Effects of multiple phase transitions in a three-dimensional spherical model of convection in Earth's mantle

Numerical models of mantle convection that incorporate the major mantle phase changes of the transition zone reveal an inherently three-dimensional flow pattern, with cylindrical features and linear features that behave differently in their ability to penetrate the 670-km discontinuity. The dynamics are dominated by accumulation of cold linear downwellings into rounded pools above the endothermic phase change at 670 km depth, resulting in frequent “avalanches” of upper mantle material into the lower mantle. The effect of the exothermic phase transition at 400 km depth is to reduce the overall degree of layering by pushing material through the 670-km phase change, resulting in smaller and more frequent avalanches, and a wider range of morphologies. Large quantities of avalanched cold material accumulate above the coremantle boundary (CMB), resulting in a region of strongly depressed mean temperature at the base of the mantle. The 670-km phase change has a strong effect on the temperature field, with three-distinct regions being visible: (1) the upper mantle, containing linear downwellings and pools of cold material in the transition zone and characterized by a high amplitude long wavelength spectrum; (2) the midmantle, containing quasi-cylindrical avalanche conduits and characterized by a low amplitude, broad spectrum; and (3) the deep mantle, containing large pools of cold, avalanched material and characterized by a high amplitude, ultra-red (i.e., long wavelength) spectrum. The effect on the velocity field is very different. Flow penetration across the 670-km phase change is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. Thus, when comparing numerical models with long wavelength seismic tomography, diagnostics based on the density field, such as the radial correlation function, are much more sensitive to the effects of phase transitions than those based on the velocity field. The amplitude of the geoid is not significantly affected by the partial layering, because the contribution from the strong heterogeneity in the transition zone is almost perfectly balanced by the contribution from deflection of the 670-km discontinuity. Avalanches are associated with geoid lows. However, a more complex viscosity structure is required to correctly match the sign of the geoid over slabs in Earth.

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

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

[3]  G. Schubert,et al.  Structure of axisymmetric mantle plumes , 1993 .

[4]  Y. Fukao.  Seismic Tomogram of the Earth's Mantle: Geodynamic Implications , 1992, Science.

[5]  Wei-jia Su,et al.  Predominance of long-wavelength heterogeneity in the mantle , 1991, Nature.

[6]  P. Shearer,et al.  Seismic constraints on mantle flow and topography of the 660-km discontinuity: evidence for whole-mantle convection , 1993, Nature.

[7]  Norman H. Sleep,et al.  Hotspots and Mantle Plumes' Some Phenomenology , 1990 .

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

[9]  D. Yuen,et al.  Geophysical inferences of thermal‐chemical structures in the lower mantle , 1993 .

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

[11]  Y. Ricard,et al.  Inferring the viscosity and the 3-D density structure of the mantle from geoid, topography and plate velocities , 1991 .

[12]  D. L. Anderson.  Theory of Earth , 2014 .

[13]  D. Anderson,et al.  Search for deep slabs in the Northwest Pacific mantle. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[14]  M. Gurnis,et al.  Viscous flow model of a subduction zone with a faulted lithosphere: Long and short wavelength topography, gravity and geoid , 1992 .

[15]  T. Katsura,et al.  The system Mg2SiO4‐Fe2SiO4 at high pressures and temperatures: Precise determination of stabilities of olivine, modified spinel, and spinel , 1989 .

[16]  F. D. Stacey,et al.  The dynamical and thermal structure of deep mantle plumes , 1983 .

[17]  T. Tanimoto.  Long-wavelength S-wave velocity structure throughout the mantle , 1990 .

[18]  D. Yuen,et al.  Instabilities from phase transitions and the timescales of mantle thermal evolution , 1993 .

[19]  W. Peltier,et al.  Avalanche effects in phase transition modulated thermal convection: A model of Earth's mantle , 1994 .

[20]  E. Ito,et al.  Refinement of enthalpy measurement of MgSiO3 perovskite and negative pressure‐temperature slopes for Perovskite‐forming reactions , 1993 .

[21]  Paul J. Tackley,et al.  Effects of strongly temperature‐dependent viscosity on time‐dependent, three‐dimensional models of mantle convection , 1993 .

[22]  Masayuki Obayashi,et al.  Subducting slabs stagnant in the mantle transition zone , 1992 .

[23]  Don L. Anderson,et al.  A seismic equation of state II. Shear properties and thermodynamics of the lower mantle , 1987 .

