Inverse modeling of electrical conductivity distributions from ERT datasets: integrated analyses of the successive linear estimator and a smoothness constrained regularization approach

Abstract

Recent field studies showed that electrical resistivity tomography (ERT) potentially is a viable tool for characterizing subsurface transport processes of substances with electrical conductivities differing from the background. Popular approaches for interpreting the electrical field measurements are based on inversion procedures including regularization terms, which force the inverse solution to be smooth. As a result, the image of a solute plume can be unsatisfactory. Furthermore most inversion procedures do not generally take advantage of in situ electrical conductivity measurements or point concentration data. We further recognize that while a solute plume in heterogeneous aquifers can be highly irregular, it can be characterized in a geostatistical sense: its mean position, lateral spreading, and spatial correlation structures. These plume statistics can serve as our prior knowledge about the plume. Based on existing stochastic theories of solute transport processes, plume statistics can be easily estimated from statistics, quantifying the heterogeneity of the hydraulic conductivity. Therefore, we hypothesize that an ERT inversion, incorporating our prior knowledge of the geostatistical characteristics of a plume and some direct point measurements of the plume concentration, could lead to more detailed images of subsurface electrical conductivity distributions associated with the solute plume. Using a synthetic salt tracer plume, we test our hypothesis by investigating the quality of inversions with a smoothness constrained regularization code as well as a geostatistic based, cokriging like code, the successive linear estimator (SLE). The results of our investigation based on measurements from different subsurface arrays show that the quality of an investigation is, as expected, strongly depending on the measurement geometry and the number of measurements. The integrated analyses of inverse modeling procedures, SLE and regularization, evidence that with only sparse measurements the conditioning of the electrical inverse problem with the statistical characteristics of the solute plume as well as with point values of the plume concentration enhances the quality of the result clearly. With an increasing number of measurements the effect of conditioning however becomes less effective.