Treatise on Geophysics : Volume 2 Mineral Physics [2, 2 ed.] 9780444538024, 044453802X

Table of contents :
Volume 1 - Deep Earth Seismology Volume 2 - Mineral Physics Volume 3 - Physical Geodesy Volume 4 - Earthquake Seismology Volume 5 - Geomagnetism Volume 6 - Crustal and Lithosphere Dynamics Volume 7 - Mantle Dynamics Volume 8 - Core Dynamics Volume 9 - Evolution of the Earth Volume 10 - Physics of Terrestrial Planets and Moons Volume 11 - Resources in the Near-Surface Earth

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2.01

Mineral Physics: An Introduction and Overview

GD Price and L Stixrude, University College London, London, UK ã 2015 Elsevier B.V. All rights reserved. This chapter is a revision of the previous edition chapter by G D Price, Volume 2, pp. 1–6, © 2007, Elsevier B.V.

Mineral physics involves the application of physics and chemistry techniques in order to understand and predict the fundamental behavior of Earth materials (e.g., Kieffer and Navrotsky, 1985) and hence provide solutions to large-scale problems in Earth and planetary sciences. Mineral physics, therefore, is relevant to all aspects of solid Earth sciences, from surface processes and environmental geochemistry to the deep Earth and the nature of the core. In this volume, however, we focus only on the geophysical applications of mineral physics (see also Ahrens, 1995; Hemley, 1998; Poirier, 2000). These applications, however, not only are constrained to understanding the structure of the Earth (see Volume 1) and its evolution (see Volume 9) but also will play a vital role in our understanding of the dynamics and evolution of other planets in our solar system (see Volume 10 and Oganov et al., 2005). As a discipline, mineral physics as such has only been recognized for some 30 years or so, but in fact, it can trace its origins back to the very foundations of solid Earth geophysics itself. Thus, for example, the work of Oldham (1906) and Gutenberg (1913), which defined the seismological characteristics of the core, led to the inference on the basis of materials physics that the outer core is liquid because of its inability to support the promulgation of shear waves. A landmark paper in the history of the application of mineral physics to the understanding of the solid Earth is the Density of the Earth by Williamson and Adams (1923). Here, the elastic constants of various rock types were used to interpret the density profile as a function of depth within the Earth that had been inferred from seismic and gravitational data. Their work was marked by taking into account the gravitationally induced compression of material at depth within the Earth, which is described by the Williamson–Adams relation that explicitly links geophysical observables (g(r), the acceleration due to gravity as a function of radius, r, and the longitudinal and shear seismic wave velocities, VP and VS) with mineral properties (KS, the adiabatic bulk modulus, and density, r), via drðr Þ gðr Þ dr ¼ rðr Þ ’ðr Þ where f(r) is the seismic parameter as a function of radius, given by 4 3

’ðr Þ ¼ VP2 ðr Þ  VS2 ðr Þ ¼

KS ðr Þ rðr Þ

Further progress in inferring the nature of the Earth’s deep interior rested upon experimental determination of the elastic properties of rocks and minerals as a function of pressure and temperature. Notably, this work was pioneered over several decades by Bridgman (1931). In parallel with experimental studies, however, a greater understanding of the theory behind the effect of pressure on compressibility was made by Murnaghan (1937) and Birch (1938). These insights into

Treatise on Geophysics, Second Edition

the equations of state of materials enabled Birch (1952) (see Figure 1) to write his classic paper entitled Elasticity and the Constitution of the Earth’s Interior, which laid the foundations of our current understanding of the composition and structure of our planet. One notable outcome from the investigation of the effect of pressure and temperature on material properties was the discovery of new high-density polymorphs of crustal minerals. Thus, Coes (1953) synthesized a new high-density polymorph of SiO2 (subsequently named coesite), and Ringwood (1959) reported the synthesis of the spinel-structured Fe2SiO4 (which had previously been predicted by Bernal, 1936). Ringwood and colleagues went on to make a variety of other high-density silicate polymorphs, including the phases that are now thought to make up the transition zone of the mantle, namely, the spinelloids wadsleyite (b-Mg2SiO4) and ringwoodite (g-Mg2SiO4), and the garnet-structured polymorph of MgSiO3 majorite. Further insights into the probable nature of deep Earth minerals came from Stishov and Popova (1961), who synthesized the rutilestructured polymorph of SiO2 (stishovite) that is characterized by having Si in octahedral coordination, and from Takahashi and Bassett (1964), who first made the hexagonal close-packed polymorph of Fe, which is today thought to be the form of Fe to be found in the Earth’s core (but see Chapter 2.06). As high-pressure and high-temperature experimental techniques evolved, still further phases were discovered, the most important of which was the perovskite-structured polymorph of MgSiO3 (Liu, 1975). It was thought for some time that this discovery and the subsequent work on the details of the high-pressure phase diagrams of silicate minerals had enabled a robust mineralogical model for the mantle to be established. More recently, this view, however, has had to be revised, after the discovery of a ‘postperovskite’ phase (Murakami et al., 2004; Oganov and Ono, 2004; Tsuchiya et al., 2004), which may be stable in the deepest part of the lower mantle (Chapter 2.05). Notwithstanding, however, the possibility of further new discoveries, the mineralogy, and composition of the mantle and the core are now relatively well defined. The current view of the mineralogy of the mantle is summarized in Figure 2, while as suggested by Birch (1952), the core is considered to be composed of iron (with minor amounts of nickel) alloyed with light elements (probably O, S, and/or Si). The solid inner core is crystallizing from the outer core and so contains less light elements. The current status of our understanding of the nature of the deep Earth is reviewed in detail in Chapters 2.03–2.05. Chapter 2.02 provides a general overview of the structure of the mantle. The nature of the lower mantle is still relatively controversial, since generating lower mantle pressures (25– 130 GPa) and temperatures (2000–3000 K) is still experimentally challenging, and mineral physics data and phase relations for the minerals thought to be found here are less robust. Furthermore, the discovery of the postperovskite phase

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Mineral Physics: An Introduction and Overview

has added even greater uncertainty to the nature of the D" zone and the core–mantle boundary. The problems of the lower mantle and the core–mantle boundary are therefore reviewed in Chapter 2.03. Although the major element chemistry of the mantle is quite well studied, it is probably fair to say that the understanding of the trace element chemistry and the role of volatiles in the deep mantle is still in its infancy. This aspect of mantle chemistry, however, is vital if we are fully to understand the processes involved in planetary formation, core segregation, and subsequent evolution of the Earth (see Volumes 9 and 10). Chapter 2.04 provides a review of our understanding of this aspect of the mantle, while the considerable progress in our understanding of the nature and evolution of the core is provided in Chapter 2.05. As indicated earlier, our understanding of the lower mantle and core is limited to some extent by our inability to easily reproduce the high-pressure and high-temperature conditions in planetary interiors. To obtain greater insight, theory and experiment must be used together, and Chapters 2.08 and 2.15 present reviews of the theory underlying high-pressure, high-temperature physics, and the major experimental methods that are being developed to probe this parameter space. Chapter 2.08 outlines the thermodynamic basis behind high-pressure and high-temperature behavior and expands in greater detail on equations of state and the way in which the density and elastic properties of materials respond to changes in pressure and temperature. The macroscopic behavior of minerals depends upon the microscopic or atomistic interactions within the mineral structure. Thus, for example, free energy (and eventually phase stability) depends in part upon entropy, which in turn is dominated (for silicates at least) by lattice vibrations. Hence, in Chapter 2.09, a detailed analysis of lattice vibrations and spectroscopy of mantle minerals is

Figure 1 Francis Birch (1903–92), Royal Astronomical Society medalist 1960; Bowie medalist 1960. Courtesy AIP Emilio Segre` Visual Archives.

Upper mantle

TZ

14

Lower mantle Pressure (GPa)

24

Core

D⬙ layer CMB 125 136

70

Ca-perovskite (cubic or tetragonal) Cpx+Opx Mineral proportions

CalrO3-type phase

Garnet

Fe- and AI-bearing Mg-perovskite

Liquid Fe

Ringwoodite Wadsleyite

Olivine

Ferropericlase 410

(High spin) (Low spin)

660

2000

2700 2900

Depth (km) Figure 2 Phase relations of pyrolitic mantle composition as a function of depth. Reproduced from Ono S and Oganov AR (2005) In situ observations of phase transition between perovskite and CaIrO3-type phase in MgSiO3 and pyrolitic mantle composition. Earth and Planetary Science Letters 236, 914–932. Courtesy AIP Emilio Segre` Visual Archives.

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presented. For the past 20 years, advances in computing power have enabled computational mineral physics to make a contribution to our understanding of the thermodynamic, thermoelastic, and dynamical properties of high-pressure minerals. Initially, the results of simulations based on interatomic potentials provided semiquantitative insights into, for example, the lattice vibrations and the thermodynamics of mantle phases (e.g., Price et al., 1987; Wall and Price, 1988). But more recently, quantum mechanical simulations of mantle and core phases have been able to achieve a precision and accuracy comparable with that achievable experimentally, and as such, ab initio modeling must now be seen as a legitimate complement to experimental study. Therefore, in this volume, the theory and results from ab initio studies of some deep Earth phases are reviewed in Chapter 2.15. Despite the power and insight provided by theory, mineral physics is dependent upon quantitative high-pressure and hightemperature experimental results. Such work was pioneered by Williamson, Adams (Figure 3), and Bridgman and then was taken up by others such as Ringwood, Bassett, Liu, and many groups in Japan (see, e.g., Akimoto, 1987 and Figure 4), but in the past 30 years, huge advances have been made and today, for

example, laser-heated diamond anvil cells can be used to access temperatures and pressures up to 6000 K and 250 GPa. Such experiments, however, can only be carried out on very small sample volumes and for very short periods of time. Multianvil experiments can be used to study much larger volumes of material and are stable over a longer time interval. These techniques are, therefore, complementary and are both developing rapidly. Chapter 2.10 provides a review of multianvil cell methods, while Chapter 2.11 gives an analysis of diamond anvil cell techniques. A third technique for producing high pressures and temperatures is via shock compression, reviewed in Chapter 2.16. In this approach, a high-velocity impact is produced by firing a projectile at a mineral target. Very high-pressure and shock-produced heating can be obtained, but only for a few 100 ns; however, this is sufficient in many applications to enable the measurement of the pressure, density, and energy of the shocked state and in certain cases to interrogate the atomic structure and bonding of the material. Achieving the high pressures and temperatures that occur in the deep Earth is, however, just the beginning of the challenge that faces experimental mineral physicists, since it is also necessary to measure a variety of physical properties under these conditions. Therefore, in Chapters 2.12–2.14, the specific techniques for measuring elastic and acoustic properties, electronic and magnetic properties, and rheological properties are described in greater detail.

Figure 3 Leason Heberling Adams (1887–1969), American Geophysical Union (AGU) president 1944–47, Bowie medalist 1950. Courtesy AIP Emilio Segre` Visual Archives.

Figure 4 Syun-iti Akimoto (1925–2004), Royal Astronomical Society medalist 1983, Bowie medalist 1983. Courtesy AIP Emilio Segre` Visual Archives.

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Mineral Physics: An Introduction and Overview

One of the long-term goals of mineral physics research is to enable a full interpretation of seismic tomographic data (see Volume 1) and to provide a three-dimensional description of the mineralogy, composition, and thermal structure of the Earth’s deep interior (Stixrude and Lithgow-Bertelloni, 2012). To this end, we need not only full descriptions of the seismic properties of rocks and minerals, as a function of composition, pressure, and temperature (see Chapter 2.02), but also an understanding of the nature and origin of anisotropy in the Earth (see Chapter 2.20) and the significance and reasons for seismic wave attenuation (see Chapter 2.17). In addition to being able to invert seismic data to provide an instantaneous picture of the Earth’s interior, we desire to be able to describe the dynamic evolution of our planet (see Volumes 7 and 8). As such, we need to be able to constrain, for example, geodynamical models of mantle convection, with the appropriate rheological descriptions of mantle phases (see Chapter 2.14), and self-consistent descriptions of heat flux and planetary thermal structure. Key to the latter is our understanding of thermal conductivity at high pressures and temperatures, which is an area where theory and experiment are still evolving and much progress is still required (see Chapter 2.22). Similarly, our ability to describe the dynamics of core convection, and hence the geodynamo, is critically dependent on our understanding of the physical properties of liquid and solid iron under core conditions (see Chapters 2.06, 2.13, and 2.19). One particular problem in our understanding of the Earth is the nature of the core–mantle boundary (Lay et al., 2008). It has been variously suggested, for example, that it is a ‘grave yard’ for subducted slabs, is a reaction zone with the core, is associated with a postperovskite phase change, is the location of pods of partially molten material, is enriched in iron, and is the source of deep mantle plumes (see Volume 7). To establish the importance of some of these hypotheses requires not only high-quality seismic data but also tight constraints on the thermal structure of the core and the high-pressure melting behavior of mantle and core material (see Chapter 2.22). The melting of mantle material also obviously plays a vital role in volcanism and planetary evolution (Stixrude et al., 2009). The migration of melts and their eruption or injection into the crust is central to our understanding of the dynamics of the upper mantle. The properties of melts are discussed in Chapter 2.19. Another long-standing problem in geophysics is the energetics of the core and the driving force behind the geodynamo (see Volume 8). To be able to model this process, accurate descriptions of the melting of iron and the chemical compositions of the inner and outer core are essential (e.g., Nimmo et al., 2004). The possible presence of radioactive elements in the core (such as 40K) would be highly significant as such internal sources of heat would greatly influence the cooling rate of the core and hence the age and rate of growth of the inner core; but it is still an open question. The stability of the geodynamo may also be affected by thermal and electrical coupling with the mantle; hence, we need to fully understand the electrical properties of mantle phases (see Chapter 2.25). Finally, for example, insights into the past nature of the geodynamo, as its paleointensity, can only be obtained from paleomagnetic data (see Volume 5), which requires a detailed understanding of rock minerals and magnetism (see Chapter 2.24).

In the following chapters in this volume, the great progress that has been made in our understanding of the physics and chemistry of minerals is clearly laid out. However, each author also highlights a number of issues that are still outstanding or that need further work to resolve current contradictions. The resolution of some of the problems outlined earlier and in the subsequent chapters will depend on more precise or higherresolution geophysical measurements (e.g., the exact density contrast between the inner and outer core), while others will be solved as a result of new experimental or computational techniques. The combination, for example, of intense synchrotron radiation and neutron sources with both diamond anvil and multianvil cell devices promises to yield much more information on high-pressure seismic (or equivalently elastic) properties of deep Earth phases. In the foreseeable future, developments in anvil design will see large-volume devices that can be used to determine phase equilibriums to 100 GPa or to study highpressure rheology to 30 GPa and beyond. But more predictably, the continued development of increasingly powerful computers will see the role of computational mineral physics grow still further, as the study of more complex problems (like rheology and thermal transport) becomes routine. In addition, the use of more sophisticated ab initio methods (like quantum Monte Carlo techniques) will become possible, and accurate studies of the band structure and electrical properties of iron bearing silicates will be performed. Finally, the pressures of the Earth’s interior (up to 360 GPa) do not represent the limit of interest for mineral physicists. Already extrasolar system, giant, Earth-like planets are being considered, and understanding their internal structure will open up even greater challenges as discussed in Chapter 2.07. In conclusion, therefore, this volume contains a comprehensive review of our current state of understanding of mineral physics, but without doubt, there is still much that is unknown, but the prospect for further progress is excellent, and it is certain that in the next decades, many issues, which are still controversial today, will have been resolved.

References Ahrens TJ (ed.) (1995) Mineral Physics and Crystallography: A Handbook of Physical Constants. Washington, DC: American Geophysical Union. Akimoto S (1987) High-pressure research in geophysics: Past, present, and future. In: Manghnani MH and Syono Y (eds.) High-Pressure Research in Mineral Physics, pp. 1–13. Washington, DC: American Geophysical Union. Bernal JD (1936) Discussion. The Observatory 59: 268. Birch F (1938) The effect of pressure upon the elastic parameters of isotropic solids, according to Murnaghan’s theory of finite strain. Journal of Applied Physics 9: 279–288. Birch F (1952) Elasticity and constitution of the earth’s interior. Journal of Geophysical Research 57: 227–286. Bridgman PW (1931) The Physics of High Pressure. London: G. Bell and Sons. Coes L (1953) A new dense crystalline silica. Science 118: 131–132. Gutenberg B (1913) On the constitution of the inner earth deduced from earthquake observations. Physikalische Zeitschrift 14: 1217–1218. Hemley RJ (ed.) (1998) Ultra-High Pressure Mineralogy: Physics and Chemistry of the Earths Deep Interior. Washington, DC: Mineralogical Society of America. Kieffer SW and Navrotsky A (eds.) (1985) Microscopic to Macroscopic: Atomic Environments to Mineral Thermodynamics. Chelsea, MI: Mineralogical Society of America. Lay T, Hernlund J, and Buffett BA (2008) Core–mantle boundary heat flow. Nature Geoscience 1: 25–32. Liu LG (1975) Postoxide phases of olivine and pyroxene and mineralogy of mantle. Nature 258: 510–512.

Mineral Physics: An Introduction and Overview

Murakami M, Hirose K, Kawamura K, Sata N, and Ohishi Y (2004) Post-perovskite phase transition in MgSiO3. Science 304: 855–858. Murnaghan FD (1937) Finite deformations of an elastic solid. American Journal of Mathematics 59: 235–260. Nimmo F, Price GD, Brodholt J, and Gubbins D (2004) The influence of potassium on core and geodynamo evolution. Geophysical Journal International 156: 363–376. Oganov AR and Ono S (2004) Theoretical and experimental evidence for a postperovskite phase of MgSiO3 in Earth’s D” layer. Nature 430: 445–448. Oganov AR, Price GD, and Scandolo S (2005) Ab initio theory of planetary materials. Zeitschrift fu¨r Kristallographie 220: 531–548. Oldham RD (1906) The constitution of the Earth as revealed by earthquakes. Quarterly Journal of the Geological Society 62: 456–475. Ono S and Oganov AR (2005) In situ observations of phase transition between perovskite and CaIrO3-type phase in MgSiO3 and pyrolitic mantle composition. Earth and Planetary Science Letters 236: 914–932. Poirier JP (2000) Introduction to the Physics of the Earth’s Interior, 2nd edn., 312 pp. Cambridge: Cambridge University Press. Price GD, Parker SC, and Leslie M (1987) The lattice-dynamics and thermodynamics of the Mg2SiO4 polymorphs. Physics and Chemistry of Minerals 15: 181–190.

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Ringwood AE (1959) The olivine-spinel inversion in fayalite. American Mineralogist 44: 659–661. Stishov SM and Popova SV (1961) A new dense modification of silica. Geokhimiya 10: 837–839. Stixrude L, de Koker N, Sun N, Mookherjee M, and Karki BB (2009) Thermodynamics of silicate liquids in the deep Earth. Earth and Planetary Science Letters 278: 226–232. Stixrude L and Lithgow-Bertelloni C (2012) Geophysics of chemical heterogeneity in the mantle. Annual Review of Earth and Planetary Sciences 40: 569–595. Takahashi T and Bassett WA (1964) High-pressure polymorph of iron. Science 145: 483–486. Tsuchiya T, Tsuchiya J, Umemoto K, and Wentzcovitch RA (2004) Phase transition in MgSiO3 perovskite in the earth’s lower mantle. Earth and Planetary Science Letters 224: 241–248. Wall A and Price GD (1988) Computer simulation of the structure, lattice dynamics, and thermodynamic properties of ilmenite-type MgSiO3. American Mineralogist 73: 224–231. Williamson ED and Adams LH (1923) Density distribution in the Earth. Journal of the Washington Academy of Sciences 13: 413–428.

2.02 Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle P Fumagalli, Universita degli Studi di Milano, Milano, Italy S Klemme, Westfa¨lische Wilhelms Universita¨t Mu¨nster, Mu¨nster, Germany ã 2015 Elsevier B.V. All rights reserved.

2.02.1 Introduction 2.02.2 Chemical and Mineralogical Composition of the Upper Mantle 2.02.3 Experimental Petrology and the Mineralogical Composition of the Earth’s Upper Mantle 2.02.3.1 Upper Mantle Bulk Compositions Used in Experiments 2.02.3.2 Experimental Methods: High-Pressure High-Temperature Apparatus 2.02.4 Phase Transitions in Dry Earth’s Upper Mantle 2.02.4.1 The Plagioclase–Spinel Transition 2.02.4.2 The Spinel–Garnet Transition 2.02.4.2.1 Phase equilibrium calculations: implications for the Hales discontinuity 2.02.4.3 Garnet–Majorite Reactions 2.02.5 Mineralogy and Transitions in the Upper Mantle at Subduction Zones 2.02.5.1 The Role of Hydrous Phases 2.02.5.2 The Basalt to Eclogite Transition 2.02.5.3 Phase Relations in Hydrous Peridotite Systems 2.02.5.3.1 Talc and amphibole 2.02.5.3.2 Serpentine and chlorite phase assemblages 2.02.5.3.3 Post antigorite–chlorite hydrous phases 2.02.5.4 Fluid/Rock Interactions and the Role of Potassic Hydrous Phases 2.02.5.5 Implications to the Geodynamics of Subduction Zones 2.02.6 Conclusions Acknowledgment References

2.02.1

Introduction

The Earth’s upper mantle extends from the base of the crust down to about 410 km where a discontinuity marks the boundary to the transition zone. Knowledge of the mineralogical composition of the upper mantle is essential to derive the density structure of the upper mantle for the interpretation of geophysical data. The knowledge of the composition and the mineralogy of the upper mantle, and therefore its physical and chemical properties, stem from both indirect investigations (e.g., experiments at P and T conditions relevant to the upper mantle and theoretical calculations) and direct petrologic and geochemical investigations of tectonically exposed mantle rocks, abyssal peridotites, and mantle xenoliths. Compared to the Earth’s crust, which consists of hundreds of different minerals and quite a few different rock types (Rudnick and Gao, 2003), the chemical and mineralogical composition of the Earth’s mantle is rather straightforward. We know that most of the upper mantle consists of peridotite, a rock type that is composed of four main minerals only (Figure 1): olivine (Mg,Fe)2SiO4, orthopyroxene (Mg,Fe)2Si2O6, clinopyroxene Ca(Mg,Fe)Si2O6, and mostly an aluminous phase (either plagioclase, spinel, or garnet as a function of pressure). In this chapter, we focus on the chemical and mineralogical composition of the upper mantle, with particular emphasis on the effect of variable bulk compositions on subsolidus phase

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relations. We will first briefly discuss the chemical composition of the mantle, taking into account information mainly from natural mantle rocks (i.e., xenoliths, ophiolites, orogenic peridotites, and abyssal peridotites) and experimental simulations. We will then discuss the mineralogical composition of the upper mantle in the context of its chemical composition, with a special focus on subsolidus phase relations and phase transformations. Here, most of the data originate from highpressure high-temperature experiments, with some additional information from natural mantle rocks and thermodynamic modeling. The concluding sections deal with the mineralogical composition of the upper mantle in subduction zones, with particular emphasis on the role of hydrous phases in the subsubduction zone mantle as they control the transport and release of water at depth. Phase relations in metasomatized lherzolite will also be addressed, focusing on the role of potassic phases stable at mantle pressures and temperatures.

2.02.2 Chemical and Mineralogical Composition of the Upper Mantle The chemical and mineralogical composition of the upper mantle may directly be studied using petrologic and field-based observations on naturally occurring mantle rocks, such as

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Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

Olivine

Plag Lhz

Dunite 90

Ha

rzb

Lherzolite

Gnt Lhz

Deeper facies

40 Pyroxenite

10 Websterite

(a)

Spl+Gar Lhz

Peridotites

Olivine websterite

Orthopyroxene

Spl Lhz

Ol

ite hrl We

urg ite

Orogenic peridotites Ophiolitic peridotites Abyssal peridotites

Plag+Spl Lhz

Clinopyroxene

Opx

Cpx Al phase (b)

Figure 1 (a) Nomenclature of ultramafic rocks as a function of modal abundances of olivine, orthopyroxene, and clinopyroxene. Modal compositions of orogenic, ophiolitic, and abyssal mantle peridotites are from review data in Bodinier and Godard (2003) (Left modified from Bodinier J-L and Godard M (2003) Orogenic, Ophiolitic, and Abyssal Peridotites. In Carlson RW (ed.) Treatise on Geochemistry, The Mantle and the Core, pp. 103–170. Amsterdam: Elsevier.); (b) schematic modal mineralogy of different mantle rocks. Pressure increases from left to right.

tectonically exhumed mantle slices (orogenic peridotites, ophiolites, and abyssal peridotites) and lithospheric mantle xenoliths incorporated in volcanic rocks erupted on the Earth’s surface. Such mantle xenoliths are common in certain alkali-rich mafic magmas and kimberlites. Field evidence suggests that the upper mantle is peridotitic in composition, although significant heterogeneities are clearly recognized. From mantle xenoliths, we know that at least the lithospheric mantle underneath continents consists of a variety of peridotite rocks, ranging from dunite to lherzolite, and some eclogite and pyroxenite. The mineralogical composition of these peridotite rocks is dominated by olivine, with much less orthopyroxene, and minor clinopyroxene, and an additional aluminous phase such as plagioclase, spinel, or garnet. Figure 1(a) shows the nomenclature of peridotite based on its mineralogical composition (Streckeisen, 1974). The observed variability in mantle rocks may be described in terms of modal abundances of olivine, orthopyroxene, and clinopyroxene (Figure 1(a)) with compositions ranging from fertile Ca- and Al-rich lherzolite to ultradepleted Mg-rich and Ca- and Al-poor dunite (e.g., Carlson et al., 2005). Among these mantle rocks, lherzolites dominate in orogenic peridotites massifs, while harzburgites and dunites predominate in ophiolites and abyssal peridotites. Most mantle xenoliths are reported in volcanic rocks found on continents and xenoliths from the oceanic mantle are rare. Only few samples have been reported from the Azores, Hawaii, and the Canary Islands (e.g., Coltorti et al., 2010; Merle et al., 2012; Yamamoto et al., 2009), which probably represent the thicker lithosphere beneath ocean islands. Alkali basalt usually contains xenoliths ranging from spinel lherzolite, spinel harzburgite, to spinel-bearing dunite. Garnet-bearing xenoliths are only rarely sampled by basalts (e.g., Bjerg et al., 2009; Goncharov and Ionov, 2012; Harris et al., 2010). Xenoliths from kimberlites, which sample the lithosphere beneath much thicker cratonic lithosphere, range from fertile garnet-bearing lherzolites to depleted harzburgites and dunites, and spinel-bearing peridotites as well. As kimberlites and lamproites sometimes contain diamonds, the

study of diamond inclusions frequently shows that olivine, garnet, spinel, pyroxene, and, sometimes, other less common phases such as sulfides or exotic oxides occur as inclusions in diamond (Bulanova et al., 2004; Haggerty et al., 1989; Nixon and Condliffe, 1989; Stachel and Harris, 2008). We will not attempt to review all the available geochemical data that explain the chemical variability of bulk upper mantle, but the interested reader is referred to the excellent review of Bodinier and Godard (2003) on orogenic and abyssal mantle rock geochemistry and to Pearson et al. (2003) on mantle xenoliths. We will instead briefly refer to the main processes that are known to cause heterogeneities in the upper mantle. There are two main processes that are known to cause heterogeneity in mantle rocks. Firstly, melt extraction from a peridotite mantle rock explains a large proportion of depleted or enriched bulk compositions recognized in tectonically emplaced peridotites as well as mantle xenoliths (e.g., Walter et al., 2004). Secondly, the interaction, at different scales and depths, of ascending melts with adjacent mantle rocks is recognized to cause further chemical variation of mantle rocks (e.g., Kelemen et al., 1997). From experimental information, we know that partial melting of lherzolite (some 10–30%) leads to ordinary basaltic melts, which, due to a much lower density than the mantle rocks, rise from the mantle into the crust. During partial melting, incompatible elements (such as Na, K, Ca, and Al) preferentially partition into the melt and compatible elements (such as Mg) preferentially stay behind in the residual mantle. Thus, melting of the mantle rocks causes chemical differentiation, which depletes the residual mantle rocks in incompatible elements. Lherzolites therefore represent a fertile bulk composition able to produce basaltic magmas by partial melting, while harzburgites or dunites represent the most depleted mantle bulk composition with poor efficiency to produce mafic partial melts. The melting process of the peridotite rock is complex (Ghiorso and Sack, 1995; Ghiorso et al., 2002; Presnall et al., 2002; Walter, 1998) and involves all mantle minerals albeit clinopyroxene and also garnet are most affected by melting.

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

This implies that the small amount of clinopyroxene present in lherzolites will completely disappear during higher degrees of partial melting. During even higher degrees of partial melting (or further reaction of mantle rock with melts), other minerals such as orthopyroxene are also significantly affected by melting, leaving behind an even more depleted mantle peridotite such as harzburgite or even dunite. From a geochemical point of view, variations of bulk composition within the mantle are conveniently represented by covariance diagrams that use major elements to illustrate magmatic processes. Al2O3 represents a good chemical marker of depletion, as it is not strongly affected by alteration or serpentinization processes and, when compared with MgO or modal olivine, reveals a large variability both in tectonically exhumed peridotites and in xenoliths (Figure 2). Most natural mantle rocks that plot on such element covariant trends also show similar variations in the XMg (XMg ¼ Mg/(Mg þ Fe)), and the resulting mineral modal proportions are consistent with variable degree of melt extraction during partial melting of asthenospheric mantle (Frey et al., 1985; Jagoutz et al., 1979; McDonough and Frey, 1989; McDonough and Sun, 1995; Ringwood, 1975). Evidence for a second source of mantle heterogeneity, caused by reactive porous flow melt percolation and melt– rock interaction, has been observed in both orogenic and abyssal peridotites. Marked FeO enrichment and SiO2 depletion at increasing MgO, and contrasting bulk versus mineral chemistry (e.g., a constant bulk XMg combined with an increase of modal olivine with constant forsterite content), reported both in natural samples (Niu et al., 1997; Rampone et al., 2004) and in experimental charges (Lambart et al., 2009) rule out that mantle differentiation occurs only by partial melting and clearly supports the melt–rock reaction processes. Summarizing, it is now widely accepted that both partial melting processes and melt–rock interaction processes operate

9

at different levels within the mantle. Depending on the melt composition, the depth at which the interaction occurs, and the thermal contrast between melts and solid rocks, different lithologies develop, which accounts for a large range of the observed mantle compositions. Dissolution of orthopyroxene and precipitation of olivine by porous flow produce ‘replacive dunites’ and ‘reactive harzburgites,’ with bulk chemical and modal depletion and peculiar structural–textural features documented in an increasing number of studies of both ‘on land’ peridotites and abyssal mantle rocks (Godard et al., 2000; Kelemen, 1990; Kelemen et al., 1992, 1995a,b, 1997; Niu et al., 1997; Quick, 1981; Rampone et al., 2004; Seyler et al., 2007; Van der Wal and Bodinier, 1996). On the other hand, at shallower levels, melt infiltration and impregnation lead to the formation of refertilized lithologies by interstitial recrystallization of percolating melts. Numerous plagioclase-rich peridotites have been documented in present-day oceanic settings, both in slow-spreading (Cannat et al., 1992; Dick, 1989; Seyler and Bonatti, 1997; Tartarotti et al., 2002) and in fast-spreading ridge/transform systems (Constantin et al., 1995; Hebert et al., 1983; Hekinian et al., 1993), as well as in ophiolites (Boudier and Nicolas, 1977; Dijkstra et al., 2003; Kaczmarek and Mu¨ntener, 2010; Nicolas, 1986; Piccardo et al., 2007; Rampone et al., 1997, 2008). These rocks have modified modal distributions and can host a greater amount of plagioclase than usually expected by metamorphic reequilibration within the plagioclase facies during tectonic exhumation of mantle rocks. Such a modal diversity can contribute, if seismically detectable, to different geophysical signals and needs to be taken into account for processes that occur in shallower mantle settings, for example, in extensional regimes. Heterogeneities have been also recognized in the deeper convective mantle. The considerable body of new trace element and radiogenic isotopic data on basalts and related residual mantle reservoirs have revealed that conventional melt

5 Orogenic and ophiolitic peridotites Abyssal peridotites - Niu, 2004

Al2O3 (wt.%)

4

Xenoliths - Pearson et al., 2003

PM - McDonough and Sun, 1995

3

HZ86 - Harte and Zindler, 1986 BRIAN - Konzett and Ulmer, 1999 HPY - Green et al., 1979

2

MPY - Green et al., 1979 FLZ - Borghini et al., 2011 KLB1 - Takahashi, 1986

1

TQ - Jaques and Green, 1979 LZ - Fumagalli and Poli, 2005 DLZ - Borghini et al., 2011

0 37

39

41 43 MgO (wt.%)

45

47

Figure 2 Al2O3 (wt.%) versus MgO (wt.%) diagram showing the variety of mantle compositions in orogenic and ophiolitic peridotites gray circles; data are from Bodinier et al. (1988, 2008), Fabrie`s et al. (1989, 1998), Lenoir et al. (2001), Le Roux et al. (2007), Rampone et al. (1995, 1996, 2004, 2005), Sinigoi et al.,(1980), Van der Wal and Bodinier (1996), and Voshage et al. (1988), abyssal peridotites (gray triangles; data are from Niu, 1997), and mantle xenoliths (gray shaded area; data are from Pearson et al., 2003) compared with various bulk compositions used in experiments (colored symbols).

10

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

extraction processes cannot explain all the observed geochemical signatures (Rampone and Hofmann, 2012; Salters et al., 2011; Stracke et al., 2005; Willbold and Stracke, 2010; Zindler et al., 1984). The latter require chemical differences within the convective mantle, that is, the source of primary basaltic magmas, which implies significant heterogeneities also in the convecting mantle. Over the last decades, many studies addressed processes that may cause heterogeneities in the upper mantle, using both field-based and experimental investigations. Three main causes have been identified in the review paper by Rampone and Hofmann (2012): (i) old depletion events not completely rehomogenized, (ii) the contribution of pyroxenite component in the mantle source (Lambart et al., 2013), and (iii) metasomatism and melt–rock interactions by deep intrusions. Although it is beyond the scope of this review to go into much detail about the rather controversial issues, the role of pyroxenites and metasomatic processes seems worth mentioning. The role of pyroxenites as an additional source in the upper mantle to generate the variable range of midocean ridge basalts (MORBs) and ocean island basalt (OIB) has been extensively investigated over the past two decades both experimentally (e.g., Hirschmann et al., 2003; Klemme et al., 2002; Lambart et al., 2013; Mallik and Dasgupta, 2012; Pertermann and Hirschmann, 2003; Sobolev et al., 2007; Yaxley and Green, 1998) and by geochemical modeling (Kogiso et al., 2004; Stracke and Bourdon, 2009; Stracke et al., 1999). This scientific interest mainly stems from the ubiquity of pyroxenites and mafic eclogites in both mantle xenoliths and ultramafic massifs and also from the chemical variability of oceanic basalts, which is not easily explained by partial melting of peridotite composition alone. Moreover, eclogites are frequently found as xenoliths especially in cratonic environments and make up some 2% on average (Schulze, 1989). In noncratonic xenoliths, pyroxenites and garnet pyroxenites are more common and eclogites are quite rare. Cratonic eclogites are distinguishable from crustal eclogites by the occurrence of diamond, the Na content in garnet, and the K content in clinopyroxenes, all features that are in agreement with a highpressure origin (Pearson et al., 2003). A different origin has been proposed for the pyroxenites (Bodinier and Godard, 2003; Downes, 2007). It seems clear that some of them are remnants of old recycled oceanic crust (Alle`gre and Turcotte, 1986; Blichert-Toft et al., 1999; Morishita et al., 2001; Morishita et al., 2003, 2004; Pearson and Nowell, 2004; Pearson et al., 1993) that was not completely remixed into the mantle, resulting in a veined mantle or ‘marble cake-like’ mantle. These pyroxenite-bearing parts of the mantle are known to melt at lower temperature than peridotites (Klemme et al., 2002; Pertermann and Hirschmann, 2003; Yaxley and Green, 1998). Other pyroxenites are clearly related to melt–rock interactions when the host peridotites were already incorporated at lithospheric environments (Bodinier and Godard, 2003; Bodinier et al., 1987a,b, 1988, 2008; Garrido and Bodinier, 1999; Takazawa et al., 1996). Subsequent interactions among pyroxenites, partial melts, and their host peridotites can account for the genesis of a second generation of pyroxenites, which cause further mantle heterogeneity on a different scale and with a larger compositional range (Lambart et al., 2013). At convergent plate boundaries, for example, in subduction zones, the recycling of the oceanic crust causes a wide range of

metasomatic reactions. Interactions of different melts or fluids derived from the subducted crust with the overlying mantle rocks create a wide range of different rocks, which commonly contain metasomatic minerals. Phlogopite–spinel peridotites (Nixon, 1987), phlogopite–garnet peridotites, phlogopite– K-richterite peridotite xenoliths, and ‘orogenic’ phlogopite peridotites of ultrahigh-pressure terrains (Bardane peridotite, Norway: van Roermund et al., 2002; Sulu garnet peridotite, China: Zhang et al., 2007; Ulten peridotite: Rampone and Morten, 2001) document efficient mass transfer from the slab toward the mantle wedge and document global chemical recycling processes in subduction zones. In summary, recent studies have clearly shown that the mineralogical and chemical compositions of the Earth’s mantle are, at least in parts, heterogeneous. However, the scale and the residence time of heterogeneities within a convecting mantle are important factors controlling the petrologic and geochemical evolution of the mantle (Xu et al., 2008). The observed heterogeneities range from cm scale to regional scale, but it is currently not fully understood (i) if the observed heterogeneities are detectable with geophysical methods and (ii) how efficient the dynamic mantle is to rehomogenize such heterogeneities. Both issues need further investigations. In this respect, a pyrolite model for the Earth’s mantle, which assumes a homogeneous mantle, represents one end-member of a range of bulk compositions (Stixrude and Lithgow-Bertelloni, 2012). In the next paragraphs, we aim to present the effects of variable chemical compositions on the mineralogical composition of the mantle. This will help investigate changes in modal mineral abundances and physical properties with depth. We will focus on experimental methods that are crucial for such endeavors, starting from chemical compositions, which are often chosen as starting material, followed by a brief overview of experimental techniques used and experimental results on important mineral phase transitions and mineral reactions observed in the upper mantle.

