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.
ASJC Scopus subject areas
- Geochemistry and Petrology