On the calculation of 3-D apparent resistivity responses with conductive plates

Abstract

An integral equation technique is applied for modeling the three-dimensional apparent resistivity response of a set of conductive plates immersed in a homogeneous or stratified earth. In implementing the algorithm, the Fredholm integral equation of the second kind is transformed into a matrix equation and solved for the components of distributed current dipoles lying on the planes of the plates. The apparent resistivity at the earth's surface is obtained from the secondary potentials produced by the current dipoles. The accuracy of the computed responses is examined in five test models. Because there is not any analytical solution for these models which could be considered as a true solution, the accuracy is defined in terms of converging numerical results or by comparison with other previously published independent numerical responses. In the first three models single-plate inhomogeneities are considered with different inclinations (horizontal, vertical, and dipping at 45 degrees). In the last two cases the approximation of solid conductive bodies with plates is tested, considering in one of these models a layered host medium. The responses are compared with six different independent solutions reported in the literature. The overall agreement between theresponses is good but not optimum. The surface charge density approach seems to show a better converging behavior than our current dipole scheme and the simulation of solid bodies shows some relatively large discrepancies (less than 20%) in the apparent resistivities right over the plates. Despite these limitations, the multiplate technique promises to be a useful tool in the interpretation of resistivity surveys in geothermal, mineral, and groundwater environments where multiple conductors may coexist.