PHYSICS AND CHEMISTRY OF THE DEEP EARTH Physics and Chemistry of the Deep Earth Edited by Shun-ichiro Karato Department of Geology and Geophysics Yale University, New Haven CT, USA A John Wiley & Sons, Ltd., Publication This edition first published 2013  2013 by John Wiley & Sons, Ltd Wiley-Blackwell is an imprint of John Wiley & Sons, formed by the merger of Wiley’s global Scientific, Technical and Medical business with Blackwell Publishing Registered office: John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial offices: 9600 Garsington Road, Oxford, OX4 2DQ, UK The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK 111 River Street, Hoboken, NJ 07030-5774, USA For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com/wiley-blackwell The right of the author to be identified as the 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in 9/11.5pt Trump Mediaeval by Laserwords Private Limited, Chennai, India 2013 Contents Contributors, vii Preface, ix PART Volatiles under High Pressure, Hans Keppler Earth’s Mantle Melting in the Presence of C–O–H–Bearing Fluid, 38 Konstantin D Litasov, Anton Shatskiy, and Eiji Ohtani Elasticity, Anelasticity, and Viscosity of a Partially Molten Rock, 66 Yasuko Takei Rheological Properties of Minerals and Rocks, 94 Shun-ichiro Karato Electrical Conductivity of Minerals and Rocks, 145 Shun-ichiro Karato and Duojun Wang Chemical and Physical Properties and Thermal State of the Core, 244 Eiji Ohtani Composition and Internal Dynamics of Super-Earths, 271 Diana Valencia MATERIALS’ PROPERTIES, 1 PART PART GEOPHYSICAL OBSERVATIONS AND MODELS OF MATERIAL CIRCULATION, 295 10 Seismic Observations of Mantle Discontinuities and Their Mineralogical and Dynamical Interpretation, 297 Arwen Deuss, Jennifer Andrews, and Elizabeth Day 11 Global Imaging of the Earth’s Deep Interior: Seismic Constraints on (An)isotropy, Density and Attenuation, 324 Jeannot Trampert and Andreas Fichtner 12 Mantle Mixing: Processes and Modeling, 351 Peter E van Keken COMPOSITIONAL MODELS, 183 Chemical Composition of the Earth’s Lower Mantle: Constraints from Elasticity, 185 Motohiko Murakami 13 Fluid Processes in Subduction Zones and Water Transport to the Deep Mantle, 372 Hikaru Iwamori and Tomoeki Nakakuki Index, 393 Ab Initio Mineralogical Model of the Earth’s Lower Mantle, 213 Taku Tsuchiya and Kenji Kawai Colour plate section can be found between pages 214–215 Contributors J E N N I F E R A N D R E W S Bullard Laboratory, Cambridge University, Cambridge, UK E L I Z A B E T H D A Y Bullard Laboratory, Cambridge University, Cambridge, UK K O N S T A N T I N L I T A S O V Department of Earth and Planetary Materials Science, Graduate School of Science, Tohoku University, Sendai, Japan A R W E N D E U S S Bullard Laboratory, Cambridge University, Cambridge, UK M O T O H I K O M U R A K A M I Department of Earth and Planetary Materials Science, Graduate School of Science, Tohoku University, Sendai, Japan A N D R E A S F I C H T N E R Department of Earth Sciences, Utrecht University, Utrecht, The Netherland T O M O E K I N A K A K U K I Department of Earth and Planetary Systems Science, Hiroshima University, Hiroshima, Japan H I K A R U I W A M O R I Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo, Japan E I J I O H T A N I Department of Earth and Planetary Materials Science, Graduate School of Science, Tohoku University, Sendai, Japan S H U N - I C H I R O K A R A T O Department of Geology and Geophysics, Yale University, New Haven, CT, USA A N T O N S H A T S K I Y Department of Earth and Planetary Materials Science, Graduate School of Science, Tohoku University, Sendai, Japan K E N J I K A W A I Department of Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo, Japan Y A S U K O T A K E I Earthquake Research Institute, University of Tokyo, Tokyo, Japan H A N S K E P P L E R Byerisched Geoinstitut, Univeră Bayreuth, Bayreuth, Germany sitat J E A N N O T T R A M P E R T Department of Earth Sciences, Utrecht University, Utrecht, The Netherland viii Contributors T A K U T S U C H I Y A Geodynamic Research Center, Ehime University, Matsuyama, Ehime, Japan D I A N A V A L E N C I A Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA P E T E R V A N K E K E N Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI, USA D U O J U N W A N G Graduate University of Chinese Academy of Sciences, College of Earth Sciences, Beijing, China Preface Earth’s deep interior is largely inaccessible The deepest hole that human beings have drilled is only to ∼11 km (Kola peninsula in Russia) which is less than 0.2 % of the radius of Earth Some volcanoes carry rock samples from the deep interior, but a majority of these rocks come from less than ∼200 km depth Although some fragments of deep rocks (deeper than 300 km) are discovered, the total amount of these rocks is much less than the lunar samples collected during the Apollo mission Most of geological activities that we daily face occur in the shallow portions of Earth Devastating earthquakes occur in the crust or in the shallow upper mantle (less than ∼50 km depth), and the surface lithosphere (‘‘plates’’) whose relative motion controls most of near surface geological activities has less than ∼100 km thickness So why we worry about ‘‘deep Earth’’? In a sense, the importance of deep processes to understand the surface processes controlled by plate tectonics is obvious Although plate motion appears to be nearly two-dimensional, the geometry of plate motion is in fact three-dimensional: Plates are created at mid-ocean ridges and they sink into the deep mantle at ocean trenches, sometimes to the bottom of the mantle Plate motion that we see on the surface is part of the three-dimensional material circulation in the deep mantle High-resolution seismological studies show evidence of intense interaction between sinking plates and the deep mantle, particularly the mid-mantle (transition zone) where minerals undergo a series of phase transformations Circulating materials of the mantle sometimes go to the bottom (the core–mantle boundary) where chemical interaction between these two distinct materials occurs Deep material circulation is associated with a range of chemical processes including partial melting and dehydration and/or rehydration These processes define the chemical compositions of various regions, and the material circulation modifies the materials’ properties, which in turn control the processes of materials circulation In order to understand deep Earth, a multidisciplinary approach is essential First, we need to know the behavior of materials under the extreme conditions of deep Earth (and of deep interior of other planets) Drastic changes in properties of materials occur under the deep planetary conditions including phase transformations (changes in crystal structures and melting) Resistance to plastic flow also changes with pressure and temperature as well as with water content Secondly, we must develop methods to infer deep Earth structures from the surface observations Thirdly, given some