The electrical conductivity of clay-free sandstones is customarily assumed to have negligible surface conductivity contribution. The Fontainebleau sandstone, a clean sandstone with relatively coarse (∼250 μm) and well-rounded silica grains and silica cement, exhibits surface conductivity along the electrical double layer coating the surface of the grains. A recently developed volume-averaging model for the electrical conductivity was used to determine intrinsic formation factor and surface conductivity from electrical conductivity measurements performed at seven salinities with NaCl solutions. The bulk tortuosity of the pore space influenced the surface conductivity in a predictable way. Formation factor and permeability can be determined as a function of the porosity using the equations developed by Archie for the formation factor, and Revil and Cathles for the permeability. In both the cases, the data emphasize the existence of a percolation threshold of about 0.02 (2%) in porosity. Once corrected for the effect of this percolation threshold, the porosity exponent of Archie's equation was approximately equal to 1.5 as predicted from the differential effective medium theory for a pack of spherical grains suspended in an electrolyte. We illustrated that permeability can be predicted, within one order of magnitude, from surface conductivity, porosity, and formation factor. Spectral-induced polarization data indicated that the in-phase conductivity was nearly frequencyindependent (in the frequency range from 1 to 10 kHz) whereas the quadrature conductivity displayed a relationship between the surface conductivity and a peak frequency likely related to the pore throat size determined from mercury porosimetry measurements.

Low-frequency quadrature conductivity spectra of siliclastic materials exhibit typically a characteristic relaxation time, which either corresponds to the peak frequency of the phase or the quadrature conductivity or a typical corner frequency, at which the quadrature conductivity starts to decrease rapidly toward lower frequencies. This characteristic relaxation time can be combined with the (intrinsic) formation factor and a diffusion coefficient to predict the permeability to flow of porous materials at saturation. The intrinsic formation factor can either be determined at several salinities using an electrical conductivity model or at a single salinity using a relationship between the surface and quadrature conductivities. The diffusion coefficient entering into the relationship between the permeability, the characteristic relaxation time, and the formation factor takes only two distinct values for isothermal conditions. For pure silica, the diffusion coefficient of cations, like sodium or potassium, in the Stern layer is equal to the diffusion coefficient of these ions in the bulk pore water, indicating weak sorption of these couterions. For clayey materials and clean sands and sandstones whose surface have been exposed to alumina (possibly iron), the diffusion coefficient of the cations in the Stern layer appears to be 350 times smaller than the diffusion coefficient of the same cations in the pore water. These values are consistent with the values of the ionic mobilities used to determine the amplitude of the low and high-frequency quadrature conductivities and surface conductivity. The database used to test the model comprises a total of 202 samples. Our analysis reveals that permeability prediction with the proposed model is usually within an order of magnitude from the measured value above 0.1 mD. We also discuss the relationship between the different time constants that have been considered in previous works as characteristic relaxation time, including the mean relaxation time obtained from a Debye decomposition of the spectra and the Cole-Cole time constant.

This paper provides an update on the fast‐evolving field of the induced polarization method applied to biogeophysics. It emphasizes recent advances in the understanding of the induced polarization signals stemming from biological materials and their activity, points out new developments and applications, and identifies existing knowledge gaps. The focus of this review is on the application of induced polarization to study living organisms: soil microorganisms and plants (both roots and stems). We first discuss observed links between the induced polarization signal and microbial cell structure, activity and biofilm formation. We provide an up‐to‐date conceptual model of the electrical behaviour of the microbial cells and biofilms under the influence of an external electrical field. We also review the latest biogeophysical studies, including work on hydrocarbon biodegradation, contaminant sequestration, soil strengthening and peatland characterization. We then elaborate on the induced polarization signature of the plant‐root zone, relying on a conceptual model for the generation of biogeophysical signals from a plant‐root cell. First laboratory experiments show that single roots and root system are highly polarizable. They also present encouraging results for imaging root systems embedded in a medium, and gaining information on the mass density distribution, the structure or the physiological characteristics of root systems. In addition, we highlight the application of induced polarization to characterize wood and tree structures through tomography of the stem. Finally, we discuss up‐ and down‐scaling between laboratory and field studies, as well as joint interpretation of induced polarization and other environmental data. We emphasize the need for intermediate‐scale studies and the benefits of using induced polarization as a time‐lapse monitoring method. We conclude with the promising integration of induced polarization in interdisciplinary mechanistic models to better understand and quantify subsurface biogeochemical processes.

For the past forty years electromagnetic prospecting instruments have played a growing role in the mapping of soil EM properties in the very low‐frequency (VLF) range for a large variety of applica tions and they are now beginning to be applied in the medium‐frequency range. Measurement interpretations, however, necessitate expressing the results in terms of physical properties. This step allows not only comparisons and joint interpretation with data generated by different electromag netic induction (EMI) instruments but also with other types of field measurements e.g., vertical electrical sounding (VES) or electrical resistivity tomography (ERT) or laboratory tests on samples. The calibration process here proposed is based on comparisons between the instrument respons es and: (1) an exact 1D multi‐layer analytical modelling that takes the three EM properties into account, i.e., the electrical conductivity, the complex magnetic susceptibility and the complex die lectric permittivity when the instrument is elevated above a layered ground; (2) the response to purely conductive metallic spheres, which only depends on the diameter of the spheres. It is applied to two instrument prototypes: one in the VLF frequency range and the other in the medium‐frequency (MF) range.