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Mantle Dynamics – A Case Study

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Advances in Geocomputing

Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 119))

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Abstract

Solid state convection in the rocky mantles is a key to understanding the thermochemical evolution and tectonics of terrestrial planets and moons. It is driven by internal heat and can be described by a system of coupled partial differential equations. There are no analytic solutions for realistic configurations and numerical models are an indispensable tool for researching mantle convection. After a brief general introduction, we introduce the basic equations that govern mantle convection and discuss some common approximations. The following case study is a contribution towards a self-consistent thermochemical evolution model of the Earth. A crude approximation for crustal differentiation is coupled to numerical models of global mantle convection, focussing on geometrical effects and the influence of rheology on stirring. We review Earth-specific geochemical and geophysical constraints, proposals for their reconciliation, and discuss the implications of our models for scenarios of the Earth’s evolution. Specific aspects of this study include the use of passive Lagrangian tracers, highly variable viscosity in 3-d spherical geometry, phase boundaries in the mantle and a parameterised model of the core as boundary condition at the bottom of the mantle.

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References

  • Albarède F (2001) Radiogenic in growth in systems with multiple reservoirs: applications to the differentiation of the mantle-crust system. Earth and Planetary Science Letters 189: 59–73

    Article  Google Scholar 

  • Albarède F, van der Hilst RD (2002) Zoned mantle convection. Philosophical Transactions of the Royal Society of London: A 360: 2569–2592

    Google Scholar 

  • Allègre CJ (2002) The evolution of mantle mixing. Philosophical Transactions: Mathematical, Physical and Engineering Sciences 360(1800): 2411–2431

    Article  Google Scholar 

  • Allègre CJ, Hamelin B, Provost A, Dupre B (1987) Topology in isotopic multispace and origin of mantle chemical heterogeneities. Earth and Planetary Science Letters 81(4): 319–337

    Article  Google Scholar 

  • Allègre CJ, Hofmann AW, O’Nions K (1996) The argon constraints on mantle structure. Geophysical Research Letters 23: 3555–3557

    Article  Google Scholar 

  • Allègre CJ, Turcotte DL (1986) Implications of a two-component marble-cake mantle. Nature 323: 123–127

    Article  Google Scholar 

  • Anderson OL (1998) The Grüneisen parameter for iron at outer core conditions and the resulting conductive heat and power in the core. Physics of the Earth and Planetary Interiors 109: 179–197

    Article  Google Scholar 

  • Andreasen R, Sharma M (2006) Solar nebula heterogeneity in p-process Samarium and Neodymium isotopes. Science 314(5800): 806–809

    Article  Google Scholar 

  • Arndt NT (2004) The Precambrian Earth: Tempos and events. In: Eriksson PG, Altermann W, Nelson DR, Mueller WU, Catuneanu O Developments in Precambrian Geology, 12, Elsevier, 155–158

    Google Scholar 

  • Arrhenius G, Lepland A (2000) Accretion of Moon and Earth and the emergence of life. Chemical Geology 169: 69–82

    Article  Google Scholar 

  • Ballentine CJ, van Keken P, Porcelli D, Hauri EH (2002) Numerical models, geochemistry and the zero-paradox noble-gas mantle. Philosophical Transactions of the Royal Society of London: A 360: 2611–2631

    Google Scholar 

  • Baumgardner JR (1983) A three-dimensional finite element model for mantle convection, Los Angeles: University of California

    Google Scholar 

  • Baumgardner JR, Frederickson PO (1985) Icosahedral discretization of the 2-sphere. Siam Journal on Numerical Analysis 22(6): 1107–1115

    Article  Google Scholar 

  • Becker TW, Kellogg JB, O’Connell RJ (1999) Thermal constraints on the survival of primitive blobs in the lower mantle. Earth and Planetary Science Letters 171: 351–365

