Magnetotelluric forward modeling on fine grid via deep learning with physical information constraints

In traditional magnetotelluric (MT) forward modeling, fine grids ensure accuracy but trap conventional methods in efficiency bottlenecks due to exponentially growing matrix computation time. Meanwhile, deep learning (DL) for MT forward modeling often loses physical information during training, failing to leverage fine grids' precision and fit real MT data well. To address these issues, this study combines DL with traditional forward techniques to achieve "high precision-efficiency" synergy, focusing on two key aspects: First, it accounts for subsurface media's volume effect and gradual resistivity variations (core real geological properties)-random synthetic resistivity models with continuous numerical changes are generated via cubic spline interpolation, ensuring training data aligns with real subsurface conditions. Second, a U-shaped DL model (Swin-UNet, with Swin Transformer as backbone) is built, and a multi-task MT forward response grid refinement model is trained under strict physical information constraints, enabling DL to efficiently fit fine grid forward processes while retaining precision and avoiding traditional methods' time costs. Synthetic data verification confirms the framework fully utilizes fine grids' precision, significantly reduces forward time, and breaks traditional bottlenecks. This work provides an efficient, high-precision MT forward solution, opens a new path for AI in fine grid forward modeling, and offers a reference for subsequent interdisciplinary geophysical modeling and interpretation.