Divergence problem in solution of direct method for two-dimensional magnetotelluric forward modelling

Abstract This study represents the first investigation into the divergence issue in the direct solution of two-dimensional magnetotelluric (MT) forward problems. In specific computational scenarios, the current density divergence in the electric field solutions obtained by the direct method is relatively large, violating the charge conservation condition and resulting in inaccurate MT responses. Using the quasi-analytical solution for the MT problem in a vertical infinite fault model as a benchmark, this paper systematically analyzes the impact of various factors on the divergence issue in direct solutions. It is found that long periods, high conductivity contrasts, and y-axis non-uniform grid discretization patterns exacerbate the divergence problem. Numerical example analyses indicate that lower residual divergence leads to higher accuracy in MT responses. Furthermore, this paper proposes an innovative improvement to the direct method for solving forward problems by incorporating divergence correction, a novel application that addresses the divergence issues in the direct solution of MT forward equations. This approach effectively restores the MT responses, which are otherwise distorted due to the divergence problem, back to their correct form. Graphical Abstract