A new method for solving the magnetotelluric forward problem in geophysics

• Proposed Half Boundary Method (HBM) for solving the Helmholtz equation in magnetotelluric (MT) forward modeling. • HBM directly computes boundary derivatives without the need for a full global field solution, improving computational efficiency. • Demonstrated higher efficiency and accuracy than conventional methods (FDM) in 1D problems across homogeneous, layered, and continuous media. • Validated for 2D MT forward modeling, demonstrating high accuracy and effectiveness. • Provides an efficient tool for MT forward modeling in uranium exploration. Solving the Helmholtz equation is a prerequisite for computing the vertical gradient of surface electromagnetic fields, both of which are crucial steps in magnetotelluric (MT) surveys for uranium exploration. Conventional methods such as FDM and FEM require full global field solutions before computing surface derivatives, leading to low efficiency in large-scale modeling. This study proposes the Half Boundary Method (HBM), which incorporates field gradients as variables and establishes nodal relations through element integration. Using recursive computation, HBM directly calculates boundary derivatives without a global solution. In 1D problems, HBM demonstrates higher efficiency and accuracy than FDM across homogeneous, layered, and continuous media. For 2D problems, comparisons with FEM validate the applicability of HBM in uniform media, anomalous bodies, and horst structures, offering an efficient tool for MT forward modeling.