The complex resistivity response of a homogeneous Earth with a finite-length contained vertical conductor

The complex resistivity response of a homogeneous Earth with a finite-length contained vertical conductor such as an oil well casing is considered. The calculational procedure developed is the equivalent of the so-called quasi-static approximation and includes a consideration of longitudinal conductor impedance and dipole-dipole array mutual coupling. The validity of the procedure is confirmed by showing that the results for long cylinder lengths are in excellent agreement with analytical calculations for infinite length cylinders available in the literature. Calculated curves of the apparent complex resistivity as a function of frequency and cylinder length for a typical field measurement are presented to indicate the effect of oil well casings on induced polarization surveys