大地电磁三维矢量有限元正演

doi:10.13278/j.cnki.jjuese.201605302

吉林大学学报(地球科学版) ›› 2016, Vol. 46 ›› Issue (5): 1538-1549.doi: 10.13278/j.cnki.jjuese.201605302

大地电磁三维矢量有限元正演

严家斌, 皇祥宇

中南大学地球科学与信息物理学院, 长沙 410083

收稿日期:2016-01-15 出版日期:2016-09-26 发布日期:2016-09-26
通讯作者: 皇祥宇(1990-),硕士研究生,主要从事大地电磁无网格化正演研究,E-mail:huangfucsu@163.com E-mail:huangfucsu@163.com
作者简介:严家斌(1969-),教授,主要从事电磁法数据处理及图像处理研究工作,E-mail:cspyry@csu.edu.cn
基金资助:
国家自然基金项目（40874055）；湖南省自然科学基金项目（14JJ2012）

Vector Finite Element Method

Yan Jiabin, Huang Xiangyu

School of Geosciences and Info-Physics, Central South University, Changsha 410083, China

Received:2016-01-15 Online:2016-09-26 Published:2016-09-26
Supported by:
Supported by the National Nature Science Foundation of China (40874055) and the Natural Science Foundation of Hunan Province, China (14JJ2012)

摘要/Abstract

摘要：

采用广义变分原理，基于矢量基函数详细推导了大地电磁三维矢量有限元方程。为了提高计算精度和效率，应用直接法强加边界条件改善总体系数矩阵的条件数，同时使用SSOR（symmetric successive over relaxation）预处理的双共轭稳定梯度法求解复对称大型稀疏线性方程组。并利用国际标准模型与相关参考文献的结果进行了对比，验证了算法的准确性。对一个典型的三维低阻体模型进行正演，得到了不同测线的视电阻率和相位断面图，并与二维正演结果进行对比分析。结果表明：在x方向测线上，ρ_yx变化幅度较ρ_xy小，中心测线上的ρ_yx和ρ_xy响应均与二维TM模式条件下的响应特征相似。

关键词: 大地电磁法, 广义变分原理, 矢量有限元方法, SSOR预条件, 边界条件强加方法

Abstract:

Based on the vector basis function,the generalized variational principle was adopted to deduce the discrete equations of magnetotelluric field.In order to increase the accuracy and efficiency of calculation, the direct method is used to impose boundary conditions, improving condition number of generalco efficient matrix. At the same time, the complex, symmetric,large sparselinear systems was solved by symmetric successive over relaxation preconditioned BICGSTAB method. The international standard model had been calculated,and the contrast with the results in related references had validated the accuracy of the algorithm. The forward modeling on a typical low resistivity model had been carried out, the response of apparent resistivity and phase had been got, and the results of 3D model and 2D model were compared.The results showed that in x direction, the change range of ρ_yx is less than that of ρ_xy. The response of both ρ_yx and ρ_xy for 3D model in thecentral survey line is similar to the 2D TM mode.

Key words: magnetotelluric method, generalized variational principle, vector finite element method, SSOR precondition, imposition of boundary conditions

中图分类号:

P631.3

严家斌, 皇祥宇. 大地电磁三维矢量有限元正演[J]. 吉林大学学报(地球科学版), 2016, 46(5): 1538-1549.

Yan Jiabin, Huang Xiangyu. Vector Finite Element Method[J]. Journal of Jilin University(Earth Science Edition), 2016, 46(5): 1538-1549.

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大地电磁三维矢量有限元正演

Vector Finite Element Method

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