QUADRIPOLE‐QUADRIPOLE ARRAYS FOR DIRECT CURRENT RESISTIVITY MEASUREMENTS—MODEL STUDIES

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Abstract
For a quadripole‐quadripole array, in which current is sequentially injected into the ground by two perpendicular dipoles, an apparent resistivity can be defined in terms of the vectorial cross product of the two electric fields measured at the receiver site. Transform equations are derived (for horizontally layered media) which relate this apparent resistivity to the apparent resistivities obtained with conventional dipole‐dipole and Schlumberger arrangements. To evaluate the method, two mathematical models are used. The first model is a half‐space with an “alpha conductivity center,” and the second model is a half‐space with a vertical contact. For an idealized quadripole‐quadripole array, simple expressions are found for the apparent resistivity, which is shown to be independent of the orientation of the current quadripole. Theoretical anomalies calculated for the quadripole‐quadripole array are compared with those obtained for a dipole‐quadripole array. It is shown that whereas the apparent resistivity map for the dipole‐quadripole array varies greatly with the azimuth of the source dipole, the results obtained with the quadripole‐quadripole array consistently display a remarkable resemblance to the assumed distribution of true resistivity. This is especially true when the current quadripole is placed at a large distance from the surveyed area.

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