2.02.3 Experimental Petrology and the Mineralogical Composition of the Earth’s Upper Mantle While it is obvious that the mineralogical composition of the mantle must be related to its chemical composition, one must consider the fact that many mantle minerals are complex solid solutions and can, therefore, incorporate several elements and display a more or less wide range of chemical compositions. This implies that small differences in chemical composition of the mantle may not stabilize additional mineral phases but can be accounted for by the rather flexible mineral compositions. Experimental petrology and geochemistry is fundamentally important in constraining the behavior of Earth materials as a function of pressure, temperature, and bulk composition, providing further constraints on the mineralogical composition of the upper mantle. The main tasks are not only related to the definition of the stability fields of upper mantle phases but also, perhaps more interestingly, related to the way in which mineral assemblages change as a result of changes in several thermodynamic variables. Changes of pressure and temperature will eventually lead to changes not only in crystallographic structure of a mineral or a phase transition, but, in complex

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

compositions, pressure and temperature variations often result in changing modal abundances of minerals and chemical reactions among minerals. In this context, petrologists distinguish two main kinds of transformations: discontinuous and continuous reactions. Discontinuous reactions imply an abrupt disappearance or appearance of a new phase and are usually represented by comparing chemographies at different pressure and temperature conditions. In contrast, continuous reactions involve continuous changes in phase compositions as a function of pressure or temperature. Continuous reactions usually occur in systems with a large number of chemical components with often extensive solid solutions. This kind of reactions is usually best described by means of divariant (or multivariant) loops in pressure–composition or temperature–composition diagrams. It should be noted that most experiments relevant to the mantle were undertaken in simplified chemical compositions, which only approximate the complex, that is, multicomponent, Earth’s mantle. Following Holloway and Wood (1988), there are two general types of experiments, namely, studies in chemically simplified compositions and experiments of individual natural rock compositions. Both approaches are valid and useful. Table 1

References SiO2 TiO2 Al2O3 Cr2O3 FeO* MnO MgO CaO Na2O NiO K2O Tot Mg# bulk XCr bulk Na2O/CaO

References SiO2 TiO2 Al2O3 Cr2O3 FeO* MnO MgO CaO Na2O NiO K2O Tot Mg# bulk XCr bulk Na2O/CaO

11

In simple systems, the bulk composition of the mantle (e.g., pyrolite, Table 1) is approximated in terms of chemical composition. While it is at the discretion of the experimentalist to choose a particular composition, often, a system is chosen that is simple but contains most (or better, all) relevant mantle phases. A system that fulfills these requirements and consequently one of the most commonly used systems is the system CaO–MgO–Al2O3–SiO2 (CMAS). While experiments in simple systems may not be directly applicable to complex natural compositions, they are useful for thermodynamic interpretation (i.e., extraction of thermodynamic data) or identification of specific mineral reactions as a function of pressure and temperature. Furthermore, quality control of experiments in simple systems is straightforward with the aid of so-called reversal experiments in which the P–T–X conditions of equilibration among different phases are constrained by approaching them from opposing directions. In this context, ‘reversal’ of an experiment means that the attainment of equilibrium between phases is tested by repeated experiments, which approach equilibrium from different (mainly compositional) sides. Having evaluated the experimental results, thermodynamic data for one or more phases may be extracted from the

Selected bulk compositions used to model mantle compositions in complex systems FLZ

DLZ

PM

LZ

HPY

Borghini et al. (2010) 44.90 0.12 3.79 0.41 7.99 0.00 39.12 3.41 0.26 0.00 0.00 100.00 0.90 0.07 0.08

Borghini et al. (2010) 44.90 0.07 2.38 0.39 8.34 0.00 41.58 2.14 0.20 0.00 0.00 100.00 0.90 0.10 0.09

McDonough and Sun (1995) 45.07 0.17 4.45 0.38 8.08 0.00 37.94 3.55 0.36 0.00 0.00 100.00 0.89 0.05 0.10

Fumagalli and Poli (2005) 45.75 0.00 3.33 0.00 7.03 0.00 40.59 3.11 0.19 0.00 0.00 100.00 0.91 0.00 0.00

Green (1973) 45.21 0.71 3.54 0.43 8.47 0.14 37.51 3.08 0.57 0.20 0.13 100.00 0.89 0.08 0.19

MPY

TQ

KLB-1

HZ86

BRIAN

Green et al. (1979) 44.30 0.17 4.33 0.45 7.48 0.11 39.18 3.35 0.40 0.26 0.00 100.00 0.90 0.06 0.12

Jaques and Green (1979) 44.96 0.08 3.22 0.45 7.66 0.14 40.04 2.99 0.18 0.26 0.02 100.00 0.90 0.09 0.06

Takahashi (1986) 44.49 0.16 3.59 0.31 8.10 0.12 39.23 3.44 0.30 0.25 0.00 100.00 0.90 0.05 0.09

Hart and Zindler (1986) 46.03 0.18 4.06 0.40 7.56 0.10 37.82 3.22 0.33 0.28 0.03 100.00 0.90 0.06 0.10

Konzett and Ulmer (1999) 45.92 0 4.43 0 7.04 0.00 37.74 3.59 0.71 0 0.57 100 0.91 – 0.20

FeO* is total iron; Mg# = Mg/(MgþFe); XCr = Cr/(CrþAl).

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

results. This leads to a comprehensive set of thermodynamic data by which, if correct and complete, one would be able to calculate phase relations in complex mantle compositions. Although such calculations are rather comprehensive in crustal compositions (e.g., Holland and Powell, 1998, 2011), we will show below that the data set is far from complete for mantle compositions. On the other hand, experiments in multicomponent systems are chemically very close to natural rocks, but quality control of such experiments is more difficult. Experiments in complex compositions are often crippled by very small crystal sizes, disequilibrium textures and compositions, and poor(er) reproducibility. Furthermore, due to a large number of components and phases, and high degree of freedom, experiments cannot be reversed as easily as in simple systems. This implies that it is not straightforward to assess the attainment of equilibrium between all phases in complex composition experiments. Nevertheless, experiments in natural (or close to natural) compositions are useful in combination with the information derived from simple systems. In the next paragraphs, we will first summarize the main bulk compositions used in experimental investigations of complex systems, then we will briefly examine the experimental techniques and high-pressure apparatus used, and finally we will examine experimental results on major mineralogical changes in the Earth’s upper mantle. In this context, we will try to show the fundamental differences between experimental results in simple versus complex systems, which are close to natural compositions. Furthermore, as computer-based phase equilibrium calculations relevant to the upper mantle are emerging, we will also present some selected results derived from thermodynamic modeling of phase relations in mantle compositions.

2.02.3.1 Upper Mantle Bulk Compositions Used in Experiments Basalts are direct products of melting processes within the Earth’s mantle. Consequently, their compositions may be used to constrain the chemical composition of the Earth’s mantle. This rationale led to the development of the so-called ‘pyrolite’ mantle model by Ringwood (1975). Pyrolite is a composite term derived from ‘pyr’oxene and ‘oli’vine and represents a peridotite mantle that is olivine and pyroxene-rich, which was calculated from complementary basaltic and depleted peridotite rock compositions (Green and Falloon, 1998). Since then, numerous experiments were conducted in fertile ‘pyrolite’ compositions, which have helped to constrain the origin of basalts (e.g., Clark and Ringwood, 1964; Green and Falloon, 1998; Green and Ringwood, 1967; Irifune, 1994; Ishii et al., 2011; Kesson et al., 1998; Robinson and Wood, 1998; Sanehira et al., 2008). Several other chemical compositions for a fertile mantle have since been proposed, based either on geochemical and cosmochemical constraints (e.g., Palme and O’Neill, 2003) or on compositions of fertile or other mantle xenoliths (e.g., Green and Falloon, 1998; Takahashi, 1986; Takahashi et al., 1993). In addition to the experiments in pyrolite-type compositions, numerous experiments have been conducted in chemical compositions based on relatively fertile mantle xenoliths, such as the Kilbourne Hole lherzolite (KLB-1) (Takahashi, 1986; Takahashi et al.,

1993) or the Tinaquillo lherzolite ( Jaques and Green, 1980; McDade et al., 2003). Starting materials close to natural compositions were taken from natural occurrences of peridotites such as the fertile lherzolite (FLZ) and depleted lherzolite (DLZ) used to investigate the plagioclase–spinel transition (Borghini et al., 2011). The effect of potassium, of relevance for the study of metasomatic reactions in subduction zones, was investigated in K-bearing lherzolites (e.g., Fumagalli et al., 2009; Konzett and Ulmer, 1999). It is worth noting that, when partial melting occurs, even small differences in incompatible element concentration (such as Na or K) of the source drastically affect the melt composition and physical properties. Subsolidus phase relations, however, are only slightly affected by small chemical differences of the bulk. Nonetheless, additional components certainly enable continuous reactions to occur, and multivariant phase assemblages to be taken into account.

2.02.3.2 Experimental Methods: High-Pressure High-Temperature Apparatus To constrain the mineralogical composition of the mantle, one needs to identify the effect of pressure, temperature, and chemical composition on phase relations of the upper mantle. To this effect, experiments at high pressure and high temperature were conducted to simulate mineralogical transformations in the laboratory. These experiments began in the early 1950 and 1960s with the development of reliable high-pressure apparatus such as the piston–cylinder apparatus and the multi-anvil apparatus (Figure 3). While there are numerous high-pressure apparatus available, two kinds of high-pressure apparatus are nowadays commonly employed to simulate the pressure– temperature conditions of the upper mantle in the laboratory. The classical paper by Boyd and England (1960) describes a piston–cylinder apparatus that is capable of routinely generating pressures up to about 4 GPa and temperatures of more than 2000  C. Hydraulic presses drive a carbide piston through 25

Multi-anvil apparatus

Pressure (GPa)

12

4.0

3.0 Piston cylinder apparatus

2.0

Hydrothermal apparatus

1.0

0

500

1000 1500 Temperature (°C)

2000

Figure 3 Pressure–temperature range of the main high-pressure apparatus used in experimental petrology.

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

2.02.4 2.02.4.1

Phase Transitions in Dry Earth’s Upper Mantle The Plagioclase–Spinel Transition

The stability of plagioclase at upper mantle conditions was pioneered in experimental studies (CaO–Al2O3–SiO2: Kushiro and Yoder, 1966; CMAS: Gasparik, 1984; Green and Hibberson, 1970; Herzberg, 1978; Kushiro and Yoder, 1966; MacGregor, 1967; Obata, 1976; O’Hara, 1967) that located the univariant transition in this simple chemical composition between 0.6 and 0.8 GPa, at 900–1200  C (Figure 4). More complex systems were investigated subsequently (Na2O–CMAS: Walter and Presnall, 1994; FeO–CMAS: Gudfinnsson and Presnall, 2000), and although these studies were primarily aimed to locate the solidus temperature of peridotites (e.g., Baker and Stolper, 1994; Baker et al., 1995; Falloon and Green, 1987, 1988; Falloon et al., 1997, 1999; Gudfinnsson and Presnall, 2000; Jaques and Green, 1980; Takahashi, 1986; Walter and Presnall, 1994), the investigators recognized a divariant field, which is characterized by the

1.0

Pressure (GPa)

a large steel-supported carbide cylinder against a top plate to provide a load. Solid-state assemblies are designed to transfer this load onto a sample to generate pressures. Typical sample size is 10–30 mg. Since then, many laboratories have built similar devices that have proven to be reliable, safe to operate, and, compared to other high-pressure apparatus, relatively cost-effective. In Europe alone, there are some 30 laboratories, including our own at Milan and Mu¨nster, which employ piston– cylinder apparatus routinely to study high-pressure phase relations, not only in a geological context but also in materials sciences. The pressure range of the piston–cylinder apparatus is limited to about 4 GPa at temperatures up to 2000  C for routine experimentation. These pressure–temperature conditions correspond to a depth of about 120 km. To investigate deeper parts of the Earth, another apparatus is needed. The high-pressure conditions needed for this kind of work can be generated with a ‘multi-anvil apparatus,’ which is capable of generating pressures of more than 20 GPa at corresponding mantle temperatures. This is more than sufficient to cover the entire range of the upper mantle, which is generally thought to extend to about 400 km depths. Multi-anvil apparatus have been pioneered in the 1950s by H. Tracy Hall who constructed the first tetrahedral apparatus (Hall, 1958). Since then, a number of multi-anvil devices have been constructed and the interested reader is referred to an excellent review paper (Liebermann, 2011). Most multi-anvil experiments of relevance to the upper mantle require pressures of only up to 15 GPa, and the most reliable and safest apparatus in this context is a modified split-sphere apparatus, the so-called ‘Walker-type’ multi-anvil module (Walker et al., 1990). This Walker-type multi-anvil apparatus is relatively straightforward to use, reliable, and safe. In Europe alone, we counted more than ten laboratories including our own, which routinely employ a Walker-type multi-anvil apparatus to study phase relations in the Earth’s upper mantle. So far, several hundred experimental studies have been conducted to constrain the chemical and mineralogical composition of the upper mantle, and the data set is far from complete, particularly in complex, natural compositions relevant to the upper mantle.

13

0.8

Spinel + cpx + opx

Plagioclase + forsterite

0.6

0.4

800

1000 1200 Temperature (°C)

1400

Figure 4 The plagioclase–spinel transition in the system CaO–MgO– Al2O3–SiO2. References are given in the text.

coexistence of plagioclase and spinel and demonstrates the continuous nature of the plagioclase–spinel transition (Green and Falloon, 1998; Green and Hibberson, 1970; Gudfinnsson and Presnall, 2000; Presnall et al., 2002; Walter and Presnall, 1994). More recently, subsolidus experiments in the complex system TiO2-Cr2O3-Na2O-FeO-CMAS quantitatively constrained the effect of different bulk compositions on the location of the reaction and described subsolidus mineral compositional variations as a result of Na and Ca partitioning between plagioclase and clinopyroxene and of Cr, Al partitioning between pyroxenes and spinel (Borghini et al., 2010). In particular, the location of the transition is described in terms of two chemical bulk parameters: the bulk Na/Ca ratio and the bulk XCr (XCr ¼ Cr/Cr þ Al) that describes the degree of depletion of the mantle rock. While higher Na in the bulk composition increases plagioclase stability, consequently shifting the transition toward higher pressure, increasing Cr in the bulk composition decreases plagioclase stability relative to spinel. As a result, bulk compositions with higher Cr spinel/anorthite normative ratios would result in Cr-rich spinels and a plagioclase-out boundary at progressively lower pressures. The available experimental data in complex systems confirm this trend (Figure 5). The experimentally derived data are also confirmed by naturally occurring mantle rocks (Figure 1(b)). Most shallow mantle xenoliths contain both spinel and plagioclase (Sen, 1988; Zipfel and Worner, 1992). Field-based studies on plagioclase peridotites from orogenic massifs (Furusho and Kanagawa, 1999; Newman et al., 1999; Ozawa and Takahashi, 1995) documented a systematic increase of anorthite from core to rim of single plagioclase crystals (referred to as ‘reverse zoning’) and interpreted this as the result of a continuous subsolidus reaction between two pyroxenes and spinel driven by progressive decompression and uplift of the peridotites (Newman et al., 1999; Ozawa and Takahashi, 1995). One of the major applications of such experimental results is related to the fact that they allow estimation of the pressure history that peridotites underwent during their uplift at extensional settings. This allows reconstructions of the exhumation

14

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

history of lithospheric upper mantle as shown recently by Borghini et al. (2011). However, the observed changes in mineral chemistry of all coexisting phases within the plagioclase stability field, and the continuous nature of the transition, additionally suggest that, as a result of mass balance condition, the modal proportions of minerals need to change as well. Borghini et al. (2010) have quantitatively examined the progressive decrease of modal plagioclase with increasing pressure up to the plagioclase-out boundary in fertile and depleted bulk composition. They find that modal plagioclase abundances varied between 8.8 and 4.8 wt.% at 0.3–0.8 GPa in a FLZ composition and between 5 and 3.2 wt.% at about 0.3–0.7 GPa in DLZs. These modal abundances are more than 60% lower than the amounts of plagioclase predicted by simple thermodynamic models that are commonly adopted in modeling phase equilibria of the uppermost lithospheric mantle (e.g., Simon and Podladchikov, 2008; Wood and Yuen, 1983). On the other hand, it should also be noted that the modal plagioclase found in the experiments probably represents an overestimation with respect to natural occurrences, where low-pressure recrystallization is generally confined to discrete microstructural domains between spinel-facies porphyroclastic minerals (Cannat and Seyler, 1995; Fabries et al., 1998; Hoogerduijn Strating et al., 1993; Montanini et al., 2006; Newman et al., 1999; Obata, 1980; Ozawa and Takahashi, 1995; Rampone et al., 1993, 1995, 2005; Takazawa et al., 1996). On the other hand, higher plagioclase 1.2 opx, cpx, ol, spinel

0.8

0.6

2.02.4.2

The transition from spinel peridotite to garnet-bearing peridotite (either FLZ or depleted harzburgite) is one of the most important phase boundaries in the upper mantle. We know from the xenolith information that spinel lherzolite xenoliths are common in alkaline volcanics and there are only a few localities worldwide where garnet-bearing xenoliths are found. Kimberlites, however, contain both spinel peridotite and garnet peridotite xenoliths, occasionally also garnet- and spinelbearing samples (e.g., Canil and O’Neill, 1996; Ganguly and Bhattacharya, 1987; Ionov et al., 1993). The transition from spinel to garnet in the Earth’s upper mantle has been studied experimentally in a variety of simple systems as well as in natural compositions, although more and better data are needed for the latter. We begin with the simplest chemical composition, which contains all relevant mantle phases. This is the system MgO– Al2O3–SiO2 (MAS) and the system CMAS. Both simple systems contain olivine (Mg2SiO4 – forsterite), Al-bearing orthopyroxene, Al-bearing clinopyroxene, spinel (MgAl2O4), and garnet ((Ca,Mg)3Al2Si3O12). These systems were studied a number of times (Brey et al., 1986; Danckwerth and Newton, 1978; Gasparik and Newton, 1984; Herzberg, 1978; Klemme and O’Neill, 2000; Lane and Ganguly, 1980; MacGregor, 1974; Nickel et al., 1985; O’Hara et al., 1971; O’Neill, 1981; Obata, 1976; Perkins and Newton, 1980), and it was shown that the spinel–garnet transition is univariant (i.e., a line in a pressure– temperature diagram) in this system. In conclusion, phase relations in simple systems, such as CMAS and MAS, are useful in constraining phase relations of the upper mantle. Figure 6 shows the garnet–spinel and the plagioclase–spinel transitions in CMAS, based on the most

opx, cpx, ol, plag + Cr-sp

1100 1000 Temperature (⬚C)

1200

1300

Figure 5 The plagioclase–spinel transition in complex compositions: pale blue: MORB Pyrolite (MPY), Niida and Green (1999); stippled gray: Hawaiian Pyrolite - HPY, Green and Ringwood (1970); black: Lherzolite in the CaO-MgO-Al_2O_3-SiO_2 system (Lherz) Presnall et al. (1979); red: Fertile Lherzolite (FLZ), Borghini et al. (2010); apple green: Depleted Lherzolite (DLZ), Borghini et al. (2010); stippled ocker: High Na Fertile Lherzolite (HNa-FLZ), Fumagalli et al. (2011). Different bulk compositions differ in the Na/Ca bulk ratio and bulk XCr (XCr ¼ Cr/(Cr þ Al): Presnall et al. (1979) investigated Cr-free system, with the lowest bulk Na2O/CaO ratio. FLZ, HNa-FLZ, MPY, and HPY have similar bulk XCr but increasing values of Na2O/CaO ratio. Depleted lherzolite has the same Na2O/CaO ratio of FLZ, but higher XCr.

25 Garnet iherzolite 20

us

900

30

oli d

0.2

35

MPY: Niida and Green, 1999 HPY: Green and Ringwood, 1970 Lherz: Presnall et al., 1979 FLZ: Borghini et al., 2010 DLZ: Borghini et al., 2010 HNa-FLZ: Fumagalli et al., 2011

Pressure (GPa)

0.4

The Spinel–Garnet Transition

Dr ys

Pressure (GPa)

1.0

abundances are expected in natural peridotites, which are refertilized by melt–rock reactions. In these cases, the modal abundance of plagioclase would be underestimated leading to the underestimation of the effect of plagioclase modes on the density profile and seismic properties of these rocks.

15 Spinel iherzolite 10 Plagioclase iherzolite 5

800

1000 1200 Temperature (°C)

1400

1600

Figure 6 The transition from garnet to spinel lherzolite in the system CaO–MgO–Al2O3–SiO (CMAS). Shown here are phase stability fields based on O’Neill (1981), Klemme and O’Neill (2000), and Milholland and Presnall (1998). See text for details.

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

recent and most consistent data set (Borghini et al., 2010; Klemme and O’Neill, 2000; Milholland and Presnall, 1998; O’Neill, 1981). The rather steep slope of the high-temperature part of the transition was confirmed recently (Walter et al., 2002). Note that the data displayed here disagree with an older set of experiments (Gasparik, 1984). This may seem insignificant here, but as the Gasparik experiments were used to calibrate the thermodynamic model employed by Holland and Powell (1998, 2011), thermodynamic calculations with the thermocalc model (Holland and Powell, 1998, 2011) are expected to yield unreliable results in mantle compositions involving spinels and garnets (Green et al., 2012). In more complex chemical compositions, the transition from spinel to garnet-bearing peridotite will have higher degrees of freedom. This implies that the line that separates the spinel from the garnet stability field in Figure 6 will be replaced with a phase stability field in which spinel and garnet coexist. The same will apply to the plagioclase to spinel transition. This also implies that in complex, multicomponent natural compositions, there must be a field in a P–T diagram where spinel and garnet (and plagioclase and spinel) coexist. This explains the coexistence of spinel and garnet in some kimberlites. O’Neill (1981) was one of the first to suggest that Cr3þ stabilizes spinel relative to garnet. Addition of Cr to the CMAS system will, therefore, result in a shift of the garnetin reaction to higher pressures. Similarly, O’Neill (1981) noted that addition of Fe2þ to the system will result in a shift of the garnet-in reaction to lower pressures. Since then, further experiments (Brey et al., 1999; Girnis and Brey, 1999; Girnis et al., 2003; Irifune et al., 1982; Nickel, 1986; Webb and Wood, 1986) and thermodynamic calculations (Ganguly and Bhattacharya, 1987) have confirmed this trend. Recently, it was shown (Klemme, 2004) that in extremely depleted compositions, the garnet–spinel transition occurs at very high

15

pressure and exhibits a negative Clapeyron slope. Note that these experiments were conducted in a model system (MgO– Cr2O3–SiO2) and that these composition are not directly relevant to the mantle, which contains always much more Al than Cr with Cr/Cr þ Al < 0.3 in even the most depleted peridotite. These experiments, however, define the maximum stability of spinel in the mantle and are important in constraining the thermodynamic properties of Cr-rich garnets (Klemme, 2004). Figure 7 shows both the effect of Cr on spinel stability (Figure 7(a)) and the stability of Cr-rich spinel in extremely depleted compositions (Figure 7(b)). Very little experimental work on the stability of garnet and spinel has been done in complex systems with near-natural compositions. The pioneering experiments of Green and Ringwood (1967) show that there is a narrow garnet plus spinel stability field, which could not be resolved any further using their experimental and analytic techniques. Additional information on the garnet–spinel transition in complex compositions can be derived from experimental studies performed on the stability of pargasite (Niida and Green, 1999) or in peridotite systems (Fumagalli and Poli, 2005; Fumagalli and Stixrude, 2007). Note, however, that, due to slow reaction rates, experiments in natural complex compositions are extremely difficult.

2.02.4.2.1 Phase equilibrium calculations: implications for the Hales discontinuity More promising perhaps, phase equilibrium calculations in fertile and depleted mantle compositions have recently emerged due to the fact that new thermodynamic data for important mantle minerals have been measured (see Klemme et al., 2009 and Ziberna et al., 2013, for discussion). With some limitations, it has been shown that in natural fertile compositions, the garnet plus spinel stability field is narrow

16

sp ine l-o

Pressure (GPa)

es

su

re

of

3.2

12

Pr

Pressure (GPa)

ut

4.0

2.4

Garnet + olivine 8

4

Spinel + orthopyroxene

1100°C 1.6

(a)

0

0.2 0.4 0.6 Spinel composition (Cr/Cr+Al)

0 1100

0.8

1300 1500 Temperature (°C)

1700

(b)

Figure 7 (a) The effect of Cr on the stability of spinel in the mantle in the system CMAS þ Cr (Redrawn from O’Neill HSC (1981) The transition between spinel lherzolite and garnet lherzolite, and its use as a geobarometer. Contributions to Mineralogy and Petrology 77: 185–194.). (b) The maximum stability of spinel in the mantle (Redrawn from Klemme S (2004) The influence of Cr on the garnet-spinel transition in the Earth’s mantle: experiments in the system MgO-Cr2O3-SiO2 and thermodynamic modelling. Lithos 77: 639–646.).

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

at high temperatures close to the solidus, but it is very wide at lower temperatures. Ziberna et al. (2013) showed in multicomponent, near-natural bulk compositions that the effect of depletion is large in subsolidus phase relations and that Cr-rich spinel can be stable in cold and depleted lithosphere up to pressures of 6 GPa (which corresponds to about 180 km depths). The implications of these results are compelling: the spinel–garnet transition in fertile and hot mantle (e.g., under mid-ocean ridges) should be relatively narrow and should show up in seismological studies as a discontinuity (Hales, 1969). However, assuming that cratonic lithosphere is much colder and also more depleted than ordinary lithosphere, the garnet–spinel transition should be much broader in cratonic regions and only a gradient zone should be observed. Thus, in continental regions with relatively hot geotherms, such as the Variscan orogen in the SW Iberian Peninsula (Palomeras et al., 2011), the Hales gradient zone is only 10–20 km thick and lies at around 70 km depth (Ayarza et al., 2010). In cratonic blocks with colder geotherms, it appears at greater depths and over broader intervals, that is, from the Moho to 150 km depth (Lebedev et al., 2009). Ziberna et al. (2013) further predict that bulk composition may control the extension of the Hales gradient zone in cold, cratonic settings, but its influence will progressively decrease at higher increasing geothermal gradients. Note that there are alternative interpretations of the Hales discontinuity, ranging from seismic anisotropy (Bostock, 1998; Fuchs, 1983; Levin and Park, 2000) to pervasive partial melts (Thybo and Perchuc, 1997) and cation ordering in mantle olivine (Mandal et al., 2012).

2.02.4.3

Garnet–Majorite Reactions

Majorite is a phase in the mantle that is related to garnet. Majorite is named after Alan Major, who synthesized this particular type of garnet at pressures of more than 6 GPa at the Australian National University in the late 1960s (Ringwood and Major, 1971). Compared to normal garnets with a chemical formula of A3B2Si3O12, majorite contains excess Si. This is reflected in the general chemical formula for majorite garnets A3B2 xSi3þxO12. The excess Si in majoritic garnets is possible to the fact that high-pressure silicates (all of them) will at some stage incorporate some of its Si not only into the normal tetrahedral site but also into an octahedral site. With increasing pressures, garnets incorporate more and more sixfold coordinated Si due to a continuous reaction with pyroxenes. This was first shown for garnets in experimental charges (Ringwood and Major, 1971), but other silicates show similar effects (e.g., Angel et al., 1988). Note that majoritic garnets are commonly found as inclusions in diamond, but majoritic garnets have been also described in the orogenic garnet peridotite in the Western Gneiss Region of Norway (e.g., Scambelluri et al., 2008; van Roermund et al., 2001). Figure 8 shows the majorite-forming reaction studied in the simple MAS system (Akaogi and Akimoto, 1977). There are very few experiments on the stability of majorite in more complex compositions; one of the few is a study in pyrolite composition (Akaogi and Akimoto, 1979; Irifune, 1987). The experimental data show that the majorite component in the upper mantle garnets (i.e., at depth less than 410 km) is only very small and does not exceed a few percent. Within the transition zone, however,

g + St + majorite 20 b + St + majorite Majoritic garnet

16 Pressure (GPa)

16

12

Pyroxene + majoritic garnet

8

4

80 MgSiO3

60

40 mol%

20 Mg3Al2Si3O12

Figure 8 Phase relations in the system MgO–Al2O3–SiO depicting the formation of majorite garnets, which are a product of increasing solution of pyroxene into the garnet structure. See text for details. Redrawn from Akaogi M and Akimoto S (1977) Pyroxene-garnet solid-solution equilibria in systems Mg4Si4012-Mg3Al2Si3O12 and Fe4Si4O12-Fe3Al2Si3O12 at high-pressures and temperatures. Physics of the Earth and Planetary Interiors 15: 90–106.

things change, and garnets are able to dissolve more and more pyroxene components (Figure 8) so that deeper parts of the transition zone are expected to be very rich in majoritic garnets (e.g., Ganguly et al., 2009; Stixrude and LithgowBertelloni, 2011). This, however, is beyond the scope of this chapter.

2.02.5 Mineralogy and Transitions in the Upper Mantle at Subduction Zones 2.02.5.1

The Role of Hydrous Phases

The upper mantle at subduction zones is unusual due to processes that occur during subduction of mafic and other crustal rocks back into the mantle. This is probably the main cause of heterogeneity in the mantle. Furthermore, geophysical observations, the evidence from subduction zone volcanoes, and the study of erupted magmas all suggest that subduction processes are associated with the presence of significant amounts of volatiles, mainly H2O, CO2, S, and halogens. Current estimates of ‘normal’ mantle water content based on cosmochemical and geochemical arguments suggest that the bulk silicate earth contains between 500 and 1900 ppm of water ( Jambon and Zimmermann, 1990). However, water is unevenly distributed: the mantle source of MORBs is expected to contain

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

be taken into account. The storage and release of water within or into the mantle and each flux are closely related to stability of hydrate minerals. Discontinuous reactions are of particular interest when they involve hydrates. The breakdown of hydrous phases will (in most cases) release fluids and therefore cause an abrupt change in the physical properties of the rock, which may be related to geophysical observations. On the other hand, the release of a free fluid phase from such a reaction may not always happen, as under some circumstances hydrates react away in the so-called fluid-conservative reactions. The triangular plots in Figure 9 represent chemographies that are useful to predict the stable phase assemblage at fixed pressure and temperature conditions as a function of variable bulk compositions. The simple system MgO–SiO2–H2O (MSH) may be taken as a reference. At P0, T0, a model hydrous peridotite (red circle) contains forsterite, talc, and enstatite. No fluid is present and the line brucite–talc–quartz defines the fluid (i.e., water) saturation condition: bulk compositions falling above will include a fluid phase and rocks below will not include a free fluid but may contain hydrous phase assemblages. This implies that the presence of hydrous phases is not precluded at fluid-absent conditions and – very similar to silicates that might be stable in SiO2-undersaturated rocks – hydrates can be stable in H2O-undersaturated compositions. At P1, T1, the phase assemblage consists of antigorite, forsterite, and enstatite. This is, again, a fluid-absent phase assemblage, and water has been simply transferred from talc to antigorite, without a free fluid phase ever being present. These so-called discontinuous reactions are water-conservative and, in the overall picture of transport and release of fluids, are of particular relevance. At P2,T2 finally, antigorite breaks down and the peridotite now includes forsterite, enstatite, and a water-rich fluid (Figure 9). Water has been released by the dehydration of antigorite, H2O saturation has been reached, and a pulse of fluid released from this reaction is expected at the corresponding depth in the mantle. As a result, fluid-present conditions can be achieved by dehydration reactions involving phase assemblages stable at fluid-absent conditions. In complex systems, continuous reactions are likely to occur. When continuous reactions involve hydrous phases, the fluid production is continuously decreasing as the reaction proceeds and fluid release is spread over a range of pressure and/or temperature. As we have seen, breakdown of a hydrated mineral may cause a fluid to be released, with significant consequences such as partial melting of the rock or changing rheological and physical properties of the rock due to the presence of a free

80–330 ppm of water, the source of OIBs from 200 to 950 ppm (Bolfan-Casanova, 2005; Hirschmann et al., 2005). The evidence from mantle xenoliths suggests that the continental upper mantle water content is around 28–175 ppm (Bell and Rossman, 1992). In contrast, however, island arc magmas suggest that upper mantle at subduction zones may contain up to 1900 ppm water, in agreement with the surficial explosive volcanism and intense seismicity observed in subduction zones. While in oceanic and continental mantle, the water can be solely stored in nominally anhydrous minerals (NAMs) such as olivine and pyroxenes, at convergent margins, additional hydrous phases and/or free water-rich fluids should be present at subsolidus conditions. Phase relations in hydrous ultramafic compositions are important to understand mantle mineralogy and phase transformations at subduction zones. Water has profound effects on most processes within the Earth’s mantle. Phase equilibriums are strongly influenced: the melting temperature of mantle rocks is lowered and phase transitions are displaced; water also weakens rocks and minerals, reduces the viscosity of mantle materials, affects the electrical conductivity of mantle rocks, and influences the seismic properties. Geophysical observations of convergent margins report subducting slabs seismically faster than the surrounding. These high-velocity zones are often marked by double seismic zones (DSZs) (Hasegawa et al., 1978): while the upper seismic plane is attributed to the interface between the slab and the overlying mantle wedge, the lower seismic plane is often explained by lithologic heterogeneity within the slab, likely related to the ultramafic portion of the slab (Brudzinski et al., 2007; Peacock, 2001; Yamasaki and Seno, 2003). The reason why these parts of the mantle are the regions where deep seismicity is recorded is often due to the embrittlement caused by dehydration of hydrated mantle minerals. Experimental investigations into these matters offer the possibility to explore the release of fluids as a function of pressure and temperature, and combining this information with the thermal structure of subduction zones, one can investigate phase transformations within the slab. In the following paragraphs, emphasis will be given to accessory hydrous phases, which may be (and have been shown to be) stable in the Earth’s upper mantle. These minerals document the transport and release of H2O during subduction, a process that has recently interested many petrologists, geochemists, and geophysicists. Before going into the detail of some experimentally derived phase diagrams, a few general petrologic considerations should

H2O Water

P0,T0 Fluid-absent br

fo + ta = atg + en atg

Water-conservative

atg

H2O Water

P1,T1

Fluid-present

per

fo

en

H2O Water

P2,T2 atg = fo + en + H2O

br atg

br

Fluid release

ta MgO

ta q

SiO2

MgO

per

fo

17

en

ta q

SiO2

MgO

per

fo

en

SiO coe 2

Figure 9 The role of hydrates in the transport and release of fluids at depth is represented in the MgO–SiO2–H2O diagrams at different pressure and temperature conditions. The red circle represents a typical simplified peridotite bulk composition. See text for details.

18

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

fluid phase. If the fluid production rate is comparable to or higher than viscous relaxation, then embrittlement is expected (Hilairet and Reynard, 2009). In contrast, the breakdown of a hydrated mineral in the upper mantle may involve a complete transfer of the H2O component into another hydrated mineral via H2O-conserving reactions. These reactions do not release fluid, but the H2O component is transferred into other minerals with higher-pressure and/or higher-temperature stability. Investigating the stability, the crystal chemical behavior, and the thermodynamic properties of hydrous phases will further our understanding of how the volatile elements are stored, transferred, or released within the mantle. Investigations on fast, slow, and ultraslow-spreading ridges suggest different structures of the oceanic crust, with the gabbroic portion less relevant, wider portion of serpentinites and mantle rocks in the latter ones as compared with the original Penrose model, where gabbros constitute the major forming blocks and a layered sequence with mantle rocks confined at the deepest levels (Dick et al., 2012). Prior to subduction, the oceanic crust is altered by hydrothermal processes at the ocean floor (Snow and Dick, 1995) and further hydrated at the outer rise inflections (Contreras-Reyes et al., 2011; Ivandic et al., 2010; Ranero and Sallares, 2004; Ranero et al., 2003). As a result, the input in a subduction zone, that is, the oceanic lithosphere, might be quite heterogeneous as a function of spreading rates and degree and depth of hydration. During subduction, relevant changes in physical properties, first of all density, are accompanied by relevant mineralogical variations, and the role of hydrous phases has been the focus of many studies over the last decades. In the following parts of our chapter, we will first briefly present experimental constraints on phase relations in mafic lithologies in subducting slabs, and then we will discuss the phase relations in hydrous peridotites, concluding with results on metasomatized lherzolites, which are thought to have formed in subduction zones as a result of interactions between fluids derived from the slab and mantle wedge peridotites.

2.02.5.2

The Basalt to Eclogite Transition

The contribution of the mafic, basaltic, and gabbroic, part of the slab to the transport and release of fluids during subduction, has been extensively investigated both at H2Osaturated conditions, that is, in the presence of water (Forneris and Holloway, 2003; Litasov and Ohtani, 2005; Okamoto and Maruyama, 2004; Pawley and Holloway, 1993; Poli, 1993; Poli and Schmidt, 1995; Schmidt and Poli, 1998), in the presence of a CO2 fluid (Molina and Poli, 2000; Yaxley and Green, 1994), and with variable C–O–H fluids (Poli et al., 2009). Besides slight discrepancies, mainly related to different experimental setup and starting materials, all experimental studies suggest that phase relations in mafic systems are dominated by solid solutions and complex continuous reactions, with significant changes in mineral chemistry with P and T and phase abundances rather than changing phase assemblages. As a result, the bulk composition exerts a fundamental role on phase stabilities, and therefore, experiments performed in certain tholeiitic compositions cannot be simply extrapolated to the wide range of compositions known to exist in basaltic oceanic crust. Furthermore, dehydration reactions occur over a considerable range of

depths and as a consequence the fluid release is expected to be continuously distributed along the slab (e.g., Bose and Ganguly, 1995; Schmidt and Poli, 1998). At blueschist facies conditions (i.e., deeper than 15 km), basalts are transformed into rock composed of chlorite, amphibole, phengite, lawsonite or zoisite, and paragonite. At these conditions, the H2O content of the rock was estimated to be around 6 wt.% (Schmidt and Poli, 2014). The hydrated oceanic crust loses up to two-third of the entire water content before the breakdown of amphibole through numerous dehydration reactions. Amphibole, however, dominates the region where high dehydration rates and fluid production are expected (Schmidt and Poli, 2014). This is why numerous experimental studies have been performed to establish the stability field of amphibole in H2O-saturated MORB both in simplified chemical compositions (Poli, 1993; Poli and Schmidt, 1995; Schmidt and Poli, 1998) and with natural starting materials (Forneris and Holloway, 2003; Liu et al., 1996; Pawley and Holloway, 1993). Available data (Figure 10) report that at 700–750  C, amphibole is stable up to a pressure of about 2.5 GPa. At pressures exceeding the stability of amphibole, other hydrates exist that can account for transport of water into greater depth. Lawsonite and zoisite dominate the higherpressure regime down to more than 200 km depths (Okamoto and Maruyama, 1999; Ono, 1998; Poli and Schmidt, 1998; Schmidt and Poli, 1998), although other minor phases can also be stable, for example, Mg chloritoid, talc, and phengite. The rock type at these depths is eclogite and the total amount of water that mafic eclogites are able to store in subarc regions is 1.5 wt.% (Schmidt and Poli, 2014). This deeper part of the subduction zone is therefore characterized by a lower dehydration rate and less fluid production. Minor amounts of K2O may stabilize phengite that, with its large stability field well beyond the stability of epidote group minerals, controls most of melting relations and geochemical signature of first partial melts (Okamoto and Maruyama, 1999; Schmidt, 1996). The addition of a CO2 component further complicates phase relations. Experimental results on mixed fluid (C–O–H) MORB compositions suggest however that, as CO2 strongly fractionates into carbonates leaving a coexistent H2O-rich fluid, amphibole stability is not significantly affected. Additionally, counterintuitively, the stability of lawsonite is slightly enhanced by the addition of CO2, extending its stability to higher temperature (Poli et al., 2009). Although the stability of lawsonite is shifted by only 30–80  C, this difference is relevant as the reaction has a slope parallel to most P–T paths, and small temperature differences control whether the rock is dry or volatiles are present in the rock. Summarizing, hydrous phases in mafic lithologies significantly contribute to the water cycle at subduction zones: while amphibole mainly controls fluid production in the forearc region, with high dehydration rate and fluid production, lawsonite and/or zoisite governs the subarc region.

