3-D Joint Inversion of Gravity and Magnetotelluric Data Based on Gaussian Mixture Model Clustering Constraints

Abstract

Joint inversion is an effective approach for reducing the nonuniqueness of geophysical inversion by integrating complementary information from different datasets. This study builds upon the petrophysically and geologically guided inversion (PGI) framework and applies a fixed-prior Gaussian mixture model (GMM) formulation to 3-D joint inversion of gravity and magnetotelluric (MT) data. In this framework, quantitative information on petrophysical classes and global prior probabilities is represented by a GMM in the joint physical-property space, and the GMM-based petrophysical regularization replaces the traditional least-squares model regularization term of the objective function. The GMM parameters in this study are estimated before the inversion and kept fixed during the inversion. To construct the prior GMM, the component means and proportions are obtained from labeled prior samples, and the within-component variability is represented by user-specified Gaussian perturbations. The resulting covariance matrices are then estimated using Ledoit–Wolf shrinkage estimation. This provides a practical way to construct the fixed-prior GMM and reduces the need for repeated trial-and-error inversions. Four synthetic examples are used to evaluate the joint inversion workflow of gravity and MT data. The results show that the fixed-prior GMM constraint can guide the joint inversion toward models consistent with the prescribed petrophysical classes and global prior probabilities. Compared with single-method inversions, the fixed-prior GMM-constrained workflow improves the consistency between recovered residual density and resistivity structures and enhances the recovery of target bodies.