observations, we need to develop a model (or models) to interpret them in the framework of physical/chemical models In this book, a collection of papers covering these three areas is presented The book is divided into three parts The first part (Keppler, Litasov et al., Takei, Karato, Karato and Wang) includes papers on materials properties that form the basis x Preface for developing models and interpreting geophysical/geochemical observations The second part (Murakami, Tsuchiya and Kawai, Ohtani, Valencia) contains papers on the composition of deep Earth and planets including the models of the mantle and core of Earth as well as models of super-Earths (Earth-like planets orbiting stars other than the Sun) And finally the third part (Deuss et al., Trampert and Fichtner, van Keken, Iwamori) provides several papers that summarize seismological and geochemical observations pertinent to deep mantle materials circulation and geodynamic models of materials circulation where geophysical/geochemical observations and mineral physics data are integrated All of these papers contain reviews of the related area to help readers understand the current status of these areas I thank all the authors and reviewers and editors of Wiley-Blackwell who made it possible to prepare this volume I hope that this volume will help readers to develop their own understanding of this exciting area of research and to play a role in the future of deep Earth and planet studies Shun-ichiro Karato New Haven, Connecticut Fabry-Perot Interferometer water cooling system scattered light Diode laser DAC X-ray X-ray CCD CO2 laser translation stage for Brilouin optics to T measurement Spectrometer with CCD M ND Temperature measurement system M CF M Laser heating system CO2 laser BS CCD L XRD measurement system BS Light TV monitor ZSP Light M Incident X-ray Monochromator SR M Slit Collimator M L L M X-ray lenses ID L DAC X-ray CCD M L ID DM PD ID CCD M L Collecting assembly M ID MS ID Focusing TV monitor RPF M M M Controller Sandercock-type tandem Fabry-Perot interferometer M assembly M M ID L VND RP ID BS CCD Diode-pumped laser, 532 nm TV monitor Brillouin scattering measurement system Plate (Fig 6.2) Whole view of the Brillouin scattering measurement system combined with synchrotron X-ray diffraction and laser heating systems at BL10XU of SPring-8 (a), and its schematic layout (b) from Murakami et al (2009) Green, white and red lines indicate the schematic optical paths for Brillouin scattering measurements, X-ray diffraction and laser heating system, respectively Light green and pale red lines indicate the scattered light and transmitted light through the sample SR, synchrotron radiation; M, mirror; L, lens; BS, beam splitter; BE, beam expander; ZSP, ZnSe plate; PD, photodiode; DM, dichroic mirror; ID, iris diaphragm; CF, color filter; VND, variable ND filter; RP, retardation plate; RPF, rotational polarized filter; MS, microscope Reproduced with permission of Elsevier Physics and Chemistry of the Deep Earth, First Edition Edited by Shun-ichiro Karato  2013 John Wiley & Sons, Ltd Published 2013 by John Wiley & Sons, Ltd 8.0 HS Shear velocity (km/s) 7.6 HS-LS LS 7.2 6.8 6.4 (Mg,Fe)O 6.0 XMg = 0.94 (Jackson et al., 2006) XMg = 0.94 (Crowhurst et al., 2008) 5.6 XMg = 0.90 (Marquardt et al., 2009) MgO (Murakami et al., 2009) 5.2 20 40 60 80 Pressure (GPa) 100 120 Plate (Fig 6.9) Representative high-pressure shear wave velocity profiles (Crowhurst et al., 2008; Jackson et al., 2006; Marquardt et al., 2009) of ferropericlase together with that of MgO (Murakami et al., 2009) Shaded area shows the possible pressure range of the spin transition HS, high-spin state of iron; LS, low-spin state of iron 6.0 Pyrolite MORB Perovskitite PREM Density (g/cm3) 5.5 5.0 4.5 4.0 50 100 150 P (GPa) Plate (Fig 7.10) Density profiles for pyrolite (solid lines), MORB (dashed lines) and perovskitite (thin line) calculated along the Brown and Shankland’s geotherm with the reference Earth value (black dots) (Dziewonski and Anderson, 1981) The perovskitite’s composition was set to 100% Pv (or PPv) with XFeSiO3 = 12 mol% Shaded areas are out of the lower mantle range Computational uncertainties were found comparable to the thickness of the lines Fluid Processes in Subduction Zones and Water Transport to the Deep Mantle ridge ocean island subduction zone (super) continent 387 subduction zone IC1 (−) IC1 (−) IC1 (+) IC2 (−) IC1 (+) IC2 (+) Fig 13.9 Schematic illustrations for a physical model of IC1 and IC2 (i.e., two overlapping differentiation processes, melting (for IC1) and aqueous fluid-rock interaction(IC2)) Irregular streaks represent recycling ‘‘melt component’’ (e.g., recycling MORB and OIB), which are accumulated near the base of the convective system, resulting in vertical IC1 variations These streaks then ascend due to thermal instability to form plumes at ocean islands The horizontally distinct light (IC2-) and shadow (IC2+) regions represent those depleted and enriched in the ‘‘aqueous fluid component,’’ respectively, possibly corresponding to the focused subduction towards the supercontinents in the past (0.3 to 0.9 Ga) the Pacific Ocean and the southern Africa to the Indian Ocean Iwamori et al (2010) have argued that an aqueous fluid component, including hydrogen, subducts to the bottom of the mantle and could affect the seismic velocity structure at CMB, although the high IC2 regions partially include non-LLSVP A possible explanation for the partial correlation between IC2 and LLSVP will be discussed later These two independent fractionation processes responsible for IC1 and IC2 variations may overlap with each other: both the recycling melt-rich components and the residual portion may exist in both the slab to be dehydrated and the mantle wedge to be hydrated beneath the volcanic arc (e.g., as in Figure 13.7) Therefore both dehydrated and hydrated melt-rich portion may be created, and similarly, dehydrated and hydrated melt-poor portion can be created through the subduction zone processes These various products will be proceeded to the source regions of MORB and OIB to create the observed isotopic variability as in Figure 13.8 Integrating all the arguments in this chapter, we propose a model for water subduction from the surface to the bottom of the mantle Focused subduction towards a supercontinent may create a source region enriched in aqueous fluid components that will bring high-IC2 values through radiogenic ingrowth with time At the shallow part in the course of water subduction, a significant amount of H2 O is released by the time it reaches the choke point to form a magmatic-hydrothermal arc above the subducting slab Aqueous fluids ascent as porous and channel flows through the solid corner flow beneath the arc The solid corner flow may contain 0.1–0.4 wt % H2 O hosted by NAMs even after breakdown of major hydrous phases (such as serpentine and chlorite), and the resultant HBL just above the slab transports it to the mantle transition zone If a stagnant slab is formed due to, e.g., buoyancy