2.02.5.3

Phase Relations in Hydrous Peridotite Systems

Hydrous peridotites have been extensively investigated at nearsolidus conditions (Green, 1973; Mysen and Boettcher, 1975;

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

19

10

9

H2O-sat. MORB

vite Stisho e it Coes

8

7

Ph en gi te

6

5

4

talc

ld

-c

Mg

Pressure (GPa)

Lawsonite

Ca, Al, H, C 3

isite

Amphibole cite

Ompha

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Amphibole e gonit Para

Garnet

Epidote 300

400

500

Epidote

2

Chlorite

Zo

Wet solidu s 600

700

800

900

Temperature (°C) Figure 10 Experimentally derived phase diagram for H2O-saturated mid-ocean ridge basalt (modified from Schmidt MW and Poli S (1998) Experimentally based water budgets for dehydrating slabs and consequences for arc magma generation. Earth and Planetary Science Letters 163: 361–379.) and at oxygen fugacity of approximately Ni-NiO buffer. Lawsonite stability is displaced toward higher temperature as anorthite (Ca, Al), H, and C increase. Shaded area represents P–T paths for slab surface from Arcay et al. (2007) with different water weakening effects: straight line represents a model reference for a ‘dry’ rock; dashed line refers to a moderate rock strength reduction due to water; narrow dashed line refers to a relevant strength reduction.

Niida and Green, 1999; Wallace and Green, 1991). These studies are of relevance for the melting behavior of the mantle (see this volume Chapter 2.19). The knowledge of the subsolidus phase relations is restricted to simplified chemical systems (MSH, MgO–Al2O3–SiO2–H2O (MASH), CaO–MgO– SiO2–H2O (CMSH), and FeO–MgO–SiO2–H2O) assumed to be representative of up to 95% of harzburgitic or lherzolitic bulk mantle or is based on a few experimental studies devoted to investigate peridotite modeled in complex, close to natural compositions (Fumagalli and Poli, 2005; Fumagalli et al., 2009; Tumiati et al., 2013). Phase relations in hydrous peridotites are shown in Figure 11. Serpentine is the dominant hydrous mineral phase in the oceanic lithosphere at slow-spreading centers, and due to its high water content, its low density, and its low mechanical strength, it is serpentine that exerts control on subduction zones dynamics and rheology (e.g., Campione and Capitani, 2013; Hattori and Guillot, 2003; Hilairet and Reynard, 2009; Scambelluri et al., 2004). As a result, serpentine has been thoroughly investigated experimentally, focusing not only on

its stability field (Bromiley and Pawley, 2003; Ulmer and Trommsdorff, 1995; Wunder and Schreyer, 1997) but also on the kinetics of serpentine dehydration reactions (Chollet et al., 2011) and on its elastic properties, both experimentally (Hilairet et al., 2006; Nestola et al., 2010) and theoretically (Capitani and Stixrude, 2012; Capitani et al., 2009; Mookherjee and Capitani, 2011; Mookherjee and Stixrude, 2009). Nonetheless, although phase assemblages are dominated by serpentine, other hydrated minerals may persist beyond the serpentine stability field in the mantle and play a pivotal role in the dehydration and fluid production during subduction. In the following paragraphs, we present the available experimental results on the most important hydrous phases in hydrated peridotites.

2.02.5.3.1 Talc and amphibole Talc (4.7 wt.% H2O, density 2.6–2.8 g cm 3) is restricted to pressures lower than 2 GPa. No significant solid solutions are expected in talc, with the exception of a moderate Tschermak substitution (Mg(VI)Si(IV) ¼ Al(VI)Al(IV)). If such an exchange is

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

7.0

6.0

Pressure (GPa)

5.0

210

Phase A

1.0

H2O-sat. lherzolite

*

ant

dry

4.0

Dvir et al (2011)

Chlorite

3.0

ant chl

3.0

110

6.5 2.0

1.0 600

chl amp ant chl tc amp

Depth (km)

20

1.3 2.5

gar

Chlorite Amphibole 700

80

Amphibole

sp 800

900

Temperature ( ⬚C) Figure 11 Experimentally derived phase diagram for H2O-saturated lherzolite modified from Fumagalli P and Poli S (2005) Experimentally determined phase relations in hydrous peridotites to 6.5 GPa and their consequences on the dynamics of subduction zones. Journal of Petrology 45: 1–24. Antigorite breakdown is from Ulmer and Trommsdorff (1995); the thermal stability of the 10 A˚ phase is from Dvir et al. (2011). Numbers in ovals are the estimated water content based on mass balance. P–T paths are from Arcay et al. (2007) as in Figure 10.

possible in the bulk composition, then the stability of talc is slightly extended to higher pressure. It is widely accepted that talc forms as a product of orthopyroxene alteration that leads to talc and serpentine in a mid-ocean ridge environment. However, the talc stability is strongly influenced by Si enrichment as a result of metasomatic fluids released by overlying sediments and oceanic rocks of the descending slab to mantle wedge peridotites. The talc dehydration reaction in mantle compositions is governed by the reaction talcþ forsterite ¼ clino-/orthoenstatite þ fluid. This reaction has been extensively investigated in the MSH system (Bose and Ganguly, 1995; Chemosky et al., 1985; Kitahara et al., 1966; Pawley, 1998; Ulmer and Trommsdorff, 1995; Wunder and Schreyer 1997; Yamamoto and Akimoto, 1977). Despite the relatively simple chemical system in which these experiments were performed, the exact location of the dehydration reaction is not well known. Melekhova et al. (2006) explained some possible causes of different experimental results using a novel rocking piston–cylinder. Such a highpressure apparatus enables experimentalists to avoid chemical zonation caused by the Soret effect within the experimental charge, a very common experimental problem when a fluid is involved (Schmidt and Ulmer, 2004). According to Melekhova et al., the differences in the location of the transition are related to a decrease of H2O activity, due to a high solubility of Mg and Si in the fluid at high pressures, and to the effect of the clinoenstatite–orthoenstatite transition. This last consequence is an excellent example of the effect that anhydrous phase (orthopyroxene) may have on a dehydration reaction. Note that talc is highly anisotropic upon compression and this should have a large effect on the seismic properties of the rock (Bailey and Holloway, 2000; Mainprice et al., 2008; Stixrude, 2002).

The role of talc on seismic anisotropy is, however, expected to be a function of its modal abundance and its preferred orientation. Hacker et al. (2003) suggested that 11–15% of talc might be hosted in harzburgite and lherzolite but up to 41% in mantle wedge assemblages related to the breakdown of serpentine. The amphibole ( 2.2 wt.% H2O, density 2.98– 3.17 g cm 3) stability in the mantle is strongly dependent on bulk composition (Niida and Green, 1999), as it forms extensive solid solutions and its composition changes drastically with pressure and temperature. Up to 1.5 GPa, the entire solid solution tremolite–pargasite is stable ( Jenkins, 1983). At higher pressure, amphibole is tremolite at relatively lower temperature, where it coexists with clinopyroxene and chlorite, and becomes pargasitic close to the solidus. At 700  C, the amphibole stability boundary in lherzolite is located at 2.5 GPa (Fumagalli and Poli, 2005). Its breakdown is related to a water-conservative reaction, that is, no release of fluids is expected during its breakdown, and consequently, water is completely transferred to chlorite at higher pressure. At higher temperature, above the stability field of chlorite, the upper pressure stability of amphibole is controlled by the reaction that leads to clinopyroxene þ orthopyroxene þ garnet þ fluid. This reaction is strongly controlled by the Na and Ca content of the bulk composition: the highest pressure stability is in fertile compositions, with high amounts of Ca and Na, where amphibole persists at 925  C to pressures of up to 3 GPa (Niida and Green, 1999). Investigating the role of water in lherzolites, Green et al. (2010) determined the maximum amount of structurally bound water in amphibole before the appearance of an aqueous fluid or melt as 0.6 wt.% H2O at 1.5 GPa, 1000  C (i.e., hosted in 30% pargasite). The change in

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

amphibole mineral chemistry as a function of pressure lowers the modal abundance to 10% and as a result lowers the water storage capacity of the rock to 0.2 wt.% H2O. Additional complexities arose by the potential dissolution of oxides, particularly of alkalis, K2O, and Na2O in high-pressure fluids. Green et al. (2010) found that the water/rock ratio plays a fundamental role: water contents >5 wt.% may inhibit the formation of amphibole at high P as alkali elements tend to partition into the vapor phase.

2.02.5.3.2 Serpentine and chlorite phase assemblages Serpentine (13 wt.% H2O, density 2.6 g cm 3), in its antigorite form, dominates the low-temperature high-pressure field and is stable up to 6 GPa (which corresponds to about 200 km depth). The stability of antigorite in complex systems, that is, natural compositions, is reasonably assumed to be that reported from experiments in the MSH systems (Bose and Ganguly, 1995; Bose and Navrotsky, 1998; Evans et al., 1976; Ulmer and Trommsdorff, 1995; Wunder and Schreyer, 1997) as no extensive solid solutions are expected for this hydrous phase. Nonetheless, Ulmer and Trommsdorff (1999) reported several discrepancies on the exact location of the upper thermal stability of antigorite. One of the main causes for these discrepancies could be down to the effect of minor components such as Cr, Fe, and Al, on the stability of serpentine. Bromiley and Pawley (2003) confirmed this, reporting a slightly increased thermal stability of antigorite due to addition of Al. The choice of the stability field adopted to envisage physical properties within the mantle should therefore be made by keeping in mind that different bulk compositions (pure antigorite vs. Cr-, Fe-, Al-bearing antigorite solid solution) have been used. At higher pressure, antigorite is replaced by a dense hydrous magnesium silicate (DHMS), the so-called phase A (Bose and Ganguly, 1995) and, even deeper in the transition zone, by phase E. In deeper parts of the mantle, when Al is considered, chlorite (13 wt.% H2O, 2.6–3.3 g cm 3) can store water up to temperatures and pressures beyond the stability of antigorite and amphibole. Chlorite has been extensively investigated in the simplified MASH system (Chernosky, 1974; Fawcett and Yoder, 1966; Fockenberg, 1995; Jenkins and Chernosky, 1986; Staudigel and Schreyer, 1977; Ulmer and Trommsdorff, 1999). However, in contrast to talc and antigorite, chlorite is expected to form extensive solid solutions, for example, hosting Fe or Cr in its structure. As a result, phase relations are expected to be strongly affected by increasing chemical complexity of the system. The thermal stability of chlorite in mantle rocks is related to the breakdown of chlorite þ pyroxene, via reactions (e.g., chlorite þ pyroxene ¼ olivine þ garnet þ water) that systematically occur at slightly lower temperature as compared with the thermal terminal stability of pure chlorite (chlorite ¼ forsterite þ pyrope þ spinel þ water). Fumagalli and Poli (2005) found that chlorite stability in lherzolite is shifted toward slightly lower temperature as a result of preferential partitioning of Fe into garnet and mass balance calculations on high-pressure experiments suggested the relevant role of clinopyroxene and grossular component in garnet in the thermal stability of chlorite. Despite the fact that Cr is a minor constituent in the Earth’s mantle, due to its uneven partitioning among major mantle minerals, MASH phase equilibriums are expected to be strongly

21

displaced (Chatterjee and Terhart, 1985) due to the presence of Cr. High-pressure mantle chlorites, found in natural peridotites, host up to 2.0 wt.% Cr2O3 (Ravna, 2006); intermediate content of Cr2O3 (up to 5–6 wt.%) has been reported for chromian chlorite found in veins in association with chromite deposits and ultramafic rocks (e.g., Nuggihalli Schist Belt, India – 5.18 wt.% Cr2O3, Phillips, 1980). In experiments, Grove et al. (2006) and Till et al. (2012) synthesized mantle chlorites in primitive mantle composition (Hart and Zindler, 1986) containing up to 1.47 wt.% Cr2O3 at 3.6 GPa, 800  C, suggesting that Cr2O3 solubility in chlorite is expected to enlarge its thermal stability. More recently, Fumagalli et al. (2014) found that in the simple Cr-MASH system, chlorite in mantle assemblages can host up to 2.2 wt% Cr2O3 and that its stability is enhanced by 50  C per 0.5 GPa.

2.02.5.3.3 Post antigorite–chlorite hydrous phases At higher pressure, phase equilibriums are complicated by the somewhat uncertain fate of chlorite and antigorite stability. Several hydrated minerals have been synthesized as products of breakdown reaction of antigorite and chlorite: phase A, the 10 A˚ phase, Mg-sursassite (formerly called MgMgAl-pumpellyite), and a newly found pyroxene-like hydrous structure, called phase-HAPY (hydrous Al-bearing pyroxene) (Gemmi et al., 2011). While chlorite-bearing peridotite and serpentinite have often been found in nature, all other hydrates have only been synthesized in high-pressure laboratories. However, the 10 A˚ phase has recently been found as inclusions in olivine crystals from ultrahighpressure rocks (Khishina and Wirth, 2008). Although it is obvious that DHMS play an important role at lower mantle conditions, the stability of the 10 A˚ phase and of phase A as reaction product of chlorite and antigorite breakdown, respectively, underlines that these hydrous phases are also relevant in the upper mantle. The stability of phase A (11.8 wt.% H2O, density 2.96 g cm 3) has been determined in the simple systems MSH and MASH (Luth, 1995; Ulmer and Trommsdorff, 1995). It was found that at 800  C phase A is stable between 7 and 10 GPa. In peridotite bulk compositions, however, the stability of phase A together with enstatite at 1050  C is extended to 6–13 GPa (Kawamoto, 2004; Kawamoto et al., 1995). At lower temperature, antigorite assemblages transfer directly H2O to phase A-bearing assemblages (Bose and Ganguly, 1995). If higher temperatures are considered, additional and intermediate hydrous phases have been found. The 10 A˚ phase (8–13 wt.% H2O, density 2.7) was first synthesized in the MSH system (Sclar et al., 1965) and has been extensively investigated in the last decades both experimentally (Chinnery et al., 1999; Chollet et al., 2009; Comodi et al., 2005, 2006; Fumagalli et al., 2001; Pawley and Wood, 1995; Pawley et al., 2011; Welch et al., 2006) and theoretically (Bridgeman and Skipper, 1997; Bridgeman et al., 1996; Fumagalli and Stixrude, 2007; Wang et al., 2004). The 10 A˚ phase is a phyllosilicate 2:1 with interlayer stably bound water molecules. Fumagalli et al. (2001) performed timeresolved experiments and found that this phase might host a variable amount of water and exhibits a swelling behavior that enables it to incorporate large molecules within its interlayer. The relevance of the 10 A˚ phase in ultramafic

22

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

rock compositions is strongly related to the talc appearance, as this phase is compositionally a hydrated form of talc. As a result, its presence is expected in Si-enriched bulk compositions, formed as a result of complex fluid/rock interactions at subduction zones. However, the reconnaissance of an Al-bearing 10 A˚ phase in peridotite systems stable at the expense of chlorite at 4.8 GPa, 650  C, emphasizes the relevance in the ultramafic portion of the slab for the water budget of subducting slabs. Dvir et al. (2011) investigated the compositions of coexisting fluids in peridotitic compositions up to 6 GPa. They confirmed the stability of this phase in mantle phase assemblages and further constrained its thermal stability, governed by the reaction 10 A˚ phase þ clinopyroxene ¼ garnet þ orthopyroxene þ H2O, between 750 and 800  C, at 5 GPa. Note that the replacement of chlorite-bearing assemblages with 10 A˚ phase-bearing rocks is not well understood, yet. Fumagalli and Poli (2005) suggested either a solid solution relation, implying a continuous reaction from chlorite to the Al-bearing 10 A˚ phase structure, or a more complex structural rearrangement as mixed layered structure with chlorite and 10 A˚ phase interconnected at the nanoscale following order–disorder relations. Additionally, its stability field overlaps those of other hydrates such as phlogopite, and high-pressure experimental results, based on the peculiar mineral chemistry of highpressure low-temperature phlogopite (see later), would suggest possible structural relations between 10 A˚ phase and phlogopite. The 10 A˚ phase thus plays an important role in transferring water into the deeper mantle of the Earth not only persisting as single phase beyond the stability of serpentine and chlorite but also, possibly, entering the structure of other hydrates such as chlorite and phlogopite. Mg-sursassite (7 wt.% H2O, density 3.3 g cm 3), previously known as MgMgAl-pumpellyite, was first synthesized by Schreyer et al. (1986) at 5.0 GPa, 700  C, and subsequently characterized by Bromiley and Pawley (2002), Gottschalk et al. (2000), and Grevel et al. (2001). Experimental studies demonstrated that Mg-sursassite is stable over a wide range of temperature, from 3.5 to 10 GPa (Fockenberg, 1995) and therefore it could play a relevant role in subduction zone environment. Its stability (in end-member composition) represents, however, a maximum stability field; in ultramafic composition, Mg-sursassite is precluded by the simultaneous stability of pyrope plus water assemblages (Artioli et al., 1999; Fockenberg, 1998; Ulmer and Trommsdorff, 1999) and its stability is likely to be reduced. Nevertheless, Mg-sursassite is considered of relevance in transferring water from antigorite–chlorite bearing assemblages to other hydrates stable at higher pressure such as phase A via reaction Mg-sursassite þ forsterite ¼ phase A þ enstatite þ pyrope by which no fluid is released and H2O content is completely transferred to phase A-bearing assemblages. Mg-sursassite in ultramafic is expected to form from chlorite-bearing assemblages via reaction chloriteþ enstatite ¼ Mg-sursassite þ forsterite þ fluid. This reaction implies that out of the 2.8 wt. % of H2O contained in a chlorite peridotite, only the 0.98% is retained in Mg-sursassite (Luth, 2003). The effect of additional components has been experimentally investigated by Wunder and Gottschalk (2002) who reported the synthesis of Fe–Mgsursassite. Fe-bearing systems are of relevance as results would

shed light on the influence of Mg–Fe partitioning on the stability of high-pressure Mg-sursassite. A previously unknown hydrous phase, a HAPY (the so-called ‘HAPY’ phase, 7 wt.% H2O, density 3.14 g cm 3), was recently found in the MASH, MSH, and Cr–MASH systems as product of chlorite breakdown at 5.4 GPa, 720  C (Fumagalli et al., 2014). Its crystal structure, characterized by automated electron diffraction tomography (Gemmi et al., 2011), is a single-chain inosilicate resembling the pyroxene structure but containing three independent cation sites. The stability of phase HAPY is far from being understood, but it might interact with other hydrates stable in the MASH system (e.g., phase A, Mg-sursassite, and 10 A˚ phase) at comparable and overlapping pressure and temperature conditions. Furthermore, from structural considerations, phase-HAPY might be able to host several additional cations via substitution such as Fe, Ca, Mg, or Tschermak exchange, making this phase of relevance in more complex systems. The discovery of phase HAPY in the MASH/Cr–MASH systems has two important implications: (i) It is a hydrous phase that persists beyond the stability of chlorite and/or antigorite and it is able to host much more water than NAMs. (ii) It has a particularly high density, higher than DHMS such as phase A and 10 A˚ phase, and as a result, it might contribute considerably to slab pull processes in subduction zones. However, its composition (MgO:Al2O3: SiO2 ¼ 2:2:1) falls in the MgO:SiO2 > 1 portion of the MASH system. As a result, its stability is restricted to unusual bulk compositions in the mantle, and it is precluded when the pyrope þ enstatite þ fluid assemblage is stable. In addition, the role of minor components in stabilizing additional hydrates able to storage water at post serpentine assemblages should be taken into account. The natural occurrence of Ti-clinohumite in ultrahigh-pressure metamorphic rocks initiated high-pressure experiments on the stability of humite-structured minerals. Stalder and Ulmer (2001), examining the stability of post antigorite phases up to 15 GPa, showed that the thermal stability of humite minerals is greatly enhanced by small amount of minor component such as F. Furthermore, the F/OH ratio in clinohumite decreases with pressure. Note that the F content of naturally occurring clinohumite from Cima di Gagnone, Switzerland (Evans and Trommsdorff, 1983), seems to indicate a pressure of origin as high as 5 GPa. Both phase A and clinohumite are unstable above 14 GPa, and in peridotite compositions, they are replaced by the assemblage phase E þ forsterite þ enstatite that persists up to the transition zone at 400 km of depth.

2.02.5.4 Fluid/Rock Interactions and the Role of Potassic Hydrous Phases In subduction zones, the extreme variability of bulk compositions and the complex relations among fluids and mantle minerals indicate that hybrid mantle compositions are common, which include chemical elements that are not commonly enriched in normal mantle compositions. Metasomatic processes are known to cause this element enrichment. Such processes in the mantle have been recognized for a long time and were documented mainly by studies on mantle xenoliths (e.g.,

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

Nixon, 1987). However, the geochemistry of the slab–mantle interface is known to be controlled by the interaction of highpressure fluids, crustal components, and ultramafic lithologies. Peridotite bodies may intrude into subducting continental crust as a result of buoyancy forces acting at the interface (Bru¨ckner, 1998). As a result, the devolatilization of felsic rocks and mass transfer toward peridotite are strongly enhanced, and a variety of volatile-bearing phases are stabilized in mantle rocks. Ti-phlogopite and diamond inclusions in Bardane peridotite, Norway (e.g., van Roermund et al., 2002), document the importance of metasomatic mass transfer and hybridization of upper mantle lithologies at depth. Phlogopite–spinel peridotites (Nixon, 1987), phlogopite– garnet peridotites, phlogopite–K-richterite peridotite xenoliths, and ‘orogenic’ phlogopite peridotites of ultrahigh-pressure terrains (Ulten peridotite: Rampone and Morten, 2001; Bardane peridotite, Norway: van Roermund et al., 2002; Sulu garnet peridotite, China: Zhang et al., 2007) document that such a process might occur both within the mantle wedge and at the slab–mantle interface, also at relatively low temperatures. The stability of potassic phases in mantle rocks has been experimentally investigated both in relatively simple systems considering phlogopite alone, phlogopite þ forsterite, and phlogopite þ enstatite þ diopside (Luth, 1997; Sudo and Tatsumi, 1990) and in bulk rocks similar to K-enriched lherzolites (Conceic¸a˜o and Green, 2004; Fumagalli et al., 2009; Konzett and Fei, 2000; Konzett and Ulmer, 1999; Mengel and Green, 1989; Wendlandt and Eggler, 1980). Phase relations are governed by the occurrence of three potassic phases, which are in order of pressure stability: phlogopite, a potassic amphibole of richteritic composition (K-amphibole), and a K-rich hydrous silicate, termed phase X (K2 xMg2Si2O7Hx, x ¼ 0–1; Yang et al., 2001). In K-enriched lherzolite, phlogopite coexists with Ca-amphibole up to 3.2 GPa and 900  C (Fumagalli et al., 2009). However, although the pressure stability of Ca-amphibole is slightly enhanced by the addition of K, its breakdown at relatively low-temperature conditions is controlled by a water-conservative reaction that leads to newly formed phlogopite but does not necessarily imply release of a free fluid phase. K-amphibole represents the breakdown product of phlogopite-bearing assemblages and phase X represents the breakdown product of K-amphibole. The potassic amphibole, which forms at the expense of phlogopite, is an Al-poor potassic amphibole and appears between 6 and 6.5 GPa at 800  C and between 6.5 and 7.0 GPa at 1100  C (Konzett and Ulmer, 1999). At pressures above 13–14 GPa (1100  C), phase X is known to replace K-amphibole. In more complex chemical compositions, the breakdown of K-amphibole occurs at lower pressures. The K-amphibole to phase X transition involves a continuous change of garnet compositions through Ca–Mg exchange and some limited majorite component (Konzett and Fei, 2000). The thermal stability of K-amphibole is determined by the appearance of the anhydrous assemblage garnet, olivine, orthopyroxene, and clinopyroxene. In the K2O–Na2O–CMASH system, it occurs between 1300 and 1400  C at 8.0 GPa and shows a positive Clapeyron slope. However, in an Fe-bearing system and in lherzolitic compositions, the effect of iron has to be taken into account. Konzett and Ulmer (1999) investigated a K-doped lherzolite modifying the composition of the Mont

23

Brianc¸on lherzolite (Massif Central, France) by adding phlogopite or K-richterite (see Table 1) components. In the lherzolitic system, the K-amphibole in reaction slightly shifts toward lower pressure (between 6.0 and 6.5 GPa at 1100  C) due to the preferential partitioning of Fe2þ into garnet, which is a product of phlogopite breakdown. The coexistence of phlogopite and K-amphibole is, however, reduced to less than 1 GPa. Konzett and Fei (2000) conducted experiments using a K-amphibole-enriched peridotite (KLB-1) from 12 to 14 GPa and 1200  C. Potassic phases, either K-amphibole or phase X, were found to coexist with garnet, low-Ca clinopyroxene, highCa clinopyroxene, and forsterite. In the Fe-bearing system, the K-amphibole to phase X transition, occurring between 12 and 13 GPa at 1200  C, is shifted by about 1.0 GPa toward lower pressure as compared with what was found in the Fe-free system. K-enriched lherzolite compositions were also investigated at relatively lower temperature (Fumagalli et al., 2009) and in the presence of C–O–H fluids (Tumiati et al., 2013). As a result of the increase of the content of alkali elements, the amphibole stability is enhanced at higher pressure, with a maximum of 3.4 GPa at 880  C. In K-enriched lherzolite with C–O–H fluids, carbonates such as magnesite and dolomite appear, but the location of the amphibole out reaction remains unchanged. At relatively low temperatures, relevant to the conditions of the slab–mantle interface, the phlogopite mineral chemistry is unusual. An excess in Si and a deficit in Al and Na þ K suggest a significant talc component in phlogopite, probably as a result of mixed layers in the phlogopite structure and the hydrated form of talc, that is, the 10 A˚ phase (Fumagalli et al., 2009). The chemical variability of phlogopite implies a continuous reaction responsible for the breakdown of amphibole that does not release a free fluid phase. Furthermore, the modal abundance of phyllosilicates is strongly enhanced at lower temperatures, that is, at the slab–mantle interface, reaching 7 wt.% modal as compared with 2 wt.% at relatively shallow depth within the stability of Ca-amphibole. Fumagalli et al. (2009) suggested that the K/OH ratio may be used to indicate the ability of a release of fluid via the transition from phlogopite to K-amphibole: At mantle wedge conditions, the K/OH ratio of phlogopite and the higher-pressure potassic phase is similar and therefore a water-conservative reaction is expected with no release of fluids. As the K/OH ratio of phlogopite is decreasing, at fixed K content in K-amphibole, a large release of fluid is expected (Figure 12).

2.02.5.5 Zones

Implications to the Geodynamics of Subduction

Here, we compare experimentally derived phase diagrams with P–T paths for slab surfaces in subduction zones (Figure 11). The thermomechanical model of Arcay et al. (2007) focuses on the degree of mechanical coupling between the slab and the mantle wedge and results in high thermal gradients within the lithosphere. Different paths take into account different amounts of water that weaken mantle rocks. Although these are typically cold thermomechanical models, they exhibit the different roles that hydrous phases can play in subduction processes rather well. Although antigorite dominates the water budget up to at least 2 GPa (Figure 11), in fertile

Mineralogy of the Earth: Phase Transitions and Mineralogy of the Upper Mantle

Slab/mantle interface

Mantle wedge 200

K-amphibole K amp in K-lherzolites KU99

6.0 phl/10 Å phase

150

K/OH> Vs Vi 6000 K). In contrast, recent first-principles calculations by Stixrude (2012) show a much wider stability field of hcp to 2300 GPa and 19 000 K (Figure 10). It is clear that, although the stable phase

20

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Figure 9 The calculated phonon dispersion curves for bcc-Fe at nine different volumes (corresponding to
40–350 GPa) (Vocˇadlo et al., 2003a). The softening in the [110] direction at
180 GPa indicates the onset of the bcc to fcc transition, and that in the [111] direction above
260 GPa corresponds to the bcc to o transition.

124

Earth’s Core: Iron and Iron Alloys

of pure iron at core conditions is hcp-Fe, the small free energy differences between the phases, together with the presence of light elements, mean that both fcc-Fe and bcc-Fe cannot be ruled out as an inner core phase. In summary, therefore, based on experiments at core conditions (Sakai et al., 2011; Tateno et al., 2010) and ab initio calculations (Stixrude, 2012; Vocˇadlo et al., 2003a,b, 2008a,b), the stable phase of pure iron at core conditions is almost

certainly the hcp phase. However, the free energies of hcp-, bcc-, and fcc-Fe are almost identical (within
35 meV atom1), only marginally favoring hcp-Fe. As a result of these small free energy differences, the relative phase stability may be greatly affected by the presence of alloying elements that are known to exist in the inner core.

2.06.4

Thermoelastic Properties of Solid Iron

4

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The only experimental data on solid iron under true core pressures and temperatures comes from either simultaneously high-P/high-T static experiments or shock experiments; however, although the measurement of temperature in shock experiments has been attempted, it is problematic (e.g., Yoo et al., 1993). There are a number of static experimental studies on pure iron at ambient pressures and high temperatures, and high pressures and ambient temperatures (see later). Simultaneously high-pressure/high-temperature experiments are very challenging, although they have been attempted (e.g., the iron phase diagram given earlier). In this section, we look at the thermoelastic properties of iron as obtained from ab initio calculations, and, where available, experimental data.

1000

2.06.4.1

Figure 10 Phase diagram of iron to extreme pressures, taken from Stixrude (2012). Bold black lines are results from Stixrude (2012); thin black lines show experimental phase boundaries. Red lines are the calculated isentrope (lower) and Hugoniot (upper). The black-dashed line is the low pressure fcc–hcp boundary where magnetic ordering has been neglected. The stability field of the liquid is shown by the gray section and is estimated from Lindemann’s law using the calculated vibrational frequencies. Reproduced from Stixrude L (2012) Structure of iron to 1 Gbar and 40,000 K. Physical Review Letters 108: 055505.

Equation of State

The equation of state for hcp-Fe has been studied both experimentally (e.g., Brown and McQueen, 1986; Mao et al., 1990) and computationally (e.g., So¨derlind et al., 1996). In Figure 11, we show the density as a function of pressure from ab initio calculations together with that from static compression measurements at 300 K (Mao et al., 1990), shock experiments (Brown and McQueen, 1986), theoretical calculations (Steinle-Neumann et al., 2002; Stixrude et al., 1997), and an

14 000 0 K 3000 K00 K 40 0 K 500 K 0 600

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Figure 11 Density as a function of pressure for hcp-Fe from ab initio calculations along isotherms between 2000 and 6000 K (modified from Vocˇadlo L, Alfe D, Gillan MJ, Wood IG, Brodholt JP, and Price GD (2003b) Possible thermal and chemical stabilisation of body-centred-cubic iron in the Earth’s core. Nature 424: 536–539). Filled circles are the static compression measurements at 300 K (Mao et al., 1990); dashed line is the calculation for the 4000 K isotherm of Stixrude et al. (1997); dotted lines are the 5000, 6000, and 7000 K isotherms of Steinle-Neumann et al., 2002; stars are from an analysis of a thermal equation of state at 6000 K (Isaak and Anderson, 2003); triangles up and down are the experiments of Brown and McQueen (1986) along the 300 K isotherm and Hugoniot, respectively.

Earth’s Core: Iron and Iron Alloys

analysis at 6000 K based on a thermal equation of state (Isaak and Anderson, 2003). All the results from both theory and experiment are in comforting agreement and provide a successful basis from which to make further comparisons of other properties.

2.06.4.2

Incompressibility

The isothermal and adiabatic incompressibility (KT and KS, respectively) are shown in Figure 12. The incompressibility increases significantly (and almost linearly) with pressure, and decreases with increasing temperature (more so in the case of KT than KS).

2.06.4.3

been reported by Stixrude and Cohen (1995a), So¨derlind et al (1996), Steinle-Neumann et al. (1999), and Vocˇadlo et al. (2003b). These values are plotted as a function of density in Figure 14(a) and 14(b). Although there is some scatter on the reported values of c12, overall the agreement between the experimental and various ab initio studies is excellent. The resulting bulk and shear moduli and the seismic velocities of hcp-Fe as a function of pressure are shown in Figures 15 and 16, along with the experimental data. The calculated values compare well with the experimental data at higher pressures; the discrepancies at lower pressures are probably due to the neglect of magnetic effects in the simulations (see Steinle-Neumann et al., 1999).

2.06.4.4.2 High-temperature elastic behavior and wave velocities

Thermal Expansion

The thermal expansivity, a, determined by ab initio computer calculations (Vocˇadlo et al., 2003b), is shown in Figure 13 together with the value determined from shock data at 5200 K (Duffy and Ahrens, 1993), the theoretical calculations of Stixrude et al. (1997), and an analysis using a thermal equation of state (Anderson and Isaak, 2002; Isaak and Anderson, 2003). It is clear that a decreases strongly with increasing pressure and increases significantly with temperature.

2.06.4.4

125

Elasticity of Solid Iron

A fundamental step toward resolving the structure and composition of Earth’s inner core is to obtain the elastic properties of the candidate phases that could be present.

2.06.4.4.1 Elastic constants of iron as a function of pressure at zero Kelvin The elastic constants of hcp-Fe at 39 and 211 GPa and ambient temperature have been measured experimentally (Mao et al., 1999). Calculations of elastic constants at 0 K for hcp-Fe have

The high-temperature elastic behavior of iron can be estimated by considering Birch’s law, which suggests that a linear relationship exists between the bulk sound speed, VF, and density, r; in the absence of reliable experimental data at very high pressures and temperatures, it has been assumed that this linearity may be extrapolated to the conditions of the inner core. Badro et al. (2007) used inelastic x-ray scattering in a DAC at high pressures, but ambient temperatures, to demonstrate a linear relationship between Vp and r for a number of systems including hcp-Fe. Figure 17 shows the fit to their results extrapolated to core density, together with the results from Vocˇadlo (2007) (where the uncertainties lie within the symbols) and also the results from shock experiments (Brown and McQueen, 1986). The agreement is generally very good; it is noteworthy that the calculated bcc-Fe and hcp-Fe velocity– density systematics are indistinguishable. More recent experimental data up to 93 GPa and 1100 K (Antonangeli et al., 2012) confirm the equivalence of temperature and density via Birch’s law as Vp scales linearly with density (Figure 18).

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Figure 12 Isothermal incompressibility, KT (solid lines), and adiabatic incompressibility, KS (dotted lines), as a function of pressure for hcp-Fe from ab initio calculations along isotherms between 2000 and 6000 K. Reproduced from Vocˇadlo L, Alfe D, Gillan MJ, Wood IG, Brodholt JP, and Price GD (2003b) Possible thermal and chemical stabilisation of body-centred-cubic iron in the Earth’s core. Nature 424: 536–539

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Earth’s Core: Iron and Iron Alloys

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P (GPa) Figure 13 Thermal expansion as a function of pressure for hcp-Fe from ab initio calculations (Vocˇadlo et al., 2003b) along isotherms between 2000 and 6000 K (solid lines). The circle is the value of Duffy and Ahrens (1993) determined from shock experiments at 5200  500 K; the dashed line is from theoretical calculations for the 4000 K isotherm (Stixrude et al., 1997); the diamonds are from an analysis of room temperature compression data at 300 K (Anderson and Isaak, 2002); the triangles (up: 6000 K, down: 2000 K) are from an analysis using a thermal equation of state applied to room temperature compression data (Isaak and Anderson, 2003). Modified from Vocˇadlo L, Alfe D, Gillan MJ, Wood IG, Brodholt JP, and Price GD (2003b) Possible thermal and chemical stabilisation of body-centred-cubic iron in the Earth’s core. Nature 424: 536–539.

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200 300 Pressure (GPa)

400

Figure 15 Plot of bulk modulus (diamonds) and shear modulus (squares) for hcp-Fe as a function of pressure, with values taken from Stixrude and Cohen (1995a), Steinle-Neumann et al. (1999), So¨derlind et al. (1996), Mao et al. (1999), and Vocˇadlo et al. (2003b). Black diamonds and squares represent ab initio values, while white diamonds and squares represent values obtained from experimentally determined elastic constants.

1000

0

1200

9

11

13

15

Density (g cc−1)

Figure 14 Combined plot of the elastic constants of hcp-Fe as a function of density calculated at 0 K from Stixrude and Cohen (1995b), So¨derlind et al (1996), Steinle-Neumann et al. (1999), and Vocˇadlo et al. (2003b) together with the experimental values of Mao et al. (1999); (a) c11 black diamonds, c12 white squares, c44 black circles, (b) c33 white diamonds, c13 black squares, and c66 white circles.

Figure 19 shows how VF varies with density for both athermal and high-temperature (up to 5500 K) ab initio calculations (Vocˇadlo, 2007), together with values from PREM (Dziewonski and Anderson, 1981), from the experiments of Brown and McQueen (1986), and from a previous computational study (6000 K; Steinle-Neumann et al., 2001). It is clear that Birch’s law holds for iron and that the velocities at constant density are almost temperature-independent.

Earth’s Core: Iron and Iron Alloys

Velocity (km s-1)

14

10

6

2

0

100

200 300 Pressure (GPa)

400

Figure 16 Plot of aggregate VP (diamonds) and VS (squares) wave velocity for hcp-Fe as a function of pressure, with values taken from Stixrude and Cohen (1995a), Steinle-Neumann et al. (1999), So¨derlind et al. (1996), Mao et al. (1999), and Vocˇadlo et al. (2003b). Black diamonds and squares represent ab initio values, while white diamonds and squares represent values obtained from experimentally determined elastic constants. White circles are the experimental data of Fiquet et al. (2001).

14

Vp (km s−1)

12 10 8 6 4 2 6000

8000

10 000

12 000

14 000

16 000

Density (kg m−3) Figure 17 P-wave velocity as a function of density for pure iron compared with the high-P ambient-T DAC experiments of Badro et al. (2007); solid line is the fit to data, dashed line is an extrapolation of the fit. Diamonds: calculated bcc-Fe VP at different temperatures; open squares: calculated hcp-Fe at different temperatures (Vocˇadlo, 2007); filled square: shock experiments of Brown and McQueen (1986).

127

hcp-Fe change dramatically as a function of temperature (Steinle-Neumann et al., 2001; Figure 21), and that compressional waves travel faster in the basal plane of hcp-Fe at high temperatures and pressures, in complete contrast to the low temperature results; this effect was also seen in ab initio molecular dynamics calculations (Vocˇadlo et al., 2009; Figures 22 and 23). The sense of the anisotropy is such that VP is fastest along the c-axis up to 5000 K but becomes reversed by 5500 K, with VP then becoming faster in the a–b plane. These results can account for the observed overall seismic anisotropy if the preferred orientation of hcp-Fe in the inner core is with the c-axis aligned parallel to the equatorial plane instead of parallel to the poles. Obviously, if the seismic anisotropy is caused by deformation, the three studies imply very different stresses and flow fields in the inner core (as described in Section 2.06.2.2). Indeed, for an iron core dominated by aligned crystals of hcpFe, with the c-axis aligned in the polar direction, the seismically observed isotropic outer–inner core could result from hcp-Fe close to melting where axial wave velocities become similar, while at greater depths, where iron is further from the melting point, a greater anisotropy can be achieved. A more recent study, however, shows that at the pressures of the center of the inner core (360 GPa) as opposed to the pressures required to produce inner core density (316 GPa) and high temperatures (just before melting), no c11–c33 crossover occurs and the sense of P-wave anisotropy is always such that the fast direction is along the c-axis (Figure 24; Martorell et al., 2013b). This work also shows significant shear softening as the melting temperature is approached. Figure 25 shows the P-wave anisotropy from ab initio molecular dynamics calculations of hcp-Fe compared to that for fcc-Fe and bcc-Fe at 316 GPa and 5500 K. For fcc-Fe, the maximum anisotropy along mutually perpendicular directions is 6% for crystals aligned along . For bcc-Fe, the maximum anisotropy that can be achieved through mutually perpendicular directions is never more than
2%. For the hcp-Fe phase, an
3% anisotropy can be achieved through mutually perpendicular directions whereby, for the polar P-wave velocity to be faster, the c-axis of the crystals would lie in Earth’s equatorial plane; this is close to the experimentally determined value of 4–5% (Antonangeli et al., 2004). Thus, for the bcc phase of iron, the observed seismic anisotropy in Earth’s inner core cannot be achieved by alignment alone, while for the hcp and fcc phases, it is just possible to achieve the required degree of anisotropy but only by a significant crystalline alignment. Such a high degree of alignment may not be necessary if the seismically observed P-wave anisotropy does not strictly require mutually perpendicular directions.

