An approximate analytical approach to compute geoelectric dipole–dipole responses due to a small buried cube |
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Authors: | Sándor Szalai László Szarka |
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Institution: | Geodetic and Geophysical Research Institute of the Hungarian Academy of Sciences, H-9401 Sopron, POB 5, Hungary. E‐mail:;and |
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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. |
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