at 660 km discontinuity associated with the phase change or viscous weaknening of the slab at 410 and/or 660 km depth also due to the phase changes (Nakakuki et al., 2010), the HBL may cause Rayleigh-Taylor 388 hikaru iwamori and tomoeki nakakuki instability to generate numerous hydrous plumes in the backarc region, redistribute water witin the mantle transition zone and the upper mantle in a relatively short time (Richard & Iwamori, 2010) If the slab penetrates into the lower mantle, several 1000 ppm H2 O may be also transported into the lower mantle As in the present-day Earth, both slab stagnation and penetration might have occurred depending on the physical conditions and the history of subduction (Fukao et al., 2001) A part of the lower mantle could be affected by the subducted components associated with slab penetration (Figure 13.7), whereas only the mantle above 660 km may be affected in the other regions A partial correlation between the seismic structure at CMB (including LLSVP) and the geochemical signature for an aqueous fluid component (i.e., IC2) may reflect such variability in terms of slab stagnation and penetration in time and space lower mantle, since fluid segregation is limited at a low fluid fraction Considering that both stagnant slabs and slab penetration are observed by the seismic tomography, the subducted H2 O is likely to distribute itself in both the mantle above 660 km and the lower mantle Finally, the mantle isotopic variability in terms of Sr, Nd and Pb has been discussed to detect such subducted fluid components Two major differentiation processes have been argued to be responsible for most of the mantle isotopic variability sampled by oceanic basalts, and one of the processes is accounted for by aqueous fluid–rock interaction Accordingly, global geographical domains have been found, which inherit the anciently subducted aqueous fluid component, possibly associated with focused subduction towards the supercontinents 13.5 Concluding Remarks The authors would like to thank Shun Karato and an anonymous reviewer for helpful comments We have examined water subduction to the deep mantle through subduction zones, associated with both slab stagnation and penetration at 660 km phase transition Based on numerical models and geophysical observations, several different stages have been recognized: (1) extensive dehydration of the subducting slab occurs between the surface and the choke point (i.e., and ∼200 km depth), above which a magmatichydrothermal arc is formed by water supply from the slab through porous and channel flows, (2) after breakdown of major hydrous phases in stage (1), a hydrous boundary layer (HBL) is formed just above the subducting slab, constituting a material and thermal boundary layer, and transport 0.1–0.4 wt % H2 O to the mantle transition zone by NAMs (and phase A depending on the thermal structure), and (3) the HBL may generate numerous hydrous plumes above the stagnant slab, hydrating the upper mantle regionally When the slab penetrates into the lower mantle, although the major lower mantle minerals could be 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Nature, 451: 326–329 391 You CF, Castillo PR, Gieskes JM, Chan LH, Spivack AJ 1996 Trace element behavior in hydrothermal experiments: Implications for fluid processes at shallow depths in subduction zones Earth Planet Sci Lett, 140: 41–52 Zhao D, Ohtani E 2009 Deep slab subduction and dehydration and their geodynamic consequences: evidence from seismology and mineral physics Gond Res, 16: 401–413 Zhao D, Tian Y, Lei J, Liu L, Zheng S 2009 Seismic image and origin of the Changbai intraplate volcano in east asia: Role of big mantle wedge above the stagnant pacific slab Phys Earth Planet Inter, 173: 197–206 Zindler A, Hart SR 1986 Chemical geodynamics Ann Rev Earth Planet Sci, 14: 493–571 Zindler A, Jagoutz E, Goldstein S 1982 Nd, Sr and Pb isotopic systematics in a three-component mantle: a new perspective Nature, 298: 519–523 Index Note: page numbers in italics refer to figures, and those in bold to tables 220 km discontinuity see Lehmann discontinuity; and seismic discontinuities 410 km discontinuity see seismic discontinuities, 410 km discontinuity 520 km discontinuity see seismic discontinuities, 520 km discontinuity 660 km discontinuity see seismic discontinuities, 660 km discontinuity ab initio finite-temperature elasticity calculations 216, 221 ab initio methods for mineral physics 214–217 ab initio mineralogical model of lower mantle 213–33 ab initio quantum-mechanical calculation method 213 accretion processes 4–5, 248, 275 albite–H2 O system complete miscibility 16 viscosity 15 alkali carbonatite melting 47–9 δ -AlOOH 228–9 ammonium ion 4, 26 amphibole, electrical conductivity 163, 167–8 anelastic effects 86–8 anelastic relaxation 85–6 anelasticity [of partially molten rock] 67 factors affecting 67 importance in seismic tomography 89 relaxation mechanisms and 85–8 anhydrous minerals see nominally anhydrous minerals anisotropic velocity tomography 329–32 ‘‘anisotropic viscosity’’ model 71–2 anisotropy of Earth 331 aragonite in alkali carbonatite systems 48 thermal stability 47 argon, mantle–atmosphere fractionation of 27, 360–361 asthenosphere 127 chemical composition 128 electrical conductivity 169, 170–171 pressure ranges 111 temperature profiles 40 attenuation tomography 337–43 3D attenuation models 341–3 description of seismic wave attenuation 337–9 averaging scheme [for electrical conductivity of multi-phase aggregate] 151–2 azimuthal anisotropy 313, 330 Beer–Lambert law ‘‘big mantle wedge’’ model 53–8 basis 53–4 melt segregation/movement mechanism 54–8 Birch’s law 121 temperature dependence 264 ‘‘box’’ models advantages 357 disadvantages 358 examples 358 Brillouin scattering spectroscopy 187–92 experimental configuration 188 high-pressure measurements 188–9 high-temperature measurements 189–90 polycrystalline samples used 189 soundwave velocity measurements under high-P–T conditions 190–192 with X-ray diffraction and laser heating 190–192 bulk quality factor 337 bulk viscosity [of partially molten rock], in textually equilibrated system 83, 84–5 buoyancy-driven porous flow 54–5 C–H–O fluids 24–5 C–O–H fluids in peridotite and eclogite systems experimental studies below 6–7 GPa 41–3 melting phase relations up to 20–30 GPa 44–9 reduced, in peridotite and eclogite systems 49 see also C–H–O fluids calcium silicate (CaSiO3 ) perovskite 223 carbon, solubility in mantle minerals 22–3 carbon-bearing phases [in mantle] 3, 23–4 Physics and Chemistry of the Deep Earth, First Edition Edited by Shun-ichiro Karato  2013 John Wiley & Sons, Ltd Published 2013 by John Wiley & Sons, Ltd 394 carbon cycle 28 carbon dioxide atmospheric and insolation 286 measurement in super-Earths 286 surface temperature regulation affected by 283 mineral/melt partition coefficients in volcanic gases 3, 4, 283 carbon–silicate cycle 283 carbonate redox melting (CRM) 52 carbonatite melts 25, 42, 43, 47–9, 52 buoyant ascent of diapir 55, 56–8 carbon