Coupled and uncoupled hydrogeophysical inversions using ensemble Kalman filter assimilation of ERT-monitored tracer test data

Recent advances in geophysical methods have been increasingly exploited as inverse modeling tools in groundwater hydrology. In particular, several attempts to constrain the hydrogeophysical inverse problem to reduce inversion errors have been made using time-lapse geophysical measurements through both coupled and uncoupled (also known as sequential) inversion approaches. Despite the appeal and popularity of coupled inversion approaches, their superiority over uncoupled methods has not been proved conclusively; the goal of this work is to provide an objective comparison between the two approaches within a specific inversion modeling framework based on the ensemble Kalman filter (EnKF). Using EnKF and a model of Lagrangian transport, we compare the performance of a fully coupled and uncoupled inversion method for the reconstruction of heterogeneous saturated hydraulic conductivity fields through the assimilation of ERT-monitored tracer test data. The two inversion approaches are tested in a number of different scenarios, including isotropic and anisotropic synthetic aquifers, where we change the geostatistical parameters used to generate the prior ensemble of hydraulic conductivity fields. Our results show that the coupled approach outperforms the uncoupled when the prior statistics are close to the ones used to generate the true field. Otherwise, the coupled approach is heavily affected by "filter inbreeding'' (an undesired effect of variance underestimation typical of EnKF), while the uncoupled approach is more robust, being able to correct biased prior information, thanks to its capability of capturing the solute travel times even in presence of inversion artifacts such as the violation of mass balance. Furthermore, the coupled approach is more computationally intensive than the uncoupled, due to the much larger number of forward runs required by the electrical model. Overall, we conclude that the relative merit of the coupled versus the uncoupled approach cannot be assumed a priori and should be assessed case by case.