Gauss-Newton inversion of ground transient electromagnetic data using COMSOL multiphysics

This study presents a Gauss-Newton inversion framework for Transient Electromagnetic (TEM) data based on the finite element software COMSOL Multiphysics. Although this platform facilitates flexible three-dimensional (3D) forward modeling, its direct application to inversion is hindered by the challenge of the sensitivity matrix computation. To address this, we introduce a virtual magnetic source at the receiver location and employ the adjoint field method, enabling the computation of the full 3D sensitivity matrix within COMSOL. This approach, integrated with the Gauss-Newton algorithm, establishes a robust iterative inversion workflow. Numerical simulations and a field case study demonstrate that: (1) Our 3D forward solutions, when applied to a homogeneous half-space model, exhibit remarkable agreement (relative error < 1.4%) with analytical solution at the center of a circular loop ; (2) For a representative "H"-shaped layered model, the inversion robustly converges in only 4 iterations, attaining a low final misfit; (3) Field application at Xiaogangou coal mine (Xinjiang, China) demonstrates the method's efficacy in delineating fault-induced water-conducting zones, with inversion results showing exceptional consistency with borehole data and geological mapping. This work delivers a convenient and high-accuracy computational solution for TEM numerical simulation and inversion under complex scenarios, significantly enhancing the practical applicability of the TEM methods.