    Article  Google Scholar 

  • Bercovici D, Karato S-I (2003) Whole-mantle convection and the transition-zone water filter. Nature 425: 39–44

    Article  Google Scholar 

  • Boehler R (2000) High-pressure experiments and the phase diagram of lower mantle and core materials. Reviews of Geophysics 38(2): 221–245

    Article  Google Scholar 

  • Boyet M, Carlson RW (2005) 142Nd evidence for early (>4.53 Ga) global differentiation of the silicate Earth. Science 309: 576–581

    Article  Google Scholar 

  • Breuer D, Spohn T (1995) Possible flush instability in mantle convection at the Archaean–Proterozoic transition. Nature 378: 608–610

    Article  Google Scholar 

  • Bunge H-P, Baumgardner JR (1995) Mantle convection modeling on parallel virtual machines. Computers in Physics 9(2): 207–215

    Article  Google Scholar 

  • Bunge H-P, Richards MA, Baumgardner JR (1997) A sensitivity study of threedimensional spherical mantle convection at 108 Rayleigh number: effects of depth-dependent viscosity, heating mode, and an endothermic phase change. Journal of Geophysical Research 102(B6): 11991–12007

    Article  Google Scholar 

  • Campbell IH (1998) The Earth’s Mantle: Composition, structure and evolution. In: Jackson I, Cambridge University Press, Cambridge, 259–310

    Google Scholar 

  • Canup RM (2004) Simulations of a late lunar-forming impact. Icarus 168(2): 433–456

    Article  Google Scholar 

  • Carlson RW, Boyet M, Horan M (2007) Chondrite Barium, Neodymium, and Samarium isotopic heterogeneity and early Earth differentiation. Science 316(5828): 1175–1178

    Article  Google Scholar 

  • Coltice N, Ricard Y (2002) On the origin of noble gases in mantle plumes. Philosophical Transactions of the Royal Society of London: A 360: 2633–2648

    Google Scholar 

  • Condie KC (1997) Plate Tectonics and Crustal Evolution. Butterworth-Heinemann

    Google Scholar 

  • Davaille A (1999) Simultaneous generation of hotspots and superswells by convection in a heterogeneous planetary mantle. Nature 402: 756–760

    Article  Google Scholar 

  • Davies GF (2005) A case for mantle plumes. Chinese Science Bulletin 50(1): 1–14

    Article  Google Scholar 

  • DeVolder B, Glimm J, Grove J, Kang Y, Lee Y, Pao K, Sharp DH, Ye K (2002) Uncertainty quantification for multiscale simulations. Journal of Fluids and Engineering 124: 29–41

    Article  Google Scholar 

  • Dixon JE, Dixon TH, Bell DR, Malservisi R (2004) Lateral variation in upper mantle viscosity: role of water. Earth and Planetary Science Letters 222(2): 451–467

    Article  Google Scholar 

  • Dziewonski AM, Anderson DL (1981) Preliminary reference Earth model. Physics of the Earth and Planetary Interiors 25: 297–356

    Article  Google Scholar 

  • Elkins-Tanton LT, Parmentier EM, Hess PC (2003) Magma ocean fractional crystallization and cumulate overturn in terrestrial planets: Implications for Mars. Meteoritics and Planetary Science 38(12): 1711–1875

    Article  Google Scholar 

  • Ferrachat S, Ricard Y (2001) Mixing properties in the Earth’s mantle: Effects of the viscosity stratification and of oceanic crust segregation. Geochemistry

    Google Scholar 

  • Glatzmaier GA (1988) Numerical simulations of mantle convection: Timedependent, three-dimensional, compressible, spherical shell. Geophysical and Astrophysical Fluid Dynamics 43: 223–264

    Article  Google Scholar 

  • Gonnermann HM, Mukhopadhyay S (2007) Non-equilibrium degassing and a primordial source for helium in ocean-island volcanism. Nature 449: 1037–1040

