Physics of Mantle Convection

This chapter presents the fundamental physics necessary to understand the complex fluid dynamics of mantle convection. The first section derives the equations of conservation for mass, momentum, and energy and the boundary and interface conditions for the various physical quantities. The thermodynamic and rheological properties of solids are discussed in the second section. The mechanism of thermal convection and the classical Boussinesq and anelastic approximations are presented in the third section. As the subject is not often included in geophysical textbooks, an introduction to the physics of multicomponent and multiphase flows is given in the fourth section. At last, the specific applications to mantle convection are reviewed in the fifth section.

[1]  G. Wasserburg,et al.  Demonstration of 26 Mg excess in Allende and evidence for 26 Al , 1976 .

[2]  M. Richards,et al.  A geodynamic model of mantle density heterogeneity , 1993 .

[3]  Ulrich R. Christensen,et al.  Dynamic Earth: Plates, Plumes and Mantle Convection , 2000 .

[4]  David Bercovici,et al.  A two-phase model for compaction and damage: 3. Applications to shear localization and plate boundary formation , 2001 .

[5]  M. Richards,et al.  Large-scale mantle convection and the history of subduction , 1992, Nature.

[6]  Donald L. Turcotte,et al.  Geodynamics : applications of continuum physics to geological problems , 1982 .

[7]  G. Schubert,et al.  Inverse problem of thermal convection: numerical approach and application to mantle plume restoration , 2004 .

[8]  Sylvaine Ferrachat,et al.  Regular vs. chaotic mantle mixing , 1998 .

[9]  P. Kelemen,et al.  Extreme chemical variability as a consequence of channelized melt transport , 2003 .

[10]  U. Christensen,et al.  Mantle convection and stability of depleted and undepleted continental lithosphere , 1997 .

[11]  Y. Ricard,et al.  Topography and geoid due to lithospheric mass anomalies , 1995 .

[12]  P. Tackley,et al.  Mantle convection and plate tectonics: toward an integrated physical and chemical theory , 2000, Science.

[13]  P. Tackley,et al.  Convective heat transfer as a function of wavelength: Implications for the cooling of the Earth , 2005 .

[14]  R. Boehler,et al.  Thermal expansivity in the lower mantle , 1992 .

[15]  B. Hager,et al.  Controls of the structure of subducted slabs , 1988, Nature.

[16]  M. Gurnis,et al.  Cenozoic subsidence and uplift of continents from time-varying dynamic topography , 1997 .

[17]  Louis Moresi,et al.  A climate induced transition in the tectonic style of a terrestrial planet , 2008 .

[18]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[19]  R. Müller,et al.  Models of mantle convection incorporating plate tectonics: The Australian region since the Cretaceous , 2000 .

[20]  D. Bercovici,et al.  Whole-mantle convection and the transition-zone water filter , 2002, Nature.

[21]  Subrahmanyan Chandrasekhar,et al.  Ellipsoidal Figures of Equilibrium , 1969 .

[22]  C. Vigny,et al.  Mantle dynamics with induced plate tectonics , 1989 .

[23]  F. Richter.  Experiments on the stability of convection rolls in fluids whose viscosity depends on temperature , 1978, Journal of Fluid Mechanics.

[24]  F. Spear.  Metamorphic phase equilibria and pressure-temperature-time paths , 1993 .

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

[26]  H. Urey.  The origin and development of the earth and other terrestrial planets , 1951 .

[27]  Donald A. Nield,et al.  Surface tension and buoyancy effects in cellular convection , 1964, Journal of Fluid Mechanics.

[28]  J. Schmalzl,et al.  The effect of rheological parameters on plate behaviour in a self-consistent model of mantle convection , 2004 .

[29]  Francis D. Murnaghan,et al.  Finite Deformation of an Elastic Solid , 1967 .

[30]  H. Dick,et al.  ABYSSAL PERIDOTITE MYLONITES : IMPLICATIONS FOR GRAIN-SIZE SENSITIVE FLOW AND STRAIN LOCALIZATION IN THE OCEANIC LITHOSPHERE , 1996 .

[31]  S. Balachandar,et al.  Three-Dimensional Instabilities of Mantle Convection with Multiple Phase Transitions , 1993, Science.

[32]  W. Peltier,et al.  Mantle phase transitions and layered chaotic convection , 1992 .

[33]  G. Schubert,et al.  Whole planet cooling and the radiogenic heat source contents of the Earth and Moon , 1980 .

