A mineralogical model for density and elasticity of the Earth's mantle

[1] We present a thermodynamic model of high-pressure mineralogy that allows the evaluation of phase stability and physical properties for the Earth's mantle. The thermodynamic model is built from previous assessments and experiments in the five-component CFMAS system (CaO-FeO-MgO-Al2O3-SiO2), including mineral phases that occur close to typical chemical models of the mantle and reasonable mantle temperatures. In this system we have performed a system Gibbs free energy minimization, including pure end-member phases and a nonideal formulation for solid solutions. Solid solutions were subdivided into discrete pseudocompounds and treated as stoichiometric phases during computation of chemical equilibrium by the simplex method. We have complemented the thermodynamic model with a model of shear wave properties to obtain a full description of aggregate elastic properties (density, bulk, and shear moduli) that provide a useful basis for the consideration of seismic and geodynamic models of the Earth's mantle. The thermodynamic model described here is made available for research and training purposes through a Web interface (http://www.earthmodel.org). We examine its validity in light of experiments from mineral physics and briefly discuss inferences for mantle structure.

[1]  Y. Ohishi,et al.  Post-Perovskite Phase Transition in MgSiO3 , 2004, Science.

[2]  James R. Harris,et al.  Ferric iron content of mineral inclusions in diamonds from S , 1997 .

[3]  R. Powell,et al.  Calculating phase diagrams involving solid solutions via non‐linear equations, with examples using THERMOCALC , 1998 .

[4]  D. L. Anderson,et al.  Seismic velocities in mantle minerals and the mineralogy of the upper mantle , 1989 .

[5]  J. Connolly.  Multivariable phase diagrams; an algorithm based on generalized thermodynamics , 1990 .

[6]  T. Katsura,et al.  A temperature profile of the mantle transition zone , 1989 .

[7]  H. Bunge,et al.  Non‐adiabaticity in mantle convection , 2001 .

[8]  C. Sotin,et al.  Comparison between tomographic structures and models of convection in the upper mantle , 1996 .

[9]  J. Bass,et al.  Effect of aluminium on the compressibility of silicate perovskite , 2003 .

[10]  G. Will,et al.  The compressibility of forsterite up to 300 kbar measured with synchrotron radiation , 1986 .

[11]  Y. Ohishi,et al.  Phase relations in Mg3Al2Si3O12 to 180 GPa: Effect of Al on post‐perovskite phase transition , 2005 .

[12]  R. Snieder,et al.  Anomalies of temperature and iron in the uppermost mantle inferred from gravity data and tomographic models , 2002 .

[13]  E. Engdahl,et al.  Finite-Frequency Tomography Reveals a Variety of Plumes in the Mantle , 2004, Science.

[14]  E. Takahashi,et al.  Subsolidus and melting experiments of K-doped peridotite KLB-1 to 27 GPa : Its geophysical and geochemical implications , 2000 .

[15]  Y. Ricard,et al.  Synthetic Tomographic Images of Slabs from Mineral Physics , 2005 .

[16]  Barbara Romanowicz,et al.  The three‐dimensional shear velocity structure of the mantle from the inversion of body, surface and higher‐mode waveforms , 2000 .

[17]  A. Ringwood.  Composition and petrology of the earth's mantle , 1975 .

[18]  P. Tackley,et al.  Plume heat flow is much lower than CMB heat flow , 2006 .

[19]  Francis Albarède,et al.  Introduction to Geochemical Modeling , 1995 .

[20]  I. Jackson,et al.  ANALYSIS OF P-V-T DATA : CONSTRAINTS ON THE THERMOELASTIC PROPERTIES OF HIGH-PRESSURE MINERALS , 1996 .

[21]  D. Komatitsch,et al.  Spectral-element simulations of global seismic wave propagation: II. Three-dimensional models, oceans, rotation and self-gravitation , 2002 .

[22]  Hans-Peter Bunge,et al.  Are splash plumes the origin of minor hotspots , 2006 .

[23]  G. Masters,et al.  On the resolution of density within the Earth , 2003 .

[24]  J. Gerald,et al.  Grain-size-sensitive seismic wave attenuation in polycrystalline olivine , 2002 .

[25]  McSween Hy,et al.  Evidence for Life in a Martian Meteorite , 1997 .

[26]  D. L. Anderson,et al.  Transition region of the Earth's upper mantle , 1986, Nature.

[27]  C. Farnetani.  Excess temperature of mantle plumes: The role of chemical stratification across D″ , 1997 .

