An approximate analytical approach to compute geoelectric dipole–dipole responses due to a small buried cube

Abstract

A simple analytical solution is presented for computing direct current (DC) electric field distortion due to a small cube in a homogeneous half‐space, measured with a dipole–dipole array on the surface. Both the transmitter and the receiver may have any orientation; furthermore their position on the horizontal surface and the depth of the cube can be freely selected. It is shown that a simple approximate analytical method may replace more complicated 3D numerical modelling algorithms. The approximation lies in the linearization of the problem: the secondary source (i.e. the cube) is considered as a system of three perpendicular electric dipoles. In spite of this first‐order approximation, in the case of realistic depths z ( z R ≈0.1–0.5, where R is the transmitter–receiver distance), this approximate solution fits very well with true 3D numerical modelling results, and with analogue modelling results if a R ≤0.1, where a is the length of the side of the cube. Due to its simplicity, this method could be used for computing DC field distortion effects, estimating parameter‐sensitivities, or even determining some initial models for further inversions.