中文摘要：

数值模拟是地球物理中重要的研究方法,针对复杂的正演问题,一般情况下不存在解析解,数值模拟方法则是一种有效的手段.有限单元法（简称有限元法）是数值模拟的一种重要方法,其优点是适用于物性分布复杂或者是几何特征不规则的地球物理问题.目前有限元法已经应用到大地电磁测深正演中,但是有关文献对其具体应用推导过程中单元刚度矩阵和单元节点编码方面描述较少.单元刚度矩阵是有限元分析中基本方程的系数矩阵,节点编码是将理论进行编程的重要环节.因此本文针对有限元大地电磁二维问题的正演过程,详细反复推导和描述其过程,给出正确结果.特别是清楚描述了单元刚度矩阵的计算过程及单元节点编码与整体结构中节点编码的关系,这对实现有限元正演的编程具有重要的意义.

英文摘要：

Numerical simulation plays an important role in geophysics. There is no analytical solution for the complex forward modeling problem. In this case the numerical simulation is an effective kind of tool. The finite element method is a significant branch of numerical simulation for it applies to the geophysical problem whose physical properties are complexly distributed or geometric feature is irregular. The finite element method has been introduced to the magnetotelluric. But there is neither literature that describe element stiffness matrix in the derivation process in detail,nor the cell node numbering. In addition,some mistaken is found in the literature. The element stiffness matrix is the coefficient matrix of the fundamental equation in the finite element analysis.Node numbering is the key link to realize the theory. Thus this paper gives the detailed and correct derivation process about the forward modeling of the magnetotelluric. It specifically describes the calculation of the element stiffness matrix and the relation between the cell node numbering and the global node numbering. It has important significance to program the forward modeling using the finite element method.