A physical interpretation of logarithmic TDR calibration equations of volcanic soils and their solid fraction permittivity based on Lichteneckerʹs mixing formulae

A physical interpretation of both logarithmic Time Domain Reflectometry (TDR) calibration equations and empirical estimates of the solid fraction permittivity of volcanic soils is given in terms of the power-law mixing formulae εeffα=∑i=1Nfiεiα. It is shown that, for most of the moisture range, the logarithmic Lichteneckerʹs law (α=0) may hold in volcanic soils, while for coarse mineral soils a Birchak model (α=1/2) may be universally valid. Two distinct logarithmic dielectric regimes dominated by free and bound water were identified for at least some soils. Such a transition from high to low water content may be predicted from the wilting point of the soil. At very low water content Lichteneckerʹs formula breaks down in volcanic soils, and a Birchak refractive index model results are more appropriate. The latter provides a generalization and physical interpretation of previous empirical estimates of the permittivity of the mineral fraction of soils, εs, and it permits the estimation of εs in volcanic soils from dry soil samples packed in air, where previous estimates (developed for mineral soils) failed to do so.