[28]  S. Saxena,et al.  Stability of Perovskite (MgSiO3) in the Earth's Mantle , 1996, Science.

[29]  D. Frost.  The structure and sharpness of (Mg,Fe)2SiO4 phase transformations in the transition zone , 2003 .

[30]  J. Ågren,et al.  A regular solution model for phases with several components and sublattices, suitable for computer applications , 1981 .

[31]  James A. D. Connolly,et al.  An automated strategy for calculation of phase diagram sections and retrieval of rock properties as a function of physical conditions , 2002 .

[32]  B. Wood,et al.  Olivine‐spinel transitions: Experimental and thermodynamic constraints and implications for the nature of the 400‐km seismic discontinuity , 1987 .

[33]  H. Mao,et al.  Thermoelasticity of Silicate Perovskite and Magnesiow�stite and Stratification of the Earth's Mantle , 1992, Science.

[34]  T. Irifune.  An experimental investigation of the pyroxene-garnet transformation in a pyrolite composition and its bearing on the constitution of the mantle , 1987 .

[35]  E. Ito,et al.  Postspinel transformations in the system Mg2SiO4‐Fe2SiO4 and some geophysical implications , 1989 .

[36]  Alan Dinsdale,et al.  The compound energy model for ionic solutions with applications to solid oxides , 1992 .

[37]  D. Frost,et al.  The effect of Al 2 O 3 on Fe-Mg partitioning between magnesiowüstite and magnesium silicate perovskite , 2002 .

[38]  M. Kunz,et al.  Thermoelastic properties and crystal structure of MgSiO3 perovskite at lower mantle pressure and temperature conditions , 2000 .

[39]  Uchida,et al.  The postspinel phase boundary in Mg2SiO4 determined by in situ X-ray diffraction , 1998, Science.

[40]  S. Ono,et al.  Post-spinel transition in Mg2SiO4 determined by high P–T in situ X-ray diffractometry , 2003 .

[41]  G. Steinle‐Neumann,et al.  Effect of Al on the sharpness of the MgSiO3 perovskite to post‐perovskite phase transition , 2005 .

[42]  H. Samuel,et al.  Heterogeneous lowermost mantle : Compositional constraints and seismological observables , 2003 .

[43]  P. Tackley.  Strong heterogeneity caused by deep mantle layering , 2002 .

[44]  A. Oganov,et al.  Theoretical and experimental evidence for a post-perovskite phase of MgSiO3 in Earth's D″ layer , 2004, Nature.

[45]  D. Komatitsch,et al.  Spectral-element simulations of global seismic wave propagation—I. Validation , 2002 .

[46]  D. McKenzie,et al.  Convection in a compressible fluid with infinite Prandtl number , 1980, Journal of Fluid Mechanics.

[47]  H. Wänke,et al.  Mantle Chemistry and Accretion History of the Earth , 1984 .

[48]  D. Yuen,et al.  Layered convection induced by phase transitions , 1985 .

[49]  Shijie Zhong,et al.  Thermochemical structures beneath Africa and the Pacific Ocean , 2005, Nature.

[50]  Y. Ohishi,et al.  Post-Perovskite Phase Transition , 2004 .

[51]  Joseph S. Resovsky,et al.  Reliable mantle density error bars: an application of the neighbourhood algorithm to normal-mode and surface wave data , 2002 .

[52]  J. Schilling.  Fluxes and excess temperatures of mantle plumes inferred from their interaction with migrating mid-ocean ridges , 1991, Nature.

[53]  M. Isshiki,et al.  Iron partitioning in a pyrolite mantle and the nature of the 410-km seismic discontinuity , 1998, Nature.

[54]  I. Jackson,et al.  Anelasticity and microcreep in polycrystalline MgO at high temperature: an exploratory study , 2003 .

[55]  D. Frost,et al.  Peridotite melting and mineral–melt partitioning of major and minor elements at 22–24.5 GPa , 2002 .

[56]  James A. D. Connolly,et al.  Computation of phase equilibria by linear programming: A tool for geodynamic modeling and its application to subduction zone decarbonation , 2005 .

[57]  D. L. Anderson,et al.  Preliminary reference earth model , 1981 .

[58]  S. Labrosse.  Hotspots, mantle plumes and core heat loss , 2002 .

[59]  Heiner Igel,et al.  Anisotropic wave propagation through finite-difference grids , 1995 .