2.06.4.4.3 P-wave anisotropy As discussed in Section 2.06.2.2, seismic observations show that the P-wave velocity though the inner core is 3–5% faster in the polar direction than in the equatorial plane (e.g., Song and Helmberger, 1998). Experiments at moderate pressure and ambient temperature (Antonangeli et al., 2004), and calculations (Stixrude and Cohen, 1995a) at high pressures but at 0 K, showed that the compressional wave velocity along the c-axis of hcp-Fe is significantly faster than that in the basal plane; this led to the conclusion that the inner core is made up of oriented hcp-Fe crystals with the c-axis parallel to the rotational axis (Figure 20). However, more recent calculations (using a particle-in-cell method) found that the elastic properties of

2.06.4.4.4 Shear-wave anisotropy of the inner core While currently very difficult to detect, shear-wave anisotropy in the inner core has been observed in a number of seismic studies. PKJKP data suggest that shear-wave anisotropy increases with depth (Cao and Romanowicz, 2009) and can be modeled by alignment of hcp-Fe crystals with the c-axis perpendicular to the rotational axis, while normal mode studies reveal an upper layer in the inner core (Irving and Deuss, 2011) in which the shearwave velocity is isotropic. Experimental studies on textured hcp-Fe at pressures up to 172 GPa show that VS is 2–4% faster along the c-axis than the a-axis (Lin et al., 2010), while theoretical studies on the bcc, fcc, and hcp phases of iron find the

128

Earth’s Core: Iron and Iron Alloys

9500 1100 K

VP (m s-1)

9000

920 K

920 K

8500 1100 K 1100 K 1110 K

8000 700 K

7500

7000

920 K 930 K

9300

9600

9900

10 200

10 500

10 800

Density (kg m-3) Figure 18 Aggregate compressional wave velocity measured at ambient temperature (solid symbols) and high temperature (open symbols) plotted as a function of density. The dotted line is the velocity reduction expected at 1100 K for a softening of 0.35 ms1 K1 at a constant density of 10 250 kg m2. Reproduced from Antonangeli D, et al. (2012) Simultaneous sound velocity and density measurements of hcp iron up to 93 GPa and 1100 K: An experimental test of the Birch’s law at high temperature. Earth and Planetary Science Letters 331: 210–214.

12.00

VΦ(km s-1)

10.00

8.00

bcc-Fe -0 K

6.00

PREM – Dziewonski and Anderson (1981) bcc-Fe - F(T) hcp ferromagnetic hcp antiferromagnetic II

4.00

hcp = f(T) Steinle-Neuman et al. (2001) Brown and McQueen (1986)

2.00 8000

9000

10 000

11 000

12 000

13 000

14 000

Density (kg m-3) Figure 19 Calculated bulk sound velocity as a function of density for pure iron (Vocˇadlo, 2007) compared with previous calculations (Steinle-Neumann et al., 2001), PREM (Dziewonski and Anderson, 1981) and the shock experiments of Brown and McQueen (1986).

maximum shear-wave anisotropy at
316 GPa and
5500 K to be considerably higher (20%, 80% and 26%, respectively; Vocˇadlo et al., 2008a). In contrast, using a different methodology, more recent calculations find that hcp-Fe becomes increasingly isotropic in both VP and VS with temperature, to the extent that, by the time Earth’s core conditions are reached, iron is elastically isotropic (Sha and Cohen, 2010).

The seismically observed anisotropy and layering in the inner core could, therefore, be accounted for if the iron crystals (of single or mixed phases) were randomly oriented in the isotropic upper layer and significantly aligned in the anisotropic lower layer. In order to draw any further conclusions about the elasticity of the inner core, however, the effect of light elements must first be taken into account (see Section 2.06.8.3).

Earth’s Core: Iron and Iron Alloys

2400

1.10 1.08

c33 Elastic moduli (GPa)

1.04 V

c11

2000

Vs(010)

1.06

1.02

Vs(001)

1.00 VP

1600 c12

1200

c13

800 c66

0.98

400

c44

0.96 001

101 Propagation direction

0

100

1500

Sound velocity (km s–1)

3000 4500 Temperature (K)

6000

VP

12

The Temperature in Earth’s Core

Having shown how mineral physics can be used to understand the properties of solid iron, we turn now to its melting behavior. An accurate knowledge of the melting properties of Fe is particularly important, as the temperature distribution in the core is relatively uncertain and a reliable estimate of the melting temperature of Fe at the pressure of the ICB would impose a muchneeded constraint on core temperatures. As with the subsolidus behavior of Fe, there is much controversy over its high-P melting behavior. Static compression measurements of the melting temperature, Tm, have been made up to
200 GPa with the DAC (e.g., Boehler, 1993) and, more recently, using a laser-heated fast x-ray diffraction technique, which provides an unambiguous signature of melting (Anzellini et al., 2013; Figure 26), but even at lower pressures, results for Tm disagree by several hundred Kelvin. Shock experiments are at present the only available method to determine melting at inner core pressures, but their interpretation is not simple, and there is a scatter of at least 2000 K in the reported Tm of Fe at ICB pressures (see Nguyen and Holmes, 2004). An alternative to experiment is theoretical calculations, which can, in principle, determine accurate melting curves to any desired pressure. Indeed, ab initio methods have successfully been used to calculate the melting behavior of transition metals such as aluminum (Vocˇadlo and Alfe, 2002) and copper (Vocˇadlo et al., 2004). Using the technique of thermodynamic integration, Alfe` et al. (1999, 2004) calculated the melting curve of iron. The condition for two phases to be in thermal equilibrium at a given temperature, T, and pressure, P, is that their Gibbs free energies, G(P, T ), should be equal. To determine Tm at any pressure, therefore, Alfe` et al. (1999, 2004) calculated G for the solid (hcp) and liquid phases of iron as a function of T and determined where they are equal. In the more recent simulations, Alfe` et al. (2004) obtained an estimate of Tm of Fe at ICB

0

(a)

Figure 20 Single-crystal velocities in hcp-Fe as a function of propagation direction with respect to the c-axis. Note that VP(90 ) < VP(0 ). Reproduced from Stixrude L and Cohen RE (1995) High pressure elasticity of iron and anisotropy of Earth’s inner core. Science 267: 1972–1975.

2.06.5

129

10 8

Vs(010)

6 Vs(001)

4 2 0

(a)

20

60 40 Angle to c-axis (⬚)

80

Figure 21 (a) Single-crystal elastic constants as a function of temperature. Note the marked reductions in c33, c44, and c66. (b) Single-crystal velocities in hcp-Fe as a function of propagation direction with respect to the c-axis. Results at 6000 K (solid lines) are compared to static results (dashed lines). Note that at 6000 K, VP(90 ) > VP(0 ). Reproduced from Steinle-Neumann G, Stixrude L, Cohen RE, and Gulseren O (2001) Elasticity of iron at the temperature of the Earth’s inner core. Nature 413: 57–60.

pressures to be
6250, with an error of 300 K. For pressures P < 200 GPa (the range covered by DAC experiments), their curve lies
900 K above the values of Boehler (1993) and
200 K above the more recent values of Shen et al. (1998) (who stress that their values are only a lower bound to Tm). The ab initio curve falls significantly below the shock-based estimates for the Tm of Yoo et al. (1993), in whose experiments temperature was deduced by measuring optical emission (however, the difficulties of obtaining temperature by this method in shock experiments are well known), but accords almost exactly with the shock data value of Brown and McQueen (1986) and the data of Nguyen and Holmes (2004), and is in identical agreement with the most recent experimental estimate of 6230  500 K (Anzellini et al., 2013; Figure 26). The ab initio melting curve of Alfe` et al. (2004, 2009) differs somewhat from the calculations of both Belonoshko et al. (2000) and Laio et al. (2000). However, the latter two authors used model potentials fitted to ab initio simulations, and so their melting curves are those of the model potential and not the true ab initio one (it is

130

Earth’s Core: Iron and Iron Alloys

2500 c33 2000 Elastic modulus (GPa)

c11 1500 c12 1000 c23 c66

500

c44 0

0

1000

2000

3000

4000

5000

Temperature (K) Figure 22 Elastic constants of hcp-Fe at 316 GPa as a function of temperature; c66 is not independent and is equal to 1/2 (c11–c12). Those at 5500 K are taken from earlier work (Vocˇadlo, 2007). Reproduced from Vocˇadlo L, Dobson D, and Wood IG (2009) Ab initio calculations of the elasticity of hcp-Fe as a function of temperature at inner-core pressure. Earth and Planetary Science Letters 288: 534–538.

important to note here that Laio et al. (2000) used a more sophisticated approach in which the model potential had an explicit dependence on the thermodynamic state that exactly matched the ab initio result). In their paper, Alfe` et al. (2004) illustrated this ambiguity by correcting for the errors associated with the potential fitting of Belonoshko et al. (2000); the result is in almost exact agreement with the true ab initio curve. Finally, using quantum Monte Carlo techniques to compute the free energies of solid and liquid iron at ICB conditions, Sola and Alfe` (2009) obtained a significantly higher iron melting temperature at 330 GPa of 6900  400 K. The addition of light elements is estimated to reduce the melting temperature of pure iron by
700 K making the likely temperature at the ICB somewhere in the region of 5500–6200 K (Alfe` et al., 2002a). An independent measure of the likely temperature in the inner core was made by Steinle-Neumann et al. (2001), who performed first-principles calculations of the structure and elasticity of iron at high temperatures; they found that the temperature for which the elastic moduli best matched those of the inner core (including light element depression) was
5700 K.

2.06.6 2.06.6.1

Physical Properties of Liquid Iron Thermoelastic Properties

The outer core of Earth is liquid Fe–Ni alloyed with 5–10% light elements. Experiments on liquid iron at core conditions are prohibitively challenging. However, once more, from the ab initio simulation of the free energy of pure iron liquid, we can obtain first order estimates for a range of thermodynamic properties at the conditions of Earth’s outer core. Figure 27(a)–27(d) shows the results of ab initio calculations for values of density, adiabatic and isothermal bulk moduli,

thermal expansion coefficient, and heat capacity (Cv), respectively, for liquid iron over a range of pressures and temperatures (see Vocˇadlo et al., 2003b). Results from the experimental analysis of Anderson and Ahrens (1994) for density and adiabatic incompressibility are also shown (as gray lines; upper: 5000 K, lower: 8000 K). The calculations reproduce the experimentally derived density and incompressibility values to within a few percent. It is worth noting that the bulk sound velocity is almost independent of temperature, confirming the conclusion of Anderson and Ahrens (1994).

2.06.6.2

Viscosity and Diffusion

Viscosity is a very important parameter in geophysics because the viscosities of materials in Earth’s core are a contributory factor in determining the overall properties of the core itself, such as convection and heat transfer; indeed, the fundamental equations governing the dynamics of the outer core and the generation and sustention of the magnetic field are dependent, in part, on the viscosity of the outer-core fluid. Quantifying viscosity at core conditions is far from straightforward, especially as the exact composition of the outer core is not known. Furthermore, although there have been many estimates made for outer-core viscosity from geodetic, seismological, geomagnetic, experimental and theoretical studies, the values so obtained span 14 orders of magnitude (see Secco, 1995). Geodetic observations (e.g., free oscillations, the Chandler wobble, length of day variations, tidal measurements, and gravitimetry) lead to viscosity estimates ranging from 10 mPas (observations of the Chandler wobble; Verhoogen, 1974) to 1013 mPas (analysis of free oscillation data; Sato and Espinosa, 1967). Theoretical geodetic studies (e.g., viscous coupling of the core and mantle, theory of rotating fluids, inner core oscillations, and core nutation) lead to viscosity estimates ranging from 10 mPas (evaluation of decay time of

Earth’s Core: Iron and Iron Alloys

2000 K

131

3000 K

Vp contours km 12.76

X1

X2

Max. velocity = 12.76 Anisotropy = 6.9% lower hemisphere

Vp contours km s-1 12.58

s-1 X1

12.56 12.48 12.40 12.32 12.24 12.16 12.08 12.00

11.91 Shading -inverse log OMin. velocity = 11.91

X2

Max. velocity = 12.58 Anisotropy = 7.8% lower hemisphere

12.40 12.30 12.20 12.10 12.00 11.90 11.80

11.63 Shading -inverse log OMin. velocity = 11.63

5000 K

4000 K

Vp contours km s-1 12.00

X1

X2

Max. velocity = 12.00 Anisotropy = 6.3% lower hemisphere

X1

11.84 11.76 11.68 11.60 11.52 11.44 11.36

11.27 Shading -inverse log OMin. velocity = 11.27

Vp contours km s-1 11.45

11.28 X2

11.20 11.12 11.04

Max. velocity = 11.45 Anisotropy = 4.9% lower hemisphere

10.90 Shading -inverse log OMin. velocity = 10.90

5500 K

X1

Vp contours km s-1 11.47

11.28 11.20 11.12 11.04 10.96

X2

Max. velocity = 11.47 Anisotropy = 6.0% lower hemisphere

10.80 Shading -inverse log OMin. velocity = 10.80

Figure 23 Single-crystal P-wave velocities as a function of propagation direction for hcp-Fe at 316 GPa and temperatures of 2000, 3000, 4000, 5000, and 5500 K. The results at 5500 K are taken from the earlier work (Vocˇadlo, 2007). Note that the velocities in the [hk0] directions, perpendicular to the c-axis, are gradually becoming more equal to that along the c-axis until above 5000 K, the direction of maximum VP changes from [001] to [hk0]. Reproduced from Vocˇadlo L, Dobson D, and Wood IG (2009) Ab initio calculations of the elasticity of hcp-Fe as a function of temperature at inner-core pressure. Earth and Planetary Science Letters 288: 534–538.

132

Earth’s Core: Iron and Iron Alloys

Simulation temperature (K)

Elastic constants (GPa)

3000

0

2000

4000 c11 c12 c33 c13 c44

2500 2000

6000

8000

6600

6900

7200

7500 2000 1500

1500

1000

1000 500

500 0

0

0.2

(a)

0.4

0.6 T/Tm

0.8

0.9

1

0.95

1

0

(b)

Figure 24 Calculated elastic constants for hcp-Fe as a function of temperature at 360 GPa. The gray band represents the minimum and maximum melting temperatures in the literature for hcp-Fe at 360 GPa. (a) The complete temperature range. (b) Results in the nonlinear regime. Reproduced from Martorell B, Brodholt J, Wood IG, and Vocˇadlo L (2013b) Strong pre melting effect in the elastic properties of hcp-Fe under inner core conditions. Science 342: 466.

inner core oscillations; Won and Kuo, 1973) to 1014 mPas (secular deceleration of the core by viscous coupling; Bondi and Lyttleton, 1948). Generally, much higher values for viscosity (1010–1014 mPas) are obtained from seismological observations of the attenuation of P- and S-waves through the core (e.g., Jeffreys, 1959; Sato and Espinosa, 1967), and from geomagnetic data (e.g., 1010 mPas; Officer, 1986). The viscosities of core-forming materials may also be determined experimentally in the laboratory and theoretically through computer simulation. Empirically, viscosity follows an Arrhenius relation of the form (see Poirier, 2002):
 Qv ∝ exp kB T where Qv is the activation energy, T is the temperature, and kB is the Boltzmann constant. Poirier (1988) analyzed data for a number of liquid metals and found that there is also an empirical relation between Qv and the melting temperature, consistent with the generalized relationship of Weertman (1970): QV ffi 2:6RTm This very important result implies that the viscosity of liquid metals remains constant (i.e., independent of pressure) along the melting curve and, therefore, equal to that at the melting point at ambient pressure, which is generally of the order of a few millipascal seconds. Furthermore, Poirier went on to state that the viscosity of liquid iron in the outer core would, therefore, be equal to that at ambient pressure (
6 mPas; Assael et al., 2006). On a microscopic level, an approximation for the viscosity of liquid metals is given by the Stokes–Einstein equation, which provides a relationship between diffusion and viscosity of the form D ¼

kB T 2pa

where a is an atomic diameter and D is the diffusion coefficient. Theoretical values for diffusion coefficients have been obtained from ab initio molecular dynamics simulations on

liquid iron at core conditions (de Wijs et al., 1998), leading to a predicted viscosity of
12–15 mPas using the Stokes–Einstein relation given earlier. However, although the Stokes–Einstein equation has proved successful in establishing a link between viscosity and diffusion for a number of monatomic liquids, it is not necessarily the case that it should be effective for alloys or at high pressures and temperatures. Alfe` et al. (2002a) used the more rigorous Green–Kubo functions to determine viscosities for a range of thermodynamic states relevant to Earth’s core (Table 1). Throughout this range, the results show that liquid iron has a diffusion coefficient and viscosity similar to that under ambient conditions, a result already suggested much earlier by Poirier (1988). Both ab initio calculations and experiments consistently give viscosities of the order of a few millipascal seconds. More recently, Desgranges and Delhommelle (2007) used classical molecular dynamics calculations to obtain estimates for viscosity of the outer core also of the order of 10 mPas. This suggests that viscosity changes little with homologous temperature, and it is now generally accepted that the viscosity of the outer core is likely to be a few millipascal seconds (comparable to that of water on Earth’s surface).

2.06.6.3

The Structure of Liquid Iron

It has long been established that liquid structure is approximately constant along the melting curve (e.g., Ross, 1969) and here, in the case of iron, there appears to be a truly remarkable simplicity in the variation of the liquid properties with thermodynamic state; indeed, not only are viscosities and diffusivities almost invariant (as described earlier), but structural properties also show a similarly consistent behavior. Alfe` et al. (2002a) calculated the radial distribution function of liquid iron as a function of temperature at a density of 10 700 kg m3, representative of that in the upper outer core (Figure 28); between 4300 and 8000 K, the effect of varying temperature is clearly not dramatic, and consists only of the expected weakening and broadening of the structure with increasing T.

Earth’s Core: Iron and Iron Alloys

X1

11.80 11.60 11.40 11.20 11.00

X2

Max. velocity = 12.21 Anisotropy = 13.5%

(a)

Vp contours (km s-1) 12.21

10.67 Shading – inverse log O Min. velocity = 10.67

upper hemisphere

X1

Vp contours (km s-1) 11.41

11.35 11.30 11.25

X2

11.20 11.10

11.04 Shading – inverse log O Min. velocity = 11.04

(b) upper hemisphere X1

Max. velocity = 11.47 Anisotropy = 6.0%

(c)

Vp contours (km s-1) 11.47

11.28 11.20 11.12 11.04 10.96

X2

Thermal and Electrical Conductivity of Liquid Iron

The geodynamo is powered by the heat flux in the outer core, which, in turn, depends upon the thermal conductivity of the material present. Estimates for heat flux across the CMB have varied over the years but have generally been estimated to be of the order of 5–15 TW. Recent calculations on iron and iron alloys at the conditions of Earth’s core have found that the thermal conductivity is up to three times higher near the top of the outer core than previously thought (de Koker et al., 2012; Pozzo et al., 2012; Figures 30 and 31). The consequences of these results are significant. Such a high conductivity means that heat would accumulate at the top of the core, generating a thick stably stratified thermal layer. As a result, convection in the outer core would be restricted to a small region beneath this layer, suppressing the magnitude and variability of the magnetic field with time. The very high thermal conductivity predicted in the inner core (100 GPa) in diamond anvils. Experiments using radial RXD of polycrystalline samples under nonhydrostatic stress have been used to estimate the single-crystal elastic constants by using the measured lattice strains and CPO combined with model polycrystalline stress distribution (e.g., Reuss uniform stress field) (e.g., Mao et al., 1998, 2008a,b,c; Merkel et al., 2005, 2006b). The uncertainties in the absolute value of the elastic constants may be on the order of 10–20%, and model-dependent stress or strain distributions may be limited by the presence of elastic and plastic strain in some cases; however, this technique provides valuable information at extreme pressures. Inelastic x-ray scattering (IXS) has provided volume-averaged P-wave velocities of hcp iron as a function of pressures to 112 GPa and temperatures up to 1100 K (Antonangeli et al., 2004, 2010, 2012; Fiquet et al., 2001). Using knowledge of the CPO combined with different scattering geometries, Antonangeli et al. (2004) had determined the P-wave velocities in two directions and C11 elastic constant of hcp iron. The nuclear-resonant IXS technique provides a direct probe of the phonon density of states. By the integration of the measured phonon density of states, the elastic and thermodynamic parameters are obtained, and when combined with a thermal equation of state (EOS), the P- and S-wave velocities of hcp iron have been determined to 73 GPa and 1700 K in a laser-heated DAC by Lin et al. (2005). However, it has only recently been realized that RXD and IXS elastic constant or velocity determinations can be compromised by nonhydrostatic stresses in DACs and the elastic lattice strain equation is violated by the presence of plastic strain caused by differential stresses above the plastic yield stress of the crystals in some cases (Antonangeli et al., 2006; Mao et al., 2008a,b,c; Merkel et al., 2006b, 2009).

2.20.2.4 Effective Elastic Constants for Crystalline Aggregates The calculation of the physical properties from microstructural information (crystal orientation, volume fraction, grain shape,

etc.) is important for upper mantle rocks because it gives insight into the role of microstructure in determining the bulk properties and it is also important for synthetic aggregates experimentally deformed at simulated conditions of the Earth’s interior. A calculation can be made for the in situ state at high temperature and pressure of the deep Earth for samples where the microstructure has been changed by subsequent chemical alteration (e.g., the transformation from olivine to serpentine) or mechanically induced changes (e.g., fractures created by decompression). The in situ temperatures and pressures can be simulated using the appropriate single-crystal derivatives. Additional features not necessarily preserved in the recovered microstructure, such as the presence of fluids (e.g., magma), can be modeled (e.g., Blackman and Kendall, 1997; Mainprice, 1997; Williams and Garnero, 1996). Finally, the effect of phase change on the physical properties can also be modeled using these methods (e.g., Mainprice et al., 1990). Modeling is essential for anisotropic properties as experimental measurements in many directions necessary to fully characterize anisotropy are not currently feasible for the majority of the temperature and pressure conditions found in the deep Earth. In the following, we will only discuss the elastic properties needed for seismic velocities, but the methods apply to all tensorial properties where the bulk property is governed by the volume fraction of the constituent minerals. Many properties of geophysical interest are of this type, for example, thermal conductivity, thermal expansion, elasticity, and seismic velocities. However, these methods do not apply to properties determined by the connectivity of a phase, such as the electrical conductivity of rocks with conductive films on the grain boundaries (e.g., carbon). We will assume the sample may be microscopically heterogeneous due to grain size, shape, orientation, or phase distribution but will be considered macroscopically uniform. The complete structural details of the sample are in general never known, but a ‘statistically uniform’ sample contains many regions, which are compositionally and structurally similar, each fairly representative of the entire sample. The local stress and strain fields at every point r in a linear elastic polycrystal are completely determined by Hooke’s law as follows: sij ðrÞ ¼ Cijkl ðrÞ ekl ðrÞ where sij(r) is the stress tensor, Cijkl(r) is the elastic stiffness tensor, and ekl(r) is the strain tensor at point r. The evaluation of the effective constants of a polycrystal would be the summation of all components as a function of position, if we know the spatial functions of stress and strain. The average stress hsi and strain hei of a statistically uniform sample are linked by an effective macroscopic modulus C* that obeys Hooke’s law of linear elasticity: C* ¼ hsihei

1

ð ð where hei ¼ V1 eðr Þdr and < s >¼ V1 sðrÞdr where V is the

volume and the notation hi denotes an ensemble average. The stress s(r) and strain e(r) distribution in a real polycrystal varies discontinuously at the surface of grains. By replacing the real polycrystal with a ‘statistically uniform’ sample, we are assuming that s(r) and strain e(r) are varying slowly and continuously with position r. A number of methods are available for determining the effective macroscopic effective modulus of an aggregate.

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

We will briefly present these methods, which try to take into account an increasing amount of microstructural information, which of course results in increasing theoretical complexity but yields estimates, which are closer to experimental values. The methods can be classified by using the concept of the order of the statistical probability functions used to quantitatively describe the microstructure (Kr€ oner, 1978). A zero-order bound is given when one has no statistical information of the microstructure of the polycrystal and, for example, we do not know the orientation of the component crystals, and in this case, we have to use the single-crystal properties. The maximum and minimum of the single-crystal property are the zero-order bounds. The simplest and best-known averaging techniques for obtaining estimates of the effective elastic constants of polycrystals are the Voigt (1928) and Reuss (1929) averages. These averages only use the volume fraction of each phase, the orientation, and the elastic constants of the single crystals or grains. In terms of statistical probability functions, these are first-order bounds as only the first-order correlation function is used, which is the volume fraction. Note that no information about the shape or position of neighboring grains is used. The Voigt average is found by simply assuming that the strain field is everywhere constant (i.e., e(r) is independent of r). The strain at every position is set equal to the macroscopic strain of the sample. C* is then estimated by a volume average of local stiffnesses C(gi) with orientation gi and volume fraction Vi: hX i C*  CVoigt ¼ V Cðgi Þ i i Reuss average is found by assuming that the stress field is everywhere constant. The stress at every position is set equal to the macroscopic stress of the sample. C* or S* is then estimated by the volume average of local compliances S(gi): hX i 1 V Sð gi Þ C*  CReuss ¼ i i hX i S*  SReuss ¼ V Sðgi Þ i i   CVoigt 6¼ CReuss and CVoigt 6¼ SReuss

1

These two estimates are not equal for anisotropic solids with the Voigt being an upper bound and the Reuss a lower bound. A physical estimate of the moduli should lie between the Voigt and the Reuss average bounds as the stress and strain distributions are expected to be somewhere between uniform strain (the Voigt bound) and uniform stress (the Reuss bound). Hill (1952) observed that arithmetic mean (and the geometric mean) of the Voigt and Reuss bounds, sometimes called the Hill or Voigt–Reuss–Hill (VRH) average, is often close to experimental values. The VRH average has no theoretical justification. As it is much easier to calculate the arithmetic mean of the Voigt and Reuss elastic tensors, all authors have tended to apply the Hill average as an arithmetic mean. In Earth sciences, the Voigt, Reuss, and Hill averages have been widely used for averages of oriented polyphase rocks (e.g., Crosson and Lin, 1971). Although the Voigt and Reuss bounds are often far apart for anisotropic materials, they still provide the limits within which the experimental data should be found. Several authors have searched for a geometric mean of oriented polycrystals using the exponent of the average of the natural logarithm of the eigenvalues of the stiffness matrix (Matthies and Humbert, 1993). Their choice of this averaging procedure was guided by the fact that the ensemble average

503

elastic stiffness hCi should equal the inverse of the ensemble average elastic compliances hSi 1, which is not true, for example, of the Voigt and Reuss estimates. A method of determining the geometric mean for arbitrary orientation distributions has been developed (Matthies and Humbert, 1993). The method derives from the fact that a stable elastic solid must have an elastic strain energy that is positive. It follows from this that the eigenvalues of the elastic matrix must all be positive. Comparison between the Voigt, Reuss, and Hill and the self-consistent estimates shows that the geometric mean provides estimates very close to the self-consistent method but at considerably reduced computational complexity (Matthies and Humbert, 1993). The condition that the macroscopic polycrystal elastic stiffness hCi must equal the inverse of the aggregate elastic compliance hSi 1 would appear to be a powerful physical constraint on the averaging method (Matthies and Humbert, 1993). However, the arithmetic (Hill) and geometric means are very similar (Mainprice and Humbert, 1994), which tends to suggest that they are just mean estimates with no additional physical significance. The second set of methods uses additional information on the microstructure to take into account the mechanical interaction between the elastic elements of the microstructure. Mechanical interaction will be very important for rocks containing components of very different elastic moduli, such as solids, liquids, gases, and voids. The most important approach in this area is the ‘self-consistent’ (SC) method (e.g., Hill, 1965). The SC method was introduced for materials with a high concentration of inclusions where the interaction between inclusions is significant. In the SC method, an initial estimate of the anisotropic homogeneous background medium of the polycrystal is calculated using the traditional volume-averaging method (e.g., Voigt). All the elastic elements (e.g., grains and voids) are inserted into the background medium using Eshelby’s (1957) solution for a single ellipsoidal inclusion in an infinite matrix. The elastic moduli of the ensemble, inclusion, and background medium are used as the ‘new’ background medium for the next inclusion. The procedure is repeated for all inclusions and repeated in an iterative manner for the polycrystal until a convergent solution is found. The interaction is notionally taken into account by the evolution of the background medium that contains information about the inclusions, albeit in a homogenous form. As the inclusion can have an ellipsoidal shape, an additional microstructural parameter is taken into account by this type of model. A hybrid self-consistent method that combines elements of the geometric mean for the calculation of the elastic properties of multiphase rock samples has been introduced by Matthies (2010, 2012). Several people (e.g., Bruner, 1976) have remarked that the SC progressively overestimates the interaction with increasing concentration. They proposed an alternative differential effective medium (DEM) method in which the inclusion concentration is increased in small steps with a reevaluation of the elastic constants of the aggregate at each increment. This scheme allows the potential energy of the medium to vary slowly with inclusion concentration (Bruner, 1976). Since the addition of inclusions to the background material is made in very small increments, one can consider the concentration step to be very dilute with respect to the current effective medium. It follows that the effective interaction between inclusions can be considered negligible and we can use the

504

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

inclusion theory of Eshelby (1957) to take into account the interaction. In contrast, the SC uses Eshelby’s theory plus an iterative evaluation of the background medium to take into account the interaction. Mainprice (1997) had compared the results of SC and DEM for anisotropic oceanic crustal and mantle rocks containing melt inclusions and found the results to be very similar for melt fractions of less than 30%. At higher melt fractions, the SC exhibits a threshold value around 60% melt, whereas the DEM varies smoothly up a 100% melt. The presence of a threshold in the SC calculations is due to the specific way that the interaction is taken into account. The estimates of both methods are likely to give relatively poor results at high fractions of a phase with strong elastic contrast with the other constituents as other phenomena, such as mechanical localization related to the percolation threshold, are likely to occur. The third set of methods uses higher-order statistical correlation functions to take into account the first- or higher-order neighbor relations of the various microstructural elements. The factors that need to be statistically described are the elastic constants (determined by composition), orientation, and relative position of an element. If the element is considered to be small relative to grain size, then grain shape and the heterogeneity can be accounted for the relative position correlation function. Nearest neighbors can be taken into account using two-point correlation function, which is also called an autocorrelation function by some authors. If we use the ‘statistically uniform’ sample introduced earlier, we are effectively assuming that all the correlation functions used to describe the microstructure up to order infinity are statistically isotropic; this is clearly a very strong assumption. In the special case where all the correlation functions up to order infinity are defined, Kr€ oner (1978) had shown that the upper and lower bounds converge for the self-consistent method so that Csc ¼ (Ssc) 1. The statistical continuum approach is the most complete description and has been extensively used for model calculations (e.g., Beran et al., 1996; Mason and Adams, 1999). Until recently, it has been considered too involved for practical application. With the advent of automated determination of crystal orientation and positional mapping using electron backscattered diffraction (EBSD) in the scanning electron microscope (Adams et al., 1993), digital microstructural maps are now available for the determination of statistical correlation functions. This approach provides the best possible estimate of the elastic properties but at the expense of considerably increased computational complexity. The fact that there is a wide separation in the Voigt and Reuss bounds for anisotropic materials is caused by the fact that the microstructure is not fully described by such methods. However, despite the fact that these methods do not take into account such basic information as the position or the shape of the grains, several studies have shown that the Voigt average or the Hill average is within 5–10% of experimental values for low-porosity rocks free of fluids. For example, Barruol and Kern (1996) showed for several anisotropic lower crust and upper mantle rocks from the Ivrea zone in Italy that the Voigt average is within 5% of the experimentally measured velocity. Finally, from a practical point of view, a free and open-source MTEX toolbox is now available (https://code.google.com/p/mtex/) for effective medium calculations, such as Voigt, Reuss, and

Hill averages for second-, third-, and fourth-rank tensors, and, plotting the results, a wide variety of graphic formats. A detailed description of the application of MTEX to elastic and seismic properties can be found in Mainprice et al. (2011).

2.20.2.5 Seismic Properties of Polycrystalline Aggregates at High Pressure and Temperature The orientation of crystals in a polycrystal can be measured by volume diffraction techniques (e.g., x-ray or neutron diffraction) or individual orientation measurements (e.g., U-stage and optical microscope, electron channeling, or EBSD). In addition, numerical simulations of polycrystalline plasticity also produce populations of crystal orientations at mantle conditions (e.g., Tommasi et al., 2004). An orientation, often given the letter g, of a grain or crystal in sample coordinates can be described by the rotation matrix between crystal and sample coordinates. In practice, it is convenient to describe the rotation by a triplet of Euler angles, for example, g ¼ (’1 f ’2) used by Bunge (1982). One should be aware that there are many different definitions of Euler angles that are used in the physical sciences. The orientation distribution function (ODF) f(g) is defined as the volume fraction of orientations with an orientation in the interval between g and g + dg in a space containing all possible orientations given by ð DV=V ¼ f ðgÞ dg where DV/V is the volume fraction of crystals with orientation g, f(g) is the texture function, and dg ¼ 1/8p2 sin f d’1 df d’2 is the volume of the region of integration in orientation space. To calculate the seismic properties of a polycrystal, one must evaluate the elastic properties of the aggregate. In the case of an aggregate with a crystallographic fabric, the anisotropy of the elastic properties of the single crystal must be taken into account. For each orientation g, the single-crystal properties have to be rotated into the specimen coordinate frame using the orientation or rotation matrix gij: Cijkl ðgÞ ¼ gip :gjq :gkr :glt Cpqrt ðgo Þ where Cijkl(g) is the elastic property in sample coordinates, gij ¼ g(’1 f ’2) is the measured orientation in sample coordinates, and Cpqrt(go) is the elastic property in crystal coordinates. The elastic properties of the polycrystal may be calculated by integration over all possible orientations of the ODF. Bunge (1982) had shown that integration is given as ð

 Cijkl m ¼ Cijkl mðgÞf ðgÞ dg

where hCijklim is the elastic properties of the aggregate of mineral m. Alternatively, it may be determined by simple summation of individual orientation measurements: X

 Cijkl m ¼ Cijkl mðgÞ:vðgÞ

where v( g) is the volume fraction of the grain in orientation g. For example, the Voigt average of the rock for m mineral phases of volume fraction v(m) is given as

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective X 

 vðmÞ Cijkl m Cijkl Voigt ¼

The final step is the calculation of the three seismic phase velocities by the solution of the Christoffel equation, details of which are given earlier. To calculate the elastic constants at pressures and temperatures, the single-crystal elastic constants are given at the pressure and temperature of their measurement by using the following relationship:     Cij ðPT Þ ¼ Cij ðP o T o Þ + dCij =dP DP + 1=2 d2 Cij =dP 2 DP 2    2  + dCij =dT DT + d Cij =dPdT DPDT

where Cij(PT ) are the elastic constants at pressure P and temperature T, Cij(PoTo) are the elastic constants at a reference pressure Po (e.g., 0.1 MPa) and temperature To (e.g., 25  C), dCij/dP is the first-order pressure derivative, dCij/dT is the firstorder temperature derivative, DP ¼ P Po, and DT ¼ T To. The equation is a Maclaurin expansion of the elastic tensor as a function of pressure and temperature, which is a special case of a Taylor expansion as the series is developed about the elastic constants at the reference condition Cij(PoTo). The series only represent the variation of the Cij in their intervals of pressure and temperature of convergence, in other words the pressure and temperature range of the experiments or atomic modeling calculations used to determine the derivatives. Note that this equation is not a polynomial and care has to be taken when using the results of data fitted to polynomials, as, for example, the second-order derivatives fitted to a polynomial should be multiplied by two for use in the equation mentioned earlier, for example, second-order pressure derivatives for MgO given by Sinogeikin et al., (2001). Also note that this equation is not a Eulerian finite strain EOS (e.g., Davies, 1974; see succeeding text), and data fit to such an equation will not have derivatives compatible with the equation mentioned earlier, for example, the pressure derivatives of brucite determined by Jiang et al. (2006). The second-order pressure derivatives d2Cij/dP2 are available for an increasing number of mantle minerals (e.g., olivine, orthopyroxene, garnet, and MgO), and the first-order temperature derivatives seem to adequately describe the temperature dependence of most minerals, although the secondorder derivatives are also available in a few cases (e.g., garnet, fayalite, forsterite, and rutile; see Isaak, 2001 for references). Experimental measurements of the cross pressure–temperature derivatives d2Cij/dPdT (i.e., the temperature derivative of the Cij/dP at constant temperature) are still very rare. For example, despite the fact that MgO (periclase) is a well-studied reference material for high-pressure studies, the complete set of singlecrystal cross derivatives were measured for the first time by Chen et al. (1998) to 8 GPa and 1600 K. The effect of the cross derivatives on the Vp and dVs anisotropy of MgO is dramatic, and the anisotropy is increased by a factor of 2 when cross derivatives are used (Figure 11). Note that when a phase transition occurs, then the specific changes in elastic constants at pressures near the phase transition will have to be taken into account, for example, the SiO2 polymorphs (Carpenter, 2006; Cordier et al., 2004a; Karki et al., 1997c). The seismic velocities also depend on the density of the minerals at pressure and temperature, which can be calculated using an appropriate EOS (Knittle, 1995). The Murnaghan EOS derived from finite strain is sufficiently accurate at

0.55 MgO at 8 GPa

0.50

Cubic anisotropy factor (A)



505

A = ((2C44+ C12)/C11) − 1

0.45 0.40 0.35 0.30 0.25 0.20 0.15

dCij /dPdT = 0 0

200

400

600 800 1000 1200 1400 Temperature (°C)

Figure 11 An illustration of the importance of the cross pressure– temperature derivatives for cubic MgO at 8 GPa pressure. With increasing temperature at constant pressure, the anisotropy measured by the cubic anisotropy factor (A) increases by a factor of 2. Data from Chen et al. (1998).

moderate compressions (Knittle, 1995) of the upper mantle and leads to the following expression for density as a function of pressure: rðP Þ ¼ ro ð1 + ðK 0 =K Þ:ðP

P o ÞÞ

1=K 0

where K is the bulk modulus, K0 ¼ dK/dP is the pressure derivative of K, and ro is the density at reference pressure Po and temperature To. For temperature, the density varies as  ð rðT Þ ¼ ro 1 avðT ÞdT  ro ½1 aav ðT T o Þ

where av(T ) ¼ 1/V(@V/@T ) is the volume thermal expansion coefficient as a function of temperature and aav is an average value of thermal expansion that is constant over the temperature range (Fei, 1995). According to Watt (1988), an error of less than 0.4% on the P and S velocity results from using aav to 1100 K for MgO. For temperatures and pressures of the mantle, the density is described for this chapter by n o 1=K 0 rðP, T Þ ¼ ro ð1 + ðK 0 =K Þ:ðP P o ÞÞ ½1 aav ðT T o Þ

An alternative approach for the extrapolation elastic constants to very high pressures is Eulerian finite strain theory (e.g., Davies, 1974). The theory is based on a Maclaurin expansion of the free energy in terms of Eulerian finite volumetric strain. For example, Karki et al. (2001) reformulated Davies’s equations for the elastic constants in terms of finite volumetric strain (f ) as   Cijkl ð f Þ ¼ ð1 + 2f Þ7=2 Coijkl + b1 f + 1⁄2 b2 f +   PDijkl where

h i f ¼ 1⁄2 ðV o =V Þ2=3 1   b1 ¼ 3K o dCoijkl =dP 5C  2  oijkl   2 b2 ¼ 9K o d Coijkl =dP 2 + 3ðK o =dP Þ b1 + 7Coijkl 16b1 49Coijkl Dijkl ¼ dij dkl dik djl dil djk

506

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

This formulation in terms of finite strain can be very useful for finding the elastic constants a given pressure from series of ab initio calculations at different pressures, for example, room pressure. With the advent of practical computational methods for applying first-principles (ab initio) methods to calculation of elastic constants of minerals at extreme pressures reduces the Eulerian finite strain theory to a descriptive tool, if tensors are available at the appropriate pressure (and temperature) conditions. The simple Maclaurin series expansions given earlier for pressure and temperature are a compact way of describing the variation of the elastic tenors in experimentations at high pressure and temperature. Extrapolation of the simple Maclaurin series expansions outside the range of experimental (or computational) data is not recommended, as the formulation is descriptive. The Eulerian finite volumetric strain formulation has the merit of a physical basis, and hence, extrapolation beyond the experimental data range may be undertaken with caution. In practice, applications of the Eulerian finite volumetric strain formulation have been mainly limited to high-symmetry crystals (e.g., Li et al., 2006b, cubic Ca-perovskite, trigonal brucite Jiang et al., 2006) but can be applied to lower symmetries (e.g., monoclinic chlorite Mookherjee and Mainprice, 2014). A thermodynamically correct formulation of the problem intermediate values in terms of pressure and temperature has been proposed by Stixrude and Lithgow-Bertelloni (2005a,b).