[34]  G. Spada,et al.  Excitation of true polar wander by subduction , 1992, Nature.

[35]  A. Hofmeister,et al.  Mantle values of thermal conductivity and the geotherm from phonon lifetimes , 1999, Science.

[36]  L. Fleitout,et al.  Topography of the ocean floor: Thermal evolution of the lithosphere and interaction of deep mantle heterogeneities with the lithosphere , 1990 .

[37]  N. Simmons,et al.  Dynamic topography and long-term sea-level variations: There is no such thing as a stable continental platform , 2008 .

[38]  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 .

[39]  U. Christensen.  The influence of trench migration on slab penetration into the lower mantle , 1996 .

[40]  W. Munk,et al.  Astronomy-Geophysics. (Book Reviews: The Rotation of the Earth. A geophysical discussion) , 1975 .

[41]  J. Gerald,et al.  Relationships between dynamically recrystallized grain size and deformation conditions in experimentally deformed olivine rocks , 1993 .

[42]  J. H. Rose,et al.  Compressibility of solids , 1987 .

[43]  Ulrich Hansen,et al.  On the Rayleigh number dependence of convection with a strongly temperature-dependent viscosity , 1998 .

[44]  L. Cserepes,et al.  Effect of depth-dependent viscosity on the pattern of mantle convection , 1993 .

[45]  C. Froidevaux,et al.  On the origin of deviatoric stresses in the lithosphere , 1992 .

[46]  C. Wolfe,et al.  Mantle flow, melting, and dehydration of the Iceland mantle plume , 1999 .

[47]  Patrice Weber,et al.  Intermittent layered convection in a model mantle with an endothermic phase change at 670 km , 1991, Nature.

[48]  W. McDonough,et al.  The composition of the Earth , 1995 .

[49]  Gary A. Glatzmaier,et al.  Three-dimensional convection of an infinite-Prandtl-number compressible fluid in a basally heated spherical shell , 1992, Journal of Fluid Mechanics.

[50]  M. Kido,et al.  Dynamic topography compared with residual depth anomalies in oceans and implications for age‐depth curves , 1994 .

[51]  C. Dumoulin,et al.  ŒDIPUS: a new tool to study the dynamics of planetary interiors , 2007 .

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

[53]  M. Kameyama,et al.  Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box , 2000 .

[54]  M. Monnereau,et al.  Spherical shell models of mantle convection with tectonic plates , 2001 .

[55]  B. Hager,et al.  Geoid Anomalies in a Dynamic Earth , 1984 .

[56]  Marc Spiegelman,et al.  Simple 2-D models for melt extraction at mid-ocean ridges and island arcs , 1987 .

[57]  J. Bass,et al.  Earth's deep mantle : structure, composition, and evolution , 2005 .

[58]  H. Samuel,et al.  Thermochemical convection and helium concentrations in mantle plumes , 2003 .

[59]  T. Ruedas,et al.  Pressure‐ and temperature‐dependent thermal expansivity and the effect on mantle convection and surface observables , 2002 .

[60]  N. Coltice,et al.  A crystallizing dense magma ocean at the base of the Earth’s mantle , 2007, Nature.

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

[62]  B. Kennett,et al.  Seismic heterogeneity in the mantle strong shear wave signature of slabs from joint tomography , 2004 .

[63]  Louis Moresi,et al.  A benchmark study on mantle convection in a 3‐D spherical shell using CitcomS , 2008 .

[64]  George Keith Batchelor,et al.  An Introduction to Fluid Dynamics. , 1969 .

[65]  David A. Yuen,et al.  Role of Phase Transitions in a Dynamic Mantle , 2007 .

[66]  A. Lenardic,et al.  Geological consequences of super‐sized Earths , 2007 .

[67]  Robert W. Clayton,et al.  Constraints on the Structure of Mantle Convection Using Seismic Observations, Flow Models, and the Geoid , 1989 .

[68]  P. Roberts.  Convection in horizontal layers with internal heat generation. Theory , 1967, Journal of Fluid Mechanics.

[69]  É. Kaminski,et al.  Anisotropic rheology of a cubic medium and implications for geological materials , 2007 .

[70]  Frank M. Richter,et al.  Dynamical Models for Melt Segregation from a Deformable Matrix , 1984, The Journal of Geology.

[71]  Ian J. Hewitt,et al.  Partial melting in an upwelling mantle column , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[72]  M. Manga,et al.  The influence of a chemical boundary layer on the fixity, spacing and lifetime of mantle plumes , 2002, Nature.