solubility in 25, 57 in deep mantle 54 H2 O content 58 infiltration into volatile-poor mantle 55–6 physical properties 54 segregation and movement of 54–8 Chandler wobble, attenuation measurements 338 channel flow 377, 378 chemical bonding, rheological properties affected by 119–21 chemical filter 410 km discontinuity as 22 transition zone as 355, 365 chemical geodynamics 351 ‘‘choke point’’ [on subducting slab] 374, 375, 376 chondritic material Mg/Si ratio in 186, 214 Ni content 263 Sm–Nd isotopes in 354 volatiles in 4–5 Christoffel equation 188 Clapeyron slope [for mineralogical phase transition] 299 clinopyroxene(s) electrical conductivity 156, 167 water in 11 Cole–Cole plot[in impedance spectroscopy] 153, 154 compositional boundary, discontinuity caused by 299 compressible convection 364–5 constitutive relationships, 95, 122 see also elastic ; mechanical ; viscous constitutive relationships contiguity, definition 68, 69 contiguity [microstructural] model 75–80 comparison with other models 75–6 contiguity vs melt fraction 80 derivation of elastic and viscous constitutive relationships 76–8 Index description of microstructures 76 microstructure-sensitive behavior of elasticity and viscosity 78–80 contiguity tensor 76, 80 continental crust extraction at subduction zones 352, 361 formation of 355–6 strength 124 structral erosion of 225 continental lithosphere depth variation in water content 168–9 strength profile 124 survival against convective erosion 126–7 continental mid and lower crust, electrical conductivity 167–8 convecting mantle, heterogeneities in 38–9, 229 convective erosion 127 core chemical and physical properties 244–5, 247–50, 254–64 thermal state 250–254 see also inner core; outer core core–mantle boundary (CMB) 195 accumulation of MORB material at 229 dense melt at 244, 246 FeO-enrichment at 246–7 seismological study of 303 temperature(s) at 253–4 Coulomb law 17–18 crustal materials, elastic properties under lower mantle conditions 222–7 crystal structure, rheological properties affected by 119–21 D discontinuity/layer anisotropy in 331 MgPv phase transition and 217 seismic characteristics 195–6, 197, 222 weakness 133 D-DIA apparatus [for deformation studies] 111, 112 applications 103 pressure–temperature range 111, 113 decarbonation reactions, carbonates with silicates 42, 43, 46, 47 deep water cycle 21–2, 28 deformation mechanism maps 107, 130 degassing [of Earth] 21, 26, 27, 28 constraint(s) on 360–361 dendritic quench texture, as melting criterion 250–251 dense hydrous magnesium silicates, stability of 7, 44, 45 dense hydrous phases 227–9 density inner core 248, 262 iron–light-element melts 254–5 at high pressures 256–8 outer core 248, 254 density/bulk modulus data 186 compared with shear velocity data 187 density deficit [of Earth’s outer core] 5, 254 density determination sink–float method 255, 256 X-ray absorption method 255, 256, 257 density functional theory (DFT) 213, 214 elastic constants determined using 215 limitations 215 density heterogeneities compared with velocity perturbations 332–3 compositional contributions 334, 335 thermal contributions 334, 335 density profiles exoplanets 276 MORB 230 pyrolite 230 density tomography 332–7 deterministic tomography 335 diabase, flow laws, 103 diamond anvil cell (DAC) applications 16, 18, 19, 113, 151, 190 combined with Brillouin scattering spectroscopy 187–92 deformation studied using 113 laser-heated 189–90, 191, 192, 218, 226, 250–251, 259, 260 melting temperature determined using 250, 253 pressure scales used 258, 259 water solubility studied in 18, 19 diamonds fluid inclusions in 4, 27 formation of 52, 57 in fluid-bearing systems 44 and native iron 52 super-deep 52, 54 diapirs, formation and buoyant ascent of 56–8, 377, 378 diffusion creep 68, 97–9, 107, 109 flow laws for 98, 103 transition to/from dislocation creep 108, 113, 114, 314 diopside carbon solubility in 22 flow laws 103 water solubility in 11 discontinuities see seismic discontinuities Index disequilibrium geometry [under stress] 70–72 dislocation creep 68, 98, 99–101, 107, 109 transition to/from diffusion creep 108, 113, 114, 314 dislocation-motion mechanism, flow law for 101 dislocations anelastic relaxation caused by 86 and plastic deformation 97, 99 dynamic recrystallization 108, 109, 125 and diffusion creep 109, 126 dynamic wetting 70 eclogite flow laws 103 in ocean island basalt source 354, 355 preferential melting of 49, 51 eclogite–CO2 systems, phase relationships [up to 21–32 GPa] 46–7 eclogite systems with C–O–H fluids, experimental studies [below 6–7 GPa] 42–3 with C–O–H volatiles, melting behavior 49–52, 58 with reduced C–O–H fluids, phase relationships [up to 16–23 GPa] 49 elastic anisotropy determination of 188 ferropericlase 222 iron alloys 261 periclase 198 elastic constitutive relationships partially molten rocks 74–5 derivation in contiguity model 76–8 elastic properties, and rheological properties 95 elasticity data [for lower mantle minerals] 186 elasticity [of partially molten rock] factors affecting 67 microstructure-sensitive behavior 78–80 in textually equilibrated system 81–3 electrical conductivity in asthenosphere 169, 170–171 basic definition 146–7 carbonatite melt 25 continental mid and lower crust 167–8 element-partitioning effects 152, 169 experimental methods 152–5 for hydrous samples 153–5 impedance spectroscopy 153, 154 experimental observations 155–67 conduction due to hydrogen-related impurities 160–166 electronic conduction due to iron-related impurities 158–60, 164 influence of partial melting 166–7 factors affecting 7, 145, 146, 152 grain boundaries affecting 152 by hydrogen conduction 150–151, 160–166, 176 impurity effects 149 intrinsic conductivity 147–8 of iron-bearing minerals 149–50, 158–60 in lower mantle 173–4, 176 Mars and the Moon 174 of multi-phase aggregate 151–2 averaging scheme for 151–2, 167 factors affecting 152 partial melting affecting 152, 166–7 planetary water content determined using 133 sensitivity to water content 7, 145, 146, 161–2, 170, 171 in transition zone 169–170, 171–2 in upper mantle 168–73 various minerals 156 enstatite carbon solubility in 22 flow laws 103 water solubility in 11, 12 equation-of-state modeling, exoplanets 277 equilibrium melt geometry 68–70, 80 characteristic dihedral angle 68, 69 exo-moons 287 exoplanets ‘‘astrophysical’’ structure models 278 composition 278–9, 281 density profiles 276 detection methods radial velocity method 272–3 transit method 273–4 discovery of 272 examples 55 Cnc-e 276, 281–2, 288 CoRoT-7b 276, 280–281, 288 GJ 1214b 275, 276, 281, 288 HD 114762b 288 HD 149026b 288 Kepler-7b 288 Kepler-10b 276, 281, 288 Kepler-11 system 276, 282 Kepler-18b 276, 282 Kepler-20b 276, 282 ‘‘geophysical’’ structure models 278 internal structure models 275–9 mass–radius relationships 277, 278 properties 276 395 rheological properties 134 transmission spectra 274, 281 see also gas giants; mini-Neptunes; super-Earths extrasolar planets see exoplanets Farallon slab 53, 317, 363 Fe–C melts, density 256, 257 Fe–FeO