大地电磁三维矢量有限元正演

3D Forward Modeling of Magnetotelluric Field by Vector Finite Element Method

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。

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 ρyx is less than that of ρxy. The response of both ρyx and ρxy for 3D model in thecentral survey line is similar to the 2D TM mode.