    Article  Google Scholar 

  • Gordon RG, Jurdy DM (1986) Cenozoic global plate motions. Journal of Geophysical Research 91: 12389–12406

    Article  Google Scholar 

  • Gottschaldt K-D (2003) Vermischung in 3D sphärischen Konvektionsmodellen des Erdmantels, Jena: Friedrich-Schiller-Universität

    Google Scholar 

  • Gottschaldt K-D, Walzer U, Hendel RF, Stegman DR, Baumgardner JR, Mühlhaus H-B (2006) Stirring in 3-d spherical models of convection in the Earth’s mantle. Philosophical Magazine 86(21–22): 3175–3204

    Article  Google Scholar 

  • Grand SP, van der Hilst RD, Widiyantoro S (1997) Global seismic tomography: a snapshot of convection in the Earth. GSA Today 7: 1–7

    Google Scholar 

  • Hanan BB, Blichert-Toft J, Pyle DG, Christie DM (2004) Contrasting origins of the upper mantle revealed by hafnium and lead isotopes from the Southeast Indian Ridge. Nature 432: 91–94

    Article  Google Scholar 

  • Hart S (1984) A large-scale isotope anomaly in the southern hemisphere mantle. Nature 309: 753–757

    Article  Google Scholar 

  • Helffrich GR, Wood BJ (2001) The Earth’s mantle. Nature 412: 501–507

    Article  Google Scholar 

  • Hirose K (2002) Phase transitions in pyrolitic mantle around 670 km depth: Implications for upwelling of plumes from the lower mantle. Journal of Geophysical Research 107(B4): 2078, doi:10.1029/2001JB000597

    Article  Google Scholar 

  • Hirose K (2006) Postperovskite phase transition and its geophysical implications. Reviews of Geophysics 44(2005RG000186): RG3001

    Article  Google Scholar 

  • Hirth G, Kohlstedt DL (1996) Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere. Earth and Planetary Science Letters 144: 93–108

    Article  Google Scholar 

  • Hofmann AW (1988) Chemical differentiation of the earth – The relationship between mantle, continental crust, and oceanic crust. Earth and Planetary Science Letters 90(3): 297–314

    Article  Google Scholar 

  • Hofmann AW (1997) Mantle geochemistry: the message from oceanic volcanism. Nature 385: 219–229

    Article  Google Scholar 

  • Holland G, Ballentine CJ (2006) Seawater subduction controls the heavy noble gas composition of the mantle. Nature 441: 186–191

    Article  Google Scholar 

  • Karato S-I, Riedel MR, Yuen DA (2001) Rheological structure and deformation of subducted slabs in the mantle transition zone: implications for mantle circulation and deep earthquakes. Physics of the Earth and Planetary Interiors 127: 83–108 Geophysics Geosystems 2: 1013, doi: 10.1029/2000GC000092

    Article  Google Scholar 

  • Kellogg JB, Jacobsen SB, O’Connell RJ (2002) Modeling the distribution of isotopic ratios in geochemical reservoirs. Earth and Planetary Science Letters 204: 183–202

    Article  Google Scholar 

  • Kellogg LH, Hager BH, van der Hilst RD (1999) Compositional stratification in the deep mantle. Science 283: 1881–1884

    Article  Google Scholar 

  • Kleine T, Mezger K, Palme H, Münker C (2004) The W isotope evolution of the bulk silicate Earth: constraints on the timing and mechanisms of core formation and accretion. Earth and Planetary Science Letters 228(1–2): 109–123

    Article  Google Scholar 

  • Labrosse S (2003) Thermal and magnetic evolution of the Earth’s core. Physics of the Earth and Planetary Interiors 140(1): 127–143

    Article  Google Scholar 

  • Labrosse S, Hernlund JW, Coltice N (2007) A crystallizing dense magma ocean at the base of the Earth’s mantle. Nature 450: 866–869

