利用多种地球物理观测资料直接反演地幔对流模型

假定地幔为一个均匀的、粘滞系数为常数、同时均匀分布放射性热源的流体球层,其内部存在的对流则由流体力学3个基本方程:运动方程、能量方程和连续性方程确定.如果假定地幔处于低瑞利数的状态（临界瑞利数1.5倍左右）,那么上述方程中的非线性项可以忽略不计.作为一类可能的模型,本文计算一组用6个边界条件确定6个未知数的线性方程组.这些条件包括板块绝对运动极型场、地球大地水准面异常和地震层析结果提供的地幔密度分布横向不均匀相应的“刚性地球”水准面异常等.模型计算表明:1.地幔中流体运动格局不仅受地幔热动力学参数（瑞利数）控制,而且强烈地受边界条件的影响.2.若不限定下边界为等温边界,则上、下地幔之间并不呈现出活动性明显差异;但是在模型瑞利数加大到一定值时,核-幔边界附近将出现一些局部的小尺度对流环.3.当模型瑞利数从很小增加时,对流格局将发生变化,这些格局可能反应由地幔热动力学参数决定的地幔固有特性.4.当瑞利数为50000和80000时,核-幔边界形变与PcP波得到的结果吻合较好.

MANTLE CONVECTION MODEL CONSTRAINED ON SEVERAL GEOPHYSICAL DATA

As a possible model the earth's geoid anomalies, plate absolute motions and a rigid earth's geoid, which is calculated by the lateral heterogeneity of the mantle, are taken as constrained conditions to inverse the thermal convection in the mantle at low Rayleigh number in this paper. The results show that （1） convection patterns in the modeling mantle are controled not only by the thermodynamical paramenter （Rayleigh number） but also by the choosing of boundary conditions, （2） assuming that the upper boundary is isothermal there is not too much different of the convection amplitude between upper and lower mantle and when the Rayleigh number of the mantle is equal to 80000 there are several small convection cell near the core-mantle boundary, （3） when the Rayleigh number of the mantle increases the convection patterns are changing and it may reflects the thermodynamical character of the mantle, （4） computed core-mantle boundary deformation at Ra = 50000 and 80000 can fit the result determinated by PcP waveforms very will.