Magnetotelluric sounding is an efficient and economical method for detecting Earth's deep structure because of its large surveying depth. We use a finite element approach to solve magnetotelluric fields in three-dimensional general anisotropic media based on the vector–scalar potentials and unstructured meshes. The implementation of a three-dimensional unstructured mesh generator TetGen with high-quality local mesh refinement can easily handle complicated models with high performance. The electromagnetic field equations are expressed in terms of Coulomb-gauged vector–scalar potentials, and the nodal-based finite element method can be used to compute the electromagnetic fields with high efficiency. The symmetric successive over-relaxation preconditioned conjugate gradient solver is used to solve the resulting linear equation system. The magnetotelluric responses in one-, two-, and three-dimensional medias are computed through our proposed approach. These results are then compared with the analytical solutions, two- and three-dimensional adaptive finite element solutions. Numerical examples demonstrate that these results are in good agreement. Because an unstructured mesh is incorporated in this approach, it has great potential for simulating the magnetotelluric responses in geometrically complicated situations.

大地电磁探测是一种探测地球深层结构的有效且经济的方法，因为它的测量深度很大。我们基于矢量标量势和非结构化网格，使用有限元方法求解三维通用各向异性介质中的大地电磁场。具有高质量局部网格细化功能的三维非结构化网格生成器TetGen的实现可以轻松处理具有高性能的复杂模型。电磁场方程用库仑计的矢量标量电势表示，基于节点的有限元方法可用于高效计算电磁场。对称连续超松弛预处理共轭梯度求解器用于求解所得线性方程组。通过我们提出的方法可以计算一维，二维和三维介质中的大地电磁响应。然后将这些结果与解析解，二维和三维自适应有限元解进行比较。数值算例表明，这些结果吻合良好。由于在这种方法中并入了非结构化网格，因此它在模拟几何复杂情况下的大地电磁响应方面具有很大的潜力。