina necropolis

The Via Nucerina necropolis, excavated by Antonio D’Ambrosio and Stefano De Caro in 1983, is slightly isolated to the east of the Porta Nocera and lies within an excavation area in the southern part of a greenspace outside the city walls (Fig. 6.2b). The most common ritual practiced within the necropolis was cremation, and the urns containing the remains were buried in pits dug into the ground bordered by the numerous funerary enclosures present in the area. The individual burials were marked by “columelles”, anthropomorphic steles, which often bore personal details of the deceased, as well as elements indicating the gender of the deceased. The two cemeteries comprised a total of 73 funerary enclosures, 15 enclosed areas delimited by simple perimeter walls, 12 areas with architectural façades, and six areas with plain façades. There are few tomb chambers, but rather a large number of certified types, e.g., the imposing “exedra” tomb with a semicircular plan datable to the Tiberian period and designed by Eumachia, priestess of Venus as a family

6.1 Site History

171

Fig. 6.3 Pompeii, Necropolis of Porta Nocera, The “exedra” tomb of Eumachia

Fig. 6.4 Pompeii, Necropolis of Porta Nocera, on a rainy day

tomb, mausoleums, house-tombs, and “podium” tombs, the latter built with one or more floors, in the form of aedicule, tetraplyon or tholos (Fig. 6.3). Based on the chronological evidence acquired by archaeological investigations, the development of the entire necropolis can be dated to between the final decades of the 1st century BC and 79 AD, when the city was destroyed. The monumental remains of the funerary structures are associated with funerary contexts, which in large part is unexplored and are the object of renewed interest and excavations (Van Andriga et al. 2013). The aim is to investigate, by examining the material traces of the rituals, the immaterial traces of customs and social self-representation, in a context in which the funerary buildings were designed to be seen and admired, as attested by the careful attention given to their decorative elements. Often, at the time of their discovery, the remains of the funerary structures still preserved substantial portions of their decoration, created using stuccowork and painted plaster. From the beginning, this presented problems linked to the long-term conservation of the monuments, through the construction of covers or restoration work to be carried out using techniques and materials that are the most compatible with those used in antiquity. In addition to the action of atmospheric agents, there is the problem of water rising from the water table, which here, in one of the lowest parts of Pompeii, is enough to cause damage to the foundations of the funerary buildings (Fig. 6.4).

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6 Site Application: The Archaeological Site of Pompeii (Italy)

6.2 Site Natural Hazard Geologically, the ancient city of Pompeii was located between the foothills of the south-western slope of the Somma–Vesuvius volcanic complex and the coastalalluvial plain of the Sarno River. It stands on a hill with a maximum height of 54 m a.s.l., due to the relict structure of an ancient volcano (Cinque and Irollo 2004), partially buried by alluvial and volcaniclastic deposits supplied from the southern slopes of the Somma–Vesuvius edifice. It is a semicircular morpho-structure mainly set in massive and scoriaceous lava flows by Strombolian activity. Its physical continuity near the archaeological area of Pompeii is interrupted by the Versilian palaeocliff along the Vesuvian coast (Cinque and Russo 1986). The activity of the Somma–Vesuvius complex in the last 17,000 years has been divided into eruptive cycles starting with the major explosive Plinian eruptions that have repeatedly shaped and changed the morphology of the volcanic edifice and ended with a minor intense, often effusive, eruption. Tephra levels covered large areas of the Campanian Plain and surrounding mountains, with a thickness of several meters. The 79 AD eruption, as described by Pliny the Younger, is one of the most important of Vesuvius, having buried the Roman cities of Herculaneum, Pompeii, Oplontis, and Stabiae, causing great destruction and casualties. Shallow instabilities that affect the site and produce monumental collapse are strongly related to the hill slope hydrological processes. Other factors are the geomorphological and stratigraphical conditions, together the climatic events. The kinematics of the shallow landslides are also related to hydro-mechanical properties and hydrological conditions. Particularly at the site, rainfall events related to surficial or sub-surficial flows strongly affect hydrological processes and subsidence events. In fact, during a rainfall event, the water reaches the ground surface causing an infiltration process within the soil that occurs at the ground surface along the slope. If the infiltration rate is greater than its infiltration capacity, the exceeded water will pond on the ground surface leading to the initiation of the runoff (Fig. 6.5). The infiltration capacity of soil/rock derives from its hydraulic properties and represents the maximum amount of water that can infiltrate in a unit of time.

Fig. 6.5 Pompeii: some example of collapsed areas at the archaeological site

6.3 NDT Geophysical Surveys

173

6.3 NDT Geophysical Surveys Integrated Ground-Penetrating Radar (GPR), passive (Self Potential—SP), and active electrical resistivity tomography (ERT) surveys were performed in three areas, labeled respectively Area 1, Area 2, and Area 3 (Fig. 6.6). Geophysical methods were chosen with the aim of obtaining information related to both the presence of archaeological structures and the causes of damage that occur to some monuments. Therefore, the need to investigate at various depths with different resolutions drove the selection of the GPR, ERT, and SP geophysical methods: GPR—because it was necessary to investigate at high resolution on the presence of archaeological structures at relatively shallow depths; ERT—to highlight at greater depth the presence of additional structures of archeological interest, the geology of the area and the depth of the foundation layers of the structures in danger of collapse; and SP—to detect possible groundwater flows related to landslides. GPR data were collected along grids with parallel and perpendicular profiles spaced at 0.5 m using the Ris Hi Mod georadar system with the dual band antennae

