A Bayesian–Gauss–Newton Inversion Framework for Electrical Resistivity Tomography with Improved Parameter Estimation and Uncertainty Quantification

Accurate subsurface parameter estimation remains challenging due to the inherent nonlinearity and non-uniqueness of geophysical inverse problems. In this study, we present an integrated Bayesian–Gauss–Newton inversion framework for Electrical Resistivity Tomography (ERT) aimed at achieving robust model parameter estimation and uncertainty quantification. The Bayesian component provides a probabilistic description of the inverse problem, enabling the incorporation of prior geological information and the assessment of posterior parameter distributions. Bayesian optimization is employed to efficiently explore the high-dimensional model space and obtain a geologically consistent initial model. Subsequently, a Gauss–Newton optimization scheme is applied to refine this solution and obtain the maximum a posteriori estimate with improved convergence characteristics. The combined approach leverages the global search capability of Bayesian optimization and the computational efficiency of the Gauss–Newton method, resulting in enhanced resolution of sharp resistivity contrasts and reduced ambiguity in subsurface models. Applications to both synthetic and field ERT datasets demonstrate that the proposed methodology improves data fitting, stabilizes inversion results, and provides a comprehensive measure of model uncertainty. The results highlight the potential of the Bayesian–Gauss–Newton framework as a reliable and efficient inversion strategy for ERT-based subsurface characterization, particularly in complex environments affected by strong resistivity contrasts and saline intrusion.