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一、引言有限单元法是根据边界条件进行应力应变正演计算最常用而又有效的数值方法。在地球动力学研究中,我们常常希望利用测得有限点的应力或应变值等来确定影响应力应变分布的动力机制,这就是地球动力学问题的反演。在线弹性有限元反演中,可以利用叠加原理获得力学方程组,解该方程组即可得到反演结果。但利用叠加原理反演的物理量种类有限,尤其该方法不能推广到非线性有限单元模型;另外,既使在边界力的反演中,由于观测资料的欠缺,使得叠加原理得到的常
I. INTRODUCTION The finite element method is the most commonly used and effective numerical method for stress-strain forward modeling based on the boundary conditions. In geodynamic studies, we often hope to use the measured stress or strain values of finite points to determine the dynamic mechanism that influences the stress-strain distribution. This is the inversion of the geodynamic problems. In the online elastic finite element inversion, the mechanical equations can be obtained by using the principle of superposition, and the inversion results can be obtained by solving the equations. However, there are limited types of physical quantities to be inverted by the superposition principle. In particular, this method can not be generalized to nonlinear finite element models. In addition, even in the inversion of the boundary force, due to the lack of observed data,