Skip to main content


Numerical models of convection in a rheologically stratified oceanic upper mantle: Early results

Article metrics

  • 184 Accesses


Recent seismological evidences imply that the boundary between the lithosphere and asthenosphere is a compositional boundary in the oceanic upper mantle, and a rapid increase of viscosity at this boundary is suggested. We modeled a thermal convection in the oceanic mantle numerically using the finite element method, and investigated geodynamical consequences of such a rheological layering. Early results from both quasi-steady state flows and time-dependent flows are presented in this report. We assumed a temperature- and depth-dependent viscosity law so that both the thermal effects and those of layering are taken into account. The effect of a high-viscosity layer (HVL) is small on the flow and the temperature field. Velocity gradients in the HVL are small in both directions, and the velocity field is well approximated by a one-dimensional channel flow. The HVL acts as a low-pass filter of the dynamic topography.


  1. Chen, Y. and J. W. Morgan, A non-linear rheology model for mid-ocean ridge axis topography, J. Geophys. Res., 95, 17583–17604, 1990.

  2. Christensen, U. R., Convection with pressure- and temperature-dependent non-Newtonian rheology, Geophys. J. R. Astr. Soc., 77, 343–384, 1984.

  3. Forte, A. M., R. L. Woodward, and A. M. Dziewonski, Joint inversion of seismic and geodynamical data for models of three-dimensional mantle heterogeneity, J. Geophys. Res., 99, 21857–21977, 1994.

  4. Gaherty, J. B., T. H. Jordan, and L. S. Gee, Depth extent of polarization anisotropy in western Pacific upper mantle, J. Geophys. Res., 101, 22291–22309, 1996.

  5. Gaherty, J. B., M. Kato, and T. H. Jordan, Seismological structure of the upper mantle: a regional comparison of seismic layering, Phys. Earth Planet. Sci., 1998 (in press).

  6. Gurnis, M. and B. H. Hager, Controls on the structure of subducting slabs, Nature, 355, 317–321, 1988.

  7. Hirth, G. and D. L. Kohlstedt, Water in the oceanic upper mantle: Implication for rheology, melt extraction, and the evolution of the lithosphere, Earth Planet. Sci. Lett., 144, 93–108, 1996.

  8. Karato, S.-I., Does partial melting reduce the creep strength of the upper mantle?, Nature, 319, 309–310, 1986.

  9. Karato, S.-I., Seismic anisotropy: mechanisms and tectonic implication, in Rheology of the Solid and of the Earth, edited by S.-I. Karato and M. Toriumi, pp. 393–422, Oxford University Press, Oxford, 1989.

  10. Karato, S.-I., Effect of water on seismic wave velocities in the upper mantle, Proc. Japan Academy, 71, Ser. B, 61–66, 1995.

  11. Karato, S.-I. and P. Wu, Rheology of the upper mantle: a synthesis, Science, 260, 771–778, 1993.

  12. Kato, M., An analysis of temperature derivative of shear-wave velocity in oceanic lithosphere in the Pacific basin, J. Phys. Earth, 45, 67–71, 1997.

  13. Kato, M. and T. H. Jordan, Seismic structure of the upper mantle beneath the western Philippine Sea, Phys. Earth Planet. Int., 1998 (in press).

  14. Katzman, R., L. Zhao, and T. H. Jordan, High-resolution, two-dimensional vertical tomography of the central Pacific mantle using ScS reverberations and frequency-dependent travel times, J. Geophys. Res., 103, 17933–17971, 1998.

  15. Kido, M. and T. Seno, Dynamic topography compared with residual depth anomalies in oceans and implication for age-depth curve, Geophys. Res. Lett., 21, 717–720, 1994.

  16. Kincaid, C., The dynamic interaction between tectosphere and large scale mantle’s convection, EOS Trans. AGU, 71, 1626, 1990.

  17. King, S. D., The interaction of subducting slab and the 670 km discontinuity, Ph.D. Thesis, Calif. Inst. Tech., Pasadena, 1990.

  18. King, S. D. and B. H. Hager, The relationship between plate velocity and trench viscosity in Newtonian and power-law subduction calculations, Geophys. Res. Lett., 17, 2409–2412, 1990.

