Skip to main content
SpringerLink
Log in
Book cover

High Performance Computing in Science and Engineering’ 05 pp 289–304Cite as

Plateness of the Oceanic Lithosphere and the Thermal Evolution of the Earth’s Mantle

  • Conference paper

  • 707 Accesses

Summary

Compared to [33], the model of the thermal evolution of the Earth’s mantle is considerably improved. The temporal development of the radial viscosity profile due to cooling of the Earth could substantially be taken into account by numerical progress using a new variant of the temperature- and pressure-dependence of the shear viscosity of the mantle, namely Eq (5). The laterally averaged heat flow, the Urey number, the Rayleigh number and the volume-averaged temperature as a function of time come up to the expectations that stem from the parameterized evolution models. The mentioned evolution parameters of the present paper better approximate the observational data. Contrary to the parameterized curves, these quantities show temporal variations. This seems to be more realistic for geological reasons. Due to the activation enthalpy, the presented viscosity profile has a highly viscous transition layer (TL) with steep viscosity gradients at the phase boundaries. A low-viscosity zone is situated above and below the TL, each. The lithosphere moves piecewise en bloc. Thin cold sheet-like downwellings have an Earth-like distribution.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Auth, C., Bercovici, D., Christensen, U.R., 2003. Two-dimensional convection with a self-lubricating, simple-damage rheology. Geophys. J. Int. 154, 783–797.

    Article  Google Scholar 

  2. Baumgardner, J.R., 1983. A three-dimensional finite element model for mantle convection. Thesis, Univ. of California, Los Angeles.

    Google Scholar 

  3. Baumgardner, J.R., 1985. Three-dimensional treatment of convective flow in the Earth’s mantle. J. Stat. Phys. 39(5-6), 501–511.

    Article  Google Scholar 

  4. Bercovici, D., 1998. Generation of plate tectonics from lithosphere-mantle flow and void-volatile self-lubrication. Earth Planet. Sci. Lett. 154, 139–151.

    Article  Google Scholar 

  5. Bina, C.R., Stein, S., Marton, F.C., Van Ark, E.M., 2001. Implications of slab mineralogy for subduction dynamics. Phys. Earth Planet. Int. 127, 51–66.

    Article  Google Scholar 

  6. Breuer, D., 2003. Thermal evolution, crustal growth, and magnetic field history of Mars. Habilitationsschrift. Univ. Münster, 176pp.

    Google Scholar 

  7. Bunge, H.-P., Richards, M.A., Baumgardner, J.R., 1997. 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. J. Geophys. Res. 102, 11991–12007.

    Article  Google Scholar 

  8. Dziewonski, A.M., Anderson, D.L., 1981. Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297–356.

    Article  Google Scholar 

  9. Funiciello, F., Morra, G., Regenauer-Lieb, K., Giardini, D., 2003. Dynamics of retreating slabs: 1. Insights from two-dimensional numerical experiments. J. Geophys. Res. 108, no. B4, 2206, doi: 10.1029/2001JB000898

    Article  Google Scholar 

  10. Gilvarry, J.J. 1956. The Lindemann and Grüneisen laws. Phys. Rev. 102, 307–316.

    Google Scholar 

  11. Glatzmaier, G.A., 1988. Numerical simulations of mantle convection: Timedependent, three-dimensional, compressible, spherical shell. Geophys. Astrophys. Fluid Dyn. 43, 223–264.

    MATH  Google Scholar 

  12. Gordon, R.G., 2000. Diffuse oceanic plate boundaries: Strain rates, vertically averaged rheology, and comparisons with narrow plate boundaries and stable plate interiors. In: Richards, M.A., Gordon, R.G., van der Hilst, R.D. (Eds.), The History and Dynamics of Global Plate Motions. Amer. Geophys. Union, Washington, DC, pp. 143–159.

    Google Scholar 

  13. Haskell, N.A., 1935. The motion of a fluid under a surface load. 1. Physics 6, 265–269.

    Article  MATH  Google Scholar 

  14. Karato, S.-I., Riedel, M.R., Yuen, D.A., 2001. Rheological structure and deformation of subducted slabs in the mantle transition zone: implications for mantle circulation and deep earthquakes. Phys. Earth Planet. Inter. 127, 83–108.

    Article  Google Scholar 

  15. McCulloch, M.T., Bennett, V.C., 1994. Progressive growth of the Earth’s continental crust and depleted mantle: geochemical constraints. Geochim. Cosmochim. Acta 58, 4717–4738.

    Article  Google Scholar 

  16. McGovern, P.J., Schubert, G., 1989. Thermal evolution of the Earth: Effects of volatile exchange between atmosphere and interior. Earth Planet. Sci. Lett. 96, 27–37.

    Article  Google Scholar 

  17. Moresi, L.N., Solomatov, V.S., 1998. Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus. Geophys. J. Int. 133, 669–682.

    Article  Google Scholar 

  18. Morra, G., Regenauer-Lieb, K., 2004. A coupled solid-fluid method for modeling subduction. Philosophical Magazine, London, submitted.

    Google Scholar 

  19. Regenauer-Lieb, K., Yuen, D.A., 2003. Modeling shear-zones in geological and planetary science: solid-and fluid-thermal-mechanical approaches. Earth Science Reviews, submitted.

    Google Scholar 

  20. Reese, C.C., Solomatov, V.S., Moresi, L.-N., 1998. Heat transport efficiency for stagnant lid convection with dislocation viscosity: Application to Mars and Venus. J. Geophys. Res. 103, 13643–13657.

    Article  Google Scholar 

  21. Reese, C.C., Solomatov, V.S., Moresi, L.-N., 1999. Non-Newtonian stagnant lid convection and magmatic resurfacing of Venus. Icarus 139, 67–80.

