A comparison between Empirical Bayes combined with Akaike’s Bayesian Information Criterion and Ensemble Smoother with Multiple data assimilation to evaluate hydrogeophisical data

Knowledge of subsurface properties is critical for appropriate groundwater resource management and predicting solute transport in aquifers. Due to the necessary field investigations such as drilling logs, pumping tests, and so on, subsurface characterization necessitates a significant amount of economic resources. As a result, this subject has received a lot of attention in the literature. Electrical resistivity tomography (ERT) is a noninvasive approach for identifying the subsurface structure based on the material's electrical resistivity. The ERT surveys yield pseudo-resistivity values and require the use of an inverse technique to estimate the resistivity field of the studied area. Two inverse procedures are applied and compared: the Empirical Bayes approach combined with Akaike's Bayesian Information Criterion (ebaPEST) and Ensemble Smoother with Multiple Data Assimilation applied via the software package genES-MDA. ebaPEST is model-independent, written in Fortran using the PEST framework, and capable of identifying both the unknown field and the prior distribution's hyper-parameters. The genES-MDA software package is a Python tool with a flexible workflow that can be easily modified for the solution of general inverse problems using a Kalman-based method. These inverse processes were tested on a synthetic example of a saturated aquifer with a resistivity field built with an exponential covariance function with a variance of 0.5 and a correlation length of 30 m. A 2D model of 96 m length and 20 m depth with a 2m x 2m computational grid represents the unknown field. In both packages, the forward problem is tackled using a 2.5-D electrical resistivity model developed with Matlab® software. It consists of computing pseudo-resistivity values while considering fully known boundary conditions and electrode configuration beginning from a resistivity field. Both approaches can quantify uncertainty, ebaPEST via the posterior probability distribution of the target quantities and genES-MDA via the ensemble of parameter realizations. The results demonstrate that both methods performed well. In this work, the advantages and drawbacks of the approaches are explored.