Accelerated Full-Waveform Time-Domain Electromagnetic Forward Modeling in Underground Full-Space Using an Octree Mesh and Model Order Reduction

Time-domain electromagnetic (TDEM) surveys commonly use diverse excitation waveforms, making accurate simulation of full-time three-dimensional responses necessary. This paper presents a fast 3-D full-space TDEM forward solver that combines octree-based local refinement with a model order reduction (MOR) strategy. The governing equation is discretized using the mimetic finite-volume (MFV) method in the magnetic flux density (b) formulation, and a source-decoupled shift-and-invert (SAI) Krylov-subspace MOR scheme is constructed to reduce the original high-dimensional system. Compared with tensor discretization, the octree mesh achieves a favorable trade-off between local resolution and memory consumption. Numerical results show that the proposed MOR solver accelerates simulations by factors of 10.5 and 4.2 relative to the conventional BDF and BDF-SAI schemes, respectively, while maintaining high accuracy. Comparisons between full-space and half-space responses reveal distinct electromagnetic field propagation characteristics in full-space environments. The results further indicate that anomalies outside the observation direction may affect measured responses, suggesting the need to mitigate interference from undesired directions in practical surveys.