  19. King, S. D., A. Raefsky, and B. H. Hager, Conman: Vectorizing a finite element code for incompressive two-dimensional convection in the earth’s mantle, Phys. Earth Planet. Sci., 59, 196–208, 1990.

  20. King, S. D., C. W. Gable, and S. A. Weinstein, Models of convection-driven tectonic plates: a comparison of models and results, Geophys. J. Int., 109, 481–487, 1992.

  21. McKenzie, D. P., J. M. Roberts, and N. O. Weiss, Convection in the earth’s mantle: towards a numerical simulation, J. Fluid. Mech., 62, 465–538, 1974.

  22. McNutt, M. K., Marine geodynamics: Depth-age revisited, Rev. Geophys., Suppl., 413–418, 1995.

  23. McNutt, M. K. and K. M. Fischer, The South Pacific superswell, in Seamounts, Islands, and Atolls, edited by B. H. Keating, P. Fryer, R. Batiza, and G. W. Boehlert, pp. 25–34, Am. Geophys. Un., Washington, 1987.

  24. McNutt, M. K. and A. V. Judge, The superswell and mantle dynamics be-neath the south Pacific, Science, 248, 969–975, 1990.

  25. Montagner, J.-P. and T. Tanimoto, Global upper mantle tomography of seismic velocity and anisotropy, J. Geophys. Res., 96, 20337–20351, 1991.

  26. Park, C.-H., K. Tamaki, and K. Kobayashi, Age-depth correlation of the Philippine Sea back-arc basins and other marginal basins in the world, Tectonophys., 181, 351–371, 1990.

  27. Parsons, B. and J. G. Sclater, An analysis of the variation of the ocean floor bathymetry and heat flow with age, J. Geophys. Res., 82, 803–827, 1977.

  28. Ribe, N. M., On the relation between seismic anisotropy and mantle flow, J. Geophys. Res., 94, 4213–4223, 1989.

  29. Richards, M. A. and B. H. Hager, Geoid anomalies in a dynamic Earth, J. Geophys. Res., 89, 5987–6002, 1984.

  30. Richter, F. M. and B. Parsons, On the interaction of two scales of convection in the mantle, J. Geophys. Res., 80, 2529–2541, 1975.

  31. Ringwood, A. E., Composition and petrology of the Earth’s mantle, 604 pp., McGraw-Hill, New York, 1975.

  32. Shapiro, S. S., B. H. Hager, and T. H. Jordan, Stability of the continental tectosphere, EOS Trans. AGU, 72, 267, 1991.

  33. Stein, C. and S. Stein, A model for the global variation in oceanic depth and heat flow with lithospheric age, Nature, 359, 123–129, 1992.

  34. Tommasi, A., A. Vauchez, and R. Russo, Seismic anisotropy in ocean basins: Resistive drag of sublithospheric mantle?, Geophys. Res. Lett., 23, 2991–2994, 1996.

  35. Turcotte, D. L. and G. Schubert, Geodynamics: Applications of Continuum Physics to Geological Problems, 450 pp., John Wiley and Sons, New York, 1982.

  36. Weinstein, S. A. and P. L. Olson, Thermal convection with non-Newtonian plates, Geophys. J. Int., 111, 515–530, 1992.

  37. Wessel, P. and W. H. F. Smith, Free software helps map and display data, EOS Trans. AGU, 72, 441, 445–446, 1991.

  38. Zhang, S. and S.-I. Karato, Lattice preferred orientation of olivine in simple shear deformation and the flow geometry of the upper mantle of the Earth, Nature, 375, 774–777, 1995.

  39. Zhong, S., M. Gurnis, and G. Hulbert, Accurate determination of surface normal stress in viscous flow from a consistent boundary flux model, Phys. Earth Planet. Sci., 78, 1–8, 1993.

Download references

Author information

Correspondence to Mamoru Kato.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kato, M. Numerical models of convection in a rheologically stratified oceanic upper mantle: Early results. Earth Planet Sp 50, 1047–1054 (1998) doi:10.1186/BF03352199

Download citation


  • Rayleigh Number
  • Asthenosphere
  • Quasi Steady State
  • Seismic Anisotropy
  • Uppermost Mantle