Stochastic inversion of time-lapse electrical resistivity tomography data by means of an adaptive ensemble-based approach

Inversion of time-lapse electrical resistivity tomography is an extension of the conventional electrical resistivity tomography inversion that aims to reconstruct resistivity variations in time. This method is widely used in monitoring subsurface processes such as groundwater evolution. The inverse problem is usually solved through deterministic algorithms, which usually guarantee a fast solution convergence. However, the electrical resistivity tomography inverse problem is ill-posed and non-linear, and it could exist more than one resistivity model that explains the observed data. This paper explores a Bayesian approach based on data assimilation, the ensemble smoother multiple data assimilation. In particular, we apply an adaptive approach in which the inflation coefficient is chosen based on the error function, that is the ensemble smoother multiple data assimilation restricted step. Our inversion approach aims to invert the data acquired at two different times simultaneously, estimating the resistivity model and its variation. In addition, the Bayesian approach allows for the assessment of the posterior probability density function needed for quantifying the uncertainties associated with the results. To test the method, we first apply the algorithm to synthetic data generated from realistic resistivity models; then, we invert field data from the Pillemark landfill monitoring station (Samsø, Denmark). Inversion results show that the ensemble smoother multiple data assimilation restricted step can correctly detect the resistivity variation both in the synthetic and in the field case, with an affordable computational burden. In addition, assessing the uncertainties allows us to interpret the reconstructed resistivity model correctly. This paper demonstrates the potential of the data assimilation approach in Bayesian time-lapse electrical resistivity tomography inversion.