Three-Dimensional Modeling for Multicoil Semi-Airborne Transient Electromagnetic With Model Reduction Method

Traditional semi-airborne transient electromagnetic (TEM) methods rely on a single source to generate electromagnetic (EM) fields, which only couple with geological bodies from one direction. In contrast, the multicoil system achieves multidirectional illumination of geological bodies, enabling more comprehensive subsurface data acquisition. However, complex 3-D multicoil forward modeling involves multisource coupling, nonlinear EM responses, and large-scale computing, which places higher demands on the computational efficiency and numerical stability of the algorithm. To address these challenges and study the working mechanism of the multicoil system, we first introduce the rational Arnoldi (RA) model reduction technique. This approach compresses high-dimensional EM systems into a low-dimensional one by constructing a mesh-independent Krylov subspace. Simultaneously, adjusting poles for rational interpolation in the low-dimensional space avoids repeated matrix decompositions. Subsequently, by combining RA with the fourth-order Runge–Kutta (RK4) time integration strategy, we ensure high-precision time-domain computations while reducing computational complexity and memory requirements. The results demonstrate that the RA-RK4 solution framework decouples the physical model from the temporal discretization dimension, thereby resolving the stability–efficiency tradeoff inherent in conventional methods for solving multiscale EM diffusion problems. This approach achieves unified high-precision simulation of time-domain EM responses across all time stages. From a physical perspective, the multicoil system enhances EM field radiation intensity while mitigating single-source volumetric effects. This configuration enables multiangle, multidepth EM coupling detection of geological targets, ultimately improving both signal strength and data resolution.