    Article  Google Scholar 

  22. Richards, M.A., Yang, W.-S., Baumgardner, J.R., Bunge, H.-P., 2001. Role of a low-viscosity zone in stabilizing plate tectonics: Implications for comparative terrestrial planetology. Geochem., Geophys., Geosystems vol. 2, paper no. 2000GC000115.

    Google Scholar 

  23. Schubert, G., Cassen, P., Young, R.E., 1979. Subsolidus convective cooling histories of terrestrial planets. Icarus 38, 192–211.

    Article  Google Scholar 

  24. Schubert, G., Stevenson, D., Cassen, P., 1980. Whole planet cooling and the radiogenic heat source contents of the Earth and Moon. J. Geophys. Res. 85, 2511–2518.

    Google Scholar 

  25. Schubert, G., Turcotte, D.L., Olson, P., 2001. Mantle Convection in the Earth and Planets. Cambridge Univ. Press, Cambridge etc, 940 pp.

    Google Scholar 

  26. Solomatov, V.S., 1995. Scaling of temperature-dependent and stressdependent viscosity convection. Phys. Fluids 7, 266–274.

    Article  MATH  Google Scholar 

  27. Stacey, F.D., Stacey, C.H.B., 1999. Gravitational energy of core evolution: implications for thermal history and geodynamo power. Phys. Earth Planet. Inter. 110, 83–93.

    Article  Google Scholar 

  28. Stein, C., Schmalzl, J., Hansen, U., 2004. The effect of rheological parameters on plate behaviour in a self-consistent model of mantle convection. Phys. Earth Planet. Inter. 142, 225–255.

    Article  Google Scholar 

  29. Tackley, P.J., 2000a. Self-consistent generation of tectonic plates in timedependent, three-dimensional mantle convection simulations. 1. Pseudoplastic yielding. Geochem. Geophys. Geosyst., 1, Paper no. 2000GC000036

    Google Scholar 

  30. Tackley, P.J., 2000b. Self-consistent generation of tectonic plates in timedependent, three-dimensional mantle convection simulations. 2. Strain weakening and asthenosphere. Geochem. Geophys. Geosyst., 1, Paper no. 2000GC000043

    Google Scholar 

  31. Trompert, R.A., Hansen, U., 1998. Mantle convection simulations with rheologies that generate plate-like behavior. Nature 395, 686–689.

    Article  Google Scholar 

  32. Vashchenko, V.Ya., Zubarev, V.N., 1963. Concerning the Grüneisen constant. Soviet Phys. Solid State 5, 653–655.

    Google Scholar 

  33. Walzer, U., Hendel, R., Baumgardner, J., 2003a. Viscosity stratification and a 3-D compressible spherical shell model of mantle evolution. In: Krause, E., Jäger, W., Resch, M. (Eds.), High Performance Computing in Science and Engineering’ 03. Springer-Verlag, Berlin Heidelberg New York. pp. 27–67. ISBN 3-540-40850-9.

    Google Scholar 

  34. Walzer, U., Hendel, R., Baumgardner, J., 2003b. Generation of platetectonic behavior and a new viscosity profile of the Earth’s mantle. In Wolf, D., Münster, G., Kremer, M. (Eds.), NIC Symposium 2004. NIC Series 20, pp. 419–428. ISBN 3-00-012372-5.

    Google Scholar 

  35. Walzer, U., Hendel, R., Baumgardner, J., 2004a. The effects of a variation of the radial viscosity profile on mantle evolution. Tectonophysics, 384, 55–90.

    Article  Google Scholar 

  36. Walzer, U., Hendel, R., Baumgardner, J., 2004b. Toward a thermochemical model of the evolution of the Earth’s mantle. In: Krause, E., Jäger, W., Resch, M. (Eds.), High Performance Computing in Science and Engineering’ 04. Springer-Verlag, Berlin Heidelberg New York. pp 395–454. ISBN 3-540-22943-4

    Google Scholar 

  37. Weidner, D.J., Chen, J. Xu, Y., Wu, Y., Vaughan, M.T., Li, L., 2001. Subduction zone rheology. Phys. Earth Planet. Inter. 127, 67–81.

    Article  Google Scholar 

  38. Yamazaki, D., Karato, S.-I., 2001. Some mineral physics constraints on the rheology and geothermal structure of the Earth’s lower mantle. American Mineralogist 86, 385–391.

    Google Scholar 

  39. Yang, W.-S., 1997. Variable viscosity thermal convection at infinite Prandtl number in a thick spherical shell. Thesis, Univ. of Illinois, Urbana-Champaign.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Uwe Walzer & Roland Hendel

  2. Dept. Earth Planet. Science, University of California, Berkeley, CA, 94720, USA

    John Baumgardner

Authors
  1. Uwe Walzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roland Hendel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John Baumgardner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Zentrum für Informationsdienste und Hochleistungsrechnen (ZIH), Technische Universität Dresden, Zellescher Weg 12-14, 01169, Dresden, Germany

    Wolfgang E. Nagel

  2. Höchstleistungsrechenzentrum Stuttgart (HLRS), Universität Stuttgart, Nobelstraße 19, 70569, Stuttgart, Germany

    Michael Resch

  3. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Willi Jäger

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Walzer, U., Hendel, R., Baumgardner, J. (2006). Plateness of the Oceanic Lithosphere and the Thermal Evolution of the Earth’s Mantle. In: Nagel, W.E., Resch, M., Jäger, W. (eds) High Performance Computing in Science and Engineering’ 05. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29064-8_23

Download citation

Publish with us

Policies and ethics

Search

Navigation