Fig. 6.6 Pompeii, Necropolis of Porta Nocera: surveyed areas

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6 Site Application: The Archaeological Site of Pompeii (Italy)

of 200 and 600 MHz. GPR data were processed in a 3D context using GPR-slice software (Goodman et al. 1994). To eliminate a small noise component and make it easier to interpret the GPR data, the following processing sequence was applied: (i) zero-time adjust (static shift) to associate zero-time with zero-depth; (ii) topographic corrections to apply the actual elevation recorded along the GPR line; (iii) frequency filtering to remove the high-frequency noise; (iv) migration to correct the shape and dimension of reflection events related to the structure present in the subsoil; and (v) trace envelop, which created a positive-valued of the amplitude of reflection events. GPR data were visualized in a 3D context using both time slice and iso-surface amplitude (Conyers 2012). In the Pompeii work, the time-slice technique has been used to display the amplitude variations within consecutive time windows of width t  5 ns. Three-dimensional amplitude, iso-surface rendering displays amplitudes of equal value in the GPR data set. Shading is usually used to illuminate these surfaces, giving the appearance of real archaeological structures. In this case, the threshold calibration is a very delicate task so as to obtain useful results. In order to define the depth of archaeological remains, the electromagnetic (EM) wave velocity, using the characteristic hyperbolic shape of a reflection from a point source (diffraction hyperbola), was used (Conyers 2012). Furthermore, an increase of the frequency content of the spectrum is obtained by a narrowing of the package in the time domain, with a consequent increase in temporal resolution. One technique to increase the length of the band in the case of radar signals consists of adding radar signals obtained with various antennae (Leucci 2012). In this case, the 200- and 600-MHz antennae radar signals were added. ERT data were collected in a 3D mode along non-conventional profiles (Leucci et al. 2016) using a dipole–dipole array (Loke 2001) and variable electrode spacing. The Syscal Kid with 24 active channels was used for geoelectrical measurements. The ErtLab inversion software (http://www.geostudiastier.it/) was used for 3D data distribution of the total volume resistivity in the subsurface. The SP were measured using the modified Syscal Kid instrument. In fact, the instrument was modified to function as a multi-channel voltmeter (Leucci et al. 2016). SP measurements overlap ERT measurements. Each electrode, non-polarizing Pb/PbCl2 (Petiau) electrodes (Perrier et al. 1997), was placed inside to 8-cm hole, filled with a moistened bentonite and gypsum mixture to ensure good contact between the electrode and the ground, and stones were placed above the electrodes. All the electrodes were scanned during a period of about 30 s. SP data were filtered in the frequency domain using a low-pass filter in order to avoid edge effects of spacedomain filters. This enabled elimination of high frequencies and preservation of low frequencies (Aubanel and Oldham 1985; Leucci et al. 2014; De Giorgi and Leucci 2015). A least-squares analysis method was used to estimate not only the depth and shape but also to determine the position of buried anomalies from the SP anomaly profile. The method is based on normalizing the residual SP anomaly using three characteristic points and their corresponding distances on the anomaly profile; then, the depth for each horizontal position of the buried anomalies is determined using the least-squares method. The computed depths are plotted against the assumed

6.3 NDT Geophysical Surveys

175

Fig. 6.7 The GPR results in Area 1: a photo; b processed radar section; c 3.0–3.5-m depth slice

horizontal positions on a graph. The solution for the depth and the horizontal position of the buried structure is read at the common intersection of the curves. Knowing the depth and the horizontal position and applying the least-squares method, the shape factor is determined using a simple linear equation. Procedures are also formulated to estimate the polarization angle and the electric dipole moment. The method is semi-automatic, and it can be applied to short or long residual SP anomaly profiles. These processed data are used to build the 3D SP maps.

6.3.1 Area 1: GPR, ERT and SP Data Interpretation With the aim of finding evidence of the presence of a Roman city defensive wall (partly dug), in Area 1, 181 profiles were acquired. The results processing the GPR data are shown in Fig. 6.7. It is possible to see the processed radar section related to the profile acquired of the hypothesized walls (Fig. 6.7b) and the time slice (depth 3.2–3.6 m) overlapped on the site map (Fig. 6.7c). The almost-horizontal reflection event (between two dashed white lines) is likely the covered ancient defensive wall. It is located, after topographical correction, at depths ranging 2.2–4 m. At the abscissa between 10 m and 35 m, the reflection event reaches its maximum depth (4 m). At this point, a collapse event occurred. This event is visible also on the visible current surface (Fig. 6.7a).

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Fig. 6.8 3D ERT processed data: a NE-SW oriented; b SW-NE oriented

Figure 6.7c shows the depth (3.0–3.5 m) of the slices with a normalized amplitude using a range defined by blue as zero and red as one. Relatively high-amplitude alignment (dashed dark line) is clearly visible. This corresponds to the prolongation of the orthostate city wall south of the amphitheater. To obtain stratigraphic information (wall foundations and collapse phenomena extension) in Area 1; a 3D ERT profile was acquired. The ErtLab software, based on tetrahedral FEM, renders the results as 3D volume; these are shown in Fig. 6.8. It is possible to note a relatively high resistivity (700  m) zone at variable depth ranging from 0.5 (SW side) to 3.5 m (NE side) in Fig. 6.8a. This corresponds to the prolongation of the orthostate city wall south of the amphitheater. Figure 6.8b shows evidence of a dense resistivity layering (“A”) above the wall. Resistivity values vary between 100 and 500  m and are probably related to the volcanic deposits. Resistivity values increase until about 1000  m below the wall. This layer reaches a depth between 4 and 6 m and could be related to the foundation layer. Using the self-potential technique helps in understanding the water flow in the subsoil. It is related to the instability condition (Leucci et al. 2016), In fact, if the values of SP anomalies are positive or negative one-hundred millivolts, the cause is the movement of the ground related to the water flow (Leucci et al. 2016). The result of this research (Fig. 6.9) shows that the self-potential values vary between −100 and 100 mV.

6.3 NDT Geophysical Surveys

177

Fig. 6.9 SP-processed data

In Fig. 6.9, it is possible to note an area where the self-potential values are zero. This indicates the absence of movements. However, it is interesting to note, below the collapse area visible on the current surface (Fig. 6.8a), a strong gradient in SP values. In this area, the self-potential values range between −100 and 40 mV. In this case, it is interesting to underline how probably the rainwater infiltrating from the surface reaches deep (dashed black arrow), carrying out minor corrosive action on the low-cemented materials and therefore producing the phenomenon.

