中文摘要：

基于双二次插值的有限单元法求解大地电磁二维正演问题，以不均匀网格剖分为基础，推导出大地电磁响应的计算公式。针对有限单元法最后形成一个线性方程组，系数矩阵是大型稀疏的带状对称正定复系数矩阵，并且其条件数远大于1，为严重病态矩阵，求解其对应方程组会遇到很多困难等问题，采用不完全LU分解（即上三角与下三角分解）处理的稳定双共轭梯度算法（BICGSTAB算法）求解该线性方程组，通过对层状介质和二维模型电磁响应进行计算，获得二维大地电磁的视电阻率曲线和阻抗相位曲线。研究结果表明，BICGSTAB算法具有速度快、精度高和稳定性好等优点。

英文摘要：

Based on the finite element method of two-dimensional magnetotelluric forward problem, quadratic interpolation in a rectangular element to solve the no-uniform mesh based magnetotelluric responses calculation formula was derived. Based on the fact that the finite element method was used to form a linear equation, and the coefficient matrix was a large sparse, banded, symmetric, conditioned and complex matrix, its condition number is far larger than 1, and it was an ill-conditioned matrix, solving large scale ill-conditioned linear equation was very difficult, and so the BICGSTAB （Bi-conjugate gradient stabilized method） algorithm with incomplete LU decomposition for preconditioning was used to solve this system linear equation. This approach was verified through the calculations of layered earth model and two-dimensional earth model. The results show that the BICGSTAB algorithm has high speed, high precision and stability. The apparent resistivity curves and the impedance phase curves are very accurate to synthetic magnetotelluric responses.