A Comparison Between Empirical Bayes Combined with Akaike’s Bayesian Information Criterion and Ensemble Smoother with Multiple Data Assimilation to Evaluate Geophysical Data

Accurate knowledge of subsurface properties is essential for effectively managing groundwater resources and predicting solute transport in aquifers. However, subsurface characterization often requires significant economic resources because of the need for field investigations such as drilling logs and pumping tests. Electrical resistivity tomography (ERT) is a noninvasive method used to determine the subsurface structure by measuring materials’ electrical resistivity. ERT surveys provide apparent resistivity values, which require inverse modeling techniques to estimate the actual resistivity distribution of the study area. This study compares two inverse approaches: the empirical Bayes approach (EBA) combined with Akaike’s Bayesian information criterion (ABIC), and the ensemble smoother with multiple data assimilation (ES-MDA) method. These methods were evaluated in a synthetic two-dimensional test case that simulates a vertical cross section of a saturated aquifer with three distinct resistivity blocks. Observations, including apparent resistivity values from a Wenner-Schlumberger electrode array and borehole resistivity data, were used to solve the inverse problem using both methodologies. The results show that although the two approaches employ different strategies, both effectively reconstruct the resistivity field. This work explores the strengths and limitations of each method.