Skip to main content
/v1/supplement/title
  • Article
  • Published:

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

Abstract

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.

References

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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

  • 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.

    Chapter  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • 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.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mamoru Kato.

Rights and permissions

Reprints and permissions

About this article

Check for updates. 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). https://doi.org/10.1186/BF03352199

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1186/BF03352199

Keywords