Comparison study of different forward modeling approaches by using the finite-element method for 3D magnetotelluric data in anisotropic media

We have examined three approaches for analyzing 3D magnetotelluric (MT) data with general anisotropy. These included the direct electromagnetic (EM) approach, which solved the electric field Helmholtz equation directly, and the Coulomb-gauged and Ungauged approaches. The three approaches are discretized using finite-element (FE) methods. First, the correctness of the three approaches is validated using a typical isotropic 3D model and a 2D anisotropic model. The FE solutions of each approach obtained by the direct solver MUMPS are compared with the analytical solutions to demonstrate that all approaches generated accurate results. Subse-quently, an anisotropic 3D model is designed to investigate the forward characteristics of the different ap-proaches. The FE solutions are obtained using the quasi-minimum residual (QMR) solver with a symmetric successive overrelaxation (SSOR) preconditioner in this model. The forward modeling results of each approach were compared in terms of stiffness matrices, the convergence of the iterative solver, and apparent resistivity and phase. We find that the FE solution of the Coulomb-gauged and Ungauged approaches produces larger stiffness matrices, but the proportion of non-zero elements in the Coulomb-gauged approach is the least. The Ungauged approach can yield faster solutions over a wide range of frequencies. Finally, a complex numerical example is provided to demonstrate the good convergence behavior of the Ungauged approach.