2.20.2.6 Anisotropy of Minerals in the Earth’s Mantle and Core To understand the anisotropic seismic behavior of polyphase rocks in the Earth’s mantle, it is instructive to first consider the properties of the component single crystals. In this section, I will emphasis the anisotropy of individual minerals rather than the magnitude of velocity. The percentage anisotropy (A) is defined here as A ¼ 200 (Vmaximum Vminimum)/ (Vmaximum + Vminimum), where the maximum and minimum are found by exploring a hemisphere of all possible propagation directions. Note that for P-wave velocities, the anisotropy is defined by the maximum and minimum velocities in two different propagation directions, for example, the maximum A is given by the maximum and minimum Vp in a hemisphere or for Vp in two specific directions such as the vertical and horizontal can be used. For S-waves in an anisotropic medium, there are two orthogonally polarized S-waves with different velocities for each propagation direction; hence, A can be defined for each direction. The consideration of the singlecrystal properties is particularly important for the transition zone (410–660 km) and lower mantle (below 660 km) as the deformation mechanisms and resulting preferred orientation of these minerals under the extreme conditions of temperature and pressure are very poorly documented by experimental investigations. In choosing the anisotropic single-crystal properties, where possible, I have included the most recent experimental determinations. A major trend in recent years is the use of computational modeling to determine the elastic constants at very high pressures and more recently at high temperatures. The theoretical modeling gives a first estimate of the pressure and temperature derivatives in a range not currently accessible to direct measurement (see review by Karki et al., 2001; also see

Chapter 2.08). Although there is an increasing amount of single-crystal data available to high temperature or high pressure, no data are available for simultaneous high temperature and pressure of the Earth’s lower mantle or inner core (see Figure 1 for the pressure and temperatures).

2.20.2.6.1 Upper mantle The upper mantle (down to 410 km) is composed of three anisotropic and volumetrically important phases: olivine, enstatite (orthopyroxene), and diopside (clinopyroxene). The other volumetrically important phase is garnet, which is nearly isotropic and hence not of great significance to our discussion of anisotropy. Olivine – A certain number of accurate determinations of the elastic constants of olivine are now available, which all agree that the anisotropy of Vp is 25% and maximum anisotropy of Vs is 18% at ambient conditions for a mantle composition of about Fo90. The first-order temperature derivatives have been determined between 295 and 1500 K for forsterite (Isaak et al., 1989a) and olivine (Isaak, 1992). The first- and second-order pressure derivatives for olivine were first determined to 3 GPa by Webb (1989). However, a determination to 17 GPa by Zaug et al. (1993) and Abramson et al. (1997) has shown that the second-order derivative is only necessary for elastic stiffness modulus C55. The first-order derivatives are in good agreement between these two studies. The second-order derivative for C55 has proved to be controversial. Zaug et al. (1993) were the first to measure nonlinear variations of C55 with pressure, but other studies have not reproduced this behavior (e.g., for olivine Chen et al., 1996; Zha et al., 1998) or forsterite Zha et al., 1996). The anisotropy of the olivine single crystal increases slightly with temperature (+2%) using the data of Isaak (1992) and reduces slightly with increasing pressure using the data of Abramson et al. (1997). Orthopyroxene – The elastic properties of orthopyroxene (enstatite or bronzite) with a magnesium number (Mg/ Mg + Fe) near the typical upper mantle value of 0.9 have also been extensively studied. The Vp anisotropy varies between 15.1% (En80 bronzite; Frisillo and Barsch, 1972) and 12.0% (En100 enstatite; Weidner et al., 1978) and the maximum Vs anisotropy between 15.1% (En80 bronzite; Webb and Jackson, 1993) and 11.0% (En100 enstatite; Weidner et al., 1978). Some of the variation in the elastic constants and anisotropy may be related to composition and structure in the orthopyroxenes (Duffy and Vaughan, 1988). Near-end-member enstatite containing Ca shows only small changes in the bulk and shear moduli by 5% and 3% from the pure Mg endmember (Perrillat et al., 2007). The first-order temperature derivatives have been determined over a limited range between 298 and 623 K (Frisillo and Barsch, 1972). An extended range of temperature derivatives has been given by Jackson et al. (2007) up to 1073 K at ambient pressure. The first- and second-order pressure derivatives for Enstatite have been determined up to 12.5 GPa by Chai et al. (1977b). This study confirms an earlier one of Webb and Jackson to 3 GPa that showed that the first- and second-order pressure derivatives are needed to describe the elastic constants at mantle pressures. The anisotropy of Vp and Vs does not vary significantly with pressure using the data of Chai et al. (1977a) to 12.5 GPa. The anisotropy of Vp and Vs does increase by about 3% when

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective extrapolating to 1000 C using the first-order temperature derivatives of Frisillo and Barsch (1972). Clinopyroxene – The elastic constants of clinopyroxene (diopside) of mantle composition have only been experimentally measured at ambient conditions (Collins and Brown, 1998; Levien et al., 1979); both studies show that Vp anisotropy is 29% and Vs anisotropy is between 20% and 24%. There are no measured single-crystal pressure derivatives. In one of the first calculations of the elastic constants of a complex silicate at high pressure, Matsui and Busing (1984) predicted the first-order pressure derivatives of diopside from 0 to 5 GPa. The calculated elastic constants at ambient conditions are in good agreement with the experimental values, and the predicted anisotropy for Vp and Vs of 35.4% and 21.0%, respectively, is also in reasonable agreement. The predicted bulk modulus of 105 GPa is close to the experimental value of 108 GPa given by Levien et al. (1979). The pressure derivative of the bulk modulus 6.2 is slightly lower than the value of 7.8  0.6 given by Bass et al. (1981). Using the elastic constants of Matsui and Busing (1984), the Vp anisotropy decreases from 35.4% to 27.7% and Vs increases from 21.0% to 25.5% with increasing pressure from ambient to 5 GPa. A recent ab inito study of the effect of pressure on the elastic constants of diopside and jadeite from 0 to 20 GPa shows a slight decrease in Vp anisotropy from 23.4% to 17.9% and a slight increase in Vs anisotropy from 20.1% to 25.2% (Walker, 2012). Isaak and

Vp (km s−1)

Ohno (2003) and Isaak et al. (2005) had measured the temperature derivatives of chrome diopside to 1300 K at room pressure that are notably smaller than other mantle minerals. The single-crystal seismic properties of olivine, enstatite, and diopside at 220 km depth are illustrated in Figure 12. Garnet is nearly isotropic with Vp anisotropy of 0.6% and Vs of 1.3%. The determination of the elastic constants of diopside with upper mantle composition (Collins and Brown, 1998) at ambient pressure agrees closely with values for chrome diopside, except for a 3% decrease in the shear modulus (C44).

2.20.2.6.2 Transition zone Over the last 20 years, a major effort has been made to experimentally determine the phase petrology of the transition zone and lower mantle. Whereas single crystals of upper mantle phases are readily available, single crystals of transition zone and lower mantle for elastic constant determination have to be grown at high pressure and high temperature. The petrology of the transition zone is dominated by garnet, majorite, wadsleyite, ringwoodite, calcium-rich perovskite, clinopyroxene, and possibly stishovite. Majorite – The pure Mg end-member majorite of the majorite–pyrope garnet solid solution has tetragonal symmetry and is weakly anisotropic with 1.8% for Vp and 9.1% for Vs (Pacalo and Weidner, 1997). A study of the majorite–pyrope system by Heinemann et al. (1997) shows that tetragonal form

dVs (%) 9.65

8.6

7.8

(100) (001)

7.59 Max. velocity = 9.65 Anisotropy = 23.8%

Min. velocity = 7.59

0.28 Max. anisotropy = 16.01

8.81

Enstatite

8.40

12.0

8.20

8.0

Min. velocity = 7.68

0.50 Max. anisotropy = 17.59

9.35

(010)

(001)

Min. velocity = 7.87

26.05

21.0 18.0 15.0 12.0 9.0 6.0

7.87 Max. velocity = 9.35 Anisotropy = 17.2 %

0.50

Min. anisotropy = 0.50

26.05

8.80 8.60 8.40 8.20

(100)

17.59

4.0

7.68 Max. velocity = 8.81 Anisotropy = 13.7 %

0.28

Min. anisotropy = 0.28

17.59

8.00

Diopside

16.01

14.0 12.0 10.0 8.0 6.0 4.0

8.2

(010)

Vs1 polarization 16.01

9.0

Olivine

507

1.02 Max. anisotropy = 26.05

1.02

Min. anisotropy = 1.02

Figure 12 Single-crystal anisotropic seismic properties of upper mantle minerals olivine (orthorhombic), enstatite (orthorhombic), and diopside (monoclinic) at about 220 km (7.1 GPa, 1250  C).

508

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

of majorite is restricted to a composition of less 20% pyrope and hence is unlikely to exist in the Earth’s transition zone. Majorite with cubic symmetry is nearly isotropic with Vp anisotropy of 0.5% and Vs of 1.1%. Pressure derivatives for majorite and majorite–pyrope have been determined by Sinogeikin and Bass (2002a) and temperature derivatives by the same authors (2002b). Cubic majorite has very similar properties to pyrope garnet (Chai et al., 1997a) as might be expected. The elastic properties of sodium-rich majorite have been studied by Reichmann et al. (2002). Wadsleyite – The elastic constants of Mg2SiO4 wadsleyite were first determined by Sawamoto et al. (1984), and this early determination was confirmed by Zha et al. (1997) with a Vp anisotropy of 16% and Vs of 17%. The (Mg,Fe)2SiO4 wadsleyite has slightly lower velocities and higher anisotropies (Sinogeikin et al., 1998). The first-order pressure derivatives determined from the data of Zha et al. (1997) to 14 GPa show that the anisotropy of Mg2SiO4 wadsleyite decreases slightly with increasing pressure. At pressures corresponding to the 410 km seismic discontinuity (ca. 13.8 GPa), the Vp anisotropy would be 11.0% and Vs 12.5%. Ringwoodite – The elastic constants of Mg2SiO4 ringwoodite were first measured by Weidner et al. (1984) and (Mg,Fe)2SiO4 ringwoodite by Sinogeikin et al. (1998) at ambient conditions with Vp anisotropy of 3.6 and 4.7% and Vs of 7.9 and 10.3%, respectively. Kiefer et al. (1997) had calculated the elastic constants of Mg2SiO4 ringwoodite to 30 GPa. Their constants at ambient conditions give a Vp anisotropy of 2.3% and Vs of 4.8% very similar to the experimental results of Weidner et al. (1984). There is a significant variation (5–0%) of the anisotropy of ringwoodite with pressure 15 GPa (ca. 500 km depth), the Vp anisotropy is 0.4%, and Vs is 0.8%; hence, ringwoodite is nearly perfectly isotropic at transition zone pressures. Single-crystal temperature derivatives have Vp (km s−1)

been measured for ringwoodite ( Jackson et al., 2000; Sinogeikin et al., 2001), but none are available for wadsleyite. Olivine transforms to wadsleyite at about 410 km, and wadsleyite transforms to ringwoodite at about 500 km; both transformations result in a decrease in anisotropy with depth. The gradual transformation of clinopyroxene to majorite between 400 and 475 km would also result in a decrease in anisotropy with depth. The seismic anisotropy of wadsleyite and ringwoodite is illustrated in Figure 13. An ab initio molecular dynamics study by Li et al. (2006a) has shown that ringwoodite is nearly isotropic at transition zone conditions with P- and S-wave anisotropies close to 1%; extrapolated experimental values to a depth of 550 km (19.1 GPa, 1520  C) suggest that the Vp anisotropy and Vs anisotropy are 3.3% and 8.2%.

2.20.2.6.3 Lower mantle The lower mantle is essentially composed of perovskite, ferropericlase, and possibly minor amount of SiO2 in the form of stishovite in the top part of the lower mantle (e.g., Ringwood, 1991). Ferropericlase is the correct name for (Mg,Fe)O with small percentage of iron, less than 50% in Mg site; previously, this mineral was incorrectly called magnesiowu¨stite, which should have more than 50% Fe. It is commonly assumed that there is about 20% Fe in ferropericlase in the lower mantle. MgSiO3 may be in the form of perovskite or possibly ilmenite. The ilmenite-structured MgSiO3 is most likely to occur at the bottom of the transition zone and the top of the lower mantle. In addition, perovskite transforms to postperovskite in the D00 layer, although extract distribution with depth (or pressure) of the phases will depend on the local temperature and their iron content. Perovskite (MgSiO3 and CaSiO3) – The first determination of the elastic constants of pure MgSiO3 perovskite at ambient conditions was given by Yeganeh-Haeri et al. (1989). However, dVs (%)

11.36

13.63

13.63

10.0

11.0

Wadsleyite

Vs1 polarization

8.0

10.8

6.0

10.6

4.0

10.4

(100) (010)

(001)

10.26 Max. velocity = 11.36 Anisotropy = 10.2 %

Min. velocity = 10.26

0.15 Max. anisotropy = 13.63

10.15

8.22

8.22

7.0

10.10 10.05

5.0

10.00

Ringwoodite

0.15

Min. anisotropy = 0.15

9.95

3.0

9.90 1.0 9.82 Max. velocity = 10.15 Anisotropy = 3.3 %

Min. velocity = 9.82

0.00 Max. anisotropy = 8.22

0.00

Min. anisotropy = 0.00

Figure 13 Single-crystal anisotropic seismic properties of transition zone minerals wadsleyite (orthorhombic) at about 450 km (15.2 GPa, 1450  C) and ringwoodite (cubic) at about 550 km (19.1 GPa, 1520  C).

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

this determination has been replaced by a more accurate study of a better quality crystal (Yeganeh-Haeri, 1994). The 1994 study gives Vp anisotropy of 13.7% and Vs of 33.0%. The [010] direction has the maximum dVs anisotropy. A new measurement of the elastic constants of MgSiO3 perovskite at ambient conditions was made by Sinogeikin et al. (2004) and gives Vp anisotropy of 7.6% and dVs of 15.4%, which has a very similar velocity distribution to the determination of Yeganeh-Haeri (1994), but the anisotropy is reduced by a factor of 2. Karki et al. (1997a) calculated the elastic constants of MgSiO3 perovskite 140 GPa at 0 K. The calculated constants are in close agreement with the experimental measurements of Yeganeh-Haeri (1994) and Sinogeikin et al. (2004). Karki et al. (1997a) found that significant variations in anisotropy occurred with increasing pressure, first decreasing to 6% at 20 GPa for Vp and to 8% at 40 GPa for Vs and then increasing to 12% and 16%, respectively, at 140 GPa. At the 660 km seismic discontinuity (ca. 23 GPa), the Vp and Vs anisotropies would be 6.5% and 12.5%, respectively. Recent progress in finite temperature first-principles methods for elastic constants has allowed their calculation at lower mantle pressures and temperatures. Oganov et al. (2001) calculated the elastic constants of Mg-perovskite at two pressures and three temperatures for the lower mantle (Figure 14). More recently, Wentzcovitch et al. (2004) had calculated the elastic constants over the complete range of lower mantle conditions and produced pressure and temperature derivatives. The results for pure Mg-perovskite from Oganov et al. and Wentzcovitch et al. agree quite closely for P-wave anisotropy, but Oganov’s elastic constants give a higher S-wave anisotropy. At ambient conditions, the results from all studies are very similar with the Vp anisotropy that is 13.7% and the Vs anisotropy that is 33.0%. When extrapolated along a geotherm using the pressure and temperature derivatives of Wentzcovitch et al. (2004), the P- and S-wave anisotropies about the same at 8% at 1000 km

Vp (km s−1)

depth and again similar anisotropies of 13% at 2500 km depth. The plasticity of Mg-perovskite has been studied using ab initio dislocation modeling to determine the critical resolved shear stresses at lower mantle pressures and viscoplastic selfconsistent (VPSC) modeling (Mainprice et al., 2008a). Using the VPSC-predicted CPO and ab initio elastic constants of Oganov et al. (2001), the predicted anisotropy at lower mantle pressures and temperatures is weak (>3% for P-waves and >2% for S-waves) and decreases with increasing temperature and pressure. The other perovskite structure present in the lower mantle is CaSiO3 perovskite; recent ab initio molecular dynamics study by Li et al. (2006b) has shown that this mineral is nearly isotropic at lower mantle conditions with P- and S-wave anisotropies close to 1%. Recent extension of experimental measurements to in situ lower mantle conditions and more refined ab initio modeling at finite temperature are starting to challenge previous results. The measurement of sound velocities at lower mantle conditions by Murakami et al. (2012) suggests that the lower mantle is composed of 93% Mg-perovskite. However, a state-ofthe-art ab initio modeling of Mg-perovskite elastic properties (Zhang et al., 2013) with the current view of a pyrolite mantle composition for lower mantle provides an alterative view. The work of Zhang et al. (2013) also allows a better understanding of the P- and S-wave anisotropies along geotherms at 1500, 2500, and 3500 K. In Figure 15, you can see that for P-wave anisotropy, there is little effect of temperature and the anisotropy increases with depth. For S-wave, there is strong increase of anisotropy with temperature and depth. Mg-perovskite may be playing more important role in the seismic anisotropy of the D00 layer than we have considered so far. MgSiO3 ilmenite – Experimental measurements by Weidner and Ito (1985) have shown that MgSiO3 ilmenite of trigonal symmetry is very anisotropic at ambient conditions with Vp anisotropy of 21.1% and Vs of 36.4%. Pressure derivatives to

(010)

(001)

16.25

12.38 Max. velocity = 13.34 Anisotropy = 7.5%

Min. velocity = 12.38

0.29 Max. anisotropy = 16.25

16.07

18.0 12.0

14.8

6.0

14.4 14.02 Min. velocity = 14.02

27.54

24.0

15.2

Max. velocity = 16.07 Anisotropy = 13.7%

0.29

Min. anisotropy = 0.29

27.54

15.6

MgO

16.25

14.0 12.0 10.0 8.0 6.0 4.0

13.20 13.10 13.00 12.90 12.80 12.70 12.60 12.50

(100)

Vs1 polarization

dVs (%) 13.34

Mg-Perovskite

509

0.04 Max. anisotropy = 27.54

0.04

Min. anisotropy = 0.04

Figure 14 Single-crystal anisotropic seismic properties of lower mantle minerals Mg-perovskite (orthorhombic) and MgO (periclase – cubic) at about 2000 km (88 GPa, 3227  C) using the elastic constants determined at high P–T by Oganov et al. (2001) and Karki et al (2000), respectively.

510

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

MgSiO3 - perovskite P- and S-wave anisotropy (%) 500

6

8 Vp

10

12

14

16

18

20

Vs

1000

Depth (km)

1500 K 2500 K 3500 K 1500

2000

Vp(%) 1500K Vs(%) 1500k Vp(%) 2500k Vs(%) 2500k Vp(%) 3500k Vs(%) 3500k

2500

3000 Figure 15 P- and S-wave seismic anisotropy for MgSiO3 perovskite with depth in the lower mantle predicted by the ab initio calculations of Zhang et al. (2013).

30 GPa have been obtained by first-principles calculation (Da Silva et al., 1999) and the anisotropy decreases with increasing pressure to 9.9% for P-waves and 24.8% for S-waves at 30 GPa. Ferropericlase – The other major phase is ferropericlase (Mg,Fe)O, for which the elastic constants have been determined. The elastic constants of the pure end-member periclase MgO of the MgO–FeO solid solution series have been measured to 3 GPa by Jackson and Niesler (1982). Isaak et al. (1989a) had measured the temperature derivatives for MgO to 1800 K. Both these studies indicate a Vp anisotropy of 11.0% and Vs of 21.5% at ambient conditions. Karki et al. (1997a,b,c) calculated the elastic constants of MgO to 150 GPa at 0 K. The thermoelasticity of MgO at lower mantle temperatures and pressures has been studied by Isaak et al. (1990) and Karki et al. (1999, 2000) (Figure 16), and more recently Sinogeikin et al. (2004, 2005); there is good agreement between these studies for the elastic constants and pressure and temperature derivatives. However, the theoretical studies do not agree with experimentally measured cross pressure–temperature derivatives of Chen et al. (1998). At the present time, only the theoretical studies permit the exploration of the seismic properties of MgO at lower mantle conditions. They find considerable changes in anisotropy preserved at high temperature with increasing pressure, along a typical mantle geotherm; MgO is isotropic near the 670 km discontinuity, but the anisotropy of P- and S-waves increases rapidly with depth reaching 17% for Vp and 36% for Vs at the D00 layer. The anisotropy of MgO increases linearly from 11.0% and 21.5% for Vp and Vs, respectively, at ambient conditions to 20% and 42%, respectively, at 1800 K according to the data of Isaak et al. (1989a,b). The effect of temperature on anisotropy is more important at low pressure than at lower mantle pressures, where the effect of pressure dominates according to the results of Karki et al. (1999). Furthermore, not only the magnitude of the anisotropy of MgO but also the orientation of the anisotropy

changes with increasing pressure according to the calculations of Karki et al. (1999), for example, the fastest Vp is parallel to [111] at ambient pressure and becomes parallel to [100] at 150 GPa pressure and fastest S-wave propagating in the [110] direction has a polarization parallel to [001] at low pressure that changes to [1–10] at high pressure. Ferropericlase – Magnesiowu¨stite solid solution series has been studied at ambient conditions by Jacobsen et al. (2002); for ferropericlase with 24% Fe, the P-wave anisotropy is 10.5% and maximum S-wave is 23.7%, slightly higher than pure MgO at the same conditions. Data are required at lower mantle pressures to evaluate if the presence of iron has a significant effect on anisotropy of ferropericlase of mantle composition. The effect of anomalous compressibility of ferropericlase through the iron spin crossover has been studied experimentally at room temperature and high pressure; in these conditions, the high to low spin produces a sharp reduction in C11 and C12 elastic moduli (e.g., Marquardt et al., 2009). Theoretical studies using ab initio methods (e.g., Wentzcovitch et al., 2009) at lower mantle conditions show that the change in elasticity is smaller and occurs in a broad depth range of 1200–2000 km for 2000 K geotherm. The elastic anomaly is increasingly attenuated with higher temperatures. It has been suggested that iron spin crossover would be seismically transparent (Antonangeli et al., 2011). It should be noted that iron spin crossover has also been proposed for perovskite, this crossover has much weaker effect on elastic properties as shown by experimental studies (e.g., Lundin et al., 2008), and ab initio modeling of the elastic properties (Caracas et al., 2010) suggests this will be difficult to detect seismically. SiO2 polymorphs – The free SiO2 in the transition zone and the top of the lower mantle (to a depth of 1180 km or 47 GPa) will be in the form of stishovite. The original experimental determination of the single-crystal elastic constants of stishovite by Weidner et al. (1982) and the more recent calculated constants of Karki et al. (1997b) both indicate Vp and Vs anisotropies at ambient conditions of 26.7–23.0% and 35.8– 34.4%, respectively, making this a highly anisotropic phase. The calculations of Karki et al. (1997a,b,c) show that the anisotropy increases dramatically as the phase transition to CaCl2-structured SiO2 is approached at 47 GPa. The Vp anisotropy increases from 23.0% to 28.9% and Vs from 34.4% to 161.0% with increasing pressure from ambient to 47 GPa. The maximum Vp is parallel to [001] and the minimum parallel to [100]. The maximum dVs is parallel to [110] and the minimum parallel to [001]. I discuss the properties of stishovite in the section on subduction zones. Postperovskite – Finally, this new phase is present in the D00 layer. Discovered and published in May 2004 by Murakami et al. (2004), the elastic constants at 0 K were rapidly established at low (0 GPa) and high (120 GPa) pressure by static atomistic calculations (Iitaka et al., 2004; Oganov and Ono, 2004; Tsuchiya et al., 2004). From these first results, we can see that Mg-postperovskite is very different to Mg-perovskite as there are substantial changes in the distribution of the velocity anisotropy with increasing pressure (Figure 16). At zero pressure, the anisotropy is very high, 28% and 47% for P- and S-waves, respectively. The maximum for Vp is parallel to [100] with small submaxima parallel to [001] and minimum near [111]. The shear wave splitting (dVs) has maxima

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

Vp (km s−1) Mg-Post-perovskite

dVs (%) 12.35

511

Vs1 Polarization 47.28

47.28

40.0 11.5

(100)

10.5

20.0

10.0

10.0

9.32 Max. velocity = 12.35

(010)

30.0

11.0

0 GPa 0 K

Min. velocity = 9.32

0.66 Max. anisotropy = 47.28

0.66

Min. anisotropy = 0.66

(001) 15.38

22.74

22.74

20.0

120 GPa 0 K

14.80

16.0

14.40

12.0

14.00

8.0

13.60

4.0

13.23 Max. velocity = 15.38 Anisotropy = 15.0 %

Min. velocity = 13.23

0.74 Max. anisotropy = 22.74

14.54

0.74

Min. anisotropy = 0.74

24.41

24.41

18.0 13.80

136 GPa 4000 K

12.0 13.40 6.0

13.00 12.69 Max. velocity = 14.54 Anisotropy = 13.6%

Min. velocity = 12.69

0.64 Max. anisotropy = 24.41

0.64

Min. anisotropy = 0.64

Figure 16 Single-crystal anisotropic seismic properties of the D00 layer mineral Mg-postperovskite (orthorhombic). Increasing the pressure from 0 to 120 GPa at a temperature of 0 K decreases the anisotropy and also changes the distribution the maximum velocities and S-wave polarizations. Elastic constants calculated by Tsuchiya et al. (2004). Increasing the pressure to 136 GPa and temperature to 4000 K, there are relatively minor changes in the anisotropy. Elastic constants calculated by Stackhouse et al. (2005).

parallel to h101i and h110i. At 120 GPa, the anisotropy has reduced to 15% and 22% for P- and S-waves, respectively. The distribution of velocities has changed, with the P maximum still parallel to [100] and submaximum parallel to [001], which is now almost the same velocity as parallel to [100]; the minimum is now parallel to [010]. The S-wave splitting maxima have also changed and are now parallel to h111i. Apparently, the compression of the postperovskite structure has caused important elastic changes as in MgO. An ab initio molecular dynamics study by Stackhouse et al. (2005) at high temperature revealed that the velocity distribution and anisotropy were little effected by increasing the temperature from 0 to 4000 K when at a pressure of 136 GPa (Figure 16). Wentzcovitch et al. (2006) produced a more extensive set of high-pressure elastic constants and pressure and temperature derivatives, similar P distributions, and slightly different shear wave splitting pattern with maximum along the [001] axis that is not present in the Stackhouse et al. velocity surfaces or in high pressure 0 K results. In conclusion, for the mantle, we can say that the general trend favors an anisotropy decrease with increasing pressure and increase with increasing temperature; olivine is a good example of this behavior for minerals in upper mantle and transition zone. The changes are limited to a few percent in most cases. The primary causes of the anisotropy changes are minor crystal structural rearrangements rather than velocity changes due to

density change caused by compressibility with pressure or thermal expansion with temperature. The effect of temperature is almost perfectly linear in many cases; some minor nonlinear effects are seen in diopside, MgO, and SiO2 polymorphs. There may be some perturbation in the seismic anisotropy due to the iron spin crossover around 1200–2000 km. Nonlinear effects with increasing pressure on the elastic constants cause the anisotropy of wadsleyite and ringwoodite to first decrease. In the case of the lower mantle minerals Mg-perovskite and MgO, there is a steady increase in the anisotropy in increasing depth; this is a very marked effect for MgO. Stishovite also shows major changes in anisotropy in the pressure range close to the transformation to the CaCl2 structure. The single-crystal temperature derivatives of wadsleyite, ilmenite MgSiO3, and stishovite are currently unknown, which makes quantitative seismic anisotropic modeling of the transition zone and upper part of the lower mantle speculative. To illustrate the variation of anisotropy as a function of mantle conditions of temperature and pressure, I have calculated the seismic properties along a mantle geotherm (Figure 17). The mantle geotherm is based on the PREM model for the pressure scale. The temperature scale is based on the continental geotherm of Mercier (1980) from the surface to 130 km and Ito and Katsura (1989) for the transition zone and Brown and Shankland (1981) for the lower mantle. The upper mantle minerals olivine (Vp, Vs) and enstatite (Vp) show a slight increase of anisotropy in the first 100 km due to the effect of

512

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

Single crystal anisotropy : Upper mantle 0 Olivine

100

Olivine

Vs

Depth (km)

Vp Vp Cpx Vp Opx

200

300 Vs Cpx

Vs Opx

400

10

15

20

25

30

35

Anisotropy (%) Single crystal anisotropy : Transition zone and lower mantle 0

Vs

400

Vp

Wadsleyite Vp

Ringwoodite

Vs

410 km

Diopside

Vp

Vs

520 km Stishovite

Vp

Vs

670 km

800 High spin

Depth (km)

High spin

Stishovite->CaCl2

1200 Vs

Vp Vp

1600

MgO

Vs

Low spin

Low spin MgPerovskite

2000

Vs

2400

CaCl2->Columbite

Vp

2230 km

Colum bite Vp

2800

CaCl2

Vp Vs

1170 km

0

10

Vs

Vp

Vs

MgO

20

30

40

50

60

Anisotropy (%) Figure 17 Variation of single-crystal seismic anisotropy with depth. The phases with important volume factions (see Figure 1) (olivine, wadsleyite, ringwoodite, Mg-perovskite, and MgO) are highlighted by a thicker line. P-wave anisotropy is the full line and the S-wave is the dashed line. See text for details.

temperature. With increasing depth, the trend is for decreasing anisotropy except for Vs of enstatite and diopside. In the transition zone and lower mantle, the situation is more complex due to the presence of phase transitions. In the transition zone, diopside may be present to about 500 km with an increasing Vs and decreasing Vp anisotropy with depth. Wadsleyite is less anisotropic than olivine at 410 km, but significantly more anisotropic than ringwoodite found below 520 km. Although the lower mantle is known to be seismically isotropic, the

constituent minerals are anisotropic. MgO shows important increase in anisotropy with depth (10–30%) at 670 km (it is isotropic) and 2800 km (it is very anisotropic), possibly being candidate mineral to explain anisotropy of the D00 layer. Mg-perovskite is strongly anisotropic (ca. 10%) throughout the lower mantle, but now, it is strongest in the lowermost mantle (Zhang et al., 2013). The SiO2 polymorphs are all strongly anisotropic, particularly for S-waves. If free silica is present in the transition zone or lower mantle, due perhaps to the presence

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

of subducted basalt (e.g., Ringwood, 1991), then even a small volume fraction of the SiO2 polymorphs could influence the seismic anisotropy of the mantle. However, to do so, the SiO2 polymorphs would have to be oriented, due to either dislocation glide (plastic flow), oriented grain growth, or anisometric crystal shape (viscous flow) (e.g., Mainprice and Nicolas, 1989). Given that the SiO2 polymorphs are likely to be less than 10% by volume (Ringwood, 1991) and hence would not be the loadbearing framework of the rock, it is more likely that the inequant shape of SiO2 polymorphs would control their orientation during viscous flow.

2.20.2.6.4 Subduction zones Subduction zones are mainly vertical structures in the Deep Earth, with a major section in the upper mantle and transition zone. In certain regions, the subducted plates have nearly horizontal sections just below 670 km seismic discontinuity. Slabs continue to descend until they reach the D00 layer and CMB. During the decent of a plate, the mineralogy changes almost continuously with the temperature and pressure changes. The subducted plate is populated with many very specific minerals because the temperature of the plate is generally lower that the surrounding mantle, whereas the depth controls the pressure. The subducting plate is a major vector for chemical exchange with deep Earth, not only hydrated minerals providing hydrogen but also minerals derived from sediments and oceanic basalts rich in potassium, sodium, aluminum, and silicon. Subduction zones are also the most seismically active regions of the planet. Here, we will focus on the seismic anisotropy of a few key subduction zone minerals. The upper part of the subduction zone is dominated by the mantle wedge, where dehydration of the plate and fluid-triggered melting are very active processes, which are directly associated with earthquake activity and volcanism, respectively. One of the reactions occurring within the mantle wedge is hydration of minerals by fluids released from the descending slab, for example, the transformation olivine to the high-pressure serpentine mineral antigorite. Bezacier et al. (2010) had reported experimental measurements of antigorite single-crystal elasticity at ambient conditions. Antigorite is monoclinic layered-structured mineral that has fast Vp in the (001) plane and low Vp normal it. Vs1 is fast in the (001) plane with a polarization parallel to the (001) plane, whereas Vs2 is slow in the (001) plane with a polarization normal to the (001) plane. The Vp and Vs anisotropies are high at 47% and 75%, respectively, with the highest S-wave splitting in the (001) plane (Figure 18). One key seismic observation in the mantle wedge because of the presence of fluids is the Vp/Vs ratio; for anisotropic crystals, there are two ratios, Vp/Vs1 and Vp/Vs2, where Vp/Vs1 corresponds to ratio with the first S-wave arrival and is probably the most frequently measured. Vp/Vs1 ranges from 2.3 to 1.1 with direction, being highest normal and lowest parallel to the (001) plane. Vp/Vs2 range is 3.8–1.4, the magnitude being highest parallel and lowest normal to the (001) plane, that is, opposite in distribution to Vp/Vs1; hence, measuring Vp/Vs2, Vp/Vs1 could provide a complementary set of data. All the velocity-related properties just described are typical of layered-structured minerals in widest sense or phyllosilicates in the present case. Information on the pressure dependence of antigorite has been provided by

513

an ab initio study by Mookherjee and Capitani (2011) up to 13.8 GPa, and more recently, an experimental study by Bezacier et al. (2013) measured a subset of the moduli to 9 GPa. Bezacier et al. (2013) indicated that there is decrease in P- and S-wave anisotropies from 47% to 75%, respectively, at ambient conditions to 22% and 63% at 7 GPa. Mookherjee and Capitani (2011) found that Vp anisotropy is 57% at zero pressure and that it decreases to 27% at 7 GPa; however, Vs anisotropy is 54% at zero pressure and increases to 63% at 7 GPa, so that both studies agree at 7 GPa, but not ambient conditions. Another potential mantle wedge mineral that has stable higher-temperature conditions than antigorite is talc; this industrially very important mineral has been studied using ab initio methods by Mainprice et al. (2008b). At zero pressure, talc is very anisotropic with P- and S-wave anisotropies of 80% and 85%, respectively; with increasing pressure, both P- and S-wave anisotropies decrease. At pressures where talc is known be stable in the Earth (up to 5 GPa), the Vp and Vs anisotropies are reduced to about 40% for both velocities, which is still a very high value. The third important layeredstructured mineral is chlorite; Mookherjee and Mainprice (2014) have studied the elastic properties to a pressure of 18.4 GPa. Chlorite is stable to higher temperatures and pressures than antigorite and talc. Chlorite has velocity characteristics very similar to antigorite, with P- and S-wave anisotropies of 30% and 52%, respectively, at zero pressure, which decrease with pressure for P-waves to 25% but increase with pressure for S-waves to 72%. Antigorite can often be seen associated with chlorite as intergrowths with the same crystal orientation (e.g., Morales et al., 2013); there are also topotactic relationships between antigorite and olivine during the phase transformation (Boudier et al., 2010; Morales et al., 2013). Both antigorite and chlorite contain 13 wt.% H2O, and hence, they are more important for the water cycle than talc, which has only 4.8 wt.% H2O. All these layered-structured minerals form CPO with strong point maximum of the (001) normal to the foliation and girdles of both (100) and (010) in the foliation plane, which will result in very strong transverse isotropic velocity distribution. At greater depths and higher pressures, there is transition to the 10 A˚ phase (13 wt.% H2O) followed with increasing depth by a series of dense hydrogen magnesium silicate (DHMS) or alphabet phases. The DHMSs have only to be observed in laboratory experiments, but hypothetically could exist along a cold slab geotherm (e.g., Mainprice and Ildefonse, 2009), and mainly present at depths of the mantle transition zone. Sanchez-Valle et al. (2006, 2008) had studied the elasticity of the phase A (12 wt.% H2O) in the laboratory at pressures up to 12.4 GPa. The velocity distribution is very different to the layered-structured minerals described earlier with fast Vp normal to (0001) and slow Vp in the (0001); Vs1 is slow in the (0001) plane, the polarization parallel to the (0001) plane, and the maximum Vs1 at 45 to the (0001) plane; and Vs2 also is slow normal to the (0001) and but fast normal to the (0001) plane. The P- and S-wave anisotropies are quite modest at 9% and 18%, respectively, at 9 GPa in the stability field of this mineral. Pressure has only a very modest effect on the anisotropy of phase A. The phase D is the DHMS that occurs at the greatest pressures and depths; being stable below 670 km discontinuity, it is the only mineral to potentially recycle

514

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

Antigorite single crystal Vp (km s−1)

dVs (%)

Vs1 polarization

Vp Contours (km s−1)

AVs Contours (%)

8.92

75.20 60.0

8.0

50.0

7.5

40.0

7.0

30.0

6.5

20.0

5.52

upper hemisphere Max. velocity = 8.92 Anisotropy = 47.1 %

75.20

0.10

Min. velocity = 5.52

Max. anisotropy = 75.20

Vs1(km s−1)

