Hydrogeophysical tracking of three-dimensional tracer migration: The concept and application of apparent petrophysical relations

[1] Direct estimation of groundwater solute concentrations from geophysical tomograms 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 because of the paucity of colocated well or core data and aquifer heterogeneity, and (3) geophysical methods exhibit spatially variable sensitivity. We show that electrical resistivity tomography (ERT) can be used to estimate groundwater solute concentrations if a relation between concentration and inverted resistivity is used to deal quantitatively with these issues. We use numerical simulation of solute transport and electrical current flow to develop these relations, which we call ‘‘apparent’’ petrophysical relations. They provide the connection between concentration, or local resistivity, and inverted resistivity, which is measured at the field scale based on ERT for media containing ionic solute. The apparent petrophysical relations are applied to tomograms of electrical resistivity obtained from field measurements of resistance from cross-well ERT to create maps of tracer concentration. On the basis of synthetic and field cases we demonstrate that tracer mass and concentration estimates obtained using these apparent petrophysical relations are far better than those obtained using direct application of Archie’s law applied to three-dimensional tomograms from ERT, which gives severe underestimates.