6.3.2 Area 2: GPR, ERT and SP Data Interpretation In Area 2, 250 GPR profiles were acquired, with results as depicted in Fig. 6.10. The reflection event labelled “A” (between two vertical dashed yellow lines) is likely the Roman road (Fig. 6.10a). Other reflection events were generated by the probable presence of buried walls (“W”) and buried pipe lines (“P”) (Figs. 6.10a, b). Reflection event labelled “A” and “W” are located at depth ranging between 1.0 and 2.0 m. Furthermore, the reflecting surface presents at the abscissa ranging between 24 and 52 m in the profile labelled R50 (Fig. 6.10a) could be interpreted as a geological surface related to volcanic materials. This reflection is present in other profiles near R50. A depression evidenced in R98 profile (Fig. 6.10b) at the abscissa ranging between 27 and 42 m was interpreted as geological surface. Several reflection events are visible inside the depression and probably related to fill material. In the slice ranging 1.0–1.5-m in depth (Fig. 6.10c), relatively high-amplitude alignments (dashed dark lines) are clearly visible. Particularly evident is the correlation between the reflection event labelled “A” and the Roman road visible in

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Fig. 6.10 The 3D visualization of GPR data: a processed radar section related to profile R50; b processed radar section related to profile R98; c 1.0–1.5-m depth slice; d iso-amplitude surface

Fig. 6.10c. In Fig. 6.10d, the same data set is displayed with iso-amplitude surfaces using a threshold value of 40% of the maximum complex-trace amplitude (De Giorgi and Leucci 2015). Obviously, lowering the threshold value increases the visibility of the main anomaly and smaller objects, but also increases heterogeneity noise. Relatively strong continuous reflections are visible on the threshold volumes. This visualization technique makes stronger the evidence of the anomalies related to the archaeological structures (road, tombs, and walls). Area 2 was divided in Areas 2a and 2b for ERT measurements. In Area 2a (Fig. 6.11), the resistivity depth slices (1.0–4.0-m depth) confirm the GPR results indicating the Roman road and other structures (dashed dark lines) that could probably be related to tombs. These structures are visible at depths up to 4.0 m. In Area 2b, the resistivity depth slice (1.0–3.0-m depth), depicted in Fig. 6.12, has high-resistivity anomalies (dashed dark line) related to archaeological structures (tombs). For SP measurements, the results are insignificant, as they do not show strong variations of the self potential.

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Fig. 6.11 ERT depth slices for Area 2a

Fig. 6.12 ERT depth slices for Area 2b

6.3.3 Area 3: GPR, ERT, and SP Data Interpretation In Area 3, the results of the GPR survey (Fig. 6.13) shows the presence of a structure that, for shape (rectangular) and dimensions (5-m long, 2-m wide), could be related to a tomb (Fig. 6.13a). Its depth ranges 1.5–1.8 m. The 3D visualization (Fig. 6.13b) well delineate the structure of the anomaly. What is interesting is the result of the 2D-ERT line acquired in Area 3 near the collapsed tombs (Fig. 6.14). In fact, in ERT profile 1 (Fig. 6.14a), the tombs foundations are clearly visibly at a depth of 0.8–1.5 m. Here, resistivity values range between 700 and 1000  m. In the western part of the 2D resistivity distribution, it

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Fig. 6.13 The 3D visualization of GPR data in Area 3: a 1.5–1.8-m depth slice; b iso-amplitude surface

Fig. 6.14 The ERT section of Area 3

is possible to note a decrease in resistivity values of 30- to 50- m. Probably in this zone, the tombs foundation lay on degraded materials (circled by the dashed black line in Fig. 6.14a). ERT profile 2 (Fig. 6.14c) shows the tombs foundations at a depth of 2–3 m, where resistivity values range between 100 and 1200  m.

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Fig. 6.15 SP processed data in Area 3

Fig. 6.16 Tomb D

A GPR profile overlapped with ERT profile 1 (Fig. 6.14b, d) evidenced a linear reflection event (yellow dashed line) related to the tomb’s foundation, thus confirming the ERT results. Processed self-potential data are used to build the 3D self-potential map shown in Fig. 6.15. The result of this research shows that the self-potential values vary between −100 and 400 mV. This result can be interpreted as indicating dangerous ground motion. The dark dashed arrows show the ground-motion direction.

6.3.4 The NDT Geophysical Survey of Tomb D Tomb D is located in the via Nucerina and shows many signs of deterioration (Fig. 6.16). NDT measurements were undertaken to understand the causes of this deterioration. The ERT, GPR, and seismic-ultrasonic NDT geophysical methods were used.

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Fig. 6.17 The locations of ERT profiles

6.3.5 2D ERT Data Analysis and Interpretation Resistivity imaging surveys have not only been carried out in space, but also in time because changes in the subsurface resistivity with time have important applications. Such studies include the flow of water through the vadose (unsaturated) zone and changes in the water table due to water extraction flow. A simple, but very interesting, experiment to map the flow of water from the ground surface downwards through the unsaturated zone was performed. This experiment was carried out in the area near the studied tomb (Fig. 6.17) where some liters of water were poured on the ground surface over a period of 3 h. The 2D resistivity model, obtained after five iterations with a final RMS error below 4.6%, is shown in Fig. 6.18. The resistivity model shows the existence of an almost horizontal stratification with the follow resistivity values ranging between 80 and 2000  m. Considering the obtained resistivity values, the first layer with low resistivity values (100–200  m) could be interpreted as the agricultural soil, the layer with higher resistivity values (500–1500  m) could be interpreted as more compact volcanic material, which could be related to the foundation line. It is visible at about 2 m in depth. Figure 6.19a shows the results of a survey carried out at the beginning of the experiment, before the irrigation started. The inversion model (Fig. 6.19a) shows that the subsurface is highly inhomogeneous. The water distribution is determined by plotting the percentage change in the subsurface resistivity of the inversion models for the data sets taken at different times (Fig. 6.19b, c), when compared with the initial data set model. The inversion

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Fig. 6.18 2D resistivity distribution related to ERT1 profile

