Three-dimensional Electromagnetic Inversion with Enhanced Boundary Resolution via Field Gradient Constraints

Geophysical electromagnetic (EM) methods are widely used to characterize subsurface electrical resistivity, typically through inversion-based imaging. While significant progress has been made, challenges remain in accurately defining boundaries and resolving fine-scale geological features, as conventional smoothness regularized EM inversions blur sharp resistivity contrasts. A novel inversion method with EM field gradient constraints is proposed to address these challenges. It incorporates EM field gradients into a robust Gauss–Newton framework, improving sensitivity to boundary variations while preserving the overall smoothness and stability of the model in homogeneous regions. An Electromagnetic-Gradient-Constraints Matrix (EMGCM), derived from the EM field gradients, is introduced to control the resolution of target areas by dynamically adjusting the weights of specific grid cells within the roughness matrix. The EM field gradients are obtained directly from observed data. A frequency-to-depth (i.e., skin-depth-weighted) operator then maps these gradients from data space into model space to construct the EMGCM, ensuring consistency between data-space gradient information and the model-space regularization. Two tests on synthetic datasets, including a realistic synthetic case in which the synthetic responses were computed from a resistivity model previously adjusted to fit field data, show that our method yields more accurate resistivity models and delineates anomalies more clearly than the standard Occam inversion, with comparable computational cost for the cases considered. By leveraging the boundary-enhancing properties of EM field gradients and employing the EM field gradient constraints, our proposed method offers a robust solution with enhanced accuracy for advancing EM data interpretation.