Quantitative inverse modelling of a cylindrical object in the laboratory using ERT: An error analysis

Electrical resistivity tomography (ERT) is a geophysical technique that can be used to obtain three-dimensional images of the bulk electrical conductivity of the subsurface. Because the electrical conductivity is strongly related to properties of the subsurface and the flow of water it has become a valuable tool for visualization in many hydrogeological and environmental applications. In recent years, ERT is increasingly being used for quantitative characterization, which requires more detailed prior information than a conventional geophysical inversion for qualitative purposes. In addition, the careful interpretation of measurement and modelling errors is critical if ERT measurements are to be used in a quantitative way. This paper explores the quantitative determination of the electrical conductivity distribution of a cylindrical object placed in a water bath in a laboratory-scale tank. Because of the sharp conductivity contrast between the object and the water, a standard geophysical inversion using a smoothness constraint could not reproduce this target accurately. Better results were obtained by using the ERT measurements to constrain a model describing the geometry of the system. The posterior probability distributions of the parameters describing the geometry were estimated with the Markov chain Monte Carlo method DREAM(ZS). Using the ERT measurements this way, accurate estimates of the parameters could be obtained. The information quality of the measurements was assessed by a detailed analysis of the errors. Even for the uncomplicated laboratory setup used in this paper, errors in the modelling of the shape and position of the electrodes and the shape of the domain could be identified. The results indicate that the ERT measurements have a high information content which can be accessed by the inclusion of prior information and the consideration of measurement and modelling errors.