Fig. 6.19 Water infiltration mapping: a Inversion model sections from the survey conducted at the beginning of the infiltration study. This shows the results from the initial data set that forms the base model in the joint inversion with the later data sets. As a comparison, the resistivity percentage change obtained from the inversion of the data set collected after 2 h of irrigation (b) and after 3 h of irrigation (c)

of the data sets was carried out using a joint inversion technique where the model obtained from the initial data set was used to constrain the inversion of the later data sets. The data set collected 2 h after the water infiltration began shows a reduction in the resistivity (of up to more than 20%) near the ground surface in the vicinity of the 2-m in depth. The near-surface low-resistivity zone reaches its maximum amplitude after about 3 h. Here, the low resistivity plume has spread downwards and slightly outwards due to infiltration of the water through the unsaturated zone. There

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Fig. 6.20 2D resistivity distribution related to ERT2 profile

is a decrease in the maximum percentage reduction in the resistivity values near the surface due to migration of the water from the near-surface zone. The model of the percentage variations of the resistivity (Fig. 6.19c) shows, particularly, the presence of zones (see the with arrow lines) in which the resistivity values decrease to about 30%. Such reduction is clearly due to an increase of the volumetric water content. These zones are therefore the preferential zones of outflow of the water. After 3 h water flow reaches the foundation line at about 2 m in depth. In this way, it is possible to estimate a hydraulic conductivity of about 1.85 × 10−4 m/s. The 2D resistivity model, obtained after five iterations with a final RMS error below 5.7%, is shown in Fig. 6.20. The resistivity model shows the existence of an almost horizontal stratification with the resistivity values ranging between 30 and 2200  m. Considering the obtained resistivity values, the first layer with low resistivity values (50–200  m) could be interpreted as the agricultural soil, and the layer with higher resistivity values (1500–2200  m) could be interpreted as volcanic material that could be related to the foundation line. It is visible at about 1.6 m in depth. Figure 6.21a shows the results of a survey carried out at the beginning of the experiment before the irrigation started. The inversion model (Fig. 6.21a) shows that the subsurface is highly inhomogeneous. The water distribution is determined by plotting the percentage changes in the subsurface resistivity of the inversion models for the data sets taken at different times (Figs. 6.21b, c) when compared with the initial data set model. The inversion of the data sets was done using a joint inversion technique where the model obtained from the initial data set was used to constrain the inversion of the later data sets. The data set collected at 2 h after the water infiltration began shows a reduction in the resistivity (of up to over 10%) near the ground surface in the vicinity of 1 m in depth. The near-surface low-resistivity zone reaches its maximum amplitude after about 3 h. Here the low resistivity plume has spread downwards and slightly outwards

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Fig. 6.21 Water infiltration mapping: a Inversion model sections from the survey conducted at the beginning of the infiltration study. This shows the results from the initial data set that forms the base model in the joint inversion with the later time data sets. As a comparison, the resistivity percentage change obtained from the inversion of the data set collected after 2 h of irrigation (b) and after 3 h of irrigation (c)

due to infiltration of the water through the unsaturated zone. There is a decrease in the maximum percentage reduction in the resistivity values near the surface due to migration of the water from the near-surface zone. The model of the percentage variations of the resistivity (Fig. 6.21c) shows, particularly, the presence of zones (see the spots with arrow lines) in which the resistivity values decrease to about 15%. Such reduction is clearly due to an increase of the volumetric water content. These zones are therefore the preferential zones of outflow of the water. After 3 h, water flow reaches the foundation line at about 1.7 m in depth. In this way, it is possible to estimate an hydraulic conductivity of about 1.57 × 10−4 m/s.

6.3.6 ERT Data Analysis and Interpretation of the Wall of the Studied Tomb Using a noninvasive micro-resistivity instrument (Fig. 6.22), a resistivity survey was performed on the north wall of the studied tomb. It enabled acquiring of a map of

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Fig. 6.22 Micro-resistivity data acquisition

Fig. 6.23 2D models: a Electrical resistivity; b Volumetric water content

resistivity values that, using an empirical relationship, enable creation of a volumetric water-content map of the same wall. Results are shown in Fig. 6.23. Results reveal an inhomogeneous distribution of resistivity values ranging from 40 to 500  m, an interesting distribution that shows increasing resistivities from the bottom to the top of the wall. The same thing is possible to say of the distribution of the volumetric water content and from the bottom upwards that varies from 35 to 10% from the bottom to the top of the wall. It seems that dampness is rising from the ground.

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(b)

Fig. 6.24 The tomb’s wall: seismic tomography. a Ray-paths in a hypothetic homogeneous wall; b Seismogram

6.3.7 Seismic Tomography Data Analysis and Interpretation of the Wall of the Studied Tomb Seismic tomography used in the evaluation of the wall consisted of 2D reconstruction based on the travel-refracted wave amplitude. Images were obtained exclusively from the first arrival of the waves, which allows the best resolution possible, because those first arrivals are always clearly detected (Fig. 6.24). A piezoelectric pulse of 55 kHz was used as the seismic source. Data were acquired with a high- frequency sensitivity accelerometer (55 kHz). In order to cover the whole space, the medium was divided into cells or elements, and the results were obtained as the sum of the values in each of the cells. In the case of non-homogeneous media, the seismic wave was refracted, because of changes in the wave velocity associated with adjacent cells, and the tomography equations

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Fig. 6.25 The tomb’s wall: a Seismic-wave velocity (Vp); b Bulk density; c Compressive-strength distribution

were solved in an iterative computational process until convergence on the solution. The computational process, the simultaneous interactive reconstruction technique (SIRT), contemplated ray curvature as a consequence of internal refractions. The characteristics of each cell were defined in the case that at least one ray path crosses the cell. The reflex software was used to invert the seismic tomography data. Seismic tomography seems to confirm the existence of a discontinuity (Fig. 6.25). Several zones presenting lower velocities (1200–1500 m/s) can be associated with cracks or more damaged parts of the wall. Irregular and small changes on the velocity are most likely caused by the irregular arrangement of materials inside the structure. However, it is noticeable that the wall exhibits high nonhomogeneity. At the top of the wall the P, wave velocity seem to be higher (about 2000–2500 m/s). This indicates the probable presence of more compact material. Irregular and small changes on the velocity are most likely caused by the irregular arrangement of materials inside the structure. However, it is noticeable that the wall exhibits high nonhomogeneity. Furthermore, using the P-wave velocity distribution, it is possible to estimate the compressive strength by using the relationship implemented in Vasanelli et al. (2015). The distribution of compressive strength, shown in Fig. 6.25c, seems to have vary in the interval, ranging from 40 to 74 kg/cm2 . This results confirm the existence of an high degree of deterioration of the wall confirmed by the low physical-mechanical characteristics of the same wall.

