Two-dimensional inversion of wideband spectral data from the capacitively coupled resistivity method – first applications in periglacial environments

The DC resistivity method is a common tool in periglacial research because it can delineate zones of large resistivities, which are often associated with frozen water. The interpretation can be ambiguous, however, because large resistivities may also have other causes, like solid dry rock. One possibility to reduce the ambiguity is to measure the frequency-dependent resistivity. At low frequencies (< 100 Hz) the corresponding method is called induced polarization, which has also been used in periglacial environments. For the detection and possibly quantification of water ice, a higher frequency range, between 100 Hz and 100 kHz, may be particularly interesting because in that range, the electrical properties of water ice exhibit a characteristic behaviour. In addition, the large frequencies allow a capacitive coupling of the electrodes, which may have logistical advantages. The capacitively coupled resistivity (CCR) method tries to combine these logistical advantages with the potential scientific benefit of reduced ambiguity. In this paper, we discuss CCR data obtained at two field sites with cryospheric influence: the Schilthorn massif in the Swiss Alps and the frozen Lake Prestvannet in the northern part of Norway. One objective is to add examples to the literature where the method is assessed in different conditions. Our results agree reasonably well with known subsurface structure: at the Prestvannet site, the transition from a frozen lake to the land is clearly visible in the inversion results, whereas at the Schilthorn site, the boundary between a snow cover and the bedrock below can be nicely delineated. In both cases, the electrical parameters are consistent with those expected from literature. The second objective is to discuss useful methodological advancements: first, we investigate the effect of capacitive sensor height above the surface and corroborate the assumption that it is negligible for highly resistive conditions. For the inversion of the data, we modified an existing 2-D inversion code originally developed for low-frequency induced polarization data by including a parametrization of electrical permittivity. The new inversion code allows the extraction of electrical parameters that may be directly compared with literature values, which was previously not possible.

Two-dimensional Inversion of wideband spectral data from the Capacitively Coupled Resistivity method – First Applications in periglacial environments

The Capacitively Coupled Resistivity (CCR) method determines the electrical resistivity and permittivity by analysing the spectra of magnitude and phase shift of the electrical impedance. The CCR is well suited for the application in cryospheric and periglacial areas, because these areas provide the required physical conditions and logistical advantages of the method regarding the problems of coupling on highly resistive grounds and in some cases hard surfaces. Since the electrical properties of ice and frozen material have a strong frequency dependence, broad spectral measurements can deliver complementary information compared to conventional low-frequency techniques. For the inversion of the data, we modified an existing 2-D inversion code originally developed for low-frequency Induced Polarization data by including a Cole-Cole parametrization of electrical permittivity. We discuss the application of the code and particular aspects related to capacitively coupled measurements using data from two sites with cryospheric influence: the Schilthorn massif in the Swiss Alps and the frozen lake Prestvannet in the northern part of Norway. We investigate the effect of capacitive sensor height above the surface and corroborate the assumption that it is negligible for highly resistive conditions. The first results agree reasonably well with known subsurface structure and measurements reported in the literature. We conclude that a spectral 2-D inversion with a Cole-Cole parametrization of permittivity is a feasible tool to invert CCR data in periglacial environments.

Inversion of capacitively coupled resistivity (line-antenna) measurements

The capacitively coupled resistivity method using line antennas (or electrodes) has been widely applied for various kinds of applications. To solve the associated inversion problem, the general practice (i.e., the indirect inversion method) for 2D surface resistivity surveys is to approximate the line-electrode array by an equivalent point-electrode array, so that the existing direct current resistivity inversion programs can still be used. Based on the experimental evidence from this study that two resistivity arrays with a similar sensitivity (1D) curve offers comparable measurement, we optimized the equivalent point-electrode array by minimizing the sensitivity (1D) difference between the line- and point-electrode arrays in terms of the depth of investigation difference (DID). The dipole length of the optimal equivalent point-electrode array can be determined by considering only the array with the shortest dipole distance. For the line-electrode arrays with the dipole lengths of 2.5, 5, and 10 m, the suggested optimal dipole lengths are 74%, 73%, and 73% of the respective dipole lengths. The numerical examples carried out in this study prove the effectiveness of the indirect inversion method for 2D surface resistivity surveys when the appropriate equivalent point-electrode array with a low DID value is chosen, and vice versa. The direct inversion of the line electrode resistivity measurements from 3D resistivity surveys is achieved with a MATLAB-based, open-source resistivity inversion package called RESINVM3D incorporating line electrodes. The usefulness of this modified code was demonstrated with a numerical example that considered cross-borehole resistivity tomography using line electrode measurements. The location of the assigned resistivity anomaly and the boundary between two soil layers were well captured by the direction inversion.