Model Reliability for 3D Electrical Resistivity Tomography: Application of the Volume of Investigation Index to a Time-Lapse Monitoring Experiment

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Solution appraisal is difficult for large 3D, nonlinear inverse problems such as electrical resistivity tomography (ERT). We construct the volume of investigation index (VOI) as the sensitivity of the inversion result to a variable-reference model. This limited exploration of the model space provides an efficient and pragmatic method of appraisal for a particular data set and a 3D model domain. We present a synthetic example to demonstrate the applicability of the VOI as a tool for characterizing model reliability for 3D ERT and as a method of survey design. We show how the VOI provides a measure of model resolution and how insight gained from VOI analysis cannot be gained through similar examination of the average sensitivity distributions. In the context of ERT monitoring of an injection/withdrawal experiment, we utilize the VOI for judging the degree of reliability of hydrogeological interpretations that stem from features observed in the estimated electrical-conductivity models. We employ the VOI for the experimental data as a comparative measure of survey performance. For this experiment, the VOI shows that a larger, more artifact-free region of reliability is achieved using a circulating vertical dipole-dipole survey geometry, as opposed to a horizontal dipole-dipole survey geometry. The experimental VOI distributions exhibit dependence on the borehole infrastructure and the actual earth model.