Efficient regularization constraints forward modeling of anisotropic magnetotelluric in spherical-coordinate system

Under China′s ongoing “Deep Earth” strategy, detailed characterization of the deep crust-mantle electrical structure has become a key prerequisite for deep-Earth research and resource-energy exploration, consequently, the magnetotelluric (MT) method is increasingly used in related studies. However, as survey scale increases, Earth′s curvature significantly affects electromagnetic propagation, and neglecting it in numerical modeling causes systematic errors. To reduce these errors, we use spherical instead of Cartesian coordinates and approximate the MT source with higher-order spherical harmonics. Moreover, widespread electrical anisotropy in the crust and upper mantle strongly affects electromagnetic field propagation, traditional isotropic models for MT data may cause large errors and misleading geological interpretations. We incorporate electrical anisotropy into the forward model to improve physical realism and accuracy. To address numerical instabilities in long-period MT data, we explicitly add a divergence correction term to the governing equations to improve stability and efficiency. To verify the proposed algorithm, we first construct an arbitrary electrically anisotropic half-space model and compare the numerical results with the theoretical solution. On this basis, two complex models (a high-resistivity HTI anomaly and a high-low resistivity anisotropic combination) are used to test the algorithm. The results show that it preserves accuracy, reduces iterations, improves efficiency, and remains stable, indicating good application potential.