[73]  A. Joachimiak,et al.  Crystal structure of trp represser/operator complex at atomic resolution , 1988, Nature.

[74]  B. Steinberger,et al.  Advection of plumes in mantle flow: implications for hotspot motion, mantle viscosity and plume distribution , 1998 .

[75]  C. Conrad,et al.  Tectonic velocities, dynamic topography, and relative sea level , 2006 .

[76]  G. I. Barenblatt.  Scaling: Self-similarity and intermediate asymptotics , 1996 .

[77]  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.

[78]  A. E. Ringwood,et al.  Nature of the 650–km seismic discontinuity: implications for mantle dynamics and differentiation , 1988, Nature.

[79]  R. Hilst,et al.  Compositional stratification in the deep mantle , 1999, Science.

[80]  J. Korenaga,et al.  Chemical composition of Earth's primitive mantle and its variance: 1. Method and results , 2007 .

[81]  C. Doglioni,et al.  Differential Rotation Between Lithosphere and Mantle' A Consequence of Lateral Mantle Viscosity Variations , 1991 .

[82]  D. Yuen,et al.  Effects of a realistic mantle thermal conductivity on the patterns of 3-D convection , 1999 .

[83]  N. Coltice,et al.  Geochemical observations and one layer mantle convection , 1999 .

[84]  I. N. Sneddon,et al.  Finite Deformation of an Elastic Solid , 1954 .

[85]  Ondřej Šrámek,et al.  Simultaneous melting and compaction in deformable two-phase media , 2007 .

[86]  Paul J. Tackley,et al.  Effects of strongly variable viscosity on three‐dimensional compressible convection in planetary mantles , 1996 .

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

[88]  Dana S. Henry,et al.  Microstructural Evidence for Grain Size Sensitive Deformation Mechanisms in Naturally Deformed Peridotites , 2002 .

[89]  Y. Podladchikov,et al.  Compaction-driven fluid flow in viscoelastic rock , 1998 .

[90]  Marc Spiegelman,et al.  Causes and consequences of flow organization during melt transport: The reaction infiltration instability in compactible media , 2001 .

[91]  V. Solomatov,et al.  Scaling of temperature‐ and stress‐dependent viscosity convection , 1995 .

[92]  M. Kurz,et al.  Experimental measurements of 3He and 4He mobility in olivine and clinopyroxene at magmatic temperatures , 1993 .

[93]  P. England,et al.  A thin viscous sheet model for continental deformation , 1982 .

[94]  Radius and Structure Models of the First Super-Earth Planet , 2006, astro-ph/0610122.

[95]  S. Balachandar,et al.  Viscous and adiabatic heating effects in three‐dimensional compressible convection at infinite Prandtl number , 1993 .

[96]  R. Hilst,et al.  Poisson's ratio in the lower mantle beneath Alaska: Evidence for compositional heterogeneity , 2004 .

[97]  John F Nye,et al.  The flow law of ice from measurements in glacier tunnels, laboratory experiments and the Jungfraufirn borehole experiment , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[98]  R. O’Connell,et al.  Deformation of a weak subducted slab and variation of seismicity with depth , 1993, Nature.

[99]  David Bercovici,et al.  A two‐phase model for compaction and damage: 1. General Theory , 2001 .

[100]  David Bercovici,et al.  Energetics of a two-phase model of lithospheric damage, shear localization and plate-boundary formation , 2003 .

[101]  P. Olson,et al.  Laboratory experiments on the structure of subducted lithosphere , 1995 .

[102]  John Hernlund,et al.  On the statistical distribution of seismic velocities in Earth's deep mantle , 2008 .

[103]  Wolfgang R. Jacoby,et al.  On modelling the lithosphere in mantle convection with non-linear rheology , 1982 .

[104]  P. Kelemen,et al.  A review of melt migration processes in the adiabatically upwelling mantle beneath oceanic spreading ridges , 1997, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[105]  G. Schubert,et al.  Three-Dimensional Spherical Models of Convection in the Earth's Mantle , 1989, Science.

[106]  G. Schubert,et al.  Numerical simulations of three-dimensional thermal convection in a fluid with strongly temperature-dependent viscosity , 1991, Journal of Fluid Mechanics.

[107]  Gabriele Morra,et al.  A benchmark comparison of spontaneous subduction models – towards a free surface , 2008 .

[108]  N. Phillips,et al.  Scale Analysis of Deep and Shallow Convection in the Atmosphere , 1962 .

