Validation of four resistivity mixing models on field time lapse geoelectrical measurements from fine-grained soil undergoing freeze-thaw cycles

Abstract

Resistivity mixing models relate porosity, phase composition and specific resistivities of ground materials to their bulk (effective) electrical properties. These models were typically derived for calculating hydrocarbon saturation from geophysical logs. In permafrost monitoring applications, they have been used to link ground electrical response to its phase composition, with focus on unfrozen water vs. ice content, and to derive changes in ground ice content from repeated resistivity acquisitions. Such quantitative interpretations rely on validity of the mixing models in a context different from the one they were derived in. To increase the reliability of the permafrost forecasts that are based on repeated resistivity surveys, we undertook validation of four selected resistivity mixing model formulations: i) the original Archie's law, ii) the Archie's law with an ice-content dependent cementation exponent $m$ (Archie-M), iii) a modification of the Archie's law for multiple conducting phases (Archie-N), and iv) the geometric mean model (GM). The model application context was permafrost monitoring and fate forecasting on natural fine-grained soil undergoing cycles of freezing and thawing, based on indirect (geophysical), in-situ time-lapse resistivity measurements. The purpose of the calibrated resistivity models was to derive the phase composition of the ground from in-situ resistivity measurements, with acceptable quantitative reliability, notably with respect to the amount and changes of ice and water content. In our validation framework, daily temperature-dependent soil phase distribution was converted into an effective resistivity distribution of the ground using each of the four resistivity mixing models. From the effective resistivity model, an apparent resistivity response was forward calculated and compared to time-lapse field apparent resistivity measurements from a permafrost monitoring field site. The performance metrics were i) the root mean square error between the forward-calculated and field-measured apparent resistivities throughout the freeze-thaw season, ii) the percentage of field apparent resistivity data explained by each resistivity model, and iii) the plausibility of the calibrated model parameter estimates. We found that despite different current conducting mechanisms involved in each of the resistivity mixing model formulations, the quantitative performance of the four evaluated models was very similar. The four models typically reproduced the field-measured resistivity variations within one to two standard deviations (STD) of the field measurements, depending on the time of the year and depth in the soil profile. In the active layer, the Archie-M model most consistently reproduced the field data within 1 STD throughout the freezing and frozen periods of the year (September – May). Meanwhile, the GM best matched the actual values of resistivities during freezing. The GM also recovered porosities of the three model layers close to the true values measured on borehole samples. All the tested models were challenged by accurately simulating the thawing period – overestimating resistivities in the temperature range from −5 °C to −2 °C and underestimating them between −2 °C and thawing point. Consequently, the choice between the models should depend on the specifics of a particular application, such as available calibration data, desired parameters or ground properties to resolve, sensitivity of the modeling framework etc. An application-specific validation of several resistivity mixing models and quantification of performance of the chosen resistivity model may be called for. Additionally, the possibility of using different mixing model and water content parameterizations should be investigated, to adequately address complex ground resistivity structures and phase change processes typical of permafrost ground.