    Article  Google Scholar 

  • Manga M (1996) Mixing of heterogeneities in the mantle: Effect of viscosity differences. Geophysical Research Letters 23(4): 403–406

    Article  Google Scholar 

  • McNamara AK, Zhong SJ (2004) Thermochemical structures within a spherical mantle: Superplumes or piles? Journal of Geophysical Research 109: B07402

    Article  Google Scholar 

  • Meibom A, Anderson DL (2003) The statistical upper mantle assemblage. Earth and Planetary Science Letters 217: 123–139

    Article  Google Scholar 

  • Monnereau M, Yuen D (2007) Topology of the postperovskite phase transition and mantle dynamics. Proceedings of the National Academy of Sciences 104:9156–9161, doi:10.1073/pnas.0608480104

    Article  Google Scholar 

  • Monnereau M, Yuen D (2007) Topology of the postperovskite phase transition and mantle dynamics. PNAS

    Google Scholar 

  • Montelli R, Nolet G, Dahlen FA, Masters G, Engdahl ER, Hung S-H (2004) Finite- frequency tomography reveals a variety of plumes in the mantle. Science 303: 338–343

    Article  Google Scholar 

  • Nakagawa T, Tackley PJ (2004) Effects of a perovskite-post perovskite phase change near core-mantle boundary in compressible mantle convection. Geophysical Research Letters 31(L16611)

    Google Scholar 

  • Nolet G, Karato S-I, Montelli R (2006) Plume fluxes from seismic tomography. Earth and Planetary Science Letters 248: 685–699

    Article  Google Scholar 

  • O’Connell RJ, Gable CW, Hager BH (1991) Toroidal-poloidal partitioning of lithospheric plate motion. In: Sabadini K, Lambeck K, Boschi E Glacial Isostasy, Sea Level, and Mantle Rheology, Kluwer Academic Publishers, Dordrecht, 535–551

    Google Scholar 

  • O’Neill HSC, Palme H, Jackson I (1998) The Earth’s mantle: Composition, structure and evolution. Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Oldham D, Davies HW (2004) Numerical investigation of layered convection in a three-dimensional shell with application to planetary mantles. Geochemistry Geophysics Geosystems 5(12): Q12C04

    Article  Google Scholar 

  • Presnall DC, Gudfinnsson GH, Walter MJ (2002) Generation of mid-ocean ridge basalts at pressures from 1 to 7 GPa. Geochimica et Cosmochimica Acta 66(12): 2073–2090

    Article  Google Scholar 

  • Ramage A, Walthan AJ (1992) Iterative solution techniques for finite element discretizations of fluid flow problems. Copper Mountain Conference on Iterative Methods, Copper Mountain, Colorado

    Google Scholar 

  • Ranen MC, Jacobsen SB (2006) Barium isotopes in chondritic meteorites: implications for planetary reservoir models. Science 314(5800): 809–812

    Article  Google Scholar 

  • Regenauer-Lieb K, Kohl T (2003) Water solubility and diffusivity in olivine: its role in planetary tectonics. Mineralogical Magazine 67(4): 697–715

    Article  Google Scholar 

  • Ritsema J, van Heijst HJ (2000) Seismic imaging of structural heterogeneity in Earth’s mantle: evidence for large-scale mantle flow. Science Progress 83(3): 243–259

    Google Scholar 

  • Ritsema J, van Heijst HJ, Woodhouse JH (1999) Complex shear wave velocity structure imaged beneath Africa and Iceland. Science 286(5546): 1925–1928

    Article  Google Scholar 

  • Rüpke L, Phipps-Morgan J, Hort M, Connolly J, Ranero C (2003) Serpentine and the chemical evolution of the earth’s mantle. Geophysical Research Abstracts 5: 09637 See: http://www.cosis.net/abstracts/EAE03/09637/EAE03-J-09637.pdf

    Google Scholar 

  • Schubert G, Turcotte DL, Olson P (2001) Mantle convection in the Earth and Planets. Cambridge University Press, Cambridge