[109]  R. C. Kerr,et al.  Fluid‐mechanical models of crack propagation and their application to magma transport in dykes , 1991 .

[110]  H. F. Astrophysics,et al.  Inevitability of Plate Tectonics on Super-Earths , 2007, 0710.0699.

[111]  Michael Manga,et al.  Buoyancy-driven interactions between two deformable viscous drops , 1993, Journal of Fluid Mechanics.

[112]  G. Spada,et al.  Polar wandering of a dynamic earth , 1993 .

[113]  D. Yuen,et al.  Effects on post-glacial rebound from the hard rheology in the transition zone , 1992 .

[114]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[115]  G. Choblet,et al.  Mantle upwelling and melting beneath slow spreading centers: effects of variable rheology and melt productivity , 2001 .

[116]  D. Turcotte,et al.  Studies of finite amplitude non‐Newtonian thermal convection with application to convection in the Earth's mantle , 1976 .

[117]  M. Paterson,et al.  Rheology of synthetic olivine aggregates: Influence of grain size and water , 1986 .

[118]  Patrick Wu,et al.  Rheology of the Upper Mantle: A Synthesis , 1993, Science.

[119]  Y. Ricard,et al.  Mantle dynamics and geoid Green functions , 1995 .

[120]  A. Davaille.  Two-layer thermal convection in miscible viscous fluids , 1999, Journal of Fluid Mechanics.

[121]  E. Garnero,et al.  Structure and Dynamics of Earth's Lower Mantle , 2008, Science.

[122]  A. C. Foweler.  Generation and creep of magma in the earth , 1989 .

[123]  D. Yuen,et al.  Pulsating diapiric flows: Consequences of vertical variations in mantle creep laws , 1992 .

[124]  U. Christensen.  Some geodynamical effects of anisotropic viscosity , 1987 .

[125]  M. Gurnis,et al.  Seismic tomography, surface uplift, and the breakup of Gondwanaland: Integrating mantle convection backwards in time , 2003 .

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

[127]  M. Richards,et al.  Role of a low‐viscosity zone in stabilizing plate tectonics: Implications for comparative terrestrial planetology , 2001 .

[128]  Paul J. Tackley,et al.  Self‐consistent generation of tectonic plates in time‐dependent, three‐dimensional mantle convection simulations , 2000 .

[129]  N. Coltice,et al.  Global warming of the mantle at the origin of flood basalts over supercontinents , 2006 .

[130]  D. Bercovici,et al.  Slab dehydration in the Earth's mantle transition zone , 2006 .

[131]  Paul B. Hays,et al.  A negative feedback mechanism for the long‐term stabilization of Earth's surface temperature , 1981 .

[132]  W. Peltier.  Mantle Viscosity and Ice-Age Ice Sheet Topography , 1996, Science.

[133]  B. Kennett,et al.  The seismic wavefield , 2001 .

[134]  D. McKenzie,et al.  The Generation and Compaction of Partially Molten Rock , 1984 .

[135]  T. Larsen,et al.  Fast plumeheads: Temperature‐dependent versus non‐Newtonian rheology , 1997 .

[136]  David A. Yuen,et al.  Mixing of passive heterogeneities by mantle convection , 1984 .

[137]  D. Tritton,et al.  Physical Fluid Dynamics , 1977 .

[138]  O. Anderson,et al.  Evidence supporting the approximation γρ = const for the Grüneisen parameter of the Earth's lower mantle , 1979 .

[139]  A. E. Ringwood,et al.  Phase transformations in a harzburgite composition to 26 GPa: implications for dynamical behaviour of the subducting slab , 1987 .

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

[141]  George Veronis,et al.  On the Boussinesq Approximation for a Compressible Fluid. , 1960 .

[142]  Louis Moresi,et al.  Free-surface formulation of mantle convection—I. Basic theory and application to plumes , 1996 .

[143]  P. Tackley,et al.  Earth's core formation aided by flow channelling instabilities induced by iron diapirs , 2008 .

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

[145]  D. Stevenson.  SPONTANEOUS SMALL-SCALE MELT SEGREGATION IN PARTIAL MELTS UNDERGOING DEFORMATION , 1989 .

[146]  Ulrich R. Christensen,et al.  3‐D Convection With Variable Viscosity , 1991 .

[147]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[148]  G. Davies.  Thermal histories of convective Earth models and constraints on radiogenic heat production in the Earth , 1980 .

