Insights into the structural properties of frozen rock from fitting a two-component model to broad-band SIP laboratory data

SUMMARY High-frequency induced polarization, which measures the complex electrical conductivity in a frequency range up to several hundred kHz, is potentially suitable to detect and quantify ice in the frozen subsurface. In order to estimate ice content from the electrical spectra, a two-component weighted power mean (WPM) model has been suggested and applied to field-scale data. In that model, ice is one of the components, whereas the solid phase, residual liquid water and potentially air form the second component, called ‘matrix’. Here, we apply the model to laboratory data previously discussed in the literature, with the aim to assess the applicability of the model and to understand the behaviour of the frequency-dependent electrical conductivity. The data were measured on an unconsolidated sediment sample with 20.8 per cent water content from the European Alps, and a consolidated sandstone with 16.6 per cent porosity. Electrical spectra have been measured over a temperature range from approx. $- 41^{\circ}$C to $+20^{\circ}$C and a frequency range from 0.01 Hz to 45 kHz. We extend the original WPM model to account for low-frequency polarization in form of a constant phase angle model. The measured data were fitted with the model by a least-squares inversion algorithm. In order to reduce the ambiguity, we constrained several of the nine underlying parameters by literature values, in particular for the electrical properties of water ice, and the expected ice content according to porosity or water content of the unfrozen sample. Both data sets can be well matched, corroborating the hypothesis that the model is in principle suitable to explain measured data of frozen samples in that frequency range. One important observation is that the mixing parameter, that is, the power in the WPM model, which is controlled by the geometric arrangement of the two components, depends on temperature. For the unconsolidated sample it even becomes negative at the coldest temperature, which is important because negative shape factors relate to specific geometries. A second observation is that relatively large permittivities of the matrix are required to fit the data, suggesting that processes at the interface between solid/liquid phase and ice, which are not included in the volumetric mixing model, might be relevant and should be considered in future extensions of the model.