2-D and 3-D interpretation of electrical tomography measurements; Part 2, The inverse problem

The interpretation of borehole-to-borehole electrical measurements requires solving an inverse problem for a given class of model geometries. The usual approach to an inverse problem includes a model dependent task (i.e., forward modeling) and a generic task (i.e., an optimization scheme). We have developed an optimization algorithm using a nonlinear inversion technique. This algorithm allows recovery of a possible resistivity distribution in an investigated zone between two boreholes or in the vicinity of them. This resistivity distribution is defined as a set of 2-D or 3-D volumes of constant resistivity. The inversion procedure minimizes a least-squares term plus a damping term. This latter term seeks to minimize the roughness of the solution. An improved form of this smoothness term may enhance the spatial resolution of the resistivity image, assuming that the resistivity contrast is known a priori. This reconstruction algorithm has been tested for both 2-D and 3-D geometries. These inversion tests were conclusive enough such that a successful interpretation on a 16X16 grid has been carried out for a field data set obtained from a mineral exploration test site.