[149]  J. Chéry,et al.  A simple parameterization of strain localization in the ductile regime due to grain size reduction: A case study for olivine , 1999 .

[150]  Z. A. Trapeznikova.  On the Interaction of , 1959 .

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

[152]  F. D. Stacey,et al.  High pressure equations of state with applications to the lower mantle and core , 2004 .

[153]  L. C. Woods,et al.  The thermodynamics of fluid systems , by L. C. Woods. Pp 359. £12·50. 1985. ISBN 0-19-856180-6 (Oxford University Press) , 1987, The Mathematical Gazette.

[154]  Paul J. Tackley,et al.  Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid , 2008 .

[155]  K. E. Bullen,et al.  The problem of the earth's density variation , 1940 .

[156]  B. Hager,et al.  Kinematic models of large‐scale flow in the Earth's mantle , 1979 .

[157]  D. Yuen,et al.  Dynamical consequences of depth-dependent thermal expansivity and viscosity on mantle circulations and thermal structure , 1993 .

[158]  Carl W. Gable,et al.  Models of convection-driven tectonic plates: a comparison of methods and results , 1992 .

[159]  Donald L. Turcotte,et al.  Mantle Convection in the Earth and Planets , 2001 .

[160]  J. Besse,et al.  Revised and synthetic apparent polar wander paths of the African, Eurasian, North American and Indian Plates, and true polar wander since 200 Ma , 1991 .

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

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

[163]  P. Tackley,et al.  Three‐dimensional structures and dynamics in the deep mantle: Effects of post‐perovskite phase change and deep mantle layering , 2006 .

[164]  V. Toussaint,et al.  Spectral decay of a passive scalar in chaotic mixing , 2000 .

[165]  M. F. Ashby,et al.  On the rheology of the upper mantle , 1973 .

[166]  P. Carman,et al.  Permeability of saturated sands, soils and clays , 1939, The Journal of Agricultural Science.

[167]  J. Sinton,et al.  Mantle Flow and Melt Generation at Mid-Ocean Ridges , 1992 .

[168]  Frank D. Stacey,et al.  Applications of thermodynamics to fundamental earth physics , 1977 .

[169]  L. Guillou,et al.  On the effects of continents on mantle convection , 2021 .

[170]  D. Yuen,et al.  The interaction of a subducting lithospheric slab with a chemical or phase boundary , 1984 .

[171]  D. Bercovici,et al.  Role of grain boundaries in magma migration and storage. , 2006 .

[172]  David A. Yuen,et al.  The interaction of viscous heating with grain‐size dependent rheology in the formation of localized slip zones , 1997 .

[173]  D. Joseph.  Nonlinear stability of the Boussinesq equations by the method of energy , 1966 .

[174]  G. Schubert,et al.  Tidal dissipation in a viscoelastic planet , 1986 .

[175]  W. Peltier,et al.  Plate tectonics and aspherical earth structure: The Importance of poloidal‐toroidal coupling , 1987 .

[176]  S. Labrosse,et al.  Effects of continents on Earth cooling: Thermal blanketing and depletion in radioactive elements , 2001 .

[177]  D. Yuen,et al.  Strongly chaotic non-newtonian mantle convection , 1992 .

[178]  N. Weiss,et al.  Dissipative heating in convective flows , 1975, Journal of Fluid Mechanics.

[179]  D. Laporte,et al.  Physics and chemistry of partially molten rocks , 2000 .

[180]  P. Tackley,et al.  Planforms of self‐consistently generated plates in 3D spherical geometry , 2008 .

[181]  David A. Yuen,et al.  Various influences on plumes and dynamics in time-dependent, compressible mantle convection in 3-D spherical shell , 1996 .

[182]  Michael Le Bars,et al.  How to anchor hotspots in a convecting mantle , 2002 .

[183]  D. Bercovici.  A source-sink model of the generation of plate tectonics from non-Newtonian mantle flow , 1995 .

[184]  A. Tarantola,et al.  A logarithmic equation of state , 1998 .

[185]  M. Richards,et al.  An Explanation for Earth's Long-Term Rotational Stability , 1997, Science.

[186]  N. A. Haskell.  The Viscosity of the Asthenosphere , 1937 .

[187]  D. Kohlstedt,et al.  Melt Segregation and Strain Partitioning: Implications for Seismic Anisotropy and Mantle Flow , 2003, Science.

[188]  Andrew C. Fowler,et al.  A mathematical model of magma transport in the asthenosphere , 1985 .

