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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.
Numerical simulation is an important research method in geophysics. For complex forward problems, there is no analytic solution in general, and numerical simulation is an effective method. Finite element method (referred to as finite element method) is a numerical simulation An important method has the advantage of being suitable for geophysical problems with complicated physical properties or irregular geometrical features. At present, the finite element method has been applied to the forward modeling of geomagnetic soundings. However, The stiffness matrix and the unit node coding are less described.The element stiffness matrix is the coefficient matrix of the basic equations in the finite element analysis.The node coding is an important part of the programming of the theory.Therefore this paper aims at the forward process of the finite element MT2D , Derive and describe the process in detail, and give correct results. Especially, the calculation process of element stiffness matrix and the relationship between element node coding and node coding in the whole structure are clearly described, which is very important for the programming of finite element forward significance.