3D Modeling for Multi-Coil 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 multi-coil system achieves multi-directional illumination of geological bodies, enabling more comprehensive subsurface data acquisition. However, complex three-dimensional multi-coil forward modeling involves multi-source 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 multi-coil system, we first introduce the Rational Arnoldi (RA) model reduction technique. This approach compresses high-dimensional EM systems into a low-dimensional 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 trade-off inherent in conventional methods for solving multi-scale EM diffusion problems. This approach achieves unified high-precision simulation of time-domain EM responses across all time stages. From a physical perspective, the multi-coil system enhances EM field radiation intensity while mitigating single-source volumetric effects. This configuration enables multi-angle, multi-depth EM coupling detection of geological targets, ultimately improving both signal strength and data resolution.