[189]  J. Booker.  Thermal convection with strongly temperature-dependent viscosity , 1976, Journal of Fluid Mechanics.

[190]  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 .

[191]  B. Evans,et al.  Paleowattmeters: A scaling relation for dynamically recrystallized grain size , 2007 .

[192]  M. Rabinowicz,et al.  Admittance for a convection in a layered spherical shell , 1984 .

[193]  J. Schmalzl,et al.  Mixing in vigorous, time-dependent three-dimensional convection and application to Earth's mantle , 1996 .

[194]  Lijun Liu,et al.  Simultaneous inversion of mantle properties and initial conditions using an adjoint of mantle convection , 2008 .

[195]  S. Weinstein.  Thermal convection in a cylindrical annulus with a non-Newtonian outer surface , 1996 .

[196]  J. Ottino.  The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[197]  Mats Hillert,et al.  On the theory of normal and abnormal grain growth , 1965 .

[198]  D. Helmberger,et al.  Sharp Sides to the African Superplume , 2002, Science.

[199]  R. Jeanloz,et al.  Is the mantle geotherm subadiabatic , 1987 .

[200]  Lee A. Segel,et al.  Averaged Equations for Two-Phase Flows , 1971 .

[201]  C. Lithgow‐Bertelloni,et al.  Origin of the lithospheric stress field , 2004 .

[202]  M. Richards,et al.  The dynamics of Cenozoic and Mesozoic plate motions , 1998 .

[203]  Carl W. Gable,et al.  Convection in three dimensions with surface plates: Generation of toroidal flow , 1991 .

[204]  Peter E. van Keken,et al.  MANTLE MIXING: The Generation, Preservation, and Destruction of Chemical Heterogeneity , 2002 .

[205]  S. Karato.  Deformation of Earth Materials: An Introduction to the Rheology of Solid Earth , 2008 .

[206]  D. Yuen,et al.  On transient rheology and glacial isostasy , 1986 .

[207]  Robert W. Clayton,et al.  Lower mantle heterogeneity, dynamic topography and the geoid , 1985, Nature.

[208]  B. Hager,et al.  Understanding the effects of mantle compressibility on geoid kernels , 1996 .

[209]  N. Coltice,et al.  Geophysical and Geochemical Models of Mantle Convection: Successes and Future Challenges , 2004 .

[210]  Guy Masters,et al.  Travel times of P and S from the global digital seismic networks: Implications for the relative variation of P and S velocity in the mantle , 2001 .

[211]  D. Yuen,et al.  Mantle stratification and long-term polar wander , 1989, Nature.

[212]  P. Wilde,et al.  Experiments on precessing flows in the Earth's liquid core , 1995 .

[213]  D. Kohlstedt,et al.  Melt migration in a silicate liquid-olivine system: An experimental test of compaction theory , 1990 .

[214]  P. Tackley.  On the penetration of an endothermic phase transition by upwellings and downwellings , 1995 .

[215]  N. Ribe.  The generation and composition of partial melts in the earth's mantle , 1985 .

[216]  L. Fleitout,et al.  Effect of lateral viscosity variations in the top 300 km on the geoid and dynamic topography , 2003 .

[217]  R. Hilst,et al.  Buckling instabilities of subducted lithosphere beneath the transition zone , 2007 .

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

[219]  Norman H. Sleep,et al.  Tapping of melt by veins and dikes , 1988 .

[220]  E. Garnero,et al.  Seismic Evidence for Partial Melt at the Base of Earth's Mantle , 1996, Science.

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

[222]  P. Tackley,et al.  A doubling of the post-perovskite phase boundary and structure of the Earth's lowermost mantle , 2005, Nature.

[223]  U. Christensen.  Influence of chemical buoyancy on the dynamics of slabs in the transition zone , 1997 .

[224]  A. Davaille,et al.  Stability of thermal convection in two superimposed miscible viscous fluids , 2002, Journal of Fluid Mechanics.

[225]  B. Parsons,et al.  The relationship between surface topography, gravity anomalies, and temperature structure of convection , 1983 .

[226]  Fabien Dubuffet,et al.  Multiple scales in mantle convection , 2000 .

[227]  M. Richards.  Hotspots and the Case for a High Viscosity Lower Mantle , 1991 .

[228]  Bradford H. Hager,et al.  A simple global model of plate dynamics and mantle convection , 1981 .

[229]  P. Silver,et al.  Dynamic topography, plate driving forces and the African superswell , 1998, Nature.

