Large-scale 3-D magnetotelluric modeling in anisotropic media using extrapolation multigrid method on staggered grids

To improve the practicality and efficiency of 3D magnetotelluric (MT) data inversion, developing a 3D MT forward modeling algorithm with low computational cost in terms of time and memory is an important prerequisite. An extrapolation cascadic multigrid (EXCMG) method is developed on rectilinear grids to accelerate the solving process of large linear systems arising from the staggered-grid finite difference (SFD) discretization of Maxwell’s equations. Arbitrary anisotropic conductivity is considered, without adding extra unknowns to the SFD scheme. A new prolongation operator based on global extrapolation and mixed-order interpolation is developed to tackle the issue caused by non-nested unknown distribution. The divergence correction scheme for arbitrary anisotropy is employed to stabilize the smoothing process, especially for low-frequency cases. Several examples are tested to validate the accuracy and efficiency of the proposed algorithm, including synthetic models with anisotropy and topography, and the real-world Cascadia model. Results show that our EXCMG solver is more efficient than traditional iterative solvers (e.g., the preconditioned BiCGStab), the algebraic multigrid method and the geometric multigrid (GMG) method. The proposed method can efficiently solve large-scale problems with large grid stretching factors and arbitrary anisotropy, providing powerful engine for large-scale MT inversion.