3D anisotropic forward modeling of controlled-source electromagnetic fields based on adaptive algebraic multi-resolution grids

In recent years, forward modeling studies of controlled-source electromagnetic (CSEM) in anisotropic media have advanced significantly, with an increasing attention focusing on numerical algorithms capable of handling arbitrary anisotropy. The finite difference method has been widely used for 3D anisotropic CSEM forward modeling due to its simplicity and ease of implementation. However, conventional structured grids often produce excessive discrete degrees of freedom when applied to geologically complex structures, resulting in substantial computational costs. To address these issues, this study proposes an efficient algebraic multi-resolution grid (AMRG) technique for 3D anisotropic CSEM forward modeling based on the secondary field formulation. By multiplying the coefficient and interpolation matrices, sub-grids of varying resolutions are applied to sub-regions at different depths. An adaptive error estimation strategy is introduced, which effectively reduces the scale of the problem to be solved while maintaining the accuracy of the multi-resolution grid. Compared with widely adopted structured-grid acceleration techniques, such as divergence correction and regularized divergence-free constraint methods, integrating AMRG with a regularized divergence-free constraint (AMRG-GD) yields a 0.9- to 16.6-fold improvement in computational efficiency. Moreover, the AMRG-GD method shows strong potential for application across a broad range of geophysical problems.