    Google Scholar 

  • Smolarkiewicz PK (1984) A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. Journal of Computational Physics 54(2): 325–362

    Article  Google Scholar 

  • Solomatov VS (2000) Fluid dynamics of a terrestrial magma ocean. In: Canup RM, Righter K Origin of the Earth and Moon, University of Arizona Press, Tucson, 323–338

    Google Scholar 

  • Stacey FD (1992) Physics of the Earth. Brookfield Press, Brisbane

    Google Scholar 

  • Stegman DR, Richards MA, Baumgardner JR (2002) Effects of depth-dependent viscosity and plate motions on maintaining a relatively uniform mid-ocean ridge basalt reservoir in whole mantle flow. Journal of Geophysical Research 107(B6): 10.1029/2001JB000192

    Google Scholar 

  • Su W-J, Woodward RL, Dziewonski AM (1994) Degree 12 model of shear velocity heterogeneity in the mantle. Journal of Geophysical Research 99(B4): 6945–6980

    Article  Google Scholar 

  • Tackley PJ (1996) Effects of strongly variable viscosity on three-dimensional compressible convection in planetary mantles. Journal of Geophysical Research 101(B2): 3311–3332

    Article  Google Scholar 

  • Tackley PJ (2000) Mantle convection and plate tectonics: Toward an integrated physical and chemical theory. Science 288: 2002–2007

    Article  Google Scholar 

  • Tackley PJ (2002) Strong heterogeneity caused by deep mantle layering. Geochemistry Geophysics Geosystems 3(4)

    Google Scholar 

  • Tackley PJ, Nakagawa T, Hernlund JW (2007) Post-Perovskite: The last mantle phase transition. Geophysical Monograph Series 174: 229–247

    Google Scholar 

  • Taylor SR, McLennan SM (1995) The geochemical evolution of the continental crust. Reviews of Geophysics 33(2): 241–265

    Article  Google Scholar 

  • Tolstikhin I, Hofmann AW (2005) Early crust on top of the Earth’s core. Physics of the Earth and Planetary Interiors 148: 109–130

    Article  Google Scholar 

  • Trampert J, Deschamps F, Resovsky J, Yuen D (2004) Probabilistic tomography maps chemical heterogeneities throughout the lower mantle. Science 306: 853–856

    Article  Google Scholar 

  • Trendall AF (2002) Precambrian sedimentary environments: A modern approach to depositional systems. In: Altermann W, Corcoran PL IAS spec. publ., 44, Blackwell, 33–66

    Google Scholar 

  • Turcotte DL, Schubert G (2002) Geodynamics. Cambridge University Press, Cambridge

    Google Scholar 

  • van der Hilst RD (2004) Changing views on Earth’s deep mantle. Science 306(5697): 817–818

    Article  Google Scholar 

  • van der Hilst RD, Widiyantoro S, Engdahl ER (1997) Evidence for deep mantle circulation from global tomography. Nature 386: 578–584

    Article  Google Scholar 

  • van Keken P, Ballentine CJ, Porcelli D (2001) A dynamical investigation of the heat and helium imbalance. Earth and Planetary Science Letters 171: 533–547

    Article  Google Scholar 

  • van Keken P, Zhong SJ (1999) Mixing in a 3D spherical model of present-day mantle convection. Earth and Planetary Science Letters 171: 533–547

    Article  Google Scholar 

  • van Keken PE, Ballentine CJ (1998) Whole-mantle versus layered mantle convection and the role of a high-viscosity lower mantle in terrestrial volatile evolution. Earth and Planetary Science Letters 156(1–2): 19–32

    Google Scholar 

  • van Keken PE, King SD, Schmeling H, Christensen UR, Neumeister D, Doin MP (1997) A comparison of methods for the modeling of thermochemical convection. Journal of Geophysical Research 102(B10): 22477–22495