system, phase relations in 248 Fe–FeS system 250–251 Fe–Ni alloy [in Earth’s core] stability line 41, 43 structure 259 volatiles sequestrated into Fe–Ni–Si alloys, density isochors 262–3 Fe–O–S system, melting relations 252–3 Fe–S system density of melt 256, 257, 258 melting relations 251, 252 Fe–Si alloys density of melt 256–7, 258 melting curves 251, 252 phase relations 260–261 Fe–Si–O system, liquidus and solidus temperatures 253, 254 feldspars alkali, dissociation of 225 flow laws 103 ferroelastic instability [post-stishovite transition] 223 ferropericlase [(Mg,Fe)O] 220–222, 299 elastic anisotropy 222 electrical conductivity 173–4 mixed-spin (MS) state 221, 222 shear elastic properties 200–201 shear wave velocity as function of pressure 201 spin transition [of iron] in 173, 200–201, 220–21, 222 water solubility in 11, 13 flow laws 136 for diffusion creep 98, 103, 122 for dislocation creep 101, 122 fluid phases, electrical conductivity affected by 152 fluid-bearing systems 18 diamond formation in 44 high-pressure experimental techniques 39–40 FMQ (fayalite–magnetite–quartz) redox buffer 26, 41, 49, 159 forsterite electrical conductivity 148, 158 influence of hydrogen on density of states of electrons 165–6 396 Fourier transform infrared (FTIR) spectroscopy, water content measured using 13, 155, 175 ´ Frechet derivatives 343, 344 Fresnel zones [for seismic waves] 302, 317 full waveform inversion 343–4 garnet flow laws 103 water solubility in 11, 46 gas giants 275 composition 277–8, 287 generalized gradient approximation (GGA) 214, 215 geodynamic models, and seismic tomography 328, 361, 363 global mass extinction events 28 grain boundaries, electrical conductivity affected by 152 grain-boundary sliding anelastic relaxation caused by 86 and diffusion creep 97, 98, 102 factors affecting 85–6 grain-scale melt redistribution 70, 71 grain-size-dependent rheology 96, 364 grain-size reduction, shear localization and 108, 109, 125 granular models 75–6 graphite, electrical conductivity affected by 152 graphite-to-diamond transition 41, 44 Griggs deformation apparatus 110, 112 applications 103 pressure–temperature range 110, 113 habitable conditions, planet’s ability to develop 289 halogens 3–4, 27–8 recycling into mantle 19, 27, 354 HARPS project 287–8 Hashin–Shtrikman averaging scheme 151, 167, 168, 216 helium behavior during mantle melting 359 He/4 He ratio 353, 354 high field strength elements (HFSE), solubility in water 18–19 high-pressure experimental techniques, fluid-bearing systems 39–40 hydrocarbon-containing inclusions see also C–O–H fluids hydrogen conduction, electrical conduction influenced by 150–151, 176 Index hydrogen–helium (H–He) atmospheres 277–8, 281, 282, 288 hydrogen-related defects electronic defects interacting with ionic defects 151, 175 in nominally anhydrous minerals 10, 161 seismic low velocities and 66–7 hydrogen-related impurities, electrical conductivity affected by 160–166 hydrous boundary layer (HBL) 378, 379, 380 formation of 378, 388 Rayleigh–Taylor instability and 380, 387 water transport by 381, 384, 387 hydrous fluids 4, 17–19 hydrous melts, quenching of 20 hydrous mineral phases 7–8, 374, 375 electrical conductivity 155, 162–3 see also ringwoodite; wadsleyite hydrous redox melting (HRM) 52 hydrous samples, electrical conductivity measurements 153–5 ice melting under pressure [in laser-heated diamond anvil cell] 192 Brillouin spectrum 192 impedance spectroscopy, electrical conductivity determined using 153, 154, 175 inclusion models 75 independent component analysis (ICA) 385 application to composition of oceanic basalts 385–7 infiltration [of carbonatite melt into volatile-poor mantle] 55–6 surface energy considerations 55 infrared spectroscopy carbon solubility in silicate melts 24 water in nominally anhydrous minerals 8–9 inner core composition 259–60, 263, 264 density 248, 262, 263 phase relations of inner-core materials 259–61 pressure scales for 258, 259, 261–2, 264 sound wave velocity studies 263–4 structure 259, 260, 264 inner core boundary (ICB) density [of inner core] at 262 temperature(s) at 253–4, 262 intrinsic conductivity 147–8 inverse problems 325 deterministic 335 factors complicating 339–40 ill-posed 330–331, 343 probabilistic formulation of 335 solving 327, 330, 332 inverse theory, linearized 325–7 iron density–compressional velocity relations 254, 264 melting temperature 250, 251, 252 phase relations 260 see also Fe ; molten iron iron–light-element systems melting and melt properties 250–254 physical properties 254–8 Ishii–Tromp density models 335 isotropic velocity tomography 327–9 IW (iron–wustite, FeFeO) redox buffer ă 23, 41, 43, 49, 5051, 50, 53 jadeite [NaAlSi2 O6 ] 225 joint velocity and density model 335 K-hollandite 225–6 KAlSi3 O8 system 225–6 Kepler space mission 272, 274, 288 Kohn–Sham equation 214 Kramers–Kronig relationship 74 Lambert–Beer law large low shear-wave velocity provinces (LLSVPs) 232, 386, 387, 388 laser-heated diamond anvil cell 189–90, 191, 192, 218, 226, 250–251, 259, 260 laser heating, melting-detection criterion during 251 lattice dynamics calculations [for elastic constants] 216 lattice-preferred orientation (LPO) 89, 101, 197–8, 261, 330 development of 110, 123 layered mantle convection model 202, 203, 204, 353 LDA + U technique 215, 220, 222 Lehmann discontinuity [at 220 km depth] 298, 313–314 light elements in core, factors affecting 248–9 linearized inverse theory 325–7 lithosphere composition 125 deformation of 107 seismological studies 304, 312 strength 124–6 temperature profiles 40 see also continental lithosphere; oceanic lithosphere Index lithosphere–asthenosphere boundary (LAB) 312–313 viscosity contrast at 89 lithospheric recycling 356–7 local density approximation (LDA) 214, 215 Love–Rayleigh discrepancy 330 Love waves, azimuthally averaged phase velocities 330 lower crust electrical conductivity 167–8 weakness 123–4 lower mantle ab initio mineralogical model 213–33 chemical composition 185–205 elasticity dataset used in modeling 202–3 electrical conductivity 173–4, 176 geotherms 202, 203 heterogeneity in deep mantle 229–33 homogeneous pyrolite model 185–6 layered mantle convection model 202, 203, 204 main phases see ferropericlase; magnesium silicate perovskite peridotitic model 185, 204, 214 perovskite-rich model 186 reflectors/scatterers 315–316 rheological properties 130, 132–3, 352 seismic observations 186, 315–316 two-phase [pv–fp] model 202 whole mantle convection model 202, 203, 204 LVZ see seismic low-velocity zone magma ocean crystallization of 27, 186 remnants 354 magmatic-hydrothermal arc 380 formation of 380–381, 387 magnesite in alkali carbonatite systems 48 thermal stability 46–7 magnesium aluminate (MgAl2 O4 ) 224–5 CF-to-CT phase transition 224 magnesium silicate (MgSiO3 ) perovskite 217–218 aluminous, Brillouin measurements 195 Brillouin spectrum 194 effect of Fe and Al 218–20 elastic constants, ab initio calculations 217 phase transition 217 physical properties 217 Raman spectrum 194 shear elastic properties 193–5, 200, 203 shear