Assessment of local hydraulic properties from electrical resistivity tomography monitoring of a three-dimensional synthetic tracer test experiment

In recent years geophysical methods have become increasingly popular for hydrological applications. Time-lapse electrical resistivity tomography (ERT) represents a potentially powerful tool for subsurface solute transport characterization since a full picture of the spatiotemporal evolution of the process can be obtained. However, the quantitative interpretation of tracer tests is difficult because of the uncertainty related to the geoelectrical inversion, the constitutive models linking geophysical and hydrological quantities, and the a priori unknown heterogeneous properties of natural formations. Here an approach based on the Lagrangian formulation of transport and the ensemble Kalman filter (EnKF) data assimilation technique is applied to assess the spatial distribution of hydraulic conductivity K by incorporating time-lapse cross-hole ERT data. Electrical data consist of three-dimensional cross-hole ERT images generated for a synthetic tracer test in a heterogeneous aquifer. Under the assumption that the solute spreads as a passive tracer, for high Peclet numbers the spatial moments of the evolving plume are dominated by the spatial distribution of the hydraulic conductivity. The assimilation of the electrical conductivity 4D images allows updating of the hydrological state as well as the spatial distribution of K. Thus, delineation of the tracer plume and estimation of the local aquifer heterogeneity can be achieved at the same time by means of this interpretation of time-lapse electrical images from tracer tests. We assess the impact on the performance of the hydrological inversion of (i) the uncertainty inherently affecting ERT inversions in terms of tracer concentration and (ii) the choice of the prior statistics of K. Our findings show that realistic ERT images can be integrated into a hydrological model even within an uncoupled inverse modeling framework. The reconstruction of the hydraulic conductivity spatial distribution is satisfactory in the portion of the domain directly covered by the passage of the tracer. Aside from the issues commonly affecting inverse models, the proposed approach is subject to the problem of the filter inbreeding and the retrieval performance is sensitive to the choice of K prior geostatistical parameters.