[24]  John R. Baumgardner,et al.  Three-dimensional treatment of convective flow in the earth's mantle , 1985 .

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

[26]  R. Jeanloz.  Effects of phase transions and possible compositional changes on the seismological structure near 650 km depth , 1991 .

[27]  S. Weinstein.  Induced compositional layering in a convecting fluid layer by an endothermic phase transition , 1992 .

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

[29]  J. R. Baumgardner.  Application of supercomputers to 3-D mantle convection. , 1986 .

[30]  G. Davies.  Role of the lithosphere in mantle convection , 1988 .

[31]  Shijie Zhong,et al.  Role of plates and temperature‐dependent viscosity in phase change dynamics , 1994 .

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

[33]  M. Richards,et al.  Hotspots, mantle plumes, flood basalts, and true polar wander , 1991 .

[34]  T. Lay.  The Fate of Descending Slabs , 1994 .

[35]  P. Wyllie.  Magma genesis, plate tectonics, and chemical differentiation of the Earth , 1988 .

[36]  D. Yuen,et al.  On the aspect ratio of Rayleigh-Benard convection cells. [in earth mantle] , 1988 .

[37]  Richard H. Rapp,et al.  The development and analysis of geopotential coefficient models to spherical harmonic degree 360 , 1990 .

[38]  Alexandra Navrotsky,et al.  Olivine-modified spinel-spinel transitions in the system Mg2SiO4-Fe2SiO4: Calorimetric measurements, thermochemical calculation, and geophysical application , 1989 .

[39]  Olafur Gudmundsson,et al.  Stochastic analysis of global traveltime data: mantle heterogeneity and random errors in the ISC data , 1990 .

[40]  J. Vidale,et al.  Seismic observation of a high‐velocity slab 1200–1600 km in depth , 1988 .

[41]  G. Schubert.  Numerical models of mantle convection , 1992 .

[42]  A. Dziewoński,et al.  Deep origin of mid-ocean-ridge seismic velocity anomalies , 1992, Nature.

[43]  G. Schubert.  Subsolidus Convection in the Mantles of Terrestrial Planets , 1979 .

[44]  T. W. Ray,et al.  Spherical disharmonies in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations , 1994 .

[45]  Guy Masters,et al.  An inversion for radial viscosity structure using seismic tomography , 1992 .

[46]  Yosihiko Ogata,et al.  Whole mantle P-wave travel time tomography , 1990 .

[47]  W. M. Kaula,et al.  A spherical harmonic analysis of the Earth's topography , 1967 .

[48]  D. Turcotte,et al.  Phase changes and mantle convection , 1971 .

[49]  A. E. Ringwood,et al.  Phase transformations and their bearing on the constitution and dynamics of the mantle , 1991 .

[50]  Wei-jia Su,et al.  On the scale of mantle heterogeneity , 1992 .

[51]  J. Vidale,et al.  Sharpness of upper-mantle discontinuities determined from high-frequency reflections , 1993, Nature.

[52]  W. Peltier,et al.  Parameterized mantle convection and the Earth's thermal history , 1978 .

[53]  J. Mitrovica.  Reply to comment by L. Cathles and W. Fjeldskaar on 'The inference of mantle viscosity from an inversion of the Fennoscandian relaxation spectrum' , 1993 .

[54]  P. Roberts,et al.  Braginsky receives Fleming Medal , 1993 .

[55]  R. Clayton,et al.  P and S wave travel time inversions for subducting slab under the island arcs of the northwest Pacific , 1990 .

[56]  P. Shearer,et al.  Global mapping of topography on the 660-km discontinuity , 1992, Nature.

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

[58]  O. Anderson,et al.  A model for the computation of thermal expansivity at high compression and high temperatures: MGO as an example , 1992 .

[59]  T. Jordan,et al.  Stochastic analysis of mantle convection experiments using two‐point correlation functions , 1994 .

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

[61]  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.

[62]  T. Spohn,et al.  Cooling of the Earth, Urey ratios, and the problem of potassium in the core , 1993 .

[63]  M. Richards,et al.  A Detailed Map of the 660-Kilometer Discontinuity Beneath the Izu-Bonin Subduction Zone , 1993, Science.

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

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

[66]  G. Houseman.  The dependence of convection planform on mode of heating , 1988, Nature.

[67]  B. Hager,et al.  Long-wavelength variations in Earth’s geoid: physical models and dynamical implications , 1989, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[68]  G. Schubert,et al.  Numerical models of thermally and mechanically coupled two-layer convection of highly viscous fluids , 1988 .

