The face‐current concept and its application to survey design in electrical exploration

Abstract

This paper presents a new method to identify the regions over a 3D geoelectrical structure that produce major contributions to the electrical potential established in response to a dc source at the ground surface. The measured potential is represented by a sum of a known primary potential (due to a homogeneous half space) plus an unknown potential caused by conductivity inhomogeneities. Because the primary potential is continuous everywhere, the interfaces with a conductivity contrast act as sources or sinks of currents in order to maintain the continuity of the current density related to the primary flux. These disturbing face currents are responsible for the generation of the secondary potential, and mapping them over a given structure allows us to assess the regions where the secondary potential is generated. In general, the face currents vanish away from the source according to the decay of the primary electric field. For this reason, deeper investigations can be expected when using pole sources because its primary field decays with the inverse of the squared distance, instead of the cubed distance as for dipole sources. For thin sheets, the polarization decay with distance is one order higher than that for large 3D bodies, which makes the detection of a sheet yet more difficult. The quantification of the total face current over the structure for different positions along a profile helps one choose the proper electrode array and determine its optimum length. This is done in two steps: (1) identification of the offset where the dc source provides the highest polarization (face current) on the targeted structure, and (2) determination of the array length by locating the potential electrodes closest to the region with the highest polarization. This second criterion came from an analogy between the face‐current and artificial current sources, where it is intuitively seen that the resulting potential is highest close to the source. The proposed survey design technique is applied to three models commonly used in electrical exploration: a shallow conductive heterogeneity, a buried contact, and a thin conductive sheet.