[230]  David Bercovici,et al.  A Simple Model of Plate Generation from Mantle Flow , 1993 .

[231]  Y. Ricard,et al.  A model for the emergence of thermal plumes in Rayleigh–Bénard convection at infinite Prandtl number , 2000, Journal of Fluid Mechanics.

[232]  Emergent anisotropy and flow alignment in viscous rock , 2004 .

[233]  P. Tackley.  Self‐consistent generation of tectonic plates in time‐dependent, three‐dimensional mantle convection simulations 2. Strain weakening and asthenosphere , 2000 .

[234]  C. Jaupart,et al.  The thermal structure and thickness of continental roots , 1999 .

[235]  R. Trompert,et al.  Mantle convection simulations with rheologies that generate plate-like behaviour , 1998, Nature.

[236]  David Bercovici,et al.  The generation of plate tectonics from mantle convection , 2003 .

[237]  C. Sotin,et al.  Turbulent 3‐D thermal convection in an infinite Prandtl number, volumetrically heated fluid: implications for mantle dynamics , 1994 .

[238]  A. Hofmann,et al.  An assessment of local and regional isotopic equilibrium in the mantle , 1978 .

[239]  Jörg Schmalzl,et al.  Mixing times in the mantle of the early Earth derived from 2‐D and 3‐D numerical simulations of convection , 2006 .

[240]  Greg Hirth,et al.  Water in the oceanic upper mantle: implications for rheology , 1996 .

[241]  G. Schubert,et al.  Three-dimensional thermal convection in a spherical shell , 1989, Journal of Fluid Mechanics.

[242]  Guillaume Fiquet,et al.  Electronic Transitions in Perovskite: Possible Nonconvecting Layers in the Lower Mantle , 2004, Science.

[243]  P. Tackley,et al.  The thermochemical structure and evolution of Earth's mantle: constraints and numerical models , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[244]  S. Carbotte,et al.  Ridge migration, asthenospheric flow and the origin of magmatic segmentation in the global mid‐ocean ridge system , 2004 .

[245]  David J. Stevenson,et al.  Magma ascent by porous flow , 1986 .

[246]  C. Vigny,et al.  Mantle heterogeneities, geoid, and plate motion: A Monte Carlo inversion , 1989 .

[247]  R. Peltier,et al.  Viscous flow models of global geophysical observables: 1. Forward problems , 1991 .

[248]  B. Hager,et al.  Subducted slabs and the geoid: 1. Numerical experiments with temperature‐dependent viscosity , 1994 .

[249]  Uriel Frisch,et al.  Chaotic streamlines in the ABC flows , 1986, Journal of Fluid Mechanics.

[250]  M. Rabinowicz,et al.  Compaction in a mantle with a very small melt concentration: Implications for the generation of carbonatitic and carbonate-bearing high alkaline mafic melt impregnations , 2002 .

[251]  C. Spiers,et al.  Grain size reduction by dynamic recrystallization: can it result in major rheological weakening? , 2001 .

[252]  J. Weertman,et al.  High Temperature Creep of Rock and Mantle Viscosity , 1975 .

[253]  D. Stevenson,et al.  A self‐consistent model of melting, magma migration and buoyancy‐driven circulation beneath mid‐ocean ridges , 1989 .

[254]  J. Korenaga.  Energetics of mantle convection and the fate of fossil heat , 2003 .

[255]  S. Balachandar,et al.  Time‐dependent three dimensional compressible convection with depth‐dependent properties , 1992 .

[256]  C. Beaumont,et al.  The evolution of sedimentary basins on a viscoelastic lithosphere: theory and examples , 1978 .

[257]  R. Jeanloz,et al.  Sediments at the top of Earth's core. , 2000, Science.

[258]  D. Bercovici,et al.  Tectonic plate generation and two‐phase damage: Void growth versus grain size reduction , 2005 .

[259]  I. Jackson.  The Earth's Mantle: Composition, Structure, and Evolution , 1998 .

[260]  S. Karato,et al.  Localization of dislocation creep in the lower mantle: implications for the origin of seismic anisotropy , 2001 .

[261]  G. Schubert,et al.  A two-phase model for compaction and damage: 2. Applications to compaction, deformation, and the role of interfacial surface tension , 2001 .

[262]  Louise H. Kellogg,et al.  Homogenization of the mantle by convective mixing and diffusion , 1987 .

[263]  U. Christensen,et al.  Convection planforms in a fluid with a temperature‐dependent viscosity beneath a stress‐free upper boundary , 1991 .

