Cross‐borehole resistivity tomography

Abstract

Electrical resistivity tomography (ERT) is a method for determining the electrical resistivity distribution in a volume from discrete measurements of current and voltage made within the volume or on its surface. We have developed an ERT algorithm that is an iterative, modified least squares inversion, based on a finite element forward solution of Laplace’s equation. We report the results of tests on this algorithm designed to determine how resistance measurements made from two boreholes may be used to image the resistivity distribution between them. A number of simple but geophysically significant structures are modeled. These include a single isolated block anomaly, two layers, a thin isolated continuous layer, and a vertical band. The main features of most resistivity models were identifiable in the reconstructions. Limited data accuracy and noise were simulated and found to cause a deterioration of the image. However, even with measurements of only one significant figure accuracy, the algorithm converged toward the desired solution for at least the first iteration and the targets were identifiable in the reconstructions. Imprecision in the data influences convergence as well as image quality; more iterations eventually lead to divergence. Spatial resolution depends on such factors as data errors and the specific target geometry.