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 (zR≈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 aR≤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.

Parameter sensitivity maps of surface geoelectric arrays I. Linear arrays

“…Szalai (1997) computed parameter sensitivity maps by using simple analytical formula, and -as it was demonstrated by Szalai and Szarka (2000) -the analitically computed parameter sensitivity values are in a good agreement with the numerical results, if the subsurface cube is relatively small (the difference is smaller than 5%, if a/R ≤ 0.1, where a is the side length of the cube, R is the transmitter-receiver distance).…”

“…-For subsurface bodies of limited size, the values provide good approximation considering even the potential difference values themselves (Szalai and Szarka 2000).…”

“…Two examples will be given: 2a. Null arrays over symmetrical inhomogeneities (Szalai et al 2000); 2b. Rotational features over elongated inhomogeneities (Szalai et al 2002).…”

Depth of Investigation of Dipole-dipole, Noncolinear and Focused Geoelectric Arrays

“…On basis of the DIC functions we compute investigation depth values from both the Roy-Apparao and the Edwards concepts. The mathematical basis of the computation for dipole-dipole arrays is given in the paper by Szalai and Szarka (2000); while the DIC functions of the other arrays were analytically computed by a new, general formula, which can be applied for any surface geoelectric array. (Roy and Apparao 1971), z e /R: median depth (Edwards 1977).…”

Electrical resistivity tomography (ERT) and sedimentological analysis applied to investigation of Upper Jurassic limestones from the Krzeszowice Graben (Kraków Upland, southern Poland)

“…Szalai and Szarka, 2000;Dahlin and Zhou, 2004). Lengths of cur rent and po ten tial di poles a = 1, 2, 3, 4, 5, 6 Dx and sep a ration fac tors (dis tances be tween cur rent and po ten tial di poles), n = 1, 2, 3, 4, 5, 6 a have been used.…”