Efficient 3D Inversion of the Marine Electrical-Source Time Domain Electromagnetic Method Based on the Footprint Technique

Marine electric-source time domain electromagnetic (TDEM) surveys typically involve the simultaneous movement of transmitters and receivers, which generates a large number of transmitter–receiver pairs. This acquisition geometry creates notable challenges for 3D inversion, mainly because of the large data volume and high computational cost. However, the electromagnetic “sensitive region” for each transmitter–receiver pair is much smaller than the full survey area. Based on this feature, we propose an efficient 3D inversion approach using the footprint technique. By clearly defining the sensitivity region, referred to as the footprint domain, for each pair, the method builds the sensitivity matrix only within localized subsurface regions that significantly affect the observed response. This approach greatly reduces both forward modeling cost and memory requirements. The forward modeling adopts an integral equation method combined with cosine transforms for fast 3D field computation, while the inversion framework uses a regularized conjugate-gradient algorithm, further accelerated by parallel computing under footprint domain constraints. Numerical simulations also examine the effects of offset, time channel, seawater thickness, and resistivity on the footprint domain, helping clarify the spatiotemporal diffusion behavior of TDEM fields in shallow marine environments. Tests on representative models show that the proposed method remains stable and accurate under complex geological conditions while significantly improving computational efficiency. In particular, the footprint domain technique improves inversion speed by about 55% compared with full domain inversion. These results indicate that the proposed approach provides a reliable and scalable option for large-scale 3D inversion of marine TDEM data.