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6.3.8 2D GPR Data Analysis and Interpretation To document the presence of structures of archaeological interest buried near the studied tomb, 2D-GPR measurements were performed. The results of the GPR processed data are shown in Figs. 6.26 and 6.27.

Fig. 6.26 Processed 2D radar section acquired near the studied tomb

Fig. 6.27 Processed 2D radar section acquired near the studied tomb

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Fig. 6.28 Processed 2D radar section acquired near the studied tomb

The almost-horizontal reflection event (between the two dashed yellow lines) is probably the buried foundation base that confirms the 2D-ERT results. At a depth ranging 0.9–1.0 m, it is possible to observe at the abscissa 7 and 13 m two reflection events (w) that could be related to a buried wall. Figure 6.28 shows the almost-horizontal reflection event (dashed yellow line) that is probably the buried foundation base that confirm the 2D-ERT results. At a depth ranging 3.0–3.2 m it is possible to observe at the abscissa 7 and 1 m two reflection events (T) that could be related to a buried tomb. More interesting is the results related to the 2D data analysis in Fig. 6.29. It shows the probable presence of two unknown tombs at depth of about 1.5–2.0 m at abscissa 8 and 10 m.

6.3.9 3D GPR Data Analysis and Interpretation The results of 3D GPR survey are shows in Fig. 6.30. In the 1.0-m depth slice, relatively high-amplitude alignments (red) are clearly visible, which could be related to archaeological structures. Relatively strong continuous reflections (red) are visible on the depth slices at about 4.0-m depth.

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Fig. 6.29 Processed 2D radar section acquired near the studied tombs

Fig. 6.30 Depth slices

6.4 GPR Data Acquisition and Analysis on the Columns Finally, an interesting study on the conservation state of three columns in the Regio VIII area is reported. The studied structures are built with irregular and fragmented bricks and mortar. The internal irregular and complex structure causes complicated 2D images, evidencing the existence of many different targets. However, the images

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Fig. 6.31 The three investigated columns in Pompeii

Fig. 6.32 GPR lines on the investigated columns

provide valuable information about the presence and the state of an internal microfracturation. Three columns were investigated (Fig. 6.31) using a GPR Ris Hi-Mod manufactured by IDS instruments and a 2-GHz frequency antenna. Vertical and horizontal lines were marked on the surface (Fig. 6.32) to acquire GPR data along each column. A 2-GHz center-frequency antenna was used. The position on the column was determined with a survey-wheel odometer. During the radar acquisition, the sampling interval was 512 samples per trace. The spatial sampling was 0.002 m, and the temporal window was 12 ns. Knowing the diameter of the column (1.3 m) and obtaining the reflection from the end on the opposite side of the antenna, an average EM wave velocity of 0.11 m/ns was estimated. Radar profiles were processed with Reflex software (Sandmeier 2003) in order to obtain 2D slices. The sequence processing applied to each radargram was: search for time, 0 ns; background removal; and migration. After the sequence processing, horizontal radargrams were transformed into cylindrical coordinates, by using a Matlab routine. Figures 6.33 and 6.34 presents the position of the vertical radar-line data on the

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(a) (b)

Fig. 6.33 Column 1: the vertical radar-data image on the column (a) and two radar-data images obtained from circular profiles (b); the main detected anomaly are marked (“D”) on the radar-data interpretation. It seem to indicate that the column is not composed of a uniform layer but rather, in these points, there are internal fractures. Also evident is the reflection that indicates the contact between the antenna and the column surface

specimen and radar data obtained from circular profiles related to columns number 1 and 2, respectively, in Fig. 6.31. The main features observed in these images correspond to some strong reflections and the irregular anomalies among them. The strong anomaly (labelled D in Figs. 6.33 and 6.34) could be due to the fractures. Other low-amplitude irregular reflection events are most likely a consequence of the internal desegregation of the material due to humidity and water actions. The strong reflection events at the sides (Figs. 6.33a and 6.34a) probably indicate contact between the antenna and the column surface.

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(b) (a)

Fig. 6.34 Column 2: the vertical radar-data image on the column (a) and two radar-data images obtained from circular profiles (b); a main detected anomaly are marked (“D”) on the radar data interpretation. It seem to indicate that the column is not composed of a uniform layer but rather that, at these points, there are internal fractures. Also evident is the reflection that indicates the contact between the antenna and the column surface

References Aubanel EE, Oldham KB (1985) Fourier smoothing without the fast Fourier transform. Byte 10(2):207–218 Cinque A, Irollo G (2004) Il “vulcano di Pompeii”: nuovi dati geomorfologici e stratigrafici. Il Quaternario 17:101–116 Cinque A, Russo F (1986) La linea di costa del 79 d.C. fra Oplonti e Stabiae nel quadro della evoluzione olocenica della Piana del Sarno (Campania). Boll Soc Geol It 105:111–121 Conyers LB (2012) Interpreting ground-penetrating radar for archaeology. Left Coast Press, Walnut Creek D’Ambrosio A, De Caro S (1983) La necropoli di Porta Nocera. In Vlad Borrelli L, D’Ambrosio A, De Caro S (eds) Un Impegno per Pompei. Studi e contributi. Fotopiano e documentazione della necropoli di Porta Nocera, Milano, 23 ss

