Numerical simulations of capacitive resistivity imaging (CRI) measurements

Electrical resistivity tomography (ERT) is a well-developed geophysical technique that is used to study a variety of geoscientific problems. In recent years it has been applied to the study of permafrost processes at both field and laboratory scale. However, highly resistive surface conditions limit its applicability due to high and variable contact resistances. The use of capacitively coupled sensors is expected to overcome this problem by providing a steady contact impedance regime. Although the theory of capacitive resistivity imaging (CRI) is well understood, a point-pole approximation of the sensors is typically used to show the similarity between CRI and ERT. Due to their nature, capacitive sensors cannot be designed as point-poles as they require a finite extent. This paper assesses the effects the finite size of sensors has on the applicability of CRI theory and aims to provide an improved understanding of the measured data. We employ finite-element numerical modelling to simulate CRI measurements over a homogeneous halfspace and on a finite rock sample. The results of a parameter study over a homogeneous halfspace are compared to an analytical solution. Observed discrepancies between the two solutions clearly indicate that large sensor sizes and small sensor separations violate the point-pole assumption of the analytical solution. In terms of data interpretation, this dictates that sensor separations smaller than twice the sensor size have to be avoided in order to remain below a generic error threshold of 5%. We show that sensor elevation, halfspace resistivity, halfspace permittivity, and measurement frequency have only minor effects on the discrepancy between simulation and analytical solution. The simulation of sequential CRI measurements on a finite rock sample suggests that, in line with expectations, the measured signals lie mainly in the 4th quadrant of the complex plane. However, we can also observe data with negative geometric factors, which are related to uncommon array. A comparison between simulated and measured data showed very good agreement; it validated the simulations and explained the measured data acquired using a prototype multisensor CRI system. We show that a comparison of simulated and measured imaginary parts of the transfer impedance can be used to assess CRI measurement errors. Our work demonstrates that finite-element numerical modelling of CRI measurements is a valuable tool with which to define limitations on array design and to assess data quality.