0.10

Min. anisotropy = 0.10

Vs2(km s−1) 5.15

a

b

4.43 4.20 4.00 3.80 3.60 3.40 3.20 3.00 2.80 2.60

4.75 4.50 4.25 4.00 3.75 3.50 3.25 3.00

c*

2.65 Max. velocity = 5.15 Anisotropy = 64.2 %

Min. velocity = 2.65

Vp/Vs1

2.32 Max. velocity = 4.43 Anisotropy = 62.8 %

Min. velocity = 2.32

Vp/Vs2 2.30

3.79 3.50 3.25 3.00 2.75 2.50 2.25 2.00 1.75

2.00 1.80 1.60 1.40

1.13 Max. ratio = 2.30 Anisotropy = 68.1 %

Min. ratio = 1.13

1.39 Max. ratio = 3.79 Anisotropy = 92.4 %

Min. ratio = 1.39

Figure 18 The seismic properties of a single crystal of antigorite at room pressure (Bezacier et al., 2010). Vp and Vs1 are both fast in the basal plane (normal to c*). Vs1 polarization is parallel to the basal plane. Vs2 is fast in directions inclined to the basal plane. Vp/Vs1 has the maximum normal to the basal plane, whereas Vp/Vs2 is highest parallel to the basal plane. Antigorite is monoclinic, so the plane normal to b and b* is a mirror plane (black vertical line containing a and c*). Note that there is some imperfect threefold symmetry.

hydrogen into the lower mantle. It is a candidate mineral for horizontal or stagnant slabs. The elasticity of phase D has been measured experimentally at ambient conditions (Rosa et al., 2012) for Mg- and Al–Fe-bearing crystals. Using ab initio methods, the elasticity of the phase D has been studied by Mainprice et al. (2007) to 84 GPa and as function of hydrogen bond symmetrization by Tsuchiya and Tsuchiya (2008) to 60 GPa. The phase D has a velocity distribution that has more in common with a layered-structured mineral than the phase A. The P-wave velocity is fast in (0001) plane and slow normal to the (0001) plane. Vs1 is fast in the basal plane and polarized parallel to the (0001) plane and Vs2 is the opposite. At ambient conditions, the P- and S-wave anisotropies are 18% and 19%, and the agreement between experimental and theoretical values is very good. At pressure of 24 GPa in the stability field of phase D, the anisotropies of P- and S-waves are 9%

and 18%, respectively, showing a decrease for the P-wave anisotropy with increasing pressure. The spin transition of Fe3+ in Al-bearing phase D occurs at around 40 GPa (Chang et al., 2013) and causes a decrease in bulk modulus from 253 to 147 GPa. The decrease in bulk modulus corresponds to bulk sound velocity drop of 2 km s 1, which could explain the exceptionally strong small-scale heterogeneity detected by direct P-waves in the mid-lower mantle beneath the circumPacific subduction zones (e.g., Kaneshima and Helffrich, 2010), a region with horizontal slabs below 670 km discontinuity. A recent study using first-principles methods has predicted a new DHMS form from breakdown of the phase D to give MgSiO4H2 plus stishovite (Tsuchiya, 2013) at pressure of about 40 GPa; at the present time, there is no experimental confirmation of this new phase. Finally, comparison with brucite Mg(OH)2 is interesting as it is a model system for

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

understanding DHMS under hydrostatic compression and an important structural unit of many layer silicates, such as chlorite, antigorite, and talc. The single-crystal elastic constants of brucite have been measured to a pressure of 15 GPa by Jiang et al. (2006). The seismic anisotropy of brucite is exceptionally high at ambient conditions with P-wave and S-wave anisotropies of 57% and 46%, respectively. Both forms of anisotropy decrease with increasing pressure being 12% and 24% at 15 GPa for P-wave and S-wave anisotropies, respectively. The stronger decrease of P-wave anisotropy compared to S-wave is probably related to the very important linear compressibility along the c-axis. The apparent symmetry of the seismic anisotropy of brucite changes with pressure (Figure 19). Brucite is stable to 80 GPa and modest temperatures, so it could be an anisotropic component of cold subducted slabs. A mineral called the phase X, which occurs as hydrous and anhydrous forms and is stable at transition zone pressures and temperatures, could contribute to mineralogy of slabs. The phase X is the reaction product of the breakdown of potassium rich amphibole (K-richterite) (Konzett and Fei, 2000). The elastic properties of the phase X have been predicted by ab initio methods to a pressure of 30 GPa (Mookherjee and Steinle-Neumann, 2009a). The anhydrous phase X has hexagonal symmetry (space group P63cm); hence, it has the equivalent elastic symmetry to a transverse isotropic sample. At transition zone pressure of 22 GPa, anhydrous phase X has P- and S-wave anisotropies of 13.1% and 12.2%, respectively. In addition to these hydrous phases, some of normally anhydrous minerals in the subducted slab can become hydrated to a limited degree; the important ones in terms of volume fraction are olivine, wadsleyite, and ringwoodite for the pyrolite mantle (Figure 1). For the upper mantle, olivine is the most important mineral being between 50% and 70% by

515

volume of a typical mantle peridotite. Single-crystal elastic constants for forsterite and olivine with 0.9 and 0.8 wt.% water have been measured by Jacobsen et al. (2008, 2009) at ambient conditions; 0.9 wt.% water is considered the maximum water storage capacity for olivine (Smyth et al., 2006). The combined effect of 3 mol% Fe and 0.8 wt.% water causes a reduction of the bulk and shear moduli of 2.9% and 4.5%, respectively. Greater modulus reductions are expected for more iron-rich than Fo90 olivine mantle compositions. New measurements for forsterite with 0.9 wt.% water to 14 GPa (Mao et al., 2010) reveal some unexpected behavior with pressure. Below  3.5 GPa, the Vp and Vs of hydrous forsterite are slower than anhydrous crystal by 0.6% and 0.4%, respectively, whereas above this pressure range, the hydrous crystal has faster velocities by 1.1% and 1.9%, respectively. At room pressure, the P- and S-wave anisotropies are, respectively, 24.7% and 18.0% for anhydrous forsterite and 23.9% and 17.8% for hydrous forsterite, indicating a decrease of 0.8% and 0.2% upon hydration. At 14 GPa, the P- and S-wave anisotropies are, respectively, 21.2% and 13.5% for anhydrous forsterite and 15.4% and 12.1% for hydrous forsterite, indicating a decrease of 6.0% and 1.4% upon hydration. Hence, the main effect of hydration on olivine elasticity is a change of velocity and reduction of P-wave anisotropy and almost no effect on S-wave anisotropy. In the transition zone (410–670 km depth), the highpressure polymorphs of olivine, wadsleyite, and ringwoodite, in their hydrous forms, have the potential to store more water as hydroxyl than the oceans on the Earth’s surface (e.g., Jacobsen, 2006). Wadsleyite and ringwoodite can be synthesized with up to 3.1 and 2.8 wt.% H2O, respectively, which is nearly three times that of olivine. The maximum water solubility in wadsleyite at transition zone conditions

Brucite P velocity (km s−1) (2110)

Vs1 polarization

dVs (%) 8.17

45.99

7.5

35.0

7.0

25.0

6.5

(0110)

P = 0 GPa

45.99

6.0

15.0

5.5

5.0

Upper hemisphere Max. velocity = 8.17 Anisotropy = 56.7 %

4.56

Min. velocity = 4.56

0.00

Max. anisotropy = 45.99

9.31

0.00

Min. anisotropy = 0.00

23.63

23.63

9.20 18.0 15.0 12.0 9.0 6.0 3.0

9.00 8.80

P = 14.6 GPa

8.60 8.40 8.25

Max. velocity = 9.31 Anisotropy = 12.1 %

Min. velocity = 8.25

0.00

Max. anisotropy = 23.63

0.00

Min. anisotropy = 0.00

Figure 19 Single-crystal anisotropic seismic properties of brucite (trigonal) at 0 and 14.6 GPa (data from Jiang et al., 2006). Note the change in velocity distribution of P-waves, dVs anisotropy, and S1 polarization orientations, which reflect the nearly hexagonal symmetry of brucite’s elastic properties at low pressure and the increasingly trigonal nature (threefold c-axis at the center of the pole figure) with increasing pressure.

516

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

(15 GPa, 1400  C) is however only about 0.9 wt.% (Demouchy et al., 2005) as temperature has an important affect on solubility. In ringwoodite, water solubility decreases with increasing temperature. In subducting slabs, hydrous wadsleyite and ringwoodite can represent volume fractions of about 50–60%, resulting in the shallower region of the mantle transition zone having a larger water storage potential than the deeper region (Ohtani et al., 2004). In upper part of the transition zone (410–520 km depth), anhydrous wadsleyite is replaced by hydrous wadsleyite in the hydrated slab. The elastic constants of hydrous wadsleyite have been determined at ambient conditions as a function of water content by Mao et al. (2008a,b). Anhydrous wadsleyite (Zha et al., 1997) has P- and S-wave anisotropies of 15.4% and 16.8%, respectively, whereas hydrous wadsleyite with 1.66 wt.% H2O has a P-wave and S-wave anisotropies of 16.3% and 16.5%, respectively. Hence, hydration increases Vp anisotropy by 0.9% and decreases Vs anisotropy by 0.3%. Anhydrous wadsleyite has Vp/Vs1 and Vp/Vs2 anisotropy values of 22.0% and 19.1%, whereas hydrous wadsleyite has Vp/Vs1 and Vp/Vs2 of 20.9% and 20.2%, respectively. For Vp/Vs1 and Vp/Vs2 anisotropies, the hydration of wadsleyite decreases Vp/Vs1 by 0.1% and increases Vp/Vs2 by 1.1%. Clearly, it is not possible to distinguish between anhydrous wadsleyite and hydrous wadsleyite on the basis of anisotropy, although there is a linear decrease of velocity with water content at room pressure (Mao et al., 2008a). A first-principles study of wadsleyite as function of water content (Tsuchiya and Tsuchiya, 2009) successfully reproduces the experimental elastic results for anhydrous wadsleyite (Zha et al., 1997) and hydrous wadsleyite (Mao et al., 2008a,b) using a Mg vacancy model for the protonation of wadsleyite. Tsuchiya and Tsuchiya (2009) also studied the effect of pressure on hydrous wadsleyite. The pressure derivatives (dCij/dP) for hydrous wadsleyite are similar to anhydrous derivatives of Zha et al. (1997). At a pressure of 20 GPa, the anhydrous wadsleyite has P- and S-wave anisotropy of 10.1% and 11.9%, whereas hydrous wadsleyite (3.3 wt.% H2O) has P- and S-wave anisotropy

of 11.3% and 12.8%. At the same pressure, the anhydrous wadsleyite has Vp/Vs1 and Vp/Vs2 anisotropies of 13.4% and 9.6%, respectively, whereas hydrous wadsleyite has Vp/Vs1 and Vp/Vs2 anisotropies of 14.6% and 11.9%. Hence, hydration of P- and S-wave anisotropies increases by 1.2% and 0.9%, respectively, and for Vp/Vs1 and Vp/Vs2 anisotropies increases by 2.2% and 1.6%, respectively. So once again hydration has more effect on velocities than the anisotropy. In the lower part of the transition zone (520–670 km depth), anhydrous ringwoodite will be replaced by its hydrated counterpart hydrous ringwoodite in the hydrated slab. The elastic constants of hydrous ringwoodite have been measured as a function of pressure to 9 GPa by Jacobsen and Smyth (2006) and to 24 GPa by Wenk et al. (2006). More recently, Mao et al. (2011, 2012) had determined the elastic constants of hydrous ringwoodite to 16 GPa and 673 K. The presence of 1.1 wt.% water lowers the elastic moduli by 5–9%, but does not affect the pressure derivatives. The reduction caused by 1.1 wt.% water is significantly enhanced by high temperature when at high pressure. Hydrous ringwoodite at 16.3 GPa and 673 K has a very low anisotropy, 1.3% for P-waves and 3.0% S-waves. The anisotropy of Vp/Vs1 and Vp/Vs2 is slightly stronger at 3.1% and 3.9%, respectively. The pressure sensitivity of the seismic anisotropy of hydrous or hydrated minerals at upper mantle and transition zone pressures is illustrated in Figure 20. Apart from hydrated phases associated with subduction, there are the phases derived from MORB and sediments (Figure 1). Compared to the pyrolite mantle composition, MORB is chemically enriched in incompatible elements (silicon, aluminum, calcium, and sodium) and depleted in compatible elements like magnesium. At deep mantle temperatures and pressures, MORB transforms to mineral assemblages with high SiO2 and aluminum content. Mineral assemblages change with pressure and depth at the top of the lower mantle in the pressure range 23–50 GPa (depth range 670–1300 km); the assemblage is composed of the new aluminum phase (NAL), aluminum-rich calcium ferrite structure (Al-CF),

25

Brucite Vs

20

Chlorite Vp

Antigorite Vp

HydoRw Vp

4

0

Vs

2

phase A Vs

Rw

5 10 Pressure (GPa)

15

0

10

Rw

5

phase A Vp

0

HydoRw

0

5

Vp

10 15 20 Pressure (GPa)

25

0

0

10

Lower mantle

Talc Vs

40

15 Rw

6

Transition zone

Talc Vp

Vs

8

phase D Vs

20

Upper mantle

Brucite Vp

Upper mantle

60

Lower mantle

HydoRw

Antigorite Vs

Transition zone

10

Chlorite Vs

Upper mantle

80

Transition zone

Anisotropy of Vp and Vs (%)

12 3-5 GPa

phase D Vp

20 30 40 Pressure (GPa)

50

Figure 20 The evolution of seismic anisotropy of hydrous or hydrated minerals in the pressure range of the upper mantle, transition zone, and lower mantle. The pressure range 3–5 GPa is typical of the mantle wedge. In the upper mantle pressure range, the strong pressure sensitivity of brucite, talc, antigorite, and chlorite contrasts with that of the DHMS phase A. Antigorite and chlorite are exceptions as the anisotropy for Vs increases with pressure. Increasing pressure reduces anisotropy with pressure for anhydrous and hydrated ringwoodite in the transition zone. Pressure has a small effect on the Vs anisotropy for DHMS phase D, but increasing pressure decreases Vp anisotropy. See text for discussion and references.

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

Mg-perovskite, Ca-perovskite, and stishovite that are stable; and of these minerals, NAL, Al-CF, and stishovite are specific to MORB chemistry. Above a pressure of 45–50 GPa (below a depth of 1200 km), NAL (hexagonal, space group P63/m) is no longer stable due to the increased in the solubility of aluminum with pressure in the Mg-perovskite (Perrillat et al., 2006; Ricolleau et al., 2010; Sanloup et al., 2013). Stishovite with rutile structure transforms to the CaCl2 structure of SiO2 at 55 GPa (depth of about 1300 km) (Andrault et al., 1998), whereas Al-CF (orthorhombic, space group Pbnm) is stable to at least 130 GPa (Hirose et al., 2005; Ono et al., 2005a,b). The aluminum-rich calcium titanate structure (Al-CT) (orthorhombic, space group Cmcm) mineral is only observed by Ono et al. (2005a,b) at CMB pressure of 143 GPa. Sediments are the other chemical source in subduction zones that can produce minerals like K-hollandite (Irifune et al., 1994). The elasticity of the relatively low-pressure NAL phase has been studied by Mookherjee et al. (2012) using ab initio methods to a pressure of 160 GPa. According to Ricolleau et al. (2010), NAL is only present in the MORB mineral assemblage in the pressure range from 22 to 50 GPa. At 27 GPa, the P- and S-wave anisotropies are 11.3% and 16.0%, respectively. As the NAL phase is hexagonal, the anisotropy has the same elastic symmetry as a transverse isotropic sample. The Al-CF phase has been studied by Tsuchiya (2011), Mookherjee (2011a), and Mookherjee et al. (2012) all using ab initio methods. The Al-CF phase has stability over a wide range of pressure in the lower mantle from 22 to 130 GPa (Hirose et al., 2005; Ono et al., 2005a,b; Perrillat et al., 2006; Ricolleau et al., 2010; Sanloup et al., 2013). The orthorhombic symmetry of Al-CF phase results in a more complex velocity distribution than the NAL phase. The elasticity of MgAl2O4 CF phase has been calculated by Tsuchiya (2011) and Mookherjee (2011a), the results for the P- and S-wave anisotropies as function of pressure are shown in Figure 21, both P- and S-wave anisotropies decrease with increasing pressure, and the results of these two studies agree very closely. At low-pressure end of the

Hollandite I and II 70

30

P- ans S-wave anisotropy (%)

Vp(%) M Vs(%) M Vp(%) T Vs(%) T

TZ LM

P- and S-wave anisotropy (%)

stability field, P-wave anisotropy is 15.2% and S-wave is 25.0%, and at the high-pressure end of the stability field, 6.5% and 15.3%, respectively. The P- and S-wave anisotropies of the Al-rich calcium titanate structure (Al-CT) at 140 GPa are 11.6% and 28.1%, respectively, near the CMB. So Al-CT has quite high S-wave anisotropy even at extreme pressures. High-pressure studies on sediments of average continental crust composition between 9 and 24 GPa found that hollandite (now called hollandite I or lingunite) represents  30% by volume of the high-pressure assemblage (Irifune et al., 1994), indicating the importance of the hollandite I phase for subducted sediments. Under ambient conditions, hollandite I has tetragonal symmetry I4/m. Using high-pressure in situ RXD techniques up to 32 GPa (Ferroir et al., 2006; Sueda et al., 2004) showed that hollandite I undergoes a phase transition from the tetragonal to a monoclinic hollandite II phase with I2/m symmetry at 20 GPa at room temperature. Phase equilibrium studies on the system KAlSi3O8–NaAlSi3O8 by Liu (2006) show that hollandite I is stable up to 18 GPa and 2200  C and hollandite II is stable up to 25 GPa and 2000  C. Hollandite I and hollandite II can be present in the transition zone and the upper part of the lower mantle and perhaps to greater depths. An elasticity study using ab initio methods by Mookherjee and Steinle-Neumann (2009b) reports the P-wave anisotropy for hollandite I as about 26% at zero pressure, which decreases at the transition pressure of about 30 GPa to 22%. The P-wave anisotropy of hollandite II at the transition pressure is 20%, and this slowly decreases to 12% at 100 GPa. The S-wave anisotropy of hollandite I is 42% at zero pressure, but rises sharply to 70% at the 30 GPa. Hollandite II at the transition pressure has Vs anisotropy of 30%, which slowly decreases with increasing pressure to 22% at 100 GPa (Figure 21). Hollandite I and hollandite II have very high S-wave anisotropies compared to other minerals in the transition zone and lower mantle. Mussi et al. (2010) had shown that hollandite I deforms plastically at transition zone temperatures and pressures and predicted CPO that would

MgAl2O4 CF phase

35

25 20 Stability field in pressure of CF phase

15 10

Vs

Vp

5 0 (a)

40

80 120 Pressure (GPa)

517

60 50

(b)

TZ LM

40

Hollandite I

30

Vp

20

Hollandite II

Vs Vp

10 0

160

Vp (%) Hollandite I Vs (%) Hollandite I Vp (%) Hollandite II Vs (%) Hollandite II

Vs

0

20

40 60 Pressure (GPa)

80

100

Figure 21 The effect of pressure on the seismic anisotropy of anhydrous phases, CF phase and hollandite I and hollandite II. The CF phase (T ¼ Tsuchiya, 2011; M ¼ Mookherjee, 2011a) shows a typical decrease of anisotropy of Vp and Vs with increasing pressure seen in minerals like talc and brucite. Hollandite I (Mookherjee and Steinle-Neumann, 2009b) is atypical with increasing Vs anisotropy with pressure, like antigorite and chlorite. In hollandite II, the Vp and Vs anisotropies decrease slightly with pressure.

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

result in seismic anisotropy very similar to stishovite (Cordier et al., 2004a), as both minerals have the same rutile structure. Aggregates of hollandite I are predicted to have P- and S-wave anisotropies of 12.8% and 15.1%, compared to stishovite aggregate with 8.9% and 7.1% at the same pressure of 17 GPa, which corresponds to a depth of about 500 km. Subducted MORB will produce SiO2 phase such as coesite, stishovite, and the poststishovite high-pressure phases. Stishovite is stable from 9 to 24 GPa in the experiments of Irifune et al. (1994) and can be stable until 55 GPa (Andrault et al., 1998). In experiments on sediments by Irifune et al. (1994), stishovite has a volume fraction between 20% and 40%, whereas in transform MORB, stishovite has volume fractions of 15–20% (Ricolleau et al., 2010). Using ab initio methods Karki et al. (1997a,b,c) has given the elastic constants of SiO2 polymorphs, and recently, full set experimental values to 12 GPa have been measured by Jiang et al. (2009), and these are in close agreement with the predictions of Karki et al. (1997a,b,c). The transformation pressure and temperature of stishovite to CaCl2-type SiO2 phase have been given by ab initio methods by Tsuchiya et al. (2004). From the anisotropy point of view, stishovite starts to become exceptional at about 670 km discontinuity when the S-wave anisotropy is greater than 50% (Figure 22). From 670 km discontinuity to the eventual transformation to CaCl2-type SiO2 at about 1200 km depth, the S-wave anisotropy sharply increases to an exceptional value of about 150% near the transition. In parallel with the evolution of the S-wave anisotropy, the Vp/Vs2 ratio also reaches unprecedented value of 10 (Figure B). Stishovite deforms plastically at high temperature and pressure (Cordier et al., 2004a,b) and is expected to form CPO as predicted by polycrystalline modeling, and a strong anisotropy is expected in real mantle samples. Kawakatsu and Niu (1994) and Vinnik et al. (2001) had observed seismic reflectivity in the lower mantle, which may be explained by the SiO2 phase transformation at around 1100–1200 km.

A wide range of temperature and pressure associated with several chemical sources represented by the pyrolite mantle, MORD, and sediments create a complex pattern of minerals with depth in subduction zones. The subduction zones are compared to the extensive volumes involved with convective mantle and are quite narrow and restricted volumes. The thermomechanical constraints of a subduction zone are a number of minerals that are very anisotropic: antigorite, talc, chlorite, brucite, hollandite I, Al-CF phase, and stishovite. In almost all minerals, the P-wave anisotropy decreases with increasing pressure. The very anisotropic minerals fall into two groups: (a) a group where the S-wave anisotropy decreases with pressure that includes talc, brucite (Figure 20), and Al-CF phase (Figure 21) and (b) a group where the S-wave anisotropy increases with pressure that includes antigorite, chlorite, hollandite I, and stishovite (Figures 20, 21, and 22, respectively).

2.20.2.6.5 Inner core Unlike the mantle, the Earth’s inner core is composed primarily of iron, with about 5 wt.% nickel and very small amounts of other siderophile elements such as chromium, manganese, phosphorus, and cobalt and some light elements such as are oxygen, sulfur, and silicon. The stable structure of iron at ambient conditions is body-centered cubic (bcc); when the pressure is increased above 15 GPa, iron transforms to an hcp structure called the e-phase; and at the high pressure and temperature, iron most likely remains hcp; however, there have been experimental observations of a double hexagonal close-packed structure (dhcp) (Saxena et al., 1996) and a distorted hcp structure with orthorhombic symmetry (Andrault et al., 1997). Atomic modeling at high pressure and high temperature suggests that the hcp structure is still stable at temperatures above 3500 K in pure iron (Vocˇadlo et al., 2003a), although the energy differences between the hcp and the bcc structures are very small and the authors speculate that

Stishovite at high pressure : Vp/Vs ratio

Stishovite at high pressure : Anisotropy

80 AVp/Vs2

60

AVp/Vs1

AVs

40 20

Maximum Vp/Vs1 and Vp/Vs2

100

Lower mantle

120

0

(a)

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P- and S-wave anisotropy (%)

140

AVp 0

200

400

600

8 6 4 Vp/Vs2 2 0

800 1000 1200

Depth (km)

10

(b)

Lower mantle

12

160

Transition zone

518

Vp/Vs1 0

200

400

600

800 1000 1200

Depth (km)

Figure 22 The effect of depth on the seismic anisotropy of anhydrous stishovite SiO2 using the ab initio predicted elastic constants of Karki et al. (1997a,b,c). The rutile-structured stishovite reaches exceptionally high Vs anisotropy (150%) near phase transition to the CaCl2 structured from of SiO2 at about 1100 km depth. In contrast, Vp anisotropy increases with depth to about 30%. The parameters associated with Vs2, such as the ratio of Vp/Vs2 and anisotropy of Vp/Vs2, both reach exceptional values near the phase transition.

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

the bcc structure may be stabilized by the presence of light elements. A suggestion is echoed by the seismic study of Beghein and Trampert (2003). To make a quantitative anisotropic seismic model to compare with observations, one needs either velocity measurements or the elastic constants of singlecrystal hcp iron at the conditions of the inner core. The measurement or first-principles calculation of the elastic constants of iron is a major challenge for mineral physics. The conditions of the inner core are extreme with pressures from 325 to 360 GPa and temperatures from 5300 to 5500 K. To date, experimental measurements have been using DACs to achieve the high pressures on polycrystalline hcp iron. IXS has been used to measure Vp at room temperature and high pressure up to 112 GPa and temperatures up to 1100 K (Antonangeli et al., 2004, 2010, 2012; Fiquet et al., 2001), and the anisotropy of Vp has been characterized in two directions up to 112 GPa (Antonangeli et al., 2004). Vp has been determined at simultaneous high pressure and temperature up to 300 GPa and up to 1200 K from x-ray Debye–Waller temperature factors (Dubrovinsky et al., 2001) and up to 73 GPa and 1700 K using IXS by Lin et al. (2005). x-Ray radial diffraction (XRD) has been used to measure the elastic constants of polycrystalline iron with simultaneous measurement of the CPO at room temperature and pressures up to 211 GPa (Singh et al., 1998; Mao et al, 1998, with corrections 1999; Merkel et al., 2005), which is still well below inner core pressures. However, as mentioned before, the high nonhydrostatic stress present in DACs has exceeded the plastic yield stress in some experiments and produced plastic strain, which violates the elastic stress analysis used to determine the elastic parameters (Antonangeli et al., 2006; Mao et al., 2008a,b,c; Merkel et al., 2006a,b, 2009). The experimental Vp data used to describe the anisotropy of textured polycrystalline samples are shown in Figure 23. The texture or CPO of the iron is induced by the compression in DAC with an axial symmetry. The original experiments of H.K. Mao et al. (1998) show the characteristic bell-shaped Vp curve with peak velocity near 45 from the compression direction, which is also the symmetry axis (Figure 23(a)). Note also that even the IXS data points of Antonangeli et al. (2004) have similar symmetry to the data

519

of Mao et al. (1998). Recently, a new combined method was introduced by Mao et al. (2008a,b,c) to avoid problems in DAC, which uses IXS and the EOS. In the 2008 paper, they reproduced the old method with bell-shaped curve and introduced the new method, which has the maximum Vp nearer the symmetry axis (Figure 23(b)). More recent work using IXS uses gas-loaded DAC to avoid or reduce nonhydrostatic stresses (Antonangeli et al., 2010, 2012), but has not studied anisotropy. In order simulate the in situ conditions, the static (0 K) elastic constants have been calculated at inner core pressures (Stixrude and Cohen, 1995). The calculated elastic constants predict maximum P-wave velocity parallel to the c-axis, and the difference in velocity between the c- and a-axes is quite small (Figure 23(a)). The anisotropy of the calculated elastic constants being quite low required that the CPO is very strong, and it was even suggested that inner core could be a single crystal of hcp iron to be compatible with the seismic observations and that c-axis is aligned with the Earth’s rotation axis. The first attempt to introduce temperature into first-principles methods for iron by Laio et al. (2000) produced estimates of the isotropic bulk and shear modulus at inner core conditions (325 GPa and 5400 K) and single-crystal elastic constants at conditions comparable with the experimental study of Mao et al. (1998) (210 GPa and 300 K). The next study to simulate inner core temperatures (4000–6000 K) and pressures by SteinleNeumann et al. (2001) produced two unexpected results: firstly the increase of the unit cell axial c/a ratios by a large amount (10%) with increasing temperature and secondly the migration of the P-wave maximum velocity to the basal plane and normal to the c-axis at high temperature. These new hightemperature results required a radical change in the seismic anisotropy model with one-third of c-axes being aligned normal to the Earth’s rotation axis (Steinle-Neumann et al., 2001) giving an excellent agreement with travel time differences. However, more recent calculations (Gannarelli et al., 2003, 2005; Sha and Cohen, 2006) have failed to reproduce the large change in c/a axial ratios with temperature, which casts some doubt on the elastic constants of Steinle-Neumann et al. at high temperature. It should be said that high-temperature

(a)

12.0 11.5 11.0 10.5 10.0 9.5 9.0 8.5 8.0 7.5 7.0

H.K. Mao et al. 1998 RXD 210 GPa Antonangeli et al. 2004 IXS 112 GPa

Vp (km s−1)

Vp (km s−1)

Experimental data : Vp curves

W.L. Mao et al. 2008 IXS+EOS 52 GPa

W.L. Mao et al. 2008 RXD 52 GPa

0

10 20 30 40 50 60 70 80 90 Angle from symmetry axis (°)

(b)

8.3 8.2 8.1 8.0 7.9 7.8 7.7 7.6 7.5 7.4 7.3

W.L. Mao et al. 2008 IXS +EOS 52 GPa

W.L. Mao et al. 2008 RXD 52 GPa

0

10 20 30 40 50 60 70 80 90 Angle from symmetry axis (°)

Figure 23 The seismic velocities at ambient temperature in single-crystal pure hexagonal close-packed e-phase iron calculated from the experimentally determined elastic constants of Mao et al. (1998, with correction 1999) and Mao et al. (2008a,b,c) or measured velocity in the case of Antonangeli et al. (2004). RXD, radial x-ray diffraction; IXS, x-ray scattering; EOS, equation of state (see text for discussion).

520

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

first-principles calculations represent frontier science in this area. What is perhaps even more troublesome is that there is very poor agreement, or perhaps one should say total disagreement, between experimental results and first principles for P- and S-wave velocity distribution in single-crystal hcp iron at low temperature and high pressure where methods are considered to be well established. The experimental techniques can be criticized as mentioned before. However, differences can be seen in the magnitude of the anisotropy and the position of the minimum velocity, minimum at 50 from the c-axis (Steinle-Neumann et al., 2001; Stixrude and Cohen, 1995) or at 90 (Laio et al., 2000; Vocˇadlo et al., 2003b). In recent years, a new consistency has appeared in the ab initio models for the inner core. In Figure 24, we have selected some original milestones like the Mao et al. (1998) experimental curve with bell shape, which today is considered an experimental artifact. The first OK ab initio model of hcp iron at core pressures by Stixrude and Cohen (1995) and an early finite temperature ab initio model by Steinle-Neumann et al. (2001) show to illustrate the degree of disagreement between these pioneering studies. All the other studies are recent from 2010 to 2013 all at inner temperatures and pressures, all for hcp iron, a part from one for bcc iron from Mattesini et al. (2010). Using the weak cylindrical seismic model for hemispherical inner core anisotropy of Lythgoe et al. (2014), we can compare with travel time residuals (dt/t) predicted by ab initio elasticity models of iron. From Figure 24, we can see that seismic anisotropy between the hemispheres is very different, and single model will not explain both hemispheres. Several models are in agreement with stronger anisotropy of the western hemisphere (hcp Stixrude and Cohen, 1995; hcp and bcc from Mattesini et al., 2010), corresponding to Vp anisotropies between 4.1% and 6.3%. Two models are also in agreement with the weaker seismic anisotropy observations for eastern hemisphere, notably (hcp, Stixrude and Cohen, 1995; hcp, Sha and Cohen, 2010)

corresponding to Vp anisotropies between 2.4% and 4.1%. All the ab initio models are present as transverse isotropic symmetry with the symmetry axis parallels to the Earth’s rotation axis. In the hcp iron, which has hexagonal symmetry, this requires that c-axis of the single crystal to be parallel to the rotation axis. In the case of bcc iron, the direction of maximum Vp is the [111] direction, and all the crystals in the model aggregate are rotated about [111] to produce transverse isotropic symmetry. So for hcp iron, the ab initio curves represent the maximum possible single-crystal anisotropy, and in the western hemisphere, there are seismic observations with anisotropy stronger than perfectly aligned c-axis of the hcp iron single crystals or bcc iron [111] axis is perfectly aligned. The bcc model of Mattesini et al. (2010) produces the strongest Vp anisotropy at 6.3%, but it is less strong than the seismic western hemisphere measurements of Lythgoe et al. (2014) at the layer three of their model (Figure 2), which corresponds to less than 550 km from the center of the Earth. In addition, it is interesting to note that recent experimental studies at 340 GPa and 4700 K favor the hcp rather than bcc as the stable structure of iron in the inner core (Tateno et al., 2012). It is not clear what mechanism would produce such perfect alignment; it seems unlikely to be caused by plasticity as this results in nonperfect statistical alignment, unless there is more anisotropic iron crystal structure than presently known in the inner core or the extreme conditions near the center of the Earth. The processes related to melting and crystallization has been recently invoked by several studies of hemispherical nature of the inner core (Alboussie`re et al., 2010; Aubert et al., 2011; Deguen and Cardin, 2009; Gubbins et al., 2011; Monnereau et al., 2010). It is possible that other compositions of iron-related phases might have greater anisotropy than pure iron and currently known alloys, for example, orthorhombic cementite (Fe3C), which has Vp anisotropy of 10.3% at inner core pressures (Mookherjee, 2011b).

Ab initio models : Vp Curves 13.0

11.5 M2010 bcc

11.0

M1998 RXD

6.3%

7.2%

M2010

10.5 10.0 (a)

SC2010

0

10

20

30

40

M2013 8.3% 7.5% M2013 FeNi

20.5%

SN2001

0.05 4.1%

SC1995

12.0

20.5%

50

60

70

Angle from symmetry axis (°)

5.7%

Vp Anisotropy (δt/t)

Vp (km s−1)

SN2001

8.3% M2013 7.5% M2013 FeNi

12.5

Ab initio models : Vp Anisotropy (δt/t) 0.10

2.4%

80

0.00

Isotropic Eastern

−0.05

Western

(b)

2.4%

SC1995 4.1%

M2010

M2010 bcc 6.3%

5.7%

−0.10 −0.15

90

SC2010

0

10

20

30

40

50

60

70

80

90

Angle from symmetry axis (°)

Figure 24 (a) The seismic velocities at 0 K or high temperature in single-crystal hexagonal e-phase iron calculated from the ab initio determined elastic constants at inner core pressures, with experimental Vp of Mao et al. (1998, 1999) at 210 GPa at room temperature for reference. (b) The predicted P-wave anisotropy for the inter core using the ab initio elastic constants, with the seismic results of Lythgoe et al. (2014) for eastern (dark gray region with black dashed line outlines) and western (light gray) hemispheres. Numbers with percent sign are the Vp-wave anisotropies for each ab initio model and the experimental data of Mao et al. (1998, 1999). All models are for pure crystal hexagonal close-packed hexagonal e-phase iron, except where otherwise specified. Bcc stands for pure body-centered cubic a-phase iron. SC1995 ¼ Stixrude and Cohen (1995) at 0 K, SN2001 ¼ Steinle-Neumann et al. (2001) at 6000 K, SC2010 ¼ Sha and Cohen (2010) at 6000 K, M2010 ¼ Mattesini et al. (2010) at 6000 K, M2010 bcc has the same authors and temperature with bcc structure, M2013 ¼ Martorell et al. (2013) at 5500 K, and M2013 FeNi has the same authors and temperature with a composition of 87.5% Fe 12.5% Ni. See text for discussion.

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

From this brief survey of recent results in this field, it is clear there is still much to do to unravel the meaning of seismic anisotropy of the inner core and physics of iron at high pressure and temperature in particular. Although the stability of hcp iron at inner core conditions has been questioned from time to time on experimental or theoretical grounds, which the inner core may not be pure iron (e.g., Poirier, 1994), the major problem at the present time is to get agreement between theory and experiment at the same physical conditions. Interpretation of the mechanisms responsible for inner core seismic anisotropy is out of the question without a reliable estimate of elastic constants of pure iron and its alloys; nowhere in the Earth is Francis Birch’s ‘high-pressure language’ (positive proof ¼ vague suggestion, Birch, 1952) more appropriate.

2.20.3 2.20.3.1

Rock Physics Introduction

In this section, I will illustrate the contribution of CPO to seismic anisotropy in the deep Earth with cases of olivine and the role of melt. The CPO in rocks of upper mantle origin is now well established (e.g., Mainprice et al., 2000; Mercier, 1985; Nicolas and Christensen, 1987) as direct samples are readily available from the first 50 km or so, and xenoliths provide further sampling down to depths of about 220 km. Ben and Mainprice (1998) created a database of olivine CPO patterns from a variety of the upper mantle geodynamic environments (ophiolites, subduction zones, and kimberlites) with a range of microstructures. However, for the deeper mantle (e.g., Wenk et al., 2004) and inner core (e.g., Merkel et al., 2005), we had to rely traditionally on high-pressure and hightemperature experiments to characterize the CPO at extreme conditions. In recent years, the introduction of various types of polycrystalline plasticity models to stimulate CPO development for complex strain paths has allowed a high degree of forward modeling using either slip systems determined from studying experimentally deformed samples using transmission electron microscopy (e.g., wadsleyite – Thurel et al., 2003; ringwoodite – Karato et al., 1998), RXD peak broadening analysis for electron radiation sensitive minerals (e.g., Mg-perovskite – Cordier et al., 2004b), or predicted systems from atomic-scale modeling of dislocations (e.g., olivine, Durinck et al., 2005a,b and ringwoodite, Carrez et al., 2006). The polycrystalline plasticity modeling has allowed forward modeling of upper mantle (e.g., Blackman et al., 1996; Chastel et al., 1993; Tommasi, 1998), transition zone (e.g., Tommasi et al., 2004), lower mantle (e.g., Mainprice et al., 2008a,b; Wenk et al., 2006), D00 layer (e.g., Merkel et al., 2006a), and the inner core (e.g., Jeanloz and Wenk, 1988; Wenk et al., 2000).

