Effects of spatially variable resolution on field-scale estimates of tracer concentration from electrical inversions using Archie's law

Two important mechanisms affect our ability to estimate solute concentrations quantitatively from the inversion of field-scale electrical resistivity tomography (ERT) data: (1) the spatially variable physical processes that govern the flow of current as well as the variation of physical properties in space and (2) the overparameterization of inverse models, which requires the imposition of a smoothing constraint (regularization) to facilitate convergence of the inverse solution. Based on analyses of field and synthetic data. we find that the ability of ERT to recover the 3D shape and magnitudes of a migrating conductive target is spatially variable. Additionally, the application of Archie's law to tomograms from field ERT data produced solute concentrations that are consistently less than 10% of point measurements collected in the field and estimated from transport modeline. Estimates of concentration from ERT using Archie's law only fit measured solute concentrations if the apparent formation factor is varied with space and time and allowed to take on unreasonably high values. Our analysis suggests that the inability to find a single petrophysical relation in space and time between concentration and electrical resistivity is largely an effect of two properties of ERT surveys: (1) decreased sensitivity of ERT to detect the target plume with increasing distance from the electrodes and (2) the smoothing imprint of regularization used in inversion.