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De Giorgi L, Leucci G (2015) Study of shallow low-enthalpy geothermal resources using integrated geophysical methods. Acta Geophys 63:125–153 Goodman D, Nishimura Y, Tobita K (1994) GPRSIM forward modeling software and time slices in ground penetrating radar surveys. In: Proceedings of 5th international conference on ground penetrating radar (GPR’94) (Kitchener, Ontario, Canada, 12–16 June) pp 31–43 Leucci G, Parise M, Sammarco M, Scardozzi G (2016) The use of geophysical prospections to map ancient hydraulic works: the Triglio underground aqueduct (Apulia, southern Italy). Archaeol Prospection 23(3):195–211. https://doi.org/10.1002/arp.1541 Leucci G, De Giorgi L, Scardozzi G (2014) Geophysical prospecting and remote sensing for the study of the San Rossore area in Pisa (Tuscany, Italy). J Archaeol Sci 52:256–276. https://doi. org/10.1016/j.jas.2014.08.028 Leucci G (2012) Ground penetrating radar a useful tool for shallow subsurface stratigraphy characterization; in stratigraphy. InTech Editor Loke, MH (2001) Electrical imaging surveys for environmental and engineering studies. A practical guide to 2-D and 3-D surveys. RES2DINV manual, IRIS Instru-ments. www.iris-instruments.com Perrier FE, Petiau G, Clerc G, Bogorodsky V, Erkul E, Jouniaux L, Lesmes D, Macnae J, Meunier JM, Morgan D, Nascimento D, Oettinger G, Schwarz G, Toh H, Valiant MJ, Vozoff K, YaziciCakin O (1997) A one-year systematic study of electrodes for long period measurements of the electric field in geophysical environments. J Geomagn Geoelectr 49(11–12):1677–1696. https:// doi.org/10.5636/jgg.49.1677 Sandmeier KJ (2003) Program for processing and interpretation of reflection and transmition data, D-76227 Karlsruha, Germany Van Andriga W, Duday H, Lepetz S, Joly D, Lind T et al (2013) Mourir à Pompéi: fouille d’un quartier funéraire de la nécropole romaine de Porta Nocera (2003–2007), vol 2. Collection de l’école française de Rome, Roma, p 468 Vasanelli E, Sileo M, Leucci G, Calia A, Aiello MA, Micelli F (2015) Mechanical characterization of building stones through DT and NDT tests: research of correlations for the in situ analysis of ancient masonry. In: Key Engineering Materials, Trans Tech Publications, Switzerland, 628: 85–89. Avilable at www.scientific.net, https://doi.org/10.4028/www.scientific.net/KEM.628.85. Accessed 28 Aug 2014

Chapter 7

Site Application: The Archaeological Site of Sagalassos (Turkey)

Abstract During the summer of 2015 (4–11 July), a passive-and-active, electricalresistivity tomography survey of two areas at the archaeological site of Sagalassos (Turkey) were undertaken. The first one, labelled Area 1, was the excavated structures of the Roman Bath, and the second one, labelled Area 2, was the stadium area. Data were collected along non-conventional profiles using a dipole–dipole array and variable electrode spacing. To obtain their distribution within a three-dimensional volume, two physical parameters were measured: the electrical resistivity and the self-potential. For Area 1, the aim of geophysical survey was to obtain information about the structural stability. For Area 2, the aim was to investigate about the existence of tombs. A two-dimensional least-squares algorithm based on the smoothness-constrained technique, implemented in Res2Dinv software, was used in order to invert the 2D apparent resistivity data, while ErtLab software was used for 3D total-volume data distribution in the subsurface.

7.1 Site Description The ancient Roman city of Sagalassos is located in the southwestern part of Turkey (Fig. 7.1), about 7 km from the village of Aglasun. The site is located on Mount Akdag at an altitude ranging between 1450 and 1700 m above sea level (m asl). The city was the first town of Pisidia in Roman Imperial times, in the region currently known as the Turkish Lakes Region, and was an important urban center of the Roman ‘imperial cult’. Two earthquakes devastated the city, first in 518 BC and then again in the middle of the seventh century, the latter of which destroyed the town and led to abandonment of the village. Since 1990, the University of Leuven (Belgium) has operated this archaeological site. The studies, including numerous geophysical investigations, performed by a multidisciplinary team revealed that, since the middle of the seventh century, the ruins of Sagalossos have been buried by eroded soil (for more information see: www.sagalassos.be).

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Fig. 7.1 The archaeological site of Sagalassos (Turkey): a Geographical location (source Google Earth). b Panoramic photo of the archaeological site (De Giorgi and Leucci 2017)

Fig. 7.2 Panoramic photos of the Roman Baths

The Roman Baths at Sagalassos formed the largest building complex in the ancient city, covering a surface of about 6825 m2 . It occupied a natural hill to the east of the lower agora, which was leveled at its top around A.D. 120 after all of the older structures had been removed (Fig. 7.2). They suffer from several subsidence phenomena that caused collapses of the structured ceiling (Fig. 7.3).

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Fig. 7.3 Collapsed ceiling of the Roman Baths

Fig. 7.4 The two areas surveyed at the archaeological site of Sagalassos

7.2 NDT Geophysical Data Acquisition, Processing and Interpretation Geophysical measurements were undertaken in two areas labeled respectively Area 1 and Area 2 (Fig. 7.4). The dipole–dipole array was applied because of its sensitivity to lateral changes in resistivity. An Iris Syscal Kid resistivity meter (appropriately modified for the storage of self-potential) with 24 active channels was used for the geoelectrical measurements.

