Three‐dimensional modeling of a hole‐to‐hole electrical method: Application to the interpretation of a field survey

Abstract

Hole‐to‐hole electrical measurements can be used to localize or define the extension of conductive bodies whether or not they are penetrated by the holes. Two promising applications of this electrical method are the optimization of mining boreholes and the delineation of fractures. Although no particular problem arises in the instrumentation of a hole‐to‐hole electrical array, the interpretation of the results has proven to be difficult. A program has been developed to compute the electrical potential caused by direct current injection in an inhomogeneous half‐space (three‐dimensional bodies embedded within a layered earth). This program allows computation of the responses of most classical electrical arrays. It is based on calculation of a disturbance potential and on resolution of a Fredholm integral equation. The modeling program is used to define the apparent‐resistivity type responses of a hole‐to‐hole pole‐pole electrical configuration for different shapes and locations of bodies in the vicinity of the boreholes. To obtain a synthetic representation, the results are plotted on a plane where the X-axis corresponds to the depth in the measuring hole and the Y-axis corresponds to the depth in the injection hole. This representation seems to be particularly convenient for the electrical configuration examined here. A detailed study of simple geometrical models has yielded interpretation rules which have been applied to the qualitative interpretation of a field survey carried out at the mining prospect of SALAU (France). The program is then applied to this interpretation to check and confirm it, by direct calculation of the response corresponding to the model.