Induced polarization as a tool to characterize permafrost 1. Theory and laboratory experiments

SUMMARY In the last decade, the dynamic Stern layer (DSL) model has proven to be a reliable petrophysical model to comprehend induced polarization data at various scales from the representative elementary volume of a porous rock to the interpretation of field data. Preliminary works have demonstrated that such model can be extended to understand the induced polarization properties of ice-bearing rocks and to interpret field-acquired induced polarization data in the context of permafrost. That being said, the direct effect of ice was let aside. We first review the DSL model in presence of ice and discuss the role of ice as an interfacial protonic dirty semiconductor in the complex conductivity spectra with an emphasis on the role of the complex-valued surface conductivity of ice crystals above 1 Hz. We propose a new combined polarization model including indirect and direct ice effects. By direct effects, we mean the effects associated with changes in the liquid water content and salinity of the pore water. By direct effect, we mean that the role of the interfacial properties of the ice surface and liquid water is still present in the pore space of the porous composite. In this case, the electrical current is not expected to cross the ice crystals. Instead, it would polarize the surface of the ice crystals (and therefore the ice crystals) and generate a very high chargeability that can reach one depending on the value of the volumetric content of ice. We apply the DSL model to a new set of complex conductivity spectra obtained in the frequency range 10 mHz–45 kHz using a collection of 25 rock samples including metamorphic and sedimentary rocks in the temperature range +15/+20 °C to −10/−15 °C. We observe that the model explains very well the observed data in the low-frequency range (10 mHz–1 Hz) without any direct contribution of ice. In the high-frequency range (above 1 Hz), we observe a weak contribution possibly associated with the contribution of ice crystals in low-porosity crystalline rocks. We establish under what conditions the direct contribution of ice can be neglected. We also investigate the role of porosity, cation exchange capacity and freezing curve parameters on the complex conductivity spectra of crystalline and non-crystalline rocks during freezing. Laboratory experiments demonstrate that in most field conditions including permafrost conditions, surface conductivity associated with conduction on the surface of clay minerals (and alumino-silicates in general) is expected to dominate the overall conductivity response. This is in sharp contract with many claims found in the literature. Therefore Archie’s law cannot be used as a conductivity equation in this context because of the contribution of surface conductivity. A large experimental and field data set at the Aiguille du Midi (3842 m a.s.l., French Alps) for the resistivity versus temperature data of granitic rocks demonstrates the role of surface conductivity in the overall conductivity of the rock.