2.20.3.2 Olivine the Most-Studied Mineral: State-of-the-ArtTemperature, Pressure, Water, and Melt Until the papers by Jung and Karato (2001), Katayama et al. (2004), and Katayama and Karato (2006) were published, the perception of olivine-dominated flow in the upper mantle was quite simple with [100] {0kl} slip being universally accepted as the mechanism responsible for plastic flow and

521

the related seismic anisotropy (e.g., Mainprice et al., 2000). The experimental deformation of olivine in hydrous conditions at 2 GPa pressure and high temperature by Karato and coworkers produced a new type of olivine CPO developed at low stress with [001] parallel to the shear direction and (100) in the shear plane, which they called C type, which is associated with high water content. They introduced a new olivine CPO classification that illustrated the role of stress and water content as the controlling factors for the development of five CPO types (A, B, C, D, and E) (Figure 25). The five CPO types are assumed to represent the dominant slip system activity on A  [100](010), B  [001](010), C  [001](100), D  [100]{0kl}, and E  [100](001). I have taken the Ben and Mainprice (1998) olivine CPO database with 110 samples and estimated the percentages for each CPO type and added an additional class called AG type (or axial b-[010] girdle by Tommasi et al., 2000), which is quite common in naturally deformed samples, particularly in samples that have been associated with melt–rock interaction (e.g., Higgie and Tommasi, 2012). The CPO types in percentage of the database are A type (49.5%), D type (23.8%), AG type (10.1%), E type (7.3%), B type (7.3%), and C type (1.8%). It is clear that CPO associated with [100] direction slip (A, AG, D, and E types) represents 90.8% of the database and therefore only 9.2% is associated with [001] direction slip (B and C types). Natural examples of all CPO types taken from the database are shown in Figure 26, with the corresponding seismic properties in Figure 27. There are only one unambiguous C-type sample and another with transitional CPO between B and C types. The database contains samples from paleo-mid-ocean ridges (e.g., Oman ophiolite), the circum-Pacific subduction zones (e.g., Philippines, New Caledonia, Canada), and subcontinental mantle (e.g., kimberlite xenoliths from South Africa). There have been some recent reports of the new olivine B-type CPO (e.g., Mizukami et al., 2004) associated with high water content, and other B and C types from ultrahigh-pressure (UHP) rocks (e.g., Xu et al., 2006) have relatively low water contents. It is instructive to look at the solubility of water in olivine to understand the potential importance of the C-type CPO. In Figure 28, the experimentally determined solubility of water in nominally anhydrous upper mantle silicates (olivine, cpw, opx, and garnet) in the presence of free water is shown over the upper mantle pressure range. The values given in the review by Bolfan-Casanova (2005) are in H2O ppm wt. using the calibration of Bell et al. (2003), so the values of Karato et al. in H/106 Si using the infrared calibration of Paterson (1982) have to be multiplied by 0.22 to obtain H2O ppm wt. If free water is available, then olivine can incorporate, especially below 70 km depth, many times the concentration necessary for C-type CPO to develop according to the results of Karato and coworkers. Why is it that the C-type CPO is relatively rare? It is certain that deforming olivine moving slowly towards the surface will lose its water due to the rapid diffusion of hydrogen. For example, even xenoliths transported to the surface in a matter of hours lose a significant fraction of their initial concentration (Demouchy et al., 2005). Hence, it very plausible that in the shallow mantle (less than about 70 km depth), the C type will not develop because the solubility of water is too low in olivine at equilibrium conditions and that ‘wet’ olivine upwelling

522

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

D -type [100]{0kl} [100] [010]

[001]

500 B-type [001](010)

D 400

(23.8%)

[001]

(7.3%)

Stress (MPa)

AG-type [100](010) [100] [010] [001]

(10.1%)

300

[100] [010] E-type [100](001)

200 A

A-type [100](010) [100] [010]

[100] [010]

[001]

[100) [010]

C-type [001](001) (1.8%)

[001]

100 (7.3%)

(73.3%) 0

(49.5%)

400

200

0

[001]

800 1000 1200 1400

600

Water content (ppm H/Si) 0

100

200

300

Water content (ppm wt) Figure 25 The classification of olivine CPO originally proposed by Jung and Karato (2001) and Karato et al. (2008) as a function of stress and water content. The water content scale in ppm H/Si is that originally used by Jung and Karato. The water content scale in ppm wt is more recent calibration used by Bolfan-Casanova (2005). The numbers in brackets are the percentage of samples with the fabric types found in the database of Ben Ismail and Mainprice (1998). On the pole figure, red indicates [100] parallel to lineation and blue indicates [001] parallel to lineation in samples from the olivine CPO database.

Effect of

Stress (MPa)

300 200 100 0

A

A

Wet

B

B

B⬘

D-type

500 400

Dry

Effect of water content

600 pressure

3.6GPa B

A

A 3.1GPa B A 3.1GPa B A 2.5GPa

C/E A

B⬘

E-type

B⬘

B⬘

C-type B⬘

B

B

A

A

B Mantle stress levels

A-type

0

C/E C D E

B-type

A

500

1000

1500

2500

Water content (ppm H/Si) Figure 26 In the left-hand panel the experimental data of Ohuchi et al. (2012) on the effect of water and stress for the development of olivine CPO. In the right-hand panel the experimental data of Jung et al. (2008) on the effect of pressure and stress on the development of dry olivine CPO. The CPO fields proposed by Jung and Karato (2001) and Karato et al. (2008) as a function of stress and water content are marked with black solid or dashed lines. In the right-handed panel the symbols with no letter next to them come from Karato et al. (2008) and symbols with a letter come from Ohuchi et al. (2012). CPO types C/E and B’ are transitional CPO defined by Ohuchi et al. (2012). Open symbol represents dry samples or no water detected. In the lefthand panel the pressure is indicated in GPa next to each symbol. See text for discussion.

from greater depths and moving towards the surface by slow geodynamic processes will lose their excess water by hydrogen diffusion. In addition, any ‘wet’ olivine coming into contact with basalt melt will tend to ‘dehydrate’ as the solubility of water in the melt phase is hundreds to thousands of times greater than olivine (e.g., Hirth and Kohlstedt, 1996). The melting will occur in upwelling ‘wet’ peridotites at a welldefined depth when the solidus is exceeded and the volume fraction of melt produced is controlled by the amount of water

present. Karato and Jung (1998) estimated that melting is initiated at about 160 km in the normal mid-ocean ridge source regions and at greater depth of 250 km in back-arctype MORB with the production of 0.25–1.00% melt, respectively. Given the small melt fraction, the water content of olivine is unlikely to be greatly reduced. As more significant melting will of course occur when the ‘dry’ solidus is exceeded with 0.3% melt per kilometer melting at about 70 km, then 3% or more percent melt is quickly produced and the water

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

[100] Z

A-Type

X

90OA61C

[010]

AG-Type 90OF22

Contours (x uni.) 8.55

Contours (x uni.) 4.65

5.0 4.0 3.0 2.0 1.0

7.0 6.0 5.0 4.0 3.0 2.0 1.0

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

Min. density = 0.00

0.00 Max. density = 8.55

B-Type NO8B

Contours (x uni.) 5.17

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

Min. density = 0.00

E-Type DC334A

Min. density = 0.04

0.06 Max. density = 3.24

Min. density = 0.00

Min. density = 0.06

0.01 Max. density = 3.98

Min. density = 0.01

Contours (x uni.) 6.23

Contours (x uni.) 6.08

Contours (x uni.) 5.44

5.0

5.0 4.0 3.0 2.0 1.0

4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

Min. density = 0.00

0.00 Max. density = 6.08

Min. density = 0.00

0.00 Max. density = 5.44

Min. density = 0.00

Contours (x uni.) 10.86

Contours (x uni.) 4.99

Contours (x uni.) 4.22

9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

3.5 3.0 2.5 2.0 1.5 1.0

Min. density = 0.00

0.00 Max. density = 4.99

Min. density = 0.00

0.00 Max. density = 4.22 Min. density = 0.00

Contours (x uni.) 14.46

Contours (x uni.) 7.37

Contours (x uni.) 6.44

12.0 10.0 8.0 6.0 4.0 2.0

6.0 5.0 4.0 3.0 2.0 1.0

5.0 4.0 3.0 2.0 1.0

0.00 Max. density = 14.46

0.00 Max. density = 2.93

3.0 2.5 2.0 1.5 1.0

0.00 Max. density = 10.86

1.0

2.5 2.0 1.5 1.0

0.00

CR24

1.5

2.5 2.0 1.5 1.0

1.0

D-Type

2.0

Contours (x uni.) 3.98

2.0

Max. density = 6.23

Contours (x uni.) 2.93

Contours (x uni.) 3.24

3.0

Optidsp42

Min. density = 0.00

Min. density = 0.00

Contours (x uni.) 3.34

4.0

C-Type

0.00 Max. density = 4.65

0.00 Max. density = 5.17

0.04 Max. density = 3.34

Min. density = 0.00

Contours (x uni.) 4.88

0.00 Max. density = 4.88

[001]

Contours (x uni.) 6.42

0.00 Max. density = 6.42

523

Min. density = 0.00

0.00 Max. density = 7.37

Min. density = 0.00

0.00 Max. density = 6.44

Min. density = 0.00

Figure 27 Natural examples of olivine CPO types from the Ben Ismail and Mainprice (1998) database, except the B-type sample NO8B from K. Michibayashi (personal communication, 2006). X marks the lineation; the horizontal line is the foliation plane. Contours given in times uniform.

524

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

Vp (km s−1) Z

dVs (%) 8.71

A-Type

10.01

8.00

90OA61C

7.80

0.37

7.57

Shading - inverse log Max. velocity = 8.71 Anisotropy = 14.0%

Min. velocity = 7.57

Shading - inverse log Max. anisotropy = 10.01

8.47

90OF22

7.17

Min. velocity = 7.66

0.29 Max. anisotropy = 7.17

8.30

NO8B

3.71

Min. velocity = 7.91

0.04 Max. anisotropy = 3.71

8.55

Optidsp42

4.0 3.0 2.0

Max. anisotropy = 6.92

Min. velocity = 7.77

0.48 Max. anisotropy = 8.74

Vp Contours (km s−1) 9.03

DC334A

Min. velocity = 7.64

AVs Contours (%) 11.26

11.26

6.0 4.0

7.64 Max. velocity = 9.03 Anisotropy = 16.7%

0.48

Min. anisotropy = 0.48

8.0

8.60 8.40 8.20 8.00

E-Type

8.74

7.0 6.0 5.0 4.0 3.0 2.0

7.77 Max. velocity = 8.76 Anisotropy = 12.0%

Min. anisotropy = 0.37

8.74

8.60 8.50 8.40 8.30 8.20 8.10 8.00 7.90

CR24

0.37

0.37

Min. velocity = 7.72

8.76

D-Type

6.92

5.0

7.72 Max. velocity = 8.55 Anisotropy = 10.1%

0.04

Min. anisotropy = 0.04

6.92

8.32 8.24 8.16 8.08 8.00 7.92 7.84

C-Type

3.71

3.0 2.5 2.0 1.5 1.0

7.91 Max. velocity = 8.30 Anisotropy = 4.8%

0.29

Min. anisotropy = 0.29

8.20 8.15 8.10 8.05 8.00

B-Type

7.17

6.0 5.0 4.0 3.0 2.0

7.66 Max. velocity = 8.47 Anisotropy = 10.0%

0.37

Shading - inverse log

Min. anisotropy = 0.37

8.24 8.16 8.08 8.00 7.92 7.84 7.76

AG-Type

10.01

9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0

8.20

X

Vs1 polarization

0.17 Max. anisotropy = 11.26

0.17

Min. anisotropy = 0.17

Figure 28 Anisotropic seismic properties of olivine at 1000˚C and 3 GPa with CPO of the samples in figure 27. X marks the lineation, the horizontal line is the foliation plane.

525

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

0

0 Di

op

70

2

sid

e

4

240

C-type CPO

300

6 O

liv

360

in

e

8

Pressure (GPa)

180

te tati Ens

Depth (km)

120

10

Pyrope

content of olivine will be greatly reduced. So the action of reduced solubility and selective partitioning of water into the melt phase are likely to make the first 70 km of oceanic mantle olivine very dry. The other region where water is certainly present is in subduction zones, where relatively water-rich sediments, oceanic crust, and partly hydrated oceanic lithosphere will add to the hydrous budget of the descending slab. Partial melting is confined in the mantle wedge to the hottest regions, where the temperatures approach the undisturbed asthenospheric conditions at 45–70 km depth, and 5–25 wt. % melt will be produced by a lherzolitic source (Ulmer, 2001). Hence, even in the mantle wedge, the presence of large volume factions of melt is likely to reduce the water content of olivine to low levels, possibly below the threshold of the C-type CPO, for depths shallower than 70 km. Is water the only reason controlling the development of the C-type fabric or [001] direction slip in general? The development of slip in the [001] direction on (010) and (100) planes at high stresses in olivine has been known experimentally since transmission electron microscopy study of Phakey et al. (1972). More recently, Couvy et al. (2004) had produced Band C-type CPO in forsterite at very high pressure (11 GPa) using nominally dry starting materials. However, as pointed out by Karato (2006), the postmortem infrared spectrophotometry of the deformed samples revealed the presence of water, presumably due to the dehydration of sample assembly at high pressure. However, concentration of water in the forsterite increases linearly with time at high pressure, whereas the CPO is acquired at the beginning of the experiment in the stress-relaxation tests conducted by Couvy et al. (2004), so it is by no means certain that significant water was present at the beginning of the experiment. Mainprice et al. (2005) suggested it was pressure that was the controlling variable, partly inspired by recent atomic modeling of dislocations in forsterite (Durinck et al., 2005b), that shows the energy barrier for [100] direction slip increases with hydrostatic pressure, whereas for [001], it is constant, which could explain the transition from [100] to [001] with pressure. More recent experiments by Jung et al. (2009) on dry olivine at pressures of 2.1–3.6 GPa report a transition from A-type CPO to B-type CPO with increasing pressure at about 3.1 GPa. Ohuchi et al. (2011) also working on dry olivine samples found the transition pressure from A type to B type is 7.1 GPa. Axial compression experiments using two single crystals of dry San Carlos olivine in series, one favorably oriented for a-direction slip and other for c-slip, find that faster c-slip occurs above 8 GPa (Raterron et al., 2007, 2009). New experiments of Ohuchi et al. (2012) on the deformation of olivine samples in the presence of water show much more complex distribution of CPO types (Figure 29) than reported by Karato et al. (2008). In Figure 29, A types are found with water contents over 500 ppm H/Si, B types are found at lower stress and very high water contents, and no definitive C types are reported by Ohuchi et al. (2012). It appears that both pressure and water content play a role in controlling CPO types, but the experimental scatter is now considerable (Figure 29) and exact relation to water content and pressure needs further calibration. If we are to accept the experimental results of Karato et al. (2008), what are the seismic consequences of the recent discovery of C-type CPO in experiments in hydrous conditions?

Upper mantle

12

410 km

420

0

1000

2000

3000

14 4000

Water content (ppm wt) Figure 29 The variation in the water content of upper mantle silicates in the presence of free water from Bolfan-Casanova (2005). The water content of the experimentally produced C-type CPO by Jung and Karato is indicated by the light blue region.

The classic view of mantle flow dominated by with [100] {0kl} slip is not challenged by this new discovery as most of the upper mantle will be dry and at low stress. The CPO associated with [100] slip, which is 90.8% of the Ben Ismaı¨l and Mainprice (1998) database, produces seismic azimuthal anisotropy for horizontal flow with maximum Vp, polarization of the fastest S-wave parallel to the flow direction, and VSH > Vsv. The seismic properties of all the CPO types are shown in Figure 27. It remains to apply the C-, B-, and possibly E-type fabrics to hydrated section of the upper mantle. Katayama and Karato (2006) proposed the mantle wedge in subduction zones is a region where the new CPO types are likely to occur, with the B-type CPO occurring in the lowtemperature (high stress and wet) subduction where an old plate is subducted (e.g., NE Japan). The B-type fabric would result anisotropy parallel normal to plate motion (i.e., parallel to the trench). In the back-arc, the A-type (or E-type reported by Michibayashi et al., 2006 in the back-arc region of NE Japan) fabric is likely dominant because water content is significantly reduced in this region due to the generation of island arc magma. Changes in the dominant type of olivine fabric can result in complex seismic anisotropy, in which the fast shear wave polarization direction is parallel to the trench in the forearc but is normal to it in the back-arc (e.g., Kneller et al., 2005). In higher-temperature subduction zones (e.g., NW America, Cascades), the C-type CPO will develop in the mantle wedge (low stress and wet) giving rise to anisotropy parallel to plate motion (i.e., normal to the trench). Although these models are attractive, trench-parallel flow was first described by Russo and Silver (1994) for flow beneath the Nazca Plate, where there is a considerable path length of anisotropic mantle to generate the observed differential arrival time of the S-waves. On the other hand, a well-exposed peridotite body analogue of arc-parallel flow of in south central Alaska reveals horizontal stretching lineations, and olivine [100] slip directions are subparallel to the Talkeetna arc for over 200 km, clearly indicating that mantle flow was parallel to the arc axis (Mehl et al., 2003).

526

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

The measured CPO of olivine shows that the E-type fabric is dominant along the Talkeetna arc; in this case, foliation is parallel to the Moho suggesting arc-parallel shear with a horizontal flow plane. Tommasi et al. (2006) also reported the E-type fabric with trench-parallel tectonic context in a highly depleted peridotite massif from the Canadian Cordillera in dunites associated with high degrees of melting and hence probably dry, whereas harzburgites have an A-type fabric. In limiting the path length to the region of no melting, in coldest part of the mantle wedge, above the plate, you are also constraining the vertical thickness to about 45–70 km depth, if one accepts the arguments for melting (Ulmer, 2001). For NE Japan, the volcanic front is about 70 km above the top of the slab defined by the hypocenter distribution of intermediatedepth earthquakes (Nakajima and Hasegawa, 2005, their Figure 1), and typical S-wave delay times are 0.17 s (maximum 0.33 s, minimum 0.07 s). The delay times from local slab sources are close to the minimum of 0.07 s for trench-parallel fast S-wave polarizations to the east of the volcanic front (i.e., above the coldest part of the mantle wedge) and are over 0.20 s for the trench normal values (i.e., the back-arc side). Are these CPOs capable of producing a recordable seismic anisotropy over such a short path length? The vertical S-wave anisotropy can be estimated from the delay time given by Nakajima and Hasegawa (2005) (e.g., 0.17 s), the vertical path length (e.g., 70 km), and the average S-wave velocity (e.g., 4.46 km s 1) to give a 1.1% S-wave anisotropy, which is less than maximum S-wave anisotropy of 1.7% given for a B-type CPO in a vertical direction given by Katayama and Karato (2006) for horizontal flow, so B-type CPO is compatible with seismic delay time, even if we allow some complexity in the flow pattern. The case for C type in the high-temperature subduction zones is more difficult to test, as the S-wave polarization pattern will be the same for C and A types (Katayama and Karato, 2006). The clear seismic observations of fast S-wave polarizations parallel to plate motion (trench normal) given for the Cascadia (Currie et al., 2004) and Tonga (Fischer et al., 1998) subduction zones, which would be compatible with A or C types. In general, some care has to be taken to separate below slab, slab, and above slab anisotropy components to test mantle wedge anisotropy. The interpretations above follow the logic of Karato et al. (2008), but as mentioned earlier, the role of C-type CPO as indicator of wet olivine is seriously questioned by the experiments of Ohuchi et al. (2012). Most of the reported B-type and C-type CPOs are associated with garnet peridotite bodies and eclogites from UHP metamorphic terranes, for example, the Sulu terrane in China (Xu et al., 2006), Alpe Arami and Cima di Gagnone in the central Alps (Dobrzhinetskaya et al., 1996; Frese et al., 2003; M€ ockel, 1969; Skemer et al., 2006), Val Malenco peridotite in northern Italy ( Jung, 2009), and the Western Gneiss Region of the Norwegian Caledonides (Katayama et al., 2005; Wang et al., 2013).

2.20.3.3

Seismic Anisotropy and Melt

The understanding of the complex interplay between plate separation, mantle convection, adiabatic decompression melting, and associated volcanism at mid-ocean ridges in the upper mantle (e.g., Solomon and Toomey, 1992) and the presence of melt in the deep mantle in the D00 layer (e.g., Williams and

Garnero, 1996) and inner core (Singh et al., 2000) are challenges for seismology and mineral physics. For the upper mantle, two contrasting approaches have been used to study mid-ocean ridges: on one hand marine geophysical (mainly seismic) studies of active ridges and on the other hand geologic field studies of ophiolites, which represent ‘fossil’ mid-ocean ridges. These contrasting methods have yielded very different views about the dimensions of the mid-ocean ridge or axial magma chambers. The seismic studies have given us threedimensional information about seismic velocity and attenuation in the axial region. The critical question is, how can this data be interpreted in terms of geologic structure and processes? To do so, we need data on the seismic properties at seismic frequencies of melt containing rocks, such as harzburgites, at the appropriate temperature and pressure conditions. Until recently, laboratory data for filling these conditions were limited for direct laboratory measurements to isotropic aggregates (e.g., Jackson et al., 2002), but deformation of initially isotropic aggregates with a controlled melt fraction in shear (e.g., Holtzman et al., 2003; Zimmerman et al., 1999) allows simultaneous development of the CPO and anisotropic melt distribution. To obtain information concerning anisotropic rocks, one can use various modeling techniques to estimate the seismic properties of idealized rocks (e.g., Mainprice, 1997; Jousselin and Mainprice, 1998; Taylor and Singh, 2002) or experimentally deformed samples in shear (e.g., Holtzman et al., 2003). This approach has been used in the past for isotropic background media with random orientation distributions of liquid-filled inclusions (e.g., Mavko, 1980; Schmeling, 1985a,b; Takei, 2002). However, their direct application to mid-ocean ridge rocks is compromised by two factors. Firstly, field observations on rock samples from ophiolites show that the harzburgites found in the mid-ocean ridges have strong CPOs (e.g., Boudier and Nicolas, 1995), which results in the strong elastic anisotropy of the background medium. For the case of the D00 layer and the inner core, the nature of the background media is not well defined and an isotropic medium has been assumed (Singh et al., 2000; Williams and Garnero, 1996). Secondly, field observations show that melt films tend to be segregated in the foliation or in veins, so that the melt-filled inclusions should be modeled with a shape preferred orientation. The rock matrix containing melt inclusions is modeled using effective medium theory, to represent the overall elastic behavior of the body. The microstructure of the background medium is represented by the elastic constants of the crystalline rock, including the CPO of the minerals and their volume factions. Quantitative estimates of how rock properties vary with composition and CPO can be divided into two classes. There are those that take into account only the volume fractions with simple homogenous strain or stress field and upper and lower bounds for anisotropic materials such as Voigt– Reuss bounds, which give unacceptably wide bounds when the elastic contrast between the phases is very strong, such as a solid and a liquid. The other class takes into account some simple aspects of the microstructure, such as inclusion shape and orientation. There are two methods for the implementation of the inclusions in effective medium theory to cover a wide range of concentrations; both methods are based on the analytic solution for the elastic distortion due to the insertion of a single inclusion into an infinite elastic

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

medium given by Eshelby (1957). The uniform elastic strain tensor inside the inclusion (eij) is given by   eij ¼ 1⁄2 Gikjl + Gjkil Cklmn e*mn

where Gikjl is the tensor Green’s function associated with displacement due to a unit force applied in a given direction, Cklmn are the components of the background medium elastic stiffness tensor, and e*mn is the eigenstrain or stress-free strain tensor due to the imaginary removal of the inclusion from the constraining matrix. The symmetrical tensor Green’s function Gikjl is given by Mura (1987) as Gikjl ¼

2p ð ðp  1 sinydy K ij 1 ðxÞxk xl df 4p 0

0

with Kip (x) ¼ Cijpl xj xl, the Christoffel stiffness tensor for direction (x), and x1 ¼ sin y cos f/a1, x2 ¼ sin y sin f/a2 and x3 ¼ cos y/a3. The angles y and f are the spherical coordinates that define the vector x with respect to the principal axes of the ellipsoidal inclusion. The semiaxes of the ellipsoid are given by a1, a2, and a3. The integration to obtain the tensor Green’s function must be done by numerical methods, as no analytic solutions exist for a general triclinic elastic background medium. Greater numerical efficiency, particularly for inclusions with large axial ratios, is achieved by taking the Fourier transform of Gikjl and using the symmetry of the triaxial ellipsoid to reduce the amount of integration (e.g., Barnett, 1972). The selfconsistent (SC) method introduced by Hill (1965) uses the solution for a single inclusion and approximates the interaction of many inclusions by replacing the background medium with effective medium. In the formulation of SC scheme by Willis (1977), a ratio of the strain inside the inclusion to the strain in the host medium can be identified as Ai: Cscs Þ

Ai ¼ ½I + GðCi

1

i¼n i¼n  X

 X eSCS ¼ V i Ai sSCS ¼ V i Ci Ai i¼1

C

SCS



SCS

¼ s

i¼1



SCS

e



1

where I is the symmetrical fourth-rank unit tensor, Iijkl ¼ 1/2 (dikdjl + dil djk), dik is the Kronecker delta, Vi is the volume fraction, and Ci are the elastic moduli of the ith inclusion. The elastic constants of the SC scheme (Cscs) occur on both sides of the equation because of the stain ratio factor (A), so that solution has to be found by iteration. This method is the most widely used in Earth sciences, being relatively simple to compute and well established (e.g., Kendall and Silver, 1996, 1998). Certain consider that when the SC is used for two phases, for example, a melt added to a solid crystalline background matrix, the melt inclusions are isolated (not connected) below 40% fluid content, and the solid and fluid phases can only be considered to be mutually fully interconnected (biconnected) between 40% and 60%. For our application to magma bodies, one would expect such interconnection at much lower melt fractions. The second method is DEM. This models a two-phase composite by incrementally adding inclusions of melt phase to a crystalline background

527

phase and then recalculating the new effective background material at each increment. McLaughlin (1977) derived the tensorial equations for DEM as follows: dCDEM 1  ¼ Ci dV ð1 V Þ

 CDEM Ai

Here, again the term Ai is the strain concentration factor coming from Eshelby’s formulation of the inclusion problem. To evaluate the elastic moduli (CDEM) at a given volume fraction V, one needs to specify the starting value of CDEM and which component is the inclusion. Unlike the SC, the DEM is limited to two components A and B. Either A or B can be considered to be the included phase. The initial value of CDEM is clearly defined at 100% of phase A or B. The incremental approach allows the calculations at any composition irrespective of starting concentrations of original phases. This method is also implemented numerically and addresses the drawback of the SC in that either phase can be fully interconnected at any concentration. Taylor and Singh (2002) attempted to take advantage of both of these methods and minimize their shortcomings by using a combined effective medium method, a combination of the SC and DEM theory. Specifically, they used the formulation originally proposed by Hornby et al. (1994) for shales; an initial meltcrystalline composite is calculated using the SC with melt fraction in the range 40–60% where they claim that each phase (melt and solid) is connected and then uses the DEM method to incrementally calculate the desired final composition that may be at any concentration with a biconnected microstructure. To illustrate the effect on oriented melt inclusions, I will use the data from the study of a harzburgite sample (90OF22) collected from the Moho transition zone of the Oman ophiolite (Mainprice, 1997). The CPO and petrology of the sample have been described by Boudier and Nicolas (1995), and the CPO of the olivine (AG Type) is given in Figure 26. The mapping area records a zone of intense melt circulation below a fast-spreading paleo-mid-ocean ridge at a level between the asthenospheric mantle and the oceanic crust. I use the DEM effective medium method combined with Gassmann’s (1951) poroelastic theory to ensure connectivity of the melt system at low frequency relevant to seismology; see Mainprice (1997) for further details and references. The harzburgite (90OF22) has a composition of 71% olivine and 29% opx. The composition combined with CPO of the constituent minerals and elastic constants extrapolated to simulate conditions of 1200  C and 200 MPa where the basalt magma would be liquid predicts the following P-wave velocities in principal structural direction: X ¼ 7.82, Y ¼ 7.69, and Z ¼ 7.38 km s 1 (X ¼ lineation, Z ¼ normal to foliation, and Y is perpendicular to X and Z). The crystalline rock with no melt has essentially an orthorhombic seismic anisotropy. Firstly, I have added basalt spherical basalt inclusions; the velocities for P- and S-waves decrease and attenuation increases (Figure 30) with increasing melt faction and the rock becomes less anisotropic, but preserves its orthorhombic symmetry. When ‘pancake’-shaped basalt inclusions with X:Y:Z ¼ 50:50:1 are added, to simulate the distribution of melt in the foliation plane observed by Boudier and Nicolas (1995), certain aspects of the original orthorhombic symmetry of the rock are preserved, such as

528

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

Melt inclusion shape X:Y:Z =1:1:1

P-waves 8

0.01

4.50

Vp(Y) Q−1

0.001

Vp(Z)

3.50

0.001 Q−1

3.00

5

4

0.01 Q−1

Vs (km s−1)

Vp (km s−1)

Q−1

6

Vs2(X) = Vs1(Z)

4.00

7

0.1

Vs1(X) = Vs1(Y)

Vp(X)

0.0001

Vs2(Y) = Vs2(Z)

2.50

0

10

20

30

40

50

0.0001

2.00

10−5

0

10

20

S-waves 0.1

5

Vp(X) Vp(Y)

Q−1 (Z)

1

Vs1(X) = Vs1(Y) = VSH

4

Q−1sv

Q−1(X) and Q−1 (Y) Q−1

5 0.001 Vp(Y)

4

3

0

10

20

30

Vs (km s−1)

Vp (km s−1)

0.01 6

10−6 50

Melt inclusion shape X:Y:Z =50:50:1

8

7

40

Melt (%)

Melt (%)

P-waves

30

0.01 Q−1

3

0.001 Q−1s1(X) = Q−1 s1(Y)

2

0.0001 50

0.0001

= Q−1SH 1

40

0.1

0

VSV

0

10

20

Melt (%)

30

10−5

40

10−6 50

Melt (%) 1

Figure 30 The effect of increasing basalt melt fraction on the seismic velocities and attenuation (Q ) of a harzburgite. See text for details.

the difference between Vp in the X direction and Vp in the Y direction. However, many velocities and attenuations change illustrating the domination of the transverse isotropic symmetry with Z direction symmetry axis associated with the ‘pancake’-shaped basalt inclusions. Vp in the Y direction decreases rapidly with increasing melt fraction, causing the seismic anisotropy of P-wave velocities between Z and X or Y to increase. The contrast in behavior for P-wave attenuation is also very strong with attenuation (Q 1) increasing for Z and decreasing for X and Y directions. For the S-waves, the effects are even more dramatic and more like a transverse isotropic behavior. The S-waves propagating in X direction with a Y polarization, VsX(Y), and Y direction with polarization X, VsY(X) (see Figure 31 for directions), are fast velocities because they are propagating the XY (foliation) plane with polarizations in XY plane; we can call these VSH waves for a horizontal foliation. In contrast, all the other S-waves have either their

propagation or polarization (or both) direction in the Z direction and have the same lower velocity; these we can call VSV. Similarly for the S-wave attenuation, VSH are less attenuated than VSV. From this study, we can see that a few percent of aligned melt inclusions with high axial ratio can change the symmetry and increase the anisotropy of crystalline aggregate (see Figure 31 for summary), completely replacing the anisotropy associated with crystalline background medium in the case of S-waves. Taylor and Singh (2002) came to the same conclusion that S-wave anisotropy is an important diagnostic tool for the study of magma chambers and regions of partial melting. One of the most ambitious scientific programs in recent years was the mantle electromagnetic and tomography (MELT) experiment that was designed to investigate the forces that drive flow in the mantle beneath a mid-ocean ridge (MELT Seismic Team, 1998). Two end-member models often proposed can be classified into two groups; the flow is a passive

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

Y

V s y ( x ) -h i g h

Vp y - intermediate

X

z

lo

w

Vs z(x) - high

X

Vp x - high V s y ( x ) -l o w Vp y - intermediate

VSV

Y

h

hig

-

VSH

Vs

(y)

sx (y )

x( y) -

hi g

h

VSV Vs z(x) - low s

Vs y(z)- low

Vsh

Vp z - high Vs y(z)- high

VSV

Z

Vsx(z) - high

Vs

) z(y

V

Vp z - low

Attenuation 1/Q

w - lo

V

VSV

Z

Vs x(z) - low

Velocities

529

Vp x - low

Figure 31 A graphical illustration of the ‘pancake’-shaped melt inclusions (red) in the foliation (XY) plane (where X is the lineation) and the relation between velocity and attenuation (Q 1). The melt is distributed in the foliation plane. The velocities have an initial orthorhombic symmetry with Vp X > Y > Z. The directions of high velocity are associated with low attenuation. P-waves normal to the foliation have the lowest velocity. S-waves with polarizations in the foliation (XY) plane have the highest velocities (VSH). Diagram inspired a figure in the thesis of Barroul (1993).

response to diverging plate motions, or buoyancy forces supplied a plate-independent component variation of density caused by pressure release partial melting of the ascending peridotite. The primary objective in this study was to constrain the seismic structure and geometry of mantle flow and its relationship to melt generation by using teleseismic body waves and surface waves recorded by the MELT seismic array beneath the superfast-spreading southern East Pacific Rise (EPR). The observed seismic signal was expected to be the product of elastic anisotropy caused by the alignment of olivine crystals due to mantle flow and the presence of aligned melt channels or pockets of unknown structure at depth (e.g., Blackman and Kendall, 1997; Blackman et al., 1996; Kendall et al., 2004; Mainprice, 1997). Observations revealed that on the Pacific Plate (western) side, the EPR had lower seismic velocities (Forsyth et al., 1998; Toomey et al., 1998) and greater shear wave splitting (Wolfe and Solomon, 1998). The shear wave splitting showed that the fast shear polarization was consistently parallel to the spreading direction and at no time parallel to the ridge axis with no null splitting being recorded near the ridge axis. In addition, the delay time between S-wave arrivals on the Pacific Plate was twice that of the Nazca Plate. P delays decreased within 100 km of the ridge axis (Toomey et al., 1998), and Rayleigh surface waves indicated a decrease in azimuthal anisotropy near the ridge axis. Any model of the EPR must take into account that the average spreading rate at 17 S on the ridge is 73 mm year 1 and the ridge migrates 32 mm year 1 to the west. Anisotropic modeling of the P and S data within 500 km of the ridge axis by Toomey et al. (2002) and Hammond and Toomey (2003) showed that a best fitting finite strain hexagonal symmetry 2-D flow model had an asymmetrical distribution of higher melt fraction and temperature, dipping to the west under the Pacific Plate and lower melt fraction and temperature with an essentially horizontal structure under the Nazca Plate. Hammond and Toomey (2003) introduced low melt fractions (>2%), in relaxed (connected) cuspate melt pockets (Hammond and Humphreys, 2000) to match the observed velocities. Blackman and Kendall (2002) used a 3-D texture flow model to predicted pattern of upper mantle flow beneath the EPR oceanic

spreading center with asymmetrical asthenospheric flow pattern. Blackman and Kendall (2002) explored a series of models for the EPR and found that asymmetrical thermal structure proposed by Toomey et al. (2002) produced the model in closest agreement with seismic observations. The 3-D model shows that shear wave splitting will be lowest at about 50 km to the west of the EPR on the Pacific Plate with similar low value at 400 km to the east on the Nazca Plate and not the ridge axis because of the underlying asymmetrical mantle structure. The MELT experiment has showed that melt flow beneath a fast-spreading ridge is more complicated than originally predicted, with a deep asymmetrical structure present to 200 km depth. The influence of the near surface configuration (e.g., ridge migration) was also important in controlling the asthenospheric return flow towards the Pacific superswell in the west (Hammond and Toomey, 2003). The influence of melt geometry appears to be small in the case of the EPR, as the essential anisotropic seismic structure is captured by models that do not have melt geometries with strong shape preferred orientation. The situation may be different for the oceanic crust at fast oceanic spreading centers. The seismic anisotropy in regions of important melt production, such as Iceland (Bjarnason et al., 2002), does not show the influence of melt geometry on anisotropy, but rather the influence of large-scale mantle flow. In other contexts, such as the rifting, for example, the Red Sea (Vauchez et al., 2000) and East African Rift (Kendall et al., 2004), the melt geometry does seem to have an important influence of seismic anisotropy.

2.20.4

Conclusions

In this chapter, I have reviewed some aspects of seismology that have a bearing of the geodynamics of the deep interior of the Earth. In particular, I have emphasized the importance of seismic anisotropy and the variation of anisotropy on a global and regional basis. In the one-dimensional PREM model (Dziewo
nski and Anderson, 1981), anisotropy was confined to the first 250 km of the upper mantle. Subsequently, other

530

Seismic Anisotropy of the Deep Earth from a Mineral and Rock Physics Perspective

studies of the mantle found various additional forms of global anisotropy associated with the transition zone, the 670 km boundary layer, and the D00 layer (e.g., Montagner, 1994a,b; Montagner and Kennett, 1996; Montagner, 1998). The most recent global studies using more complete data sets and new methods of analysis emphasize the exceptionally strong nature of the upper mantle anisotropy, the anisotropy of the D00 layer, and no significant deviation from the original isotropic PREM for the rest of the mantle (e.g., Beghein et al., 2006; Panning and Romanowicz, 2006). To explain velocity variations that are observed in the mantle studies using probabilistic tomography places the emphasis on chemical heterogeneity and lateral temperature variations in the mantle (Deschamps and Trampert, 2003; Trampert et al., 2004). Trampert and van der Hilst (2005) argued that spatial variations in bulk major element composition dominate buoyancy in the lowermost mantle, but even at shallower depths, its contribution to buoyancy is comparable to thermal effects. The case of the D00 layer is perhaps even more challenging, as it is clearly a region with not only strong temperature and compositional gradients (e.g., Lay et al., 2004) but also a regionally varying seismic anisotropy (e.g., Maupin et al., 2005; van der Hilst et al., 2007; Wookey et al., 2005a) with an overall global signature (e.g., Beghein et al., 2006; Montagner and Kennett, 1996; Panning and Romanowicz, 2006). The inner core has well-known travel time variations that can be modeled to fit various single or double concentric layered anisotropy scenarios. Some studies (Beghein and Trampert, 2003; Ishii and Dziewo
nski, 2002) tend to favor a difference in anisotropy between the outermost inner core and innermost inner core; however, they disagree in the magnitude and symmetry of the anisotropy. Calvet et al. (2006) suggested that the data set is too poor to distinguish between several of the current models, whereas new highquality data (Lythgoe et al., 2014) clearly favor a strongly anisotropic western hemisphere and weakly anisotropic eastern one. Lythgoe et al. (2014) also questioned if the outermost and innermost inner core model is an artifact of not taking into account the hemispherical structure of the inner core. In the mantle and the inner core, there are often differences between studies at the global and regional scales and differences between 1-D and 3-D global models. The seismic sampling over different radial and lateral length scales using surface and body waves of variable frequency has made reference models very important in the reporting and understanding of complex data sets. Kennett (2006) had shown, for example, it is difficult to achieve comparable P- and S-wave definition for the whole mantle. Mineral physics can play important role as a representation based on elastic moduli rather than wave speeds that would provide a better comparator for interpretation in terms of composition, temperature, and anisotropy. In addressing the basics of elasticity, wave propagation in anisotropic crystals, and the nature of the anisotropy polycrystalline aggregates with CPO, I hope I have provided some of keys necessary for the interpretation of seismic anisotropy. CPO produced by plastic deformation is the link between deformation history and the seismic anisotropy of the Earth’s deep interior. We have seen earlier that many regions of the mantle (e.g., lower mantle) do not have a pronounced seismic anisotropy. However, from mineral physics, we have seen that in the upper mantle, olivine has a strong elastic anisotropy; in

the transition zone, wadsleyite is quite anisotropic; in the lower mantle, Mg-perovskite and MgO have increasing anisotropy with depth; in the D00 layer, postperovskite is very anisotropic; and the inner core, hcp iron is moderately anisotropic. In addition, if we add minerals from the hydrated mantle in subduction regions, such as the antigorite, chlorite, talc, and brucite, they can be very anisotropic at low pressure and S-wave anisotropy and can be very high for antigorite and chlorite even at high pressure. Subduction-related nonhydrous minerals, such as Al-CF phase, hollandite I, and stishovite, can have exceptionally high anisotropy in the transition zone and lower mantle. Potentially, the mineralogy suggests that seismic anisotropy could be present if these minerals have a CPO. Aligned melt inclusions and compositional layers can also produce anisotropy. To understand why there are regions in the deep Earth that have no seismic anisotropy is clearly a challenge for mineral physics, seismology, and geodynamics.

