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

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 a nd 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 complic ated 3D numerical modelling algorithms. The approximation lies in the linearization of the problem: the secondary s ource (i.e. the cube) is considered as a system of three perpendicular elec tric dipoles. In spite of this first-order approximation, in the case of re alistic depths z (z/R approximate to 0.1-0.5, where R is the transmitter-re ceiver distance), this approximate solution fits very well with true 3D num erical modelling results, and with analogue modelling results if a/R less t han or equal to 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 init ial models for further inversions.