基于二次场算法的大地电磁二维有限单元法正演

Secondary Field Based Two Dimensional Magnetotelluric Numerical Simulation by Finite Element Method

摘要:

推导了同时考虑电阻率与磁导率变化的大地电磁二维方程，并应用有限单元法进行数值模拟.为了提高计算精度与效率、简化计算节点生成，采用格林定理处理二次场方程源项，并设计实现了一种基于二叉树结构的收缩网格剖分算法；采用基于最少填入元思想的稀疏矩阵符号分析方法，实现了稀疏线性方程组的LDLT求解.利用二次场算法进行模型试算，结果表明所采用的新计算方法大大减少了计算单元数量，提高了计算精度与效率.

关键词:大地电磁; 有限单元法; 数值模拟; 稀疏矩阵

Abstract:

The Helmholtz equations for the secondary fields are almost the same as those for the total fields; the main differences are the addition of source terms involving the primary fields and the conductivity (TM mode) or magnetic permeability (TE mode) difference between the abnormal body and the host. In this paper a forward code was proposed using the finite element method, in which not only the conductivity but also the magnetic permeability differences were considered. In order to increase the calculation accuracy and efficiency, some special technologies were adopted. First, Green’s theorem was used to treat the source term of the secondary field equations as the volume integral and boundary integrals at elements. Next, the contraction grid algorithm was designed based on the binary tree structure. The advantage of the mesh was that it greatly reduced the number of nodes with almost the same precision as the uncontracting mesh. Moreover, sparse linear system of equations was solved by using the LDLT method, in order to reduce the calculation time. The sparse matrix symbolic analysis method based on the minimum fill in element were adopted before the LDLT. Finally, the two models were tested. The results showed that the calculation accuracy and efficiency were greatly improved by using the treatment method of secondary filed source term, the domain discrete method and the LDLT.

Key words:magnetotellurics; finite element method; numerical simulation; sparse matrix