3-D Fourier Finite Element Modeling of Controlled-Source Electromagnetic Responses in Anisotropic Media

Current forward modeling approaches for 3-D controlled-source electromagnetic (CSEM) problems in anisotropic media exhibit limited capability in addressing large-scale models. Given that, we have developed an innovative 3-D forward modeling algorithm for anisotropic CSEM problems by using the Fourier finite element method (FFEM). Starting from Maxwell’s equations, the 3-D governing equations of the secondary vector and scalar potentials based on the Coulomb gauge are derived. That secondary field approach can not only effectively eliminate source singularities but also maintain flexibility for various source configurations. Then, a horizontal 2-D Fourier transform is employed to convert the 3-D governing equations from the spatial domain into a system of 1-D ordinary differential equations in the space–wavenumber domain. The resulting equations are discretized and solved via the 1-D finite element method (FEM). Additionally, a contraction operator is applied to iteratively correct the total electric field. By leveraging the computational efficiency of Fourier transform and the stability of iterative techniques, the proposed approach achieves enhanced computational efficiency without compromising numerical accuracy. The validity, performance, and convergence of the proposed approach were verified by using a 1-D isotropic canonical offshore hydrocarbon model and a 3-D anisotropic prism model. Compared with the open source package parallel edge-based tool for geophysical electromagnetic modeling (PETGEM) based on the high-order edge FEM (HEFEM), the proposed approach using FFEM exhibits obvious efficiency advantages for a 1-D isotropic canonical offshore hydrocarbon model. Finally, two sophisticated geological models were employed to validate the robustness of FFEM in handling complex subsurface conditions, and the influence of frequency on electromagnetic field distribution was also investigated.