[60]  G. Glatzmaier.  Numerical simulations of mantle convection: time-dependent, three-dimensional, compressible, spherical shell , 1988 .

[61]  T. Duffy,et al.  The equation of state of forsterite to 17.2 GPa and effects of pressure media , 1996 .

[62]  T. Kikegawa,et al.  Thermal expansivity of MgSiO3 perovskite under high pressures up to 20 GPa , 1995 .

[63]  J. Gerald,et al.  Mineralogy and dynamics of a pyrolite lower mantle , 1998, Nature.

[64]  E. R. Engdahl,et al.  Constraints on seismic velocities in the Earth from traveltimes , 1995 .

[65]  Albrecht W. Hofmann,et al.  The chemical composition of the Earth , 1995 .

[66]  Mark A. Richards,et al.  A sensitivity study of three-dimensional spherical mantle convection at 108 Rayleigh number: Effects of depth-dependent viscosity, heating mode, and an endothermic phase change , 1997 .

[67]  Lapo Boschi,et al.  A comparison of tomographic and geodynamic mantle models , 2002 .

[68]  Robert M. Hazen,et al.  Effects of temperature and pressure on the crystal structure of forsterite , 1976 .

[69]  J. Matas.  Modelisation thermochimique des proprietes de solides a hautes pressions et hautes temperatures. Applications geophysiques , 1999 .

[70]  J. Bass,et al.  Lower mantle composition and temperature from mineral physics and thermodynamic modelling , 2005 .

[71]  J. Maclennan,et al.  Joint inversion of seismic and gravity data for lunar composition and thermal state , 2007 .

[72]  N. Guignot,et al.  Equation of state of lower mantle (Al,Fe)-MgSiO3 perovskite , 2001 .

[73]  G. D. Price,et al.  Comparative study of quasiharmonic lattice dynamics, molecular dynamics and Debye model applied to MgSiO3 perovskite. , 2000 .

[74]  Mark A. Richards,et al.  The origin of large scale structure in mantle convection: Effects of plate motions and viscosity stratification , 1996 .

[75]  L. Stixrude,et al.  Petrology, elasticity, and composition of the mantle transition zone , 1992 .

[76]  M. Reed,et al.  Calculation of Simultaneous Chemical Equilibria in Aqueous-Mineral-Gas Systems and its Application to Modeling Hydrothermal Processes , 1998 .

[77]  C. McCammon.  Perovskite as a possible sink for ferric iron in the lower mantle , 1997, Nature.

[78]  B. Kennett,et al.  Spatial and temporal evolution of the subducting Pacific plate structure along the western Pacific margin , 2006 .

[79]  K. Hirose,et al.  Experimentally determined postspinel transformation boundary in Mg2SiO4 using MgO as an internal pressure standard and its geophysical implications , 2004 .

[80]  R. Hilst,et al.  High resolution global tomography : a snapshot of convection in the Earth , 1997 .

[81]  O. Fabrichnaya.  The phase relations in the FeO-MgO-Al2O3-SiO2 system: assessment of thermodynamic properties and phase equilibria at pressures up to 30 GPa , 1999 .

[82]  Jianzhong Zhang,et al.  Pressure and temperature dependence of elastic wave velocity of MgSiO3 perovskite and the composition of the lower mantle , 2005 .

[83]  Introduction to the Physics of the Earth's Interior , 1991 .

[84]  P. Richet,et al.  Thermal expansion of forsterite up to the melting point , 1996 .

[85]  Shijie Zhong,et al.  Constraints on thermochemical convection of the mantle from plume heat flux, plume excess temperature, and upper mantle temperature , 2006 .

[86]  Richards,et al.  Time scales and heterogeneous structure in geodynamic earth models , 1998, Science.

[87]  Raymond Jeanloz,et al.  Temperature distribution in the crust and mantle , 1986 .

[88]  S. Saxena.  Earth mineralogical model: Gibbs free energy minimization computation in the system MgOFeOSiO2 , 1996 .

[89]  K. Leinenweber,et al.  In situ high P‐T X ray diffraction studies on three polymorphs (α, β, γ) of Mg2SiO4 , 1993 .

[90]  H. Mao,et al.  The fate of subducted basaltic crust in the Earth's lower mantle , 1999, Nature.

[91]  S. Sutton,et al.  Thermal equation of state of akimotoite MgSiO3 and effects of the akimotoite–garnet transformation on seismic structure near the 660 km discontinuity , 2004 .