Acknowledgments I thank Guilhem Barruol, Franc¸ois Boudier, Patrick Cordier, Brian Kennett, Bob Liebermann, Katsuyoshi Michibayashi, Sebastien Merkel, Adolphe Nicolas, Andrea Tommasi, and the late Paul Silver for their helpful discussions. I thank Don Issak for providing a copy of his 2001 publication on Elastic Properties of Minerals and Planetary Objects, which is an excellent compliment to this work. I also thank Steve Jacobsen for providing preprints of his work on hydrous minerals. I thank Mainak Mookherjee for providing data in digital format from his publications. I thank James Wookey for his constructive review of the first version of this chapter and useful suggestions. Finally, I thank volume editors G. David Price and Lars Stixrude for providing the occasion to write this chapter and both them and series editor Gerald Schubert for their patience during long gestation of this manuscript. I dedicate this chapter to the memory of Paul G. Silver, extraordinary seismologist, genial colleague, and great friend.

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2.21 Properties of Rocks and Minerals: Physical Origins of Anelasticity and Attenuation in Rock I Jackson, Australian National University, Canberra, ACT, Australia ã 2015 Elsevier B.V. All rights reserved.

2.21.1 2.21.2 2.21.2.1 2.21.2.1.1 2.21.2.2 2.21.2.2.1 2.21.2.2.2 2.21.2.3 2.21.2.3.1 2.21.2.3.2 2.21.2.4 2.21.2.4.1 2.21.2.4.2 2.21.2.5 2.21.3 2.21.3.1 2.21.3.1.1 2.21.3.1.2 2.21.3.1.3 2.21.3.2 2.21.3.3 2.21.3.3.1 2.21.3.3.2 2.21.3.3.3 2.21.3.4 2.21.4 2.21.4.1 2.21.4.1.1 2.21.4.1.2 2.21.4.2 2.21.4.3 2.21.4.4 2.21.4.5 2.21.4.6 2.21.4.7 2.21.5 References

Introduction Theoretical Background Phenomenological Description of Viscoelasticity Thermodynamic description of anelasticity Intragranular Processes of Viscoelastic Relaxation Stress-induced rearrangement of point defects Stress-induced motion of dislocations Intergranular Relaxation Processes Effects of elastic and thermoelastic heterogeneity in polycrystals and composites Grain-boundary sliding Relaxation Mechanisms Associated with Phase Transformations Stress-induced variation of the proportions of coexisting phases Stress-induced migration of transformational twin boundaries Anelastic Relaxation Associated with Stress-Induced Fluid Flow Insights from Laboratory Studies of Geologic Materials Dislocation Relaxation Linearity and recoverability Laboratory measurements on single crystals Laboratory measurements on natural rocks and synthetic polycrystals Stress-Induced Migration of Transformational Twin Boundaries in Ferroelastic Perovskites Grain-Boundary Relaxation Processes Grain-boundary migration in b.c.c. and f.c.c. Fe Grain-boundary sliding in melt-free materials Melt-related viscoelastic relaxation Viscoelastic Relaxation in Cracked and Water-Saturated Crystalline Rocks Geophysical Implications Dislocation Relaxation Vibrating-string model Kink model Grain-Boundary Processes Partial Melting and the Seismic Signature of the Asthenosphere The Role of Water in Seismic Wave Dispersion and Attenuation Bulk Attenuation in the Earth’s Mantle Migration of Transformational Twin Boundaries as a Relaxation Mechanism in the Lower Mantle Solid-State Viscoelastic Relaxation in the Earth’s Inner Core Summary and Outlook

Nomenclature A

a ad B b C CW

Measure of anisotropy or interphase variability in elastic moduli or thermal expansivity involved in thermoelastic relaxation strength Spacing between adjacent Peierls valleys Period of kink potential measured parallel to dislocation line Dislocation drag coefficient Burgers vector Rate constant for phase transformation (m s 1 Pa 1) Concentration of water (wt ppm)

Treatise on Geophysics, Second Edition

541 542 542 544 545 545 545 549 549 550 552 552 553 554 556 556 556 556 557 557 558 558 558 559 561 562 562 562 563 564 565 566 566 567 567 567 568

Diffusivity (of either matter or heat) Grain size; characteristic separation of vacancy sources D(t) Normalized distribution of anelastic relaxation times Db Grain-boundary diffusivity Diffusivity for high-temperature background DB(t) dissipation Dk Kink diffusivity DP(ln t) Normalized distribution of ln t to model the dissipation peak associated with elastically accommodated grain-boundary sliding D d

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539

540

E Ed EP Eup f G g GHS Gm GR GRS GU h H(x) Hint hj Hk Hkp Hm Hmc J(t) J* J1 J2 JU K k Kf Ki Km KR Ks KU L L Lc M

ma ml mv N

Properties of Rocks and Minerals: Physical Origins of Anelasticity and Attenuation in Rock

Activation energy for relaxation time Elastic strain energy per unit length of dislocation or line tension Activation energy describing position (period) of dissipation peak Binding energy of dislocation to pinning point Frequency; the reciprocal of du/dx ¼ tan f (Figure 4(c)) Shear modulus Dimensionless multiplier of Tm/T in exponent for thermal activation of relaxation time Mean of the Hashin–Shtrikmann bounds on the shear modulus of a polycrystalline aggregate Free energy of kink migration Relaxed value of shear modulus (anelastic relaxation only) Reuss average of single-crystal elastic constants for shear Unrelaxed shear modulus Separation of closely spaced dislocations in subgrain wall Heaviside step function Kink interaction energy jth coefficient in Fourier series representing grainboundary topography Formation energy for a single geometric kink Kink-pair formation energy Enthalpy of kink migration Activation enthalpy for multicomponent diffusion Creep function Dynamic compliance Real part of J* Negative imaginary part of J* Unrelaxed compliance (e/s) Bulk modulus of composite of coexisting phases Boltzmann constant Bulk modulus of fluid Bulk modulus partially relaxed by phase transformation Bulk modulus of melt Bulk modulus fully relaxed by phase transformation Bulk modulus of solid matrix Unrelaxed bulk modulus Length of dislocation segment between adjacent pinning points Subgrain diameter Critical dislocation segment length for dislocation multiplication Ratio (te/td) of characteristic times for elastically and diffusionally accommodated grainboundary sliding Grain-size exponent of anelastic relaxation time Effective mass per unit length of dislocation Grain-size exponent for viscous (Maxwell) relaxation time Number of terms retained in Fourier series representing grain-boundary topography

n Nv p p0 pL(L) ps Q 1 QD1 r

R

Re s

Sm t T Tm To u U U(u) u0 um VSH VSV wk X x x1 y Y a

ab

Exponent in term btn representing transient creep in the Andrade model Number of dislocation segments of given length L per unit volume Internal variable providing link between stress and anelastic strain Stress-dependent equilibrium value of p Distribution of dislocation segment lengths Small fluctuation in pressure P Inverse quality factor (¼tan d); a measure of strain energy dissipation Height of the Debye dissipation peak of the standard anelastic solid Exponent describing sensitivity of relaxation time te to water content; radius of minor phase in concentric-sphere model of phase-transforming material Radius of curvature of dislocation bowed out under applied stress; gas constant; radius of grain-edge tubule Outer radius for concentric-sphere model of phase-transforming material Laplace transform variable; distance measured along dislocation line; exponent describing grain-size sensitivity of Q 1; ratio (r/Re) of radii in concentric-sphere model of phasetransforming material Entropy of kink migration Time Absolute temperature Melting temperature Oscillation period (¼2p/o) Displacement of dislocation segment, or position of grain boundary, in the y-direction Equilibrium distance for grain-boundary sliding Peierls potential x-Independent amplitude of u; position of straight dislocation segment under static stress s Maximum displacement for newly formed kink pair Wave speed for horizontally polarized seismic shear wave Wave speed for vertically polarized seismic shear wave Width of a single geometric kink Chemical composition Coordinate measuring distance parallel to dislocation line or grain boundary Unstable equilibrium spacing of kinks of opposite sign Coordinate measuring distance perpendicular to dislocation line Young’s modulus Negative of exponent describing frequency dependence of Q 1; exponent used in specifying the distribution D(t) of anelastic relaxation times for the monotonic high-temperature background dissipation Aspect ratio of grain-boundary region (¼d/d)

Properties of Rocks and Minerals: Physical Origins of Anelasticity and Attenuation in Rock

ae at b G g gs D d d(x) DB dG dJ DP

dP dT0 dTs Dv df (dr/r)0 (dr/r)a

(dr/r)e « «0 «a «e «m h h1 hb hf hm l

2.21.1

Aspect ratio (minimum/maximum dimension) of ellipsoidal inclusion Aspect ratio of grain-edge tubule (¼2R/d) Coefficient of term btn representing transient creep in the Andrade model Gamma function Multiplicative constant of order unity Multiplicative constant Anelastic relaxation strength Phase lag between stress and strain; width of grain-boundary region (d) Dirac delta function Anelastic relaxation strength for hightemperature background dissipation Anelastic relaxation of the shear modulus Anelastic relaxation of the compliance Anelastic relaxation strength for the dissipation peak of elastically accommodated grainboundary sliding Width in pressure of binary loop Width of melting interval Pressure-induced perturbation to solidus and liquidus temperatures Anelastic relaxation strength for the relaxation of the bulk modulus Pressure-induced perturbation in melt fraction Fractional density contrast between coexisting polymorphs Fractional change in density resulting from small change in proportions of coexisting phases; anelastic volumetric strain Fractional change in density caused by pressure ps Strain Amplitude of sinusoidally time-varying strain Anelastic strain Elastic strain Maximum anelastic strain due to migration of geometric kinks on a dislocation segment Viscosity or effective viscosity Viscosity of dashpot in parallel with spring in the anelastic element of the Burgers model Grain-boundary viscosity Fluid viscosity Melt viscosity Wavelength of periodic grain-boundary topography or of seismic wave

Introduction

The Earth and its constituent materials are subjected to naturally applied stresses that vary widely in intensity and timescale. At sufficiently high temperatures, nonelastic behavior will be encountered – even at the low-stress amplitudes of seismic wave propagation, tidal forcing, and glacial loading (Figure 1). For harmonic loading, nonelastic behavior is manifest in a phase lag between stress and strain, giving rise to strain energy dissipation and associated frequency dependence

L Lm mk n nk0 r rk , rþ k rk0, rþ k0 req k s s0 sn sP st sup t tA td tdr te tH tL tM tP ts,e ts,t w f v V v0

541

Dislocation density, that is, dislocation length per unit volume ¼ NvL Density of mobile dislocations Kink mobility (¼Dk/kT ) Poisson’s ratio Attempt frequency of dislocation vibration Crystal density; dislocation density Densities of kinks of opposite sign (number per unit length of dislocation line) Densities of kinks of opposite sign, under conditions of zero stress Equilibrium kink density; number of kinks per unit length of dislocation line Stress, usually shear stress; measure of width of normal distribution, DP(ln t) Amplitude of sinusoidally time-varying stress Normal stress Peierls stress Tectonic shear stress Unpinning shear stress Relaxation time Anelastic relaxation time associated with simple Burgers creep function Duration of transient diffusional creep Timescale for draining of cylindrical laboratory specimen Relaxation time for elastically accommodated grain-boundary sliding Upper cutoff for distribution DB(t) of anelastic relaxation times for high-temperature background Lower cutoff for distribution DB(t) of anelastic relaxation times for high-temperature background Maxwell (viscous) relaxation time Relaxation time associated with dissipation peak Relaxation time for melt squirt between ellipsoidal inclusions Relaxation time for melt squirt between grainedge tubules Grain-boundary slope Melt fraction; the angle between a dislocation segment and its Peierls valley Angular frequency Molecular volume of diffusing species (Angular) resonance frequency of dislocation segment

(dispersion) of the relevant modulus or wave speed. In the case of glacial loading, the transient creep of mantle material of sufficiently low viscosity allows time-dependent relaxation of the stresses imposed by the growth and decay of ice sheets with consequent time-dependent surface deformations. Departures from elastic behavior have long been studied in metals. Notable early successes came from the application of resonance (pendulum) methods at fixed frequencies near 1 Hz that revealed low-temperature dissipation peaks attributable to various types of point-defect relaxation (e.g., Nowick and

542

Properties of Rocks and Minerals: Physical Origins of Anelasticity and Attenuation in Rock

Berry, 1972; Zener, 1952). Until recently, most of the available information concerning elastic wave speeds in geologic materials and their variations with pressure and temperature came from ultrasonic and optoacoustic techniques (Chapter 2.12) at frequencies at least six orders of magnitude higher than those of teleseismic waves (Figure 1). However, there is growing recognition of the need, first clearly articulated by Goetze (1977), for a thorough understanding of viscoelastic behavior in minerals and rocks at low strains and seismic frequencies. It is the purpose of this chapter to assess the relaxation mechanisms most likely to produce significant departures from elastic behavior under the high-temperature conditions of the Earth’s interior. Among these are intragranular mechanisms involving the motion of point defects and dislocations, grain-boundary migration and sliding, stress-induced redistribution of an intergranular fluid phase, and effects associated with phase transformations. Section 2.21.2 focuses on the theoretical framework for the description of viscoelasticity provided by broad phenomenological considerations and models for the operation of specific microphysical relaxation mechanisms. A thorough review of this subject in a materials science context is provided by Schaller et al. (2001). In Section 2.21.3, an attempt will be made to integrate the results of the still relatively few seismicfrequency laboratory experiments on geologic materials into

Tectonism

Glacial loading

Tidal deformation

Teleseismic band

Viscous fluid

log10(frequency, Hz) 10

2.21.2 2.21.2.1

Theoretical Background Phenomenological Description of Viscoelasticity

For sufficiently small stresses, the stress–strain behavior is expected to be linear and the response is represented in the time domain by the ‘creep function’ J(t), which is defined as the strain resulting from the application at time t ¼ 0 of unit step-function stress, that is, sðt Þ ¼ 0, ¼ 1,

5

0

-5

-10

-15

Figure 1 A schematic mechanical relaxation spectrum for the Earth. The mechanical behavior of the Earth’s hot interior and its constituent materials changes progressively from that of an elastic solid to that of a viscous fluid with decreasing frequency or increasing timescale. This transition involves the thermally activated mobility of crystal defects including vacancies, dislocations, twin-domain and grain boundaries, and phase boundaries and intergranular melt. The resulting viscoelastic behavior is manifest in the dissipation of strain energy and associated frequency dependence of the shear modulus and wave speed. Adapted from Jackson I, Webb SL, Weston L, and Boness D (2005) Frequency dependence of elastic wave speeds at high-temperature: A direct experimental demonstration. Physics of the Earth and Planetary Interiors 148: 85–96.

t 0.01 s (Lu and Jackson, 2006). Recent broadband studies of water-saturated rocks employing both ultrasonic wave-propagation and forced-oscillation methods provide additional insight into the dispersion associated with squirt flow. Long-period (100 s) oscillating-pressure tests on an Icelandic basalt containing both cracks and pores yielded a substantially lower bulk modulus than ultrasonic wave speed measurements (10 6 s) – the difference being attributed to squirt flow between cracks and pores in the oscillating-pressure tests (Adelinet et al., 2010). In a study of a thermally cracked quartzite, Schijns et al. (2012) showed that water saturation results in a dramatic increase of elastic wave speeds measured at microsecond period, whereas the corresponding moduli were insensitive to water saturation at the much longer periods (>1 s) of forced-oscillation experiments. Moreover, Adelinet et al. (2010) measured a lower bulk modulus on the Icelandic basalt under drained, water-saturated conditions than for dry conditions – suggestive of a role for adsorbed water in increasing the compliance of grain contacts.

2.21.4 2.21.4.1

Geophysical Implications Dislocation Relaxation

2.21.4.1.1 Vibrating-string model The possibility that viscoelastic relaxation associated with the stress-induced motion of dislocations might explain the

attenuation and dispersion of seismic waves, especially in the Earth’s upper mantle, has been widely canvassed (Gue´guen and Mercier, 1973; Karato, 1998; Karato and Spetzler, 1990; Minster and Anderson, 1981). Gue´guen and Mercier (1973) invoked the vibrating-string model of dislocation motion as an explanation for the upper-mantle zone of low wave speeds and high attenuation. They associated an intragranular dislocation network with any observable high-temperature relaxation peak and suggested that a grain-boundary network of more closely spaced dislocations might explain the high-temperature background attenuation. It was suggested that impurity control of dislocation mobility might yield relaxation times appropriate for the seismic-frequency band. A more ambitious attempt to produce a model of dislocation-controlled rheology consistent with both seismic wave attenuation and the long-term deformation of the mantle was made by Minster and Anderson (1981). They envisaged a microstructure established by dislocation creep in response to the prevailing tectonic stress st and comprising subgrains of dimension L L ¼ gs Gb=st ¼ gs Lc

[80]

with a mobile dislocation density Lm ¼ gðst =GbÞ2 ¼ gLc

2

[81]

where Lc ¼ Gb/st is the critical dislocation link length for multiplication by the Frank–Read mechanism (see discussion following eqn [12], and Chapter 2.18). From laboratory experiments on olivine (Durham et al., 1977), it was estimated that gs  20 for well-annealed mantle olivine; g is a constant of order unity (Frost and Ashby, 1982). Furthermore, it was argued that the distribution of dislocation segment lengths will be dominated by those of length L  ð5=3ÞLc

[82]

for which the dislocation multiplication time, calculated with a migration velocity given by eqn [14], is a minimum. It follows from eqns [80]–[82] that the dislocation density within the

Properties of Rocks and Minerals: Physical Origins of Anelasticity and Attenuation in Rock subgrains is essentially that (L 2) of the Frank network with dislocation relaxation strength D  0.1 (eqn [23]). For st  1 MPa (strain rate of 10 15 s 1 with effective viscosity of 1021 Pa s), Lc  30 mm and Lm  10 3 mm 2. It was suggested that the total dislocation density should be much higher – being dominated by dislocations organized into the subgrain walls. The climb-controlled motion of these latter dislocations was invoked to explain deformation at tectonic stresses and timescales (Minster and Anderson, 1981). Their suggestion of a dominant link length disallows an absorption band based on a wide distribution of segment lengths (eqn [50]). Minster and Anderson (1981) suggested instead that the seismic absorption band reflects a spectrum of activation energies. A frequency-independent upper-mantle Q 1 of 0.025 was shown to require a range dE of about 80 kJ mol 1 and to produce an absorption band only two to three decades wide. A unified dislocation-based model for both seismic wave attenuation and the tectonic deformation of the Earth’s mantle has been sought more recently by Karato and Spetzler (1990) and Karato (1998). Karato and Spetzler (1990) emphasized the apparent paradox whereby a Maxwell model based on reasonable steady-state viscosities seriously underestimates the level of seismic wave attenuation (their Figure 3). Equally, a transient-creep description of seismic wave attenuation extrapolated to tectonic timescales ( Jeffreys, 1976) seriously overestimates the mantle viscosity. For a unified dislocation-based model, it is thus required that dislocations have much greater mobility (velocity/stress) at seismic frequencies than for tectonic timescales. Karato and Spetzler’s assessment of relaxation strengths and relaxation times, based on the vibrating-string model of dislocation motion (eqn [23]) and revisited with a somewhat higher dislocation density of 10 3 mm 2 (eqn [81]) applied to the upper mantle as in the preceding paragraph, is in general accord with that of Minster and Anderson. In particular, reasonable levels of seismic wave attenuation (10 1 > D > 10 3) would require segment lengths L of 1–10 mm, and a specific range of dislocation mobilities (b/B in eqn [14]) would be needed for relaxation times in the seismic band (Karato and Spetzler, 1990, Figure 7). The issue in all such analyses is to relate key parameters controlling D, t, and indeed the steady-state effective viscosity , to the intrinsic and/or extrinsic properties of dislocations, as appropriate. Karato and Spetzler noted that dislocation mobility is expected to increase with increasing temperature and water content but to decrease with increasing pressure. The segment length L for the vibrating-string model was shown to depend in different ways on the tectonic stress according to whether pinning is effected by interaction with impurities or other dislocations.

2.21.4.1.2 Kink model The feasibility of seismic wave attenuation resulting from the stress-induced migration of kinks was also briefly explored by Karato and Spetzler (1990) and analyzed in more detail by Karato (1998). In the latter study, Karato identified three distinct stages of dislocation relaxation to be expected with progressively increasing temperature or stress and/or decreasing frequency. Stage I involves the reversible migration of preexisting geometric kinks along Peierls valleys with characteristic timescale and relaxation strength given by eqns [27] and

563

[28]. The maximum anelastic strain resulting from migration of geometric kinks (eqn [30]) is of order 10 6 for a Frank network of dislocations with L  L 2  10 3 mm 2 – consistent with the large relaxation strength for this mechanism (eqn [28]). Stage II is associated with the spontaneous nucleation of isolated kink pairs followed by the separation of the newly formed kinks of opposite sign. The resulting anelastic relaxation, usually associated with the Bordoni dissipation peak for deformed metals (e.g., Fantozzi et al., 1982; Seeger, 1981), is described in detail by Seeger’s theory outlined in the preceding text and culminating in eqns [43]–[45]. At the still higher temperatures/larger stresses of stage III, it was envisaged by Karato that continuous nucleation and migration of kinks, possibly enhanced by unpinning of dislocations, would allow the arbitrarily large, irrecoverable strains of viscous behavior. The relaxation times expected for geometric kink migration and kink-pair formation and migration in the Earth’s upper mantle were shown by Karato (1998) to be broadly compatible with strain energy dissipation at teleseismic and lower frequencies. It was thus concluded that attenuation and associated dispersion, microcreep, and large-strain creep possibly share a common origin in dislocation glide. The results of such calculations, repeated with eqns [27], [28], and [43]–[45], are presented in Figure 14. For this purpose, we have used ad  b  a  0.5 nm, Gu ¼ 60 GPa, and vk0 exp(Sm/k)  1013 Hz (Seeger and Wu¨thrich, 1976) and have chosen a relatively large value of Hm ¼ 200 kJ mol 1 intended to reflect kink interaction with impurities and sP/G ¼ 0.01, which, through eqn [39], fixes Hk at 162 kJ mol 1 (so that 2Hk þ Hm is of order 500 kJ mol 1: cf. Karato, 1998, Figure 3). Substantially larger values of sP/G have been suggested (Frost and Ashby, 1982, p. 106; Karato and Spetzler, 1990, p. 407) but, when combined with Seeger’s theory, yield implausibly high kink formation energies. Relaxation times have been calculated for indicative lengths of 1 and 100 mm for dislocation segments. The results of these calculations (Figure 14), like those of Karato (1998), indicate that the migration of geometric kinks could result in anelastic relaxation within the seismic-frequency band at typical upper-mantle temperatures. The much higher activation energy for the formation and migration of kink pairs (here 2Hk þ Hm ¼ 524 kJ mol 1) results in much longer relaxation times – ranging from  104 to 106.5 s at the highest plausible upper-mantle temperatures  1700 K. An effective activation energy lower by about 100 kJ mol 1 would be required to bring the relaxation involving kink-pair formation and migration into substantial overlap with the seismic-frequency band for typical temperatures of the convecting upper mantle as indicated by the broken line in Figure 14. Alternatively, kinkpair formation and migration might result in relaxation at the day-to-month timescales of Earth tides. Similarly, high activation energies for attenuation and creep in olivine are interpreted by Karato (1998) to imply the need for kink nucleation for both processes, whereas the low reported activation energy for attenuation in single-crystal MgO might reflect a dominant role for the migration of geometric kinks. Emerging extrapolations of experimental forced-oscillation data for olivine to upper-mantle grain sizes and dislocation densities suggest that seismic wave attenuation might involve subequal contributions from intragranular (dislocation-related)

564

Properties of Rocks and Minerals: Physical Origins of Anelasticity and Attenuation in Rock

L = 100 mm

Kink-pair formation and migration

Log10(relaxation time, s)

8 6

Heff = Hk + Hm

4

Convecting upper mantle

L = 1 mm

10

d Heff = -100 kJ mol-1 Heff = 2Hk + Hm L = 100 mm L = 1 mm

2

Teleseismic band

0 Geometrical kink migration

-2 Heff = Hm 4

8

6

10

104/T(K) Figure 14 Computed relaxation times for Seeger’s (1981) kink model of dislocation mobility. The green band represents relaxation associated with the migration of geometric kinks with segment lengths of 1–100 mm and an activation energy for kink migration Hm ¼ 200 kJ mol 1. Relaxation times calculated from eqns [36]–[39] for the formation and migration of kink pairs are indicated by the red band for the same range of segment lengths and an activation energy for the formation of a single kink of 162 kJ mol 1 corresponding through Seeger’s (1981) theory with sP/G ¼ 0.01. The effect of an effective activation energy lower by 100 kJ mol 1 is shown by the broken line.

and intergranular (grain-boundary sliding) relaxation mechanisms (Farla et al., 2012a,b). The observation by the same authors that prior deformation in torsion is more effective than prior compressive deformation in enhancing dissipation by dislocation relaxation in torsional oscillation tests suggests that seismic wave attenuation may be anisotropic. For example, the azimuthal anisotropy of the compressional wave speed in the oceanic upper mantle and the associated polarization anisotropy whereby horizontally polarized shear waves travel faster than those with vertical polarization are both attributed to the preferred orientation of olivine resulting from activation of the dominant [10 0](0 1 0) dislocation slip system during horizontal simple shear (Figure 15; Chapters 1.19, 2.17, and 2.20). Within this fabric, dislocations are favorably oriented for reactivation by the stress field associated with near-vertically propagating shear waves polarized parallel with the spreading direction, and accordingly, such waves should be preferentially attenuated by dislocation relaxation.

2.21.4.2

Grain-Boundary Processes

Gribb and Cooper (1998a) explained their observations of high-temperature absorption band behavior (eqn [49] with a  0.35) for a reconstituted dunite of 3 mm grain size in terms of the transient diffusional creep modeled by Raj (1975). The strong Q 1  d 1 grain-size sensitivity implied by this model (eqn [62]) extrapolated to millimeter–centimeter grain size seriously underestimates upper-mantle seismic wave attenuation. Gribb and Cooper (1998a) sought to resolve this discrepancy by invoking diffusionally accommodated sliding on subgrain boundaries rather than on grain boundaries. It

Mid-ocean ridge

Simple shear

[010]

Passive upwelling

[100] II spreading direction Azimuthal (VP) and polarisation (VSH > VSV) anisotropy

Shear wave propag’n and polaris’n directions optimal for dissipation Figure 15 Anisotropy of dislocation-related seismic shear wave attenuation. Simple shear deformation in the oceanic upper mantle involves glide of the dominant [1 0 0](0 1 0) dislocations that is responsible for preferred orientation of olivine grains. The observed anisotropy of seismic wave speeds is conventionally attributed to this fabric, which is also well suited to the attenuation of subvertically propagating shear waves polarized parallel with the spreading direction (Farla et al., 2012a).

was suggested that this mechanism could also reconcile the Gribb and Cooper data with those of Gue´guen et al. (1989) for predeformed single-crystal forsterite. The increased attenuation resulting from prior deformation has been more naturally interpreted by others (including Gue´guen et al., 1989) as prima facie evidence of dislocation relaxation as discussed in Section 2.21.3.1.3. The milder grain-size sensitivity Q 1  d 1/4 subsequently directly measured by Jackson et al. (2002) for melt-free

Properties of Rocks and Minerals: Physical Origins of Anelasticity and Attenuation in Rock

2.21.4.3 Partial Melting and the Seismic Signature of the Asthenosphere Although solid-state viscoelastic relaxation in a dry, melt-free upper mantle can explain much of the observed variability of seismic wave speeds and attenuation, other effects, associated with partial melting (e.g., Anderson and Sammis, 1970) and/ or the presence of water (Karato and Jung, 1998), may be required to explain some of the distinctive seismological characteristics of the asthenosphere. Analyses of surface wave dispersion indicate that the upper mantle beneath oceanic lithosphere is characterized by low seismic shear wave speeds at depths of 50–150 km, significant radial anisotropy with VSH > VSV, and enhanced attenuation – these effects being most pronounced and shallowest beneath young oceanic lithosphere (Chapters 1.19, 1.25, and 2.17). Furthermore, body wave studies reveal azimuthal variation of compressional wave speeds in the oceanic lithosphere, and receiver functions involving short wavelength-converted phases provide evidence for a sharp transition ( s[010] > s[001] at constant hydrogen content. Yoshino et al. fitted activation enthalpies of H[100] ¼ 70 kJ mol1, H[010] ¼ 90 kJ mol1, and H[001] ¼ 84 kJ mol1. However, extrapolated to slightly higher temperatures of 1273 K, the conductivity of hydrogen-bearing olivine becomes nearly isotropic, whereas at the same temperature, hydrogen diffusivity is strongly anisotropic. Yoshino et al. interpreted this difference to indicate different mechanisms for hydrogen mobility in diffusion and conductivity. Poe et al. fitted activation enthalpies of H[100] ¼ 122 kJ mol1 , H[010] ¼ 145 kJ mol1, and H[001] ¼ 78 kJ mol1, which are only slightly lower (30 kJ mol 1) than those measured for hydrogen diffusion (Du Frane and Tyburczy, 2012; Kohlstedt and Mackwell, 1998). Hydrogen may affect other charge-carrying defects in olivine. Calculations based on density functional theory indicate that hydrogen creates an impurity level in the electronic bandgap of olivine (Wang et al., 2011, 2012). It is unknown whether this causes an electronic conductivity sufficiently large to affect the overall electrical properties of olivine. HierMajumder et al. (2005) measured Mg–Fe interdiffusion in hydrous olivine and found a small enhancement in the presence of water, but not sufficient to yield a conductivity increase of the magnitude measured for hydrous olivine. These topics have been discussed by Yoshino (2010), Karato and Wang (2013), Pommier (2013), and Yoshino and Katsura (2013).

2.25.4 Melts

Electrical Conductivity of Melts and Partial

Naturally occurring silicate melt conductivity has been examined at elevated pressure in dry systems to 2.5 GPa (Tyburczy and Waff, 1983, 1985) and in a hydrous silicic melt to 0.4 GPa (Gaillard, 2004). Conductivity of a basaltic melt decreases with increasing pressure up to about 0.8 GPa and then is independent of pressure to 2.5 GPa (Tyburczy and Waff, 1983). Dry silicic melts have greater pressure dependence, with activation volumes on the order of a few cm3mol 1 at 2.5 GPa (Tyburczy and Waff, 1985). Gaillard (2004) examined conductivity of an obsidian melt with up to 3 wt.% water and found an increase of about ½ order of magnitude or less over the dry obsidian at 0.2 GPa corresponding to an activation volume of about 20 cm3 mol 1. Pommier et al. (2008) studied dry and hydrous melts from Mt. Vesuvius with similar results. Pommier and Le-Trong (2011) developed a method for calculation of natural silicate melt conductivity as a function of SiO2, Na2O, H2O, T, and P. Conductivities of molten carbonates are 100–1000 times greater than those of molten silicates with much lower activation energies (Gaillard et al., 2008). Waff (1974) discussed the importance of the textural distribution of melt on the bulk electrical properties of a partially molten rock and the importance of textural equilibration

Properties of Rocks and Minerals – The Electrical Conductivity of Rocks, Minerals, and the Earth

(Bulau et al., 1979). Studies of texturally equilibrated partially molten systems include those of Roberts and Tyburczy (1999) and ten Grotenhuis et al. (2005). Roberts and Tyburczy (1999) showed that for an Fo80-melt system, the melt was highly interconnected at low melt fractions (0–5 vol.%) and that paralleltype bulk conduction models (Hashin–Shtrikman upper bound, simple parallel conductors, or Archie’s law) describe the data (see text later). Archie’s law (sbulk/smelt ¼ CXm, where C and m are constants and X is volume fraction melt) constants C ¼ 0.73 and m ¼ 0.98 were determined. They pointed out that melt composition changes significantly with changes in melt fraction at very low melt fractions and that these changes may need to be considered when modeling low melt fraction systems. ten Grotenhuis et al. (2005) examined an iron-free olivine–enstatite– melt system and observed a change from nearly dry grain faces (with melt mostly in tubules or triple junctions) at 1 vol.% melt to mostly wetted grain faces at a melt fraction of 10 vol.%. The change was discontinuous, with the most abrupt change occurring at around 2 vol.% melt. They determined Archie’s law constants of C ¼ 1.47 and m ¼ 1.30. Caricchi et al. (2011) examined the effect of torsional deformation on electrical conductivity of a partially molten olivine–melt system. Conductivity is enhanced (melt is interconnected) in the direction of maximum shear and is lower (melt is not interconnected) perpendicular to maximum shear (i.e., radially in the torsion experiment) consistent with melt segregation studies (King et al., 2010). Such anisotropy of melt distribution and bulk conductivity could explain anisotropy of conductivity parallel and perpendicular to mid-ocean ridges (Baba et al., 2006; Caricchi et al., 2011).

2.25.5

The bulk conductivity of a rock consisting of several minerals depends on the textural distribution of the minerals, which is generally not well known. A variety of relations have been employed to do so. Series and parallel solutions yield the maximum and minimum values, respectively, of a mixture of materials ss1 ¼ x1 =s1 þ x2 =s2

[23]

sp ¼ x1 s1 þ x2 s2

[24]

where ss is the series conductivity, sp is the parallel conductivity, s1 and s2 are the conductivities of the constituent phases, and x1 and x2 are the volume fractions. The geometric mean conductivity sGM is given by [25]

Archie’s law (Archie, 1942) is often used for fluid- or meltrock mixtures sbulk =smelt ¼ Cxm

[26]

where sbulk is the conductivity of the mixture, C and m are constants, and x is volume fraction melt or fluid. For very low porosities, a modified expression is used (Hermance, 1979) sbulk ¼ srock þ ðsfluid  srock Þxm

sHS ¼ s2 þ x1 ðs1  s2 Þ1 þ x2 =ð3s2 Þ


[27]

The Hashin–Shtrikman bounds describe the narrowest upper and lower bounds in the absence of geometric information (Hashin and Shtrikman, 1962)

1

[28] [29]

where s1> s2, and sHSþ and sHS correspond to the upper and lower bounds, respectively. The effective medium bounds (Landauer, 1952) lie between the HS upper and lower bounds sEM ¼ ¼fð3x1  1Þs1 þ ð3x2  1Þs2 þ ½fð3x1  1Þs1 þð3x2  1Þs2 g2 þ 8s1 s2 Š1=2 g

[30]

These and other relationships have been applied to the conductivities of multiphase materials in the mantle (e.g., Xu et al., 2000a,b) including partial melts. They yield the widest ranges when the conductivities of the two phases in question are greatly different, for example, in the transition zone (Xu et al., 2000a,b) or for partial melts.

2.25.6

Application to MT Studies

We discuss here a small number of MT field studies as representative of those for which these laboratory results have been influential in modeling or interpreting mantle conditions. In MT studies, orthogonal components of electrical Ex and magnetic Hy fields as a function of period t are measured at the Earth’s surface. From these, the apparent resistivity r(t) and phase ’(t) are determined according to rðtÞ ¼ ðt=2pmÞ Ex =Hy
¼ tan 1 Ex =Hy

Mixing Relationships

sGM ¼ s1 x1 s2 x2


1 sHSþ ¼ s1 þ x2 ðs2  s1 Þ1 þ x1 =ð3s1 Þ

669


2

and

’ðtÞ [31]

where m is the magnetic permeability (Cagniard, 1953; see Simpson and Bahr, 2005 for a recent discussion of MT methods). Conductivity–depth models are fit to or derived from such field results using smooth or discontinuous models. The D þ inversions provide the best fitting model to the data r(t) and ’(t) that can be achieved; they consist of a series of delta functions in conductivity as a function of depth (Parker, 1980). Occam’s razor inversions yield the smoothest possible conductivity–depth models to the data (Constable et al., 1987). Neither of these approaches corresponds to a real physical Earth. The existing framework of experimental results on electrical conductivity of Earth materials under mantle conditions allows for modeling and interpretation of electromagnetic field results in terms of realistic mineralogies reflecting known seismic discontinuities and mantle conditions. Xu et al. (2000b) showed that using their nominally anhydrous laboratory data, a mineral physics-based conductivity– depth model for the upper mantle and transition zone provides a very good fit (via forward modeling) to resistivity r(t) and phase ’(t) for a European MT data set (Olsen, 1999) (Figure 7). This agreement indicates that the laboratory data provide a robust framework for interpreting MT results. Note, however, that recent experimental results on water-containing minerals indicate that some of the earlier nominally anhydrous experiments contained significant amounts of hydrogen (Huang et al., 2005). Other models based on MT studies include effects of water in mantle and transition zone minerals (Karato, 2006; Lizzaralde et al., 1995; Simpson and Tommasi,

Log (conductivity (S m-1)) 0

-3

-2

0

-1

1

2

Xu et al. (2000) 500

Depth (km)

1000

1500 Olsen (1999) smooth 2000

2500

(a)

Olsen (1999) D+

3000

90

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80 70 60 50

Xu et al. (2000) Olsen (1999) D+ Olsen (1999) smooth inversion Olsen (1999) data

40 1.E+04

1.E+05

(b)

1.E+06 1.E+07 Period (s)

1.E+08

1.E+09

Apparent resistivity (W-m)

1000

100

10

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0.1

0.01 1.E+04 (c)

Xu et al. (2000) Olsen (1999) D+ Olsen (1999) Smooth Inversion Olsen (1999) Data

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

Period (s)

Figure 7 (a) Electrical conductivity versus depth profile for Europe from Olsen (1999) with D þ and smooth inversions and mineral physics-based model of Xu et al. (2000a,b). Smooth inversion is from Tarits et al. (2004). (b) Phase and (c) apparent resistivity as a function of frequency data and the models. Adapted from Xu YS, Shankland TJ, and Poe BT (2000b) Laboratory-based electrical conductivity in the earth’s mantle. Journal Geophysical Research 105, 27865–27875; Tarits P, Hautot S, and Perrier F (2004) Water in the mantle: Results from electrical conductivity beneath the French Alps. Geophysical Research Letters 31, L06612, http://dx.doi.org/10.1029/2003GL019277, with permission.

Properties of Rocks and Minerals – The Electrical Conductivity of Rocks, Minerals, and the Earth

2005; Tarits et al., 2004). There are significant regional differences in transition zone conductivity that may be attributable to variations in water content (Karato, 2006; Tarits et al., 2004). Conductivity–depth profiles as a function of water content down to the mantle transition zone have been published based on widely varying laboratory measurements on hydrous minerals ( Jones et al., 2012; Karato, 2011; Khan and Shankland, 2012). Just off of the southern East Pacific rise, Evans et al. (2005) observed strong electrical conductivity anisotropy at a depth of 100 km, with the ridge perpendicular (plate motion parallel) value approximately a factor of 10 greater than the ridge parallel value. They interpreted this result using the earlier diffusion-based model of hydrogen-enhanced olivine conductivity to indicate hydrous (103 H/106 Si) shear-oriented olivine ([1 0 0] parallel to flow direction, perpendicular to the ridge). However, Yoshino et al. (2006) pointed out that their the highpressure conductivity measurements indicate a much smaller amount of electrical conductivity anisotropy in hydrous olivine, suggesting that partial melt may be the cause of the conductivity anisotropy near the ridge.

2.25.7

Summary

Many aspects of the electrical conductivity of mantle minerals and its dependence on environmental factors are well measured and understood. Laboratory measurement of electrical conductivity of mantle and transition zone minerals has advanced to the point where interesting and provocative interpretations of mantle MT profiles in terms of mineralogy, temperature, composition, and water content are possible. The coming years promise significant new revelations from the study of electrical properties of Earth materials and the application to Earth interior issues.

Acknowledgments We are very grateful to Daniel Toffelmier for enthusiastically helping prepare this manuscript. Lisa Gaddis provided crucial inspiration, guidance, and assistance. Susan Selkirk was invaluable in helping prepare the figures. This work was supported by NSF grants EAR0073987 and EAR0739050.

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