Fundamentals of the capacitive resistivity technique

Abstract

Capacitive resistivity (CR) is an emerging geophysical technique designed to extend the scope of the conventional methodology of dc resistivity to environments where galvanic coupling is notoriously difficult to achieve — for example, across engineered structures (roads, pavements), hard rock, dry soil, or frozen ground. Conceptually, CR is based on a four-point array capacitively coupled to the ground. Under certain conditions, capacitive measurements of resistivity are equivalent to those obtained with the dc technique, thus making dc interpretation schemes applicable to CR data. The coupling properties of practical sensor realizations are shown to be a function of their geometrical arrangement. Separate bodies of theory are associated with two complementary but distinct sensor types: the capacitive-line antenna and the plate-wire combination. The use of plate-wire combinations results in localized coupling, which, in conjunction with a quasi-static (low-frequency) formulation of the transfer impedance, provides a valid emulation of the dc measurement with point electrodes. A parametric study of the complex, quasi-static transfer impedance reveals the existence of a restricted range of practical parameters that permits successful operation of CR instruments at low induction numbers. Theory predicts that emulating the dc measurement is compromised if low-induction-number operation is not maintained throughout a survey area, as in a zone of high conductivity. Validation of the theory is achieved using specially designed field-scale experiments carried out with a CR instrument capable of measuring the full complex transfer impedance. At intermediate dipole separations, the results are consistent with the predictions of quasi-static theory. Deviations observed in the near and far separation zones can be explained by geometric effects or the breakdown of quasi-static conditions, respectively. Finally, under suitable conditions the phase-sensitive expression for apparent resistivity as a function of the complex transfer impedance is shown to reduce to the classical dc formula for the in-phase component. CR, while capable of emulating dc resistivity, also can be regarded as a physical complement of the inductively coupled ground-conductivity method.