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Numerical simulation for the prediction of the plate motions: Effects of lateral viscosity variations in the lithosphere
Earth, Planets and Space volume 53, pages709–721(2001)
A numerical simulation of Newtonian viscous flow without inertia terms in a 3-D spherical shell driven by the negative buoyancy due to the slabs has been conducted to understand the effects of weak plate margins on the plate motions. Density loads are inferred from the seismicity and the reconstruction of the subduction history. The toroidal energy of plate motion comparable to the poloidal energy appears, when γ (ratio of the viscosity at margins to that of interiors) becomes O(0.01). For the whole mantle density model, all the plates move too fast relative to the Pacific plate. The direction of major plate motions is generally improved by the inclusion of weak plate boundaries. The density loads in the upper mantle appear to explain the overall plate motions, although some of the plate motions may require hidden and/or deeper density anomalies to be consistent with the observations. As γ decreases, the geoid anomalies associated with the upper mantle slabs change their signs. This reversal affects the long-wavelength components of the geoid anomalies. A considerable part of the horizontal stress field shows a horizontal extension suggesting that another type of density anomalies is necessary to explain the general compressional field of the real Earth.
Argus, D. F. and R. G. Gordon, No-net-rotation model of current plate velocities incorporating plate motion model NUVEL-1, Geophys. Res. Lett., 18, 2039–2042, 1991.
Bai, W., C. Vigny, Y. Ricard, and C. Froidevaux, On the origin of deviatoric stresses in the lithosphere, J. Geophys. Res., 97, 11729–11737, 1992.
Christensen, U. and H. Harder, 3-D convection with variable viscosity, Geophys. J. Int., 104, 213–226, 1991.
Corrieu, V., C. Thoraval, and Y. Ricard, Mantle dynamics and geoid Green functions, Geophys. J. Int., 120, 516–523, 1995.
Forsyth, D. W. and S. Uyeda, On the relative importance of the driving force of plate motion, Geophys. J. R. Astron. Soc., 43, 163–200, 1975.
Gordon, R. J. and D. M. Jurdy, Cenozoic global plate motions, J. Geophys. Res., 91, 12389–12406, 1986.
Gurnis, M., J. X. Mitrovica, J. Ritsema, and H.-J. van Heijst, Constraining mantle density structure using geological evidence of surface uplift rates: The case of the African superplume, Geochemist. Geophys. Geosyst., 1, 1999GC000035, 2000.
Hager, B. H., Oceanic plate motions driven by lithospheric thickening and subducted slabs, Nature, 276, 541–545, 1978.
Hager, B. H., Subducted slabs and the geoid: Constraints on mantle rheology and flow, J. Geophys. Res., 89, 6003–6015, 1984.
Hager, B. H. and R. W. Clayton, Constraints on the structure of mantle convection using seismic observations, flow models and the geoid, in Mantle Convection: Plate Tectonics and Global Dynamics, edited by W. R. Peltier, The fluid mechanics of astrophysics and geophysics 4, pp. 657–763, Gordon and Breach Science Publishers, New York, 1989.
Hager, B. H. and R. J. O’Connell, Subduction zone dip angles and flow driven by plate motion, Tectonophys., 50, 111–133, 1978.
Hager, B. H. and R. J. O’Connell, A simple global model of plate dynamics and mantle convection, J. Geophys. Res., 86, 4843–4867, 1981.
Hager, B. H., R. W. Clayton, M. A. Richards, R. P. Comer, and A. M. Dziewonski, Lower mantle heterogeneity, dynamic topography and the geoid, Nature, 313, 541–545, 1985.
Iwase, Y., Three-dimensional infinite Prandtl number convection in a spherical shell with temperature-dependent viscosity, J. Geomag. Geoelector., 48, 1499–1514, 1996.
Karato, S.-I. and P. Wu, Rheology of the upper mantle: A synthesis, Science, 260, 771–778, 1993.
Lerch, F. J. and 19 others, A geopotential model from satellite tracking, altimeter and surface gravity data: GEM-T3, J. Geophys. Res., 99, 2815–2839, 1994.
Moresi, L. and M. Gurnis, Constraints on the lateral strength of slabs from three-dimensional dynamic flow models, Earth Planet. Sci. Lett., 138, 15–28, 1996.
Ricard, Y. and C. Vigny, Mantle dynamics with induced plate tectonics, J. Geophys. Res., 94, 17543–17559, 1989.
Ricard, Y., M. A. Richards, C. Lithgow-Bertelloni, and Y. L. Stunff, A geodynamics model of mantle density heterogeneity, J. Geophys. Res., 98, 21895–21909, 1993.
Richards, M. A. and B. H. Hager, Effects of lateral viscosity variations on long-wavelength geoid anomalies and topography, J. Geophys. Res., 94, 10299–10313, 1989.
Richardson, R. M., Ridge forces, absolute plate motions, and the intraplate stress field, J. Geophys. Res., 97, 11739–11748, 1992.
Tackley, P. J., Three-dimensional simulations of mantle convection with a thermo-chemical basal boundary layer: D”?, in The Core-Mantle Boundary Region, edited by M. Gurnis, M. E. Wysession, E. Knittle, and B. A. Buffett, Geodynamics series 28, pp. 231–253, American Geophysical Union, Washington, D.C., 1998.
Turcotte, D. L. and G. Schubert, Geodynamics: Applications of Continuum Physics to Geological Problems, pp. 450, John Wiley and Sons, New York, 1982.
Wen, L. and D. L. Anderson, Present-day plate motion constraint on mantle rheology and convection, J. Geophys. Res., 102, 24639–24653, 1997.
Zhang, S. and U. Christensen, Some effects of lateral viscosity variations on geoid and surface velocities induced by density anomalies in the mantle, Geophys. J. Int., 114, 531–547, 1993.
Zhong, S. and G. F. Davies, Effects of plate and slab viscosities on the geoid, Earth Planet. Sci. Lett., 170, 487–496, 1999.
Zhong, S. and M. Gurnis, Interaction of weak faults and non-Newtonian rheology produces plate tectonics in a 3D model of mantle flow, Nature, 383, 245–247, 1996.
Zhong, S., M. Gurnis, and L. Moresi, Role of faults, nonlinear rheology, and viscosity structure in generating plates from instantaneous mantle flow models, J. Geophys. Res., 103, 15255–15268, 1998.
Zoback, M. L., First- and second-order patterns of stress in the lithosphere: The world stress map project, J. Geophys. Res., 97, 11703–11728, 1992.
Zoback, M. L., and 27 others, Global patterns of tectonic stress, Nature, 341, 291–298, 1989.
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Yoshida, M., Honda, S., Kido, M. et al. Numerical simulation for the prediction of the plate motions: Effects of lateral viscosity variations in the lithosphere. Earth Planet Sp 53, 709–721 (2001) doi:10.1186/BF03352399
- Root Mean Square
- Plate Motion
- Lower Mantle
- Mantle Convection
- Plate Margin