A mantle convection model to fit in with the surface observations

Abstract

Based on fundamental equations governing thermal convection and taking features of mantle convection, especially self-gravitation and the non-linear effects of advective heat transportation, into account, this paper presents an appropriate numerical simulation method for solving mantle convection problems in which the observed long wavelength geopotential anomalies and the surface velocity field up to degree 8 are taken as the restrictions. The mantle is assumed to behave dynamically as a self-gravitating, incompressible Newtonian viscous fluid shell with spherically symmetric viscosity structure (a value of 10 21 Pas in the upper mantle and 10 22 Pas in the lower mantle). The PREM Earth model is used as a reference hydrostatic model. Using the technique developed by Backus, the momentum, energy, continuity and Poisson equations are simultaneously converted to a set of non-linear ordinary equations which are solved by means of the Born approximation and the multi-point shooting method. The calculated patterns of the horizontal divergence of the surface velocity field and long wavelength geoid have a good fit to observed patterns, verifying the accuracy of the applied method. The predicted dynamic topography at the Earth's surface up to degree 8 displays the characteristic that most parts of the ocean regions show a downwelling, while the continental regions are elevated. The degree correlation coefficients between observed and predicted surface topography up to degree 8 are calculated, and good correlations are revealed in degrees 2 and 3. The dynamic topography generated at the core-mantle boundary is also calculated, and this shows a different pattern from the surface topography. Non-adiabatic temperature anomalies in the upper and lower mantles are correlated with seismic velocity anomalies obtained by tomography. A complicated flow pattern appears, which characterizes high Rayleigh number convection.