Effective medium theories for modelling the relationships between electromagnetic properties and hydrological variables in geomaterials: a review

The paper reviews the effective medium theories used for modelling the relationships between electromagnetic properties (low-frequency conductivity and high-frequency permittivity) and hydrological variables (water content, salinity, suction, permeability) in soils and rocks. It aims a) to provide a simple presentation of these theoretical approaches, b) to present their theoretical and practical limitations and c) to establish some connections with empirical equations usually used in hydrogeophysics (i.e., Archie relationships, Topp equation and complex refractive index model). This review demonstrates that two groups of effective medium theories can be clearly identified. The first group constituted by the Maxwell-Wagner and Symmetric-Bruggenian rules is characterized by easy-to-use models. When the volumetric water content and the texture are known, they allow to obtain fast estimates of effective electromagnetic properties. In the second group, the differential effective medium schemes that are more complex from a mathematical point of view are preferred when frequency-dependent properties are studied. In particular, differential effective medium schemes are used for providing some insights into the physical basis of spectral induced polarization measurements in hydrogeophysical applications.