Bayesian Inversion of Electrical Resistivity Tomography Data for Uranium Exploration Through a Localized Ensemble‐Based Approach

ABSTRACT The electrical resistivity tomography (ERT) is a geophysical method commonly used in mining exploration to reconstruct the subsurface resistivity. The associated inverse problem is typically addressed using deterministic approaches that minimize an objective function and guarantee fast convergence. However, due to the ill‐posedness and nonlinearity of the ERT inverse problem, the solution is not unique and the deterministic algorithm can remain trapped in local minima of the objective function. Additionally, the uncertainty of the solution can be assessed using a local approximation of the inverse of the Hessian matrix. For this reason, we focus on an inversion algorithm based on the Kalman filter, the ensemble smoother multiple data assimilation algorithm, which produces an ensemble of models as a solution that approximates the posterior probability density function. The algorithm iteratively updates the models by estimating the sensitivity information using correlation matrices. When the ensemble size is finite, the correlation matrices and then the Kalman filter, can be affected by spurious correlations, introducing errors in the sampling of the posterior probability density function sampling. To mitigate this issue, we follow a strategy commonly used in other fields, such as in reservoir history matching and meteorology, which involves a distance‐based function to smooth out the components of the Kalman filter affected by spurious correlations. This strategy, known as localization, ensures the attenuation of model updates driven by spurious correlations. To assess the effectiveness of the proposed approach and evaluate the impact of ensemble size on the propagation of spurious correlations, we first invert synthetic data generated through a realistic resistivity model representing a typical unconformity‐related uranium setting. We then apply the method to a field dataset from the Athabasca Basin, one of the World's major uranium plays. The inversion results illustrate the propagation of spurious correlations and its attenuation when the localization strategy is employed. Moreover, the localization allows for obtaining a reasonable solution even reducing the ensemble size. Finally, the field data inversion suggests the presence of at least two low‐resistivity anomalies below the unconformity zone, starting at a depth of approximately 500 m. The posterior distribution we obtain with the proposed approach allows for the evaluation of the uncertainty, enabling a more reliable interpretation of the result. Overall, this paper highlights the potential of the localized ensemble‐based inversion method for estimating the subsurface resistivity and quantifying the associated uncertainties in the resistivity model.