Three-Dimensional Borehole–Surface TEM Forward Modeling with a Time-Parallel Method

The three-dimensional borehole-to-surface transient electromagnetic (BSTEM) method plays a critical role in resolving subsurface conductivity structures under complex geological conditions. However, its application is often constrained by the high computational costs associated with large-scale simulations and fine temporal resolution. In this study, a time-parallel forward modeling strategy is employed by integrating the finite volume method (FVM) with the Multigrid Reduction-in-Time (MGRIT) algorithm. Maxwell’s equations are discretized in space using unstructured octree meshes, while the MGRIT algorithm enables parallelism along the time axis through coarse–fine temporal grid hierarchy and multilevel iterative correction. Numerical experiments on synthetic and field-scale models demonstrate that the MGRIT-based solver significantly reduces computational time compared to conventional direct solvers, particularly when a large number of processors are utilized. In a field-scale hematite mine model, the MGRIT-based solver reduces the total runtime by more than 40% while maintaining numerical accuracy. The method exhibits parallel scalability and is especially advantageous in problems involving a large number of time channels, where simultaneous time-step updates offer substantial performance gains. These results confirm the effectiveness and robustness of the proposed approach for large-scale 3D TEM simulations under complex conditions and provide a practical foundation for future applications in high-resolution electromagnetic modeling and imaging.