Induced Polarization of Clayey Rocks and Soils: Non-Linear Complex Conductivity Models

The past decades have witnessed the increased applications of induced polarization (IP) method in the critical zone studies with ubiquitous clay minerals. Although IP outperforms traditional electrical and electromagnetic methods through its unique ability to measure quadrature conductivity, the nonlinearity that quadrature conductivity behaves with salinities and frequencies greatly tortures IP practitioners, as (a) salinity-dependency makes the quadrature conductivity a varyingly unstable parameter to quantitatively estimate hydraulic properties and clay content; (b) frequency-dependent Cole-Cole and Debye/Warburg decomposition models, although mathematically sound, physically mingle the properties of pore water and clay minerals and are empirical in nature. From basic principles, we demonstrate that quadrature conductivity remains a hybrid property involving both clay and water, and develop relevant models to distinguish them. Our models are validated by theories, experiments, simulations, and comparisons, all of which proclaim considerable advantages over previous models and offer the prospect of quantitative applications. As habitually appears in the first chapter of many geophysics textbooks, rock and soil models (i.e., petrophysics) lay the base for geophysical applications, bridging the gap between macro-scale field and micro-scale rock/soil parameters such as porosity and permeability. In contrast to "clean" rocks and soils where Archie's law is readily used, the additional interfacial conduction and polarization arising from the electrical double layer of "dirty" rocks and soils, especially clayey ones, greatly complicate this issue and bring both challenges and opportunities. On the one hand, this interfacial conduction nullifies Archie's law, making the porosity evaluation challenging, but, on the other hand, these interfacial properties provide an opportunity to assess the pore structure and clay properties, making the permeability estimation possible. Although IP is highly commendable to separate the interfacial attribution from the bulk water, complex conductivity models that can both physically and mathematically explain clayey rock/soil behaviors are lacking, which is the goal of our work. We expect our developed models to deepen the understanding of IP mechanisms and lead to more quantitative IP applications. Salinity- and frequency-dependent nonlinearities lie at the crux of induced polarization mechanisms Quadrature conductivity increases with salinity mainly by virtue of the coupling between electrical double layer (EDL) and water Frequency dependency of clayey rocks and soils stems from the leaky-capacitor behavior of the EDL