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 usua l approach to an inverse problem includes a model dependent task (i.e., for ward modeling) and a generic task (i.e. an optimization scheme). We have de veloped an optimization algorithm using a nonlinear inversion technique. Th is algorithm allows recovery of a possible resistivity distribution in an i nvestigated zone between two boreholes or in the vicinity of them. This res istivity distribution is defined asa 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 impro ved 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 geomet ries. These inversion tests were conclusive enough such that a successful i nterpretation on a 16 x 16 grid has been carried out for a field data set o btained from a mineral exploration test site.