Tracking 3D Tracer Migration: Non-stationary Conditioning of Resistivity Tomograms to Simulated Concentrations

To quantitatively use electrical resistance tomography (ERT) to estimate groundwater solute concentrations, a relation must exist between concentration and resistivity. Obtaining site-specific relations between geophysical and hydrogeologic state variables traditionally entails application of empirical petrophysical expressions to tomographic geophysical images, such as resistivity tomograms. In field applications, direct estimation of solute concentrations has been only moderately successful because (1) reconstructed tomograms are often highly uncertain and subject to inversion artifacts; (2) the range of subsurface conditions represented in data sets is incomplete due to the paucity of co-located well or core data and aquifer heterogeneity; and (3) geophysical methods exhibit spatially variable sensitivity. We use numerical simulation of solute transport and electrical resistance processes to create local non-stationary relations between the resistivity and tracer concentration. These relations are applied to tomograms of electrical resistivity obtained from field measurements of resistance using cross-well ERT. Based on synthetic and field cases, we demonstrate that tracer mass and concentration estimates obtained using this non-stationary estimation approach are far better than those obtained using direct application of empirical petrophysical relations such as Archie's law; the application of petrophysical relations directly to inverted 3D ERT tomograms produces severe mass and concentration underestimates.