3D edge-based and nodal finite element modeling of magnetotelluric in general anisotropic media

Abstract

Research on the magnetotelluric (MT) forward modeling response in anisotropic media has been important since the discovery of anisotropic electric fields in the Earth's interior. In this study, we presented an edge-based and nodal finite-element method (FEM) for three-dimensional (3D) MT forward modeling problems in general anisotropic media. Partial differential equations are derived using the Coulomb-gauged approach from Maxwell's equation and discretized by the edge-based and nodal FEM. The magnetic vector A was discretized by an edge-based FEM and the electric scalar ψ was discretized by nodal FEM. The computational domain was refined using a hexahedral mesh. The Galerkin variant of the weighted residuals method was used to obtain a sparse linear system for magnetic vector A and electric scalar ψ. Three models were designed to validate and analyze our forward modeling code by comparing it with a one-dimensional analytical solution and with the results from codes developed by other scholars. A direct solver and iterative solvers with preprocessors were used to evaluate the performance of our code. Numerical experiments showed that our forward modeling code is accurate and robust and converges faster. In addition, the stiffness matrix assembled by our algorithm was smaller than that assembled by the nodal FEM, which further demonstrates the advantage of our algorithm in terms of computational memory.