Computation of Optimized Electrode Arrays for 3-D Electrical Resistivity Tomography Surveys

Abstract

The present study explores the applicability and effectiveness of an optimization technique applied to electrical resistivity tomography data. The procedure is based on the Jacobian matrix, where the most sensitive measurements are selected from a comprehensive data set to enhance the least resolvable parameters of the reconstructed model. Two existing inversion programs in two and three dimensions are modified to incorporate this new approach. Both of them are selecting the optimum data from an initial comprehensive data set which is comprised of merged conventional arrays. With the two-dimensional (2-D) optimization approach, the most sensitive measurements are selected from a 2-D survey profile and then a clone of the resulting optimum profile reproduces a three-dimensional (3-D) optimum data set composed of equally spaced parallel lines. In a different approach, with the 3-D optimization technique, the optimum data are selected from a 3-D data set of equally spaced individual parallel lines. Both approaches are compared with Stummer’s optimization technique which is based on the resolution matrix. The Jacobian optimization approach has the advantage of selecting the optimum data set without the need for the solution of the inversion problem since the Jacobian matrix is calculated as part of the forward resistivity problem, thus being faster from previous published approached based on the calculation of the sensitivity matrix. Synthetic 3-D data based on the extension of previous published works for the 2-D optimization case and field data from two case studies in Greece are tested, thus verifying the validity of the present study, where fewer measurements from the initial data set (about 15–50%) are able to reconstruct a model similar with the one produced from the original comprehensive data set.