Theoretical and experimental examinations of the capacitively coupled resistivity (line antenna) method

Abstract

The capacitively coupled (CC) resistivity method is an emerging geophysical technique for near-surface investigations. However, there are two major problems associated with using the CC resistivity (line antenna) system in ground investigations. These two problems are (1) the geometrical factor and (2) measurement biases. We first derive the geometric factor for the line-antenna array in a dipole-dipole configuration. The new expression of the geometric factor considers the separation between the two current (and the two potential) line antennas, thereby improving the accuracy of the measured apparent resistivity. Second, from the electroquasistatic point of view, a quadruline model that can describe the characteristics of the CC resistivity (line antenna) system is derived based on the previously published quadrupole model. The validity of the quadruline model is verified experimentally. Based on the quadruline model, it is found that the dielectric properties of the line-to-ground capacitor and the ground permittivity produce measurement bias at low and high current frequencies, respectively. If the operating current frequency is around the kHz range and the ground resistivity is relatively high, such as in permafrost areas, the ground permittivity can also create measurement bias to cause the actual value to be underestimated. The experimental results and the predictions by the quadruline model suggest that the measurement bias induced by the gap between the line antenna and the ground surface becomes significant and cannot be ignored as the gap height is large and the associated ground resistivity is low. In general, the CC resistivity (line antenna) measurements are not biased by the gap effect when the gap height is less than 0.01 m, which can easily be achieved for tests on flat ground.