wave velocity as function of pressure 195 synthesis in situ [in DAC] 194 water solubility in 11, 13–14 magnesium silicate (MgSiO3 ) post-perovskite Brillouin spectrum 197 effect of Fe and Al 218–20 low-pressure analogs 218 physical properties 217 shear elastic properties 196–8 in super-Earths 279 see also post-perovskite phase magnetic fields effect on atmosphere 283 super-Earths 285–6 majorite [garnet], water content 13, 46, 155 majorite–perovskite transition 317 mantle pressure ranges in 111 water storage in 4, 6, 13 see also lower mantle; transition zone; upper mantle mantle convection 94 2D models 358–9 3D spherical models 359, 364 dynamical models 358, 361 improvements 364 effect of water frequencies 67 isotopic models 361, 362 modeling of 186, 357–9 rheological barriers to 128–9 seismic studies 317–318 mantle discontinuities see seismic discontinuities mantle heterogeneity 38–9, 229 addition of 354–7 evidence for 353–4 sampling 359–60 mantle melting effect of carbon 25–6, 38, 46–7 effect of water 19–21, 38, 44–6, 146, 357 mantle mixing processes and modeling 357–9 see also mantle convection mantle plumes, seismic studies 316–317 mantle temperature profiles 40–41 mantle transition zone see transition zone mantle viscosity, effect of water mantle wedge water in 381, 384 see also ‘‘big mantle wedge’’ model ‘‘marble cake’’ mantle model 359 397 Mars electrical conductivity distribution 174 rheological properties 134 MEarth project 274, 281 mechanical constitutive relationships, partially molten rocks 72–3 melt fraction and contiguity 80 viscosity [of partially molten rocks] plotted against 83–4 melt geometry 68–72 3D images 70 disequilibrium geometry under stress 70–72 equilibrium geometry 68–70 melt phase, anelastic relaxation affected by 86 melt segregation 55–6 frequencies 67 into melt-rich bands 71 mantle dyanamics and 66 ‘‘millefeuille cake’’ model 89 shear-induced, multiscale dynamics for 89 melt segregation and movement 54–8 buoyancy-driven porous flow 54–5 formation and buoyant ascent of melt diapir 56–8 infiltration of volatile-poor mantle 55–6 melting criteria, in high-pressure experiments 250–251 methane-containing inclusions MgO–SiO2 system, aqueous fluids in 18 microstructural models 67–8, 75–6 see also contiguity model mid-ocean ridge basalts (MORBs) 6, 222–3 accumulation at core–mantle boundary 229, 232, 386 compositional variability 359, 385 density profiles 230 elastic wave velocity profiles 230–231, 233 electrical conductivity 173 influence of hydrogen and iron content 164 generation of 26 isotopic variations in 353, 359, 385 phase relations 226–7 sources 22, 222, 353 volatiles and 6, 51 water content 374 mid-ocean ridges CO2 degassing at 26 melting under 20–21, 43, 51, 359 water degassing at 21 398 ‘‘millefeuille cake’’ model [of melt segregation] 89 mineral/melt partition coefficients carbon dioxide noble gases 27 water 6, 21 mineralogical phase transitions Clapeyron slopes 299 and seismic discontinuities 298, 299 mini-Neptunes 275, 276, 288 misfit functionals 344 MMO (molybdenum–molybdenum oxide) redox buffer 49, 50 molecular dynamics calculations [for elastic constants] 216 molten iron dissolution of O and/or Si into 245, 246–7, 249 partitioning of FeO in 252–3 molten rock see partially molten rock Moon electrical conductivity distribution 174, 175 rheological properties 133 multi-phase aggregate, electrical conductivity 151–2 muon tomography 337 NaAlSi3 O8 system 225 NAL phase 226–7 Nernst–Einstein relation 149, 164 neutral [hydrogen-related] defects 150, 163 ionization of 161 neutrino tomography 337 nickel content of inner core 263 effect in sulfur-bearing systems 249–50 excess in mantle 248 see also Fe–Ni alloy nitrogen volatiles 4, 26 see also ammonium ion NNO (nickel–nickel oxide) redox buffer 27 noble gases 27 as markers 4, 27 mineral/melt partition coefficients 27 recycling into mantle 27, 354 in volcanic gases nominally anhydrous minerals electrical conductivity 162, 163 hydrogen-bearing defects in 9–10, 10, 161 hydrous minerals stored in 227–8 Index thermodynamic models for water solubility 10–11 water in 8–14, 21–2, 374 ocean island basalts (OIBs) compositional variability 385 isotopic variations in 353, 385 sources 22 recycled oceanic crust in 354–5 volatiles and 6, 51 oceanic crust density 365 formation and recycling of 352, 354–5, 363 oceanic lithosphere, strength profile 124, 125 oceans, origins 21–2 OH point defects, water as 6, olivine carbon solubility in 22 creep strength affected by pressure 116 deformation mechanism map 107 electrical conductivity 156, 158, 159, 160 factors affecting creep strength 116, 117, 118, 119 flow laws 103 high-pressure polymorphs see ringwoodite; wadsleyite phase transitions 186, 299 polarized infrared spectra 8, solubility of water in 11–12, 46, 308 olivine–wadsleyite phase transition 299, 306–7 Orowan equation 99 orthopyroxene dynamic recrystallization of 125 electrical conductivity 156, 159, 166, 167 infrared spectra 10 stability pressure range 111 water in 11, 12 outer core and core formation processes 248–9 density 248, 254 light elements in 247–50 melting and melt properties of core materials 247–58 oxidation state [of mantle] 41 oxygen, as light element in core 248 oxygen fugacity, dissolution of light elements into molten iron affected by 249 partial melting 21, 51 electrical conductivity affected by 152, 166–7 mechanical properties affected by 66, 128 plastic deformation affected by 106, 121–2, 128 partially molten rocks contiguity [microstructural] model 75–80 comparison with other models 75–6 contiguity vs melt fraction 80 derivation of elastic and viscous constitutive relationships 76–8 description of microstructures 76 microstructure-sensitive behavior of elasticity and viscosity 78–80 melt geometry 68–72 phenomenological representation 72–5 elastic and viscous constitutive relationships 74–5 generalization to viscoelastic solids 73–4 mechanical constitutive relationships 72–3 textually equilibrated system 68, 70 properties 80–85 Paterson deformation apparatus 110–111, 112 applications 103 pressure–temperature range 109, 110, 113 Peierls mechanism 101, 107, 113, 114, 125 Peierls potential, dislocation glide over 100, 101 Peierls stress 101, 122, 123 periclase [MgO] Brillouin spectrum 199 elastic properties 198–200 shear elastic properties 200, 203 shear wave velocity as function of pressure 199, 201 shear wave velocity measurements 192, 198–9 stability 220 stress–strain relations 216 peridotite electrical conductivity, influence of hydrogen and iron content 164 flow laws 103 peridotite–CO2 systems, phase relationships [up to 21–32 GPa] 46–7 peridotite–H2 O systems, phase relationships [up to 25–30 GPa] 44–6 peridotite systems with C–O–H fluids, experimental studies [below 6–7 GPa] 41–3 with C–O–H volatiles, melting behavior 49–52, 58 Index with reduced C–O–H fluids, phase relationships [up to 16–23 GPa] 49 peridotitic model [of lower mantle] 185, 204, 214 Mg/Si ratio 185–6, 214 perovskite 217 spin transition [of iron] in 173, 195, 219 stability pressure range 