Three-Dimensional Magnetotelluric Forward Modeling in the Mixed Space-Wavenumber Domain with Divergence Correction

Three-dimensional magnetotelluric (MT) forward modeling remains constrained by the difficulty of achieving both high numerical accuracy and computational efficiency. To address this limitation, we propose a mixed space-wavenumber domain method based on coupled equations for the magnetic vector potential and electric scalar potential under the Lorenz gauge. Our method incorporates a divergence correction scheme and employs the Gaussian Fourier transform technique to solve the three-dimensional MT forward problem. The vector-potential equation reduces the number of unknowns and computational cost, while simplifying the treatment of boundary conditions at conductivity interfaces. The divergence correction suppresses spurious solutions at anomalous-body boundaries in low-induction-number regimes. We use Gauss-FFT instead of the traditional FFT to reduce the errors due to aliasing and imposed periodicity as well as edge effects in the MT forward modeling. Numerical experiments demonstrate that both iterative solution time and memory consumption scale linearly with the number of computational nodes. On refined meshes, the proposed method requires approximately one-eighth of the iterative solution time and one-quarter of the memory required by the finite element method. Together, these improvements substantially enhance computational efficiency without compromising numerical accuracy. The method is therefore well suited for large-scale 3D MT forward modeling on laterally regular grids with layered or vertically heterogeneous media, as required in high-resolution mineral exploration and regional crustal-structure imaging, where both accuracy and efficiency are essential.