    Article  Google Scholar 

  • van Thienen P (2003) Evolving dynamical regimes during secular cooling of terrestrial planets: insights and inferences from numerical models, Universiteit Utrecht, Utrecht

    Google Scholar 

  • Walzer U, Hendel R (2008) Mantle convection and evolution of growing continents. Journal of Geophysical Research 113: B09405, doi: 10.1029/2007JB005459

    Article  Google Scholar 

  • Walzer U, Hendel RF (1999) A new convection-fractionation model for the evolution of the principal geochemical reservoirs of the Earth’s mantle. Physics of the Earth and Planetary Interiors 112: 211–256

    Article  Google Scholar 

  • Walzer U, Hendel RF, Baumgardner JR (2003) Viscosity stratification and a 3D compressible spherical shell model of mantle evolution. High Performance Computing in Science and Engineering 2003: 419–428

    Google Scholar 

  • Walzer U, Hendel RF, Baumgardner JR (2004a) The effects of a variation of the radial viscosity profile on mantle evolution. Tectonophysics 384: 55–90

    Article  Google Scholar 

  • Walzer U, Hendel RF, Baumgardner JR (2004b) Toward a thermochemical model of the evolution of the Earth’s mantle. High Performance Computing in Science and Engineering 2004: 395–454

    Google Scholar 

  • Watson EB, Thomas JB, Cherniak DJ (2007) 40Ar retention in the terrestrial planets. Nature 449: 299–304

    Article  Google Scholar 

  • Weiss D, Bassias Y, Gautier I, Mennesier J-P (1989) Dupal anomaly in existence 115 ma ago: Evidence from isotopic study of the Kerguelen plateau (South Indian Ocean). Geochimica et Cosmochimica Acta 53: 2125–2131

    Article  Google Scholar 

  • Xie S, Tackley PJ (2004) Evolution of Helium and Argon Isotopes in a convecting mantle. Physics of the Earth and Planetary Interiors 146(3–4): 417–439

    Article  Google Scholar 

  • Yang W-S (1997) Variable viscosity thermal convection at infinite Prandtl number in a thick spherical shell, University of Illinois, Urbana-Champaign

    Google Scholar 

  • Zaranek SE, Parmentier EM (2004) Convective cooling of an initially stably stratified fluid with temperature-dependent viscosity – Implications for the role of solid-state convection in planetary evolution. Journal of Geophysical Research 109(B3): B03409

    Article  Google Scholar 

  • Zerr A, Boehler R (1993) Melting of (Mg,Fe)SiO3-perovskite to 625 kilobars: Indication of a high melting temperature in the lower mantle. Science 262: 553–555

    Article  Google Scholar 

  • Zerr A, Boehler R (1994) Constraints on the melting temperature of the lower mantle from high-pressure experiments on MgO and magnesiowüstite. Nature 371: 506–508

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Queensland ESSCC, PO Box 6067, St Lucia, QLD 4067, Australia

    Klaus-D. Gottschaldt

  2. Friedrich-Schiller-Universität Jena Institut für Geowissenschaften, Burgweg 11 07749 Jena, Germany

    Uwe Walzer

  3. Earth Sciences The University of Melbourne, Victoria 3010, Australia

    Dave R. Stegman

  4. Department of Earth & Planetary Science, University of California, 307 McCone Hall, Berkeley, CA 94720-4767, USA

    John R. Baumgardner

  5. University of Queensland, ESSCC, 36067, St Lucia QLD 4067, Australia

    Hans B. Mühlhaus

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  1. Klaus-D. Gottschaldt
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  4. John R. Baumgardner
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  5. Hans B. Mühlhaus
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Gottschaldt, KD., Walzer, U., Stegman, D.R., Baumgardner, J.R., Mühlhaus, H.B. (2009). Mantle Dynamics – A Case Study. In: Advances in Geocomputing. Lecture Notes in Earth Sciences, vol 119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85879-9_5

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