地幔对流的数值模拟及其与表面观测的关系

THE NUMERICAL MODELLING OF MANTLE CONVECTION AND ITS RELATIONSHIP TO SURFACE OBSERVATIONS

本文从基本的热对流方程出发,并结合地幔对流特点,特别考虑到自重及非线性影响,探讨地幔对流及其与表面观测的关系,发展了相应的数值方法.结果表明,计算得到的长波大地水准面、地表地形、板块速度场水平散度与观测值符合程度较好.上、下地幔的非绝热温度异常与由地震层析得到的地震波速异常显示一定的相关性.地幔内部的流动呈现复杂形态,反映了高瑞利数对流的特征.

Based on fundamental equations governing thermal convection and taking features of man-the convection, especially self-gravitation and non-linear effect of advective thermal transportation into account, this paper presents a appropriate numerical simulation method to solve mantle convection problem in which the observed long wavelength geopotencial anomalies and surface velocity field up to 8 degree is taken as the restictions. The mantle is assumed to behave dynamically as a self-gravitating, incompressible Newtonian viscous fluid shell with sphericaly symmetric viscosity structure, a value of 1021 Pa.s in the upper mantle and 1022 Pa.s in the lower mantle. The PREM Earth model is used as a reference hydrostatic model. The calculated patterns of the horizontal divergence of the surface velocity field and long wavelength geoid have a good fit to observed ones, verifying the accuracy of the applied method. The calculated dynamic topography at the Earth's surface for degree 2-8 displayed a characterization that most part of ocean region showed a downwelling while the continental region is elevated. The degree correlations between observed and predicted surface topography up to 8 degree are calculated and showed a good correlation, especially in degree 2 and 3. Non-adia-batic temperature anomalies in upper and lower mantle are correlated with seismic velocity anomalies obtained by tomography. A complicated flow pattern appeared, which characterized high Rayleigh number convection.