Comparison of smoothness-constrained and geostatistically based cross-borehole electrical resistivity tomography for characterization of solute tracer plumes

Experiments using electrical resistivity tomography (ERT) have shown promising results in reducing the uncertainty of solute plume characteristics related to estimates based on the analysis of local point measurements only. To explore the similarities and differences between two cross-borehole ERT inversion approaches for characterizing salt tracer plumes, namely the classical smoothness-constrained inversion and a geostatistically based approach, we performed two-dimensional synthetic experiments. Simplifying assumptions about the solute transport model and the electrical forward and inverse model allowed us to study the sensitivity of the ERT inversion approaches towards a variety of basic conditions, including the number of boreholes, measurement schemes, contrast between the plume and background electrical conductivity, use of a priori knowledge, and point conditioning. The results show that geostatistically based and smoothness-constrained inversions of electrical resistance data yield plume characteristics of similar quality, which can be further improved when point measurements are incorporated and advantageous measurement schemes are chosen. As expected, an increased number of boreholes included in the ERT measurement layout can highly improve the quality of inferred plume characteristics, while in this case the benefits of point conditioning and advantageous measurement schemes diminish. Both ERT inversion approaches are similarly sensitive to the noise level of the data and the contrast between the solute plume and background electrical conductivity, and robust with regard to biased input parameters, such as mean concentration, variance, and correlation length of the plume. Although sophisticated inversion schemes have recently become available, in which flow and transport as well as electrical forward models are coupled, these schemes effectively rely on a relatively simple geometrical parameterization of the hydrogeological model. Therefore, we believe that standard uncoupled ERT inverse approaches, like the ones discussed and assessed in this paper, will continue to be important to the imaging and characterization of solute plumes in many real-world applications.