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7.2.1 Area 1 With the aim of assessing the degree of integrity of the Roman Bath’s structure, the ERT survey was conducted in an area 78 × 127 m (Fig. 7.5). The measurements were collected along 74 lines placed in a non-standard manner. The length of lines varied from 80 to 155 m, with variable line spacing ranging from 1 to 5 m. A total of about 5,000,000 apparent-resistivity measurements were collected (n 1 to n 9). The vertical stack was set to four. The relative standard deviation for each stack is a good indicator of the quality of the data, so it was checked during the measurements. When the relative standard deviation of the stacked data was greater than 3%, the vertical stack was increased to six. The standard deviation of the measurements was mostly below 1%. Measurements, stored in the data logger of the resistivity meter, were transferred to the computer using an RS232 port. As a first step, we applied a two-dimensional inversion method to obtain a more reliable image of both the structure and the subsurface using Res2Dinv software. This program iteratively calculates a resistivity model, trying to minimize the differences between the observed apparent-resistivity values and those calculated from the model. The maximum number of iteration was set to four or eight for all profiles to avoid overfitting the data. The inversion process resulted in a satisfactory fit with an RMS error of 4–12%. Due to the low RMS error, the obtained results can be considered as a reliable representation of the true resistivity distribution of the subsurface. Figure 7.6 show the results of 2D inversion related to the ERT profile labelled 1, which is located near the wall of the Roman Bath. Figure 7.6 shows a layered resistivity profile in the top 12 m; (1) a zone of medium resistivity values (ranging from 300 to 1000  m) from the surface to a depth of about 4 m; this may be linked to the foundation of the structure; (2) a zone of high resistivity values (ranging from 6000 to 26,000  m); his may be linked to the bedrock;

Fig. 7.5 Area 1: ERT profiles

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Fig. 7.6 Area 1: electrical resistivity distribution in the subsoil related to the ERT profile labelled 1

(3) a zone of relativity low resistivity values (ranging from 20 to 60  m); due to the shape and dimensions (about 1 m in diameter); this could be linked to the presence of the discharge pipe of the cloaca. The bedrock was interrupted by a fault located at the bottom of two fractures (inside the foundations). In this zone, an event of instability could be hypothesized. The same considerations can be made for profiles 2 and 3 which line the structure (Figs. 7.7 and 7.8).

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Fig. 7.7 Area 1: electrical-resistivity distribution in the subsoil related to the ERT profile labelled 2

For the profiles performed on the structure (Figs. 7.9 and 7.10), what is noteworthy is: (1) the collapsed roof zone; it is surrounded by areas completely filled with water. Two fractures are also visible (Fig. 7.9); and (2) the very dangerous condition of the closed zone of the baths. In this zone (Fig. 7.10), several fractures are present. Furthermore, the roof is completely filled with water.

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Fig. 7.8 Area 1: electrical-resistivity distribution in the subsoil related to the ERT profile labelled 3

Next, we jointly show the geo-electrical sections processed using a 3D software ErtLab manufactured by Multi-Phase Technologies, LLC. Its numerical core is based on tetrahedral FEM, and inversion was performed robustly (using data-variance iterative reweighting). The results of the inversion of the ERT data set, arranged as horizontal slices (parallel to the surface) through the ground, are shown in Fig. 7.11. Figure 7.11 shows the electrical-resistivity model at six various depths. It is possible to note a low-resistivity zone (10–60  m) that is probably linked to the presence of a flow of water coming from the north. Part of water flow is directed towards the thermal baths, and it spreads out within them. It is possible also to discern the fault line that crosses the baths.

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Fig. 7.9 Area 1: electrical-resistivity distribution in the subsoil related to the ERT profile labelled 4

The 3D images of electrical resistivity can easily be visualized by 3D contouring of iso-resistivity volumes (Fig. 7.12). In this representation, the transparency function is defined by two threshold values of ρ, ρ1, and ρ2 (ρ < ρ2). In the intervals ρ < ρ1 and ρ > ρ2, the data are rendered as transparent, therefore only the data in the interval ρ1 < ρ < ρ2 are visualized. The threshold calibration is a very delicate task. In fact, by lowering the threshold value, not only the visibility of the main anomaly is raised, but also that of the smaller objects and noise increases. In Fig. 7.12, the ρ data set is displayed with iso-ρ volumes using two threshold values ranging respectively from 1500 to 2000  m and from 10 to 60  m. This kind of visualization makes it possible to emphasize both the bedrock variation depth (ranging from about 5 to about 12 m in depth) and the water flow.

7.3 The Roman Bath Stability Study To better understand the stability condition of Roman Bath, Area 1 was subdivided in two sub areas labelled respectively zone 1 and zone 2 (Fig. 7.13).

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Fig. 7.10 Area 1: electrical-resistivity distribution in the subsoil related to the ERT profile labelled 5

Fig. 7.11 Area 1: 3D electrical-resistivity distribution in the subsoil

7.3.1 Zone 1 The results of the inversion of the ERT data set, given as horizontal slices (parallel to the surface) through the ground, are shown in Fig. 7.14.

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Fig. 7.12 Area 1: 3D iso-resistivity volume

Fig. 7.13 Area 1: zone 1 and zone 2

Figure 7.14 shows the electrical-resistivity model at eight various depths. It is possible to note the probable ancient drainage system in the first slices (+9 m) positioned at about 3 m in depth (referring to the current actual surface). It is characterized by high-resistivity values ranging from about 4000 to about 5000  m. These values suggest that the system is empty and partially collapsed. A low resistivity zone (10–60  m) indicates probable water flow coming from the north. Due to the collapsed ancient drainage system, the water path is random, and therefore the water diffuses randomly along paths that for centuries have been opened in the building. Other high-resistivity zones (labelled “C”) are visible on the

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Fig. 7.14 Area 1: zone 1: 3D electrical-resistivity distribution in the subsoil

Fig. 7.15 Area 1: zone 1: 3D electrical-resistivity distribution crossing the Roman Bath

roof. These zones are probably related to a fracture system. It is possible also to discern the fault line that crosses the baths. To better understand the distribution of water on the roof, vertical distributions of resistivity are depicted in Fig. 7.15. Figure 7.15 shows the electrical-resistivity model at four various vertical sections that cross the Roman Bath structure. It is possible to note the probable ancient drainage system. It is characterized by high-resistivity values ranging from about 4000 to about 5000  m. These values suggest that the system is empty and partially collapsed. A low resistivity zone (10–60  m) indicates probable water distribution on the roof. Other high resistivity zones (labelled “C”) are visible on the roof. These zones are probably related to a fracture system.