[69]  T. Jordan,et al.  Comparisons Between Seismic Earth Structures and Mantle Flow Models Based on Radial Correlation Functions , 1993, Science.

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

[71]  D. L. Anderson,et al.  The effect of post Pangea subduction on global mantle tomography and convection , 1992 .

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

[73]  G. Schubert,et al.  Mantle circulation and the lateral migration of subducted slabs , 1986 .

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

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

[76]  T. Ahrens,et al.  Thermal expansion of mantle and core materials at very high pressures , 1993 .

[77]  W. Peltier,et al.  Lateral heterogeneity in the convecting mantle , 1986 .

[78]  S. Honda,et al.  Multiple phase transitions and the style of mantle convection , 1992 .

[79]  G. Schubert,et al.  Chaotic, subduction-like downflows in a spherical model of convection in the Earth's mantle , 1990, Nature.

[80]  S. Honda,et al.  Development of Diapiric Structures in the Upper Mantle Due to Phase Transitions , 1991, Science.

[81]  S. Zhong,et al.  Generation of Long Wavelength Heterogeneity in the Mantle by the Dynamic Interaction Between Plates and Convection (Paper 91GL00823) 581 , 1991 .

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

[83]  D. L. Anderson.  Hotspots, polar wander, Mesozoic convection and the geoid , 1982, Nature.

[84]  P. Olson,et al.  Three‐Dimensional Convection Planforms With Internal Heat Generation , 1990 .

[85]  G. Schubert,et al.  On the penetration of the 660 km phase change by mantle downflows , 1993 .

[86]  D. Yuen,et al.  The effects of multiple phase transitions on Venusian mantle convection , 1992 .

[87]  Shijie Zhong,et al.  Dynamic feedback between a continentlike raft and thermal convection , 1993 .

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

[89]  D. Yuen,et al.  Internal heating and thermal constraints on the mantle , 1989 .

[90]  G. Schubert,et al.  Three‐dimensional spherical models of layered and whole mantle convection , 1993 .

[91]  A. E. Ringwood,et al.  Phase Transformations and Differentiation in Subducted Lithosphere: Implications for Mantle Dynamics, Basalt Petrogenesis, and Crustal Evolution , 1982, The Journal of Geology.

[92]  D. L. Anderson,et al.  Measurement of mantle wave velocities and inversion for lateral heterogeneity and anisotropy: 1. Analysis of Great Circle Phase Velocities , 1983 .

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

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

[95]  S. Weinstein.  Catastrophic overturn of the Earth's mantle driven by multiple phase changes and internal heat generation , 1993 .

[96]  A. Navrotsky,et al.  Negative Pressure-Temperature Slopes for Reactions Formign MgSiO3 Perovskite from Calorimetry , 1990, Science.

[97]  Gary A. Glatzmaier,et al.  Mantle dynamics in Mars and Venus: Influence of an immobile lithosphere on three-dimensional mantle convection , 1990 .

[98]  G. Davies,et al.  Mantle convection model with a dynamic plate: topography, heat flow and gravity anomalies , 1989 .

[99]  S. Karato,et al.  Importance of anelasticity in the interpretation of seismic tomography , 1993 .

[100]  Michael Gurnis,et al.  Large-scale mantle convection and the aggregation and dispersal of supercontinents , 1988, Nature.

[101]  M. Osako,et al.  Thermal diffusivity of MgSiO3 perovskite , 1991 .

[102]  P. Richards,et al.  Borovoye Geophysical Observatory, Kazakhstan , 1992 .

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

[104]  Olafur Gudmundsson,et al.  Spectra of mantle shear wave velocity structure , 1992 .

[105]  Guust Nolet,et al.  Tomographic imaging of subducted lithosphere below northwest Pacific island arcs , 1991, Nature.

[106]  S. Balachandar,et al.  Various influences on three-dimensional mantle convection with phase transitions , 1994 .

[107]  G. Schubert,et al.  Plume formation in the D″-layer and the roughness of the core–mantle boundary , 1987, Nature.

[108]  Toshiro Tanimoto,et al.  Predominance of Large-Scale Heterogeneity and the Shift of Velocity Anomalies between the Upper and Lower Mantle , 1990 .

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

[110]  T. Jordan,et al.  Slab penetration into the lower mantle , 1984 .

[111]  S. Karato,et al.  Diffusion Creep in Perovskite: Implications for the Rheology of the Lower Mantle , 1992, Science.