[264]  M. Gurnis,et al.  Dynamics of subduction initiation at preexisting fault zones , 1998 .

[265]  A. Davaille,et al.  Transient high-Rayleigh-number thermal convection with large viscosity variations , 1993, Journal of Fluid Mechanics.

[266]  Seismic Anisotropy in the Deep Mantle, Boundary Layers and the Geometry of Mantle Convection , 1998 .

[267]  E. Boschi,et al.  FAST TRACK PAPER: Linear or non-linear rheology in the Earth's mantle: the prevalence of power-law creep in the postglacial isostatic readjustment of Laurentia , 2004 .

[268]  D. Bercovici,et al.  Two-phase damage theory and crustal rock failure: the theoretical ‘void’ limit, and the prediction of experimental data , 2003 .

[269]  A. Hofmann,et al.  Segregation of subducted oceanic crust in the convecting mantle , 1994 .

[270]  G. Davies.  Stirring geochemistry in mantle convection models with stiff plates and slabs , 2002 .

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

[272]  Ulrich R. Christensen,et al.  Convection with pressure- and temperature-dependent non-Newtonian rheology , 1984 .

[273]  N. Ribe.  The deformation and compaction of partial molten zones , 1985 .

[274]  A. Lenardic.  On the partitioning of mantle heat loss below oceans and continents over time and its relationship to the Archaean paradox , 1998 .

[275]  Frank M. Richter,et al.  Convection experiments in fluids with highly temperature-dependent viscosity and the thermal evolution of the planets , 1982 .

[276]  Ulrich R. Christensen,et al.  Some effects of lateral viscosity variations on geoid and surface velocities induced by density anomalies in the mantle , 1993 .

[277]  Don L. Anderson,et al.  Top-Down Tectonics? , 2001, Science.

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

[279]  U. Christensen.  Heat transport by variable viscosity convection and implications for the Earth's thermal evolution , 1984 .

[280]  Louis Moresi,et al.  Role of temperature‐dependent viscosity and surface plates in spherical shell models of mantle convection , 2000 .

[281]  Chris Kincaid,et al.  An experimental study of subduction and slab migration , 1987 .

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

[283]  M. Richards,et al.  The history and dynamics of global plate motions , 2000 .

[284]  Stuart A. Weinstein,et al.  Thermal convection with non-Newtonian plates , 1992 .

[285]  D. Bercovici,et al.  Two-dimensional convection with a self-lubricating, simple-damage rheology , 2003 .

[286]  D. Tozer.  The present thermal state of the terrestrial planets , 1972 .

[287]  Giorgio Ranalli,et al.  Rheology of the earth , 1987 .

[288]  W. Landuyt,et al.  Variations in planetary convection via the effect of climate on damage , 2008 .

[289]  R. Bruce Lindsay,et al.  Thermodynamics of Irreversible Processes , 1971 .

[290]  S. K. Runcorn,et al.  Satellite Gravity Measurements and a Laminar Viscous Flow Model of the Earth's Mantle , 1964 .

[291]  Louis Moresi,et al.  Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus , 1998 .

[292]  D. Yuen,et al.  Temperature‐dependent Newtonian and non‐Newtonian convection: Implications for lithospheric processes , 1993 .

[293]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .

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

[295]  A. E. Ringwood,et al.  Phase transformations in subducted oceanic crust and buoyancy relationships at depths of 600–800 km in the mantle , 1993 .

[296]  J. Tromp,et al.  Theoretical Global Seismology , 1998 .

[297]  M. Gurnis,et al.  Numerical study of high Rayleigh number convection in a medium with depth-dependent viscosity , 1986 .

[298]  C. R. Hagelberg,et al.  Mantle circulation models with variational data assimilation: inferring past mantle flow and structure from plate motion histories and seismic tomography , 2001 .

[299]  J. Mitrovica,et al.  Radial profile of mantle viscosity: Results from the joint inversion of convection and postglacial , 1997 .

[300]  D. Pepper,et al.  Ascent and decompression of viscous vesicular magma in a volcanic conduit , 2001 .

[301]  C. Froidevaux,et al.  Geoid heights and lithospheric stresses for a dynamic Earth. , 1984 .

[302]  P. Tackley.  Self-consistent generation of tectonic plates in three-dimensional mantle convection , 1998 .

[303]  R. Rudnick,et al.  Nature and composition of the continental crust: A lower crustal perspective , 1995 .