[92]  Lars Stixrude,et al.  Thermodynamics of mantle minerals – I. Physical properties , 2005 .

[93]  F. Birch.  Elasticity and Constitution of the Earth's Interior , 1952 .

[94]  Thomas H. Brown,et al.  The computation of chemical equilibrium in complex systems containing non-ideal solutions , 1987 .

[95]  S. Stein,et al.  A model for the global variation in oceanic depth and heat flow with lithospheric age , 1992, Nature.

[96]  D. Giardini,et al.  Inferring upper-mantle temperatures from seismic velocities , 2003 .

[97]  David J. Stevenson,et al.  Effects of an endothermic phase transition at 670 km depth in a spherical model of convection in the Earth's mantle , 1993, Nature.

[98]  T. Irifune.  Absence of an aluminous phase in the upper part of the Earth's lower mantle , 1994, Nature.

[99]  T. Kikegawa,et al.  Complicated effects of aluminum on the compressibility of silicate perovskite , 2004 .

[100]  H. Mao,et al.  Effect of pressure, temperature, and composition on lattice parameters and density of (Fe,Mg)SiO3‐perovskites to 30 GPa , 1991 .

[101]  E. R. Engdahl,et al.  Evidence for deep mantle circulation from global tomography , 1997, Nature.

[102]  J. Tromp,et al.  Normal-mode and free-Air gravity constraints on lateral variations in velocity and density of Earth's mantle , 1999, Science.

[103]  G. M. Anderson,et al.  Thermodynamics of Natural Systems , 1995 .

[104]  R. Hazen,et al.  High-pressure crystal chemistry of MgSiO3 perovskite , 1990 .

[105]  Y. Ohishi,et al.  Post‐perovskite phase transition and mineral chemistry in the pyrolitic lowermost mantle , 2005 .

[106]  N. Olsen,et al.  Constraining the composition and thermal state of the mantle beneath Europe from inversion of long‐period electromagnetic sounding data , 2006 .

[107]  N. Weiss,et al.  Convection in the earth's mantle: towards a numerical simulation , 1974, Journal of Fluid Mechanics.

[108]  J. Connolly,et al.  An algorithm and computer program for calculating composition phase diagrams , 1987 .

[109]  C. Sotin,et al.  Computation of seismic profiles from mineral physics: the importance of the non-olivine components for explaining the 660 km depth discontinuity , 1998 .

[110]  L. Dubrovinsky,et al.  Thermodynamic data for the phases in the CaSiO3 system , 1997 .

[111]  T. Yoshino,et al.  Phase relations and equation-of-state of aluminous Mg-silicate perovskite and implications for Earth's lower mantle , 2004 .

[112]  T. Kondo,et al.  Thermoelastic properties of MgSiO3 perovskite determined by in situ X ray observations up to 30 GPa and 2000 K , 1996 .

[113]  S. Akimoto,et al.  High-pressure phase equilibria in a garnet lherzolite, with special reference to Mg2+Fe2+ partitioning among constituent minerals , 1979 .

[114]  Don L. Anderson,et al.  Composition of the upper mantle: Geophysical tests of two petrological models , 1984 .

[115]  Hans-Peter Bunge,et al.  Low plume excess temperature and high core heat flux inferred from non-adiabatic geotherms in internally heated mantle circulation models , 2005 .

[116]  W. Spakman,et al.  Mesozoic subducted slabs under Siberia , 1999, Nature.

[117]  B. Kennett,et al.  Joint seismic tomography for bulk sound and shear wave speed in the Earth's mantle , 1998 .

[118]  N. Ross,et al.  Crystal structure and equation of state of MgSiO3 perovskite , 2006 .

[119]  Harmen Bijwaard,et al.  Closing the gap between regional and global travel time tomography , 1998 .

[120]  S. Sinogeikin,et al.  Elasticity of single crystal and polycrystalline MgSiO3 perovskite by Brillouin spectroscopy , 2004 .

[121]  M. Kunz,et al.  P-V-T EQUATION OF STATE OF MGSIO3 PEROVSKITE , 1998 .

[122]  K. Hirose.  Phase transitions in pyrolitic mantle around 670‐km depth: Implications for upwelling of plumes from the lower mantle , 2002 .

[123]  Gabi Laske,et al.  The Relative Behavior of Shear Velocity, Bulk Sound Speed, and Compressional Velocity in the Mantle: Implications for Chemical and Thermal Structure , 2013 .