111 see also calcium silicate perovskite; magnesium silicate perovskite perovskite-rich lower mantle model 186 phase D [dense hydrous phase] 7, 45, 228, 374 phase egg [AlSiO3 (OH)] 228, 374 phase relations, in subduction zones 374–7 phase transition, discontinuity caused by 298, 299 phase X [hydrous phase] 7, 8, 46 plagioclase, electrical conductivity, 156 167 plastic anisotropy 101–2 estimation of 102, 111 plastic deformation atomic processes involved in 95 deformation mechanism map 107 and diffusion creep 97–9 and dislocation creep 99–101 effect of partial melting 121–2 effect of water 117–119 and electrical conductivity 95–6 experimental methods 108–113 experimental observations 113–22 grain-boundary sliding in 102 grain-size dependence 113, 114 in multi-phase mixtures 106 shear localization and 107–8 stress dependence 113, 114 temperature dependence 113, 114 theoretical studies 122–3 see also rheological properties plate tectonics early Earth 356 Earth compared with Venus 126 factors influencing 123, 124–5, 126, 283, 284, 285, 357 super-Earths 135, 271, 283, 283–5 platinum melting point 251 see also Pt pressure scales point defects anelastic relaxation caused by 85 and plastic deformation 97 ‘‘polaron’’, meaning of term 150 pore geometry mechanical properties affected by 67 seismological indicator 88 poroelastic effect 87, 88 porous flow 377, 378 buoyancy-driven 54–5 post-perovskite phase bondary, double crossing of 245–6 post-perovskite phase [of MgSiO3 ] 195–8 elastic anisotropy 198 shear wave velocity measurements 196–7 post-perovskite/post-spinel phase transition 196, 310 power-law constitutive relationships, 122 power-law creep, flow laws for, 103 PREM seismic model inner core 262, 340 Lehmann discontinuity 313 lower mantle 203, 204 outer core 254 pressure, rheological properties affected by 115–117 pressure ranges, in Earth’s interior 111 pressure-solution creep 97, 106 principal component analysis (PCA) 385 probabilistic tomography 335–6 Pt pressure scales 258, 259, 261–2, 264 PT-profiles lower mantle 41, 42 shallow mantle 40–41, 43 pyrolite density profiles 230 elastic wave velocity profiles 230–231, 233 electrical conductivity 173 pyrolite model [of mantle] 185–6 phase transitions in 310 pyrope [garnet] carbon solubility in 22 electrical conductivity 156, 159, 160 water solubility in 11, 46 pyroxenes electrical conductivity 167 water content 5–6 QFM buffer see FMQ buffer quality factor frequency-dependence of 338 temperature-dependence of 337 quartz, flow laws, 103 radial shear attenuation structure, constraints on 340, 341 radio emissions [from magnetic fields] 287 radiogenic nuclides 225, 360, 385 399 Rayleigh number 360 Rayleigh–Taylor instability 377, 378, 384, 387 Rayleigh waves azimuthally averaged phase velocities 330 inversion of phase and amplitude measurements 342 redox buffers see FMQ ; IW ; MMO ; NNO redox buffer redox freezing 52, 57 redox melting 3, 26, 51, 52–3 relaxation mechanisms, anelasticity affected by 85–8 remote sensing electrical conductivity 5, 133, 145 exoplanets 272 magnetic fields 286–7 rheological properties [of minerals and rocks] comparison with other physical properties 95–7 effect of chemical bonding and crystal structure 119–21 factors influencing 113–22 grain-size dependence 96, 364 lower crust 123–4 lower mantle 130, 132–3 plate tectonics influenced by 124–5, 283 pressure effects 115–117 stress dependence 96, 113–115 temperature dependence 96, 113–115 and terrestrial dynamics and evolution 94–5 theoretical studies 122–3 in transition zone 128–30 upper mantle 124–8 water content dependence 96, 117–119, 146, 357 see also plastic deformation rifting, factors influencing 126, 127 ringwoodite deformation mechanism map 130 electrical conductivity 155, 156, 159 phase transitions 299, 310 solubility of water in 3, 7, 13, 22, 46, 58, 155, 308, 374 rotational Drickamer apparatus (RDA) [for deformation studies] 111, 112 applications 103, 116, 129 pressure–temperature range 111, 113 runaway gas accretion 275 rutile [TiO2 ], solubility in water 18, 19 400 S40RTS tomographic model 363, 364 secondary ion mass spectrometry (SIMS), water content measured using 9, 13, 21, 155 seismic anisotropy 89, 330 absence in lower mantle 132 in asthenosphere 128 cause(s) in D layer 196, 222 and dislocation creep 125, 128, 132 in inner core 261 in transition zone 128 seismic data types 300 seismic discontinuities 297–300, 304–315 220 km [Lehmann] discontinuity 298, 313–314 410 km discontinuity 298, 304–8 as chemical filter 22 melt layer at 3, 22, 308 pressure range 111 as rheological barrier to mantle convection 128–9 as water filter 308 520 km discontinuity 298, 304, 308–9 660 km discontinuity 298, 304, 309–10 melt layer at pressure range 111 as rheological barrier to mantle convection 128–9 D discontinuity/layer anisotropy in 331 MgPv phase transition and 217 seismic characteristics 195–6, 197, 222 weakness 133 effect of water 6–7 geodynamical interpretation 316–318 Lehmann discontinuity 298, 313–314 and mineralogical phase transitions 298, 299 publications on 298 X-discontinuity 298, 314–315 seismic frequencies 66, 67 shear velocity model S40RTS 329 seismic low-velocity zone (LVZ), partial melt in 21, 25, 66 seismic tomography 324–5 compared with geodynamic models 328, 361, 363 limiting factors 325 P-wave velocity models 327, 329 S-wave velocity models 327 travel time models 327 typical global model 328 Index seismic wave propagation, anisotropy 329 seismic wave velocities, factors affecting 146 seismic waves converted waves 300, 303–4 reflected waves 300, 301–3 refracted waves 301 surface waves 312 seismological data types P-to-S receiver functions 303–4 applications 305, 306, 308, 309, 310, 311, 312, 314, 315, 316 PP precursors 302–3 applications 304, 305, 306, 308–9, 310, 315 P’P’ precursors 302 applications 306, 308, 309–10, 315, 316 S-to-P receiver functions 304 applications 308, 312, 316 ScS reverberations 301, 303 applications 314 SS precursors 302–3 applications 304, 305, 306, 308, 310–316 seismological detection of mantle discontinuities 300–304 of small amounts of melt 88–9 seismological methods 300–304 migration techniques 300, 302 stacking techniques 300, 302, 306, 308 seismological observability, of pore geometry 88 ‘‘self-diffusion coefficients’’, hydrogen-related species 163 semiconductors, impurity conduction in 148 serpentine, dehydration of 374, 379 shape-preferred orientation (SPO) 330 shear elastic properties experimental methods 190–192 experimental results 192–201 (Mg,Fe)O 200–201 MgO 198–200 MgSiO3 perovskite 193–5 MgSiO3 post-perovskite 195–8 shear localization 107–8, 123 factors affecting 108, 109, 125–6 in modelling studies 126 shear quality factor 337 shear velocity data, compared with density/bulk modulus data 187 shear viscosity [of partially molten rock], in textually equilibrated system 83–4 shear-wave attenuation 342 global models 342, 343 shear-wave velocity anomalies 353–4 shock experiments melting temperature of iron determined by 253, 254 pressure scale(s) and 258 silica phase