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本文首先从麦克斯韦方程出发,研究了三维大地电磁场所满足的方程和边界条件,利用加权余量法推导了与大地电磁场边值问题等价的变分方程.用六面体单元对计算区域进行剖分,通过矢量有限元分析形成大型复系数线性方程组,采用不完全Cholesky预处理结合双复共轭梯度算法对方程进行求解.建立均匀半空间模型和三层层状模型进行数值模拟,并与解析解进行对比,验证了矢量有限元方法以及程序的正确,然后对三维异常体模型进行正演模拟,并对结果进行了分析.在验证过程中发现利用矢量有限元方法进行三维大地电磁正演时,传统的边界条件结果不理想,还需要给定四个垂直侧面的边界条件,另外认识到网格剖分的重要性,得到了一些在用矢量有限元方法进行三维大地电磁正演时关于剖分的有意义的结论.
Starting from the Maxwell equation, the paper studies the equations and boundary conditions that are satisfied by the three-dimensional magnetosphere, and deduces the equivalent variational equations with the boundary value problem of the magnetotelluric field by using the weighted residue method. The computational domain is decomposed by the hexahedron element, The large complex coefficient linear equations were formed by vector finite element analysis, the incomplete Cholesky pretreatment combined with double complex conjugate gradient algorithm was used to solve the equation.Uniform half-space model and three-layer layered model were established for numerical simulation, The results show that the vector finite element method and the correct program are validated, and then the forward modeling of the three-dimensional abnormal body model is carried out and the results are analyzed.In the verification process, The traditional boundary conditions result is not ideal, but also given the boundary conditions of the four vertical sides, in addition to recognize the importance of meshing, obtained some finite element method using the vectorial three-dimensional Meaningful conclusion.