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Fig. 7.16 Area 1: zone 1: SP maps

Self-potential (SP) data were filtered with a low-pass filter in the frequency domain to avoid edge effects of the space-domain filters, so that high frequencies were eliminated and low frequencies were preserved. A least-squares analysis method to estimate not only the depth and shape but also to determine the horizontal position of a buried structure from the SP anomaly profile was used. The method is based on normalizing the residual SP anomaly using three characteristic points and their corresponding distances on the anomaly profile and then determining the depth for each horizontal position of the buried structure using the least-squares method. The computed depths are plotted against the assumed horizontal positions on a graph. The solution for the depth and the horizontal position of the buried structure is read at the common intersection of the curves. Knowing the depth and the horizontal position and applying the least-squares method, the shape factor is determined using a simple linear equation. Procedures are also formulated to estimate the polarization angle and the electric-dipole moment. The method is semi-automatic, and it can be applied to short or long residual SP anomaly profiles. Large anomalous potentials are often observed over sulfide and graphite ore bodies, magnetite and several other electrically conductive minerals, and groundwater accumulations. Self-potential anomalies are also associated with water in subsurface structures and flows of water through the ground. The streaming self-potential of groundwater is usually indicated as a negative anomaly in the profile. Self-potential anomalies vary in value according to their source. If the value of self-potential is a positive or negative one of one hundred millivolts, the cause is the movement of water. The motion direction is from the negative to the positive potential. These processed data are used to build the self-potential map sheen in Fig. 7.16. The result of this research shows that the self-potential values vary between −100 and 20 mV. Observing Fig. 7.16, it is possible to note a probable water micro-flow on the roof of the Roman Bath.

7.3 The Roman Bath Stability Study

209

Fig. 7.17 Area 1: zone 2: 3D electrical-resistivity distribution in the subsoil

Fig. 7.18 Area 1: zone 2: 3D electrical-resistivity distribution crossing the Roman Bath

7.3.2 Zone 2 The results of the inversion of the ERT data set, given as horizontal slices (parallel to the surface) through the ground, are shown in Fig. 7.17. Figure 7.17 shows the electrical-resistivity model at eight various depths, and it is possible to detect the Roman Bath system. It is characterized by high-resistivity values ranging from about 5000 to about 10,000  m. A low resistivity zone (10–60  m) indicates probable water distribution in the surveyed area. To better understand the distribution of the water on the roof, vertical distributions of resistivity are show in Fig. 7.18.

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7 Site Application: The Archaeological Site of Sagalassos (Turkey)

Fig. 7.19 Area 1: zone 2: SP map

Figure 7.18 shows the electrical-resistivity model at four various vertical sections that cross the Roman Bath structure. It is possible to note the probable ancient bath system. It is characterized by high resistivity values ranging from about 5000 to about 10,000  m. A low resistivity zone (10–60  m) indicates probable water distribution on the roof. Other high resistivity zones (labelled “fracture”) are visible on the roof, and these zones are probably related to a fracture system. Also in this case, the self-potential map was drawn (Fig. 7.19). The result of this research shows that the self-potential values vary between −5 and 20 mV. Observing Fig. 7.19, it is possible to note a probable water microflow on the roof of the Roman Bath. The low SP values indicate a stable water flow that tends to stagnate on the roof, with a slow exchange of water coming from the north.

7.3.3 Analysis of the Probability of Long-Term Collapse The empirical analysis of the stability of the roof was performed considering the crown pillar’s thickness and its span as the variables and functions of its length and width, respectively. The thickness of the material that forms the roof of the cave is defined as the crown-pillar thickness (Fig. 7.20). The width of the roof is defined as the crownpillar span. Empirical analysis methods can be used to assess the stability of a crown pillar. The method of assessment is known as the scaled crown-pillar span method (Leucci and De Giorgi 2015). This method was developed from extensive databases

7.3 The Roman Bath Stability Study

211

Fig. 7.20 Crown-pillar definition scheme (Leucci and De Giorgi 2015)

containing information about the geometry, physical-mechanical parameters, and stability of crown pillars. The method relies upon two input parameters: one related to the crown-pillar geometry and the other related to the roof-material quality. The roof-material quality is quantified by Q (Tunneling Quality Index proposed by Barton (2002)). Instability of a crown pillar is likely to occur if the scaled crown-pillar span, Cs, is greater than the critical span, Sc, calculated by the equations (Leucci and De Giorgi 2015): Sc  3.3 × Q 0.43

(7.1)

and  CS  S

S.G.   T 1 + LS (1 − 0.4 cos θ )

(7.2)

where S  crown pillar span (m), L  crown pillar length (m), T  crown pillar thickness (m), SG  rock mass specific gravity (=3.5 for high grade ore; 3 for moderate grade ore; 2.7 for waste rock), and θ  ore body/foliation dip. The method is applied by comparing the scaled crown-pillar span for the pillar of interest to the critical span value deemed appropriate for the controlling rock mass. When the scaled crown-pillar span is determined to be less than the critical span, the crown pillar is considered to be stable. On the other hand, when Cs is greater than Sc, the probability of failure is high. Because of its empirical basis, application of the scaledspan method at least makes possible a rational assessment of the failure likelihood if the method is applied probabilistically. The index is known as the factor of safety: F  Sc/Cs

(7.3)

where instability of a crown pillar is likely to occur if F < 1. Table 7.1 shows how the method can help in defining acceptable or allowable risk. The next step is to study the stability of the roof using the empirical analysis described above. In this case, the thickness T varies with the distances x and y because it takes into account the variations in thickness of the roof of the bath structure. Therefore, T is treated as a matrix. Consider a parametric surface parameterized by two independent variables, i and j, which vary continuously over a rectangle, for example, 1 ≤ i ≤ m and 1 ≤ j ≤ n. Matrix T was constructed considering the

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Table 7.1 Crown-pillar probability-failure definition in the long term [Carter and Miller 1995 (modified)] Class Prob. of failure Minimum factor Serviceable life Years (%) of safety A

50–100