transitions 222–4, 314–316 solubility in water 18 silicate melts CO2 solubility in 24 nitrogen solubility in 26 sulfur solubility in 26 water solubility in 14–17 silicates carbon solubility in 22–3, 39 water solubility in 9–10, 39 silicon content of inner core 263 as light element in outer core 249 singularity, viscosity [of partially molten rocks] 78–80, 84 SiO2 –H2 O system complete miscibility in 16, 18 melting relationships in 16–17 ‘‘snowball glaciation’’ 28 sound-wave velocity data 187 determination of 187–92, 256, 257 in inner core 263–4 iron–light-element systems 256, 257 simultaneous measurements with X-ray diffraction 190 under high-pressure and/or high-temperature conditions 187, 192–201 spheroid free oscillations, effect of density variations 333–4 spin transition [of iron] effect on various properties 245 elastic properties affected by 195 electrical conductivity affected by 173 in ferropericlase 173, 200–201, 220–221, 222 in MgSiO3 perovskite 219 in perovskite 173, 195, 219 plastic deformation affected by 132 shear wave velocity affected by 200–201, 245 splitting function measurements 331, 336, 337 ‘‘stagnant lid convection’’ 124–5, 134, 285 stagnant slab(s) 41, 42, 186 dehydration of 53 formation of 58, 387 stishovite [SiO2 polymorph] aluminous 46 Index phase transitions involving 223, 314–316 subducting plates/slabs 38–9 deformation of 129–30, 131 dehydration of 19, 20, 53, 171, 357, 375, 388 role in water transport to deep mantle 22, 227, 378–84 temperature 40 subduction, change from ‘‘dry’’ to ‘‘wet’’ form 357, 361 subduction zone fluids 19, 27 subduction zone processes 373–8 phase relations 373–7 water-transport mechanisms 377–8 subduction zones amount of water loss in 355, 356 continental crust extraction at 352, 361 hydrous phases in 8, 374, 375 maximum water content in 374, 375 melting in 3, 19–20 seismic discontinuities in 302 seismological investigations 304, 316 sulfur depletion in mantle 248 as light element in core 248 volatiles 26–7 super-Earths 272 atmosphere composition 281, 282–3 composition 278–9, 281 density–mass relationships 280 differentiation into layered structure 279 distinguished from mini-Neptunes 275 examples 55 Cnc-e 276, 281–2, 288 CoRoT-7b 276, 280–281, 288 GJ 1214b 276, 281, 288 Kepler-10b 276, 281, 288 Kepler-11 system 276, 282 Kepler-18b 276, 282 Kepler-20b 276, 282 interior dynamics 282–7 interior dynamics observables 286–7 magnetic fields 285–6 mass–radius relationships 278, 279 plate tectonics 135, 283–5 pressure–temperature relationships 277 representative compositions 280 rheological properties 135 terrestrial planets [and satellites] electrical conductivity distribution 174 rheological properties 133–5 see also exoplanets; super-Earths textually equilibrated system [partially molten rocks] continguity determined for 68–9 properties 80–85 elasticity 81–3 viscous rheology 83–5 thermal runaway instability 107–8 thermochemical models convection models 365 mixing models 361 oceanic crust formation and mixing 352 thermochemical piles [in deep mantle] 229, 232, 335 tidal energy dissipation, of Moon 133 tidal tomography 337 tidally locked exoplanets 274, 281 transition zone addition of water to 355 as chemical filter 355, 365 deformation of cold slabs in 129–30 electrical conductivity 169–70, 171–2 melting in 364 phase transitions in 299, 307, 309, 310 rheological properties 128–30 seismic discontinuities 303, 304–310 thickness 310–312 factors affecting 311–312, 317 water in 3, 7, 9, 12–13, 22, 45, 46, 53 see also ringwoodite; wadsleyite transmission spectroscopy, exoplanets 274, 281, 286 tectonics early Earth 356, 361 see also plate tectonics temperature–depth profiles 42, 43, 136 temperature profiles [in mantle] 40–41 velocity–density correlations 335 Venus absence of plate tectonics 126 atmosphere 286 rheological properties 133–4 ultra-low seismic wave velocity layer/zone 217, 244, 245, 246 ultrasonic frequencies 67 ultrasonic interferometry combined with X-ray diffraction 198 soundwave velocity measurements by 187, 193, 205 upper–lower mantle boundary 309 upper mantle electrical conductivity 168–73 rheological properties 124–8, 352 seismic discontinuities 303, 312–315 water in 11 see also asthenosphere; lithosphere 401 viscoelastic representation, partially molten rocks 73–4 viscosity [of partially molten rock] factors affecting 67, 68, 283–4, 357 microstructure-sensitive behavior 78–80 in textually equilibrated system 83–5 viscous constitutive relationships partially molten rocks 74–5 derivation in contiguity model 76–8 Voigt–Ruess–Hill averaging scheme 188, 203, 216, 230 volatile budget [of Earth] 4–7, 58 volatiles abundance 3–4 effects on planetary evolution 4, 28 volcanic eruptions effects on atmosphere 28, 283 sulfur emissions 26–7 volcanic gases, composition 3–4, 27 volcanism, on super-Earths 285 von Mises criterion 101 wadsleyite electrical conductivity 155, 156, 159, 160, 171 solubility of water in 3, 7, 9, 13, 22, 46, 58, 155, 308, 374 stability pressure range 111 wadsleyite–ringwoodite phase transition 299, 309 water chemical evolution [of Earth] affected by 355 content measurement techniques 9, 13, 21, 155 distribution in Earth’s interior 3, 6, 7, 9, 12–13, 22, 373 electrical conductivity affected by 7, 145, 146, 161–2, 170, 171 mantle melting affected by 19–21, 38, 44–6, 146, 357 in nominally anhydrous minerals 8–14, 21–2 physico-chemical properties of mantle minerals affected by 6–7, 133, 145, 146, 372–3 rheological properties affected by 96, 117–119, 146, 357 as solvent under ambient/standard conditions 17–18 in transition zone 3, 7, 9, 12–13, 22, 53, 375 transport to deep mantle 21–2, 227, 355, 378–84 transport to lower mantle 381–4 transport to transition zone 378–81 402 water (continued) in volcanic gases 3, see also hydrous fluids; hydrous minerals water filter, 410 km discontinuity as 308 water solubility 10 nominally anhydrous minerals 11–13 water-transport integrated model 387–8 water-transport mechanisms 377–8 whole mantle convection model 202, 203, 204 Index whole mantle shear attenuation 342 wustite [FeO] ă phase transition 220 shear elastic properties 200, 203 X-discontinuity [at 250–350 km depth] 298, 314–315 X-ray absorption method, density determined by 255, 256 X-ray diffraction (XRD) density determined by 258 melting detected by 251 with shear wave velocity measurements 190, 198–9 xenoliths carbon in 23 fluid inclusions in 4, 24 hydrous minerals in Zeeman effect 287 ... composition of deep Earth and planets including the models of the mantle and core of Earth as well as models of super-Earths (Earth- like planets orbiting stars other than the Sun) And finally the third... understand deep Earth, a multidisciplinary approach is essential First, we need to know the behavior of materials under the extreme conditions of deep Earth (and of deep interior of other planets)... in the contents of water, carbon and other volatiles between the different kinds of chondritic meteorites and the Earth, likely formed by accretion of a mixture of these different materials, the