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

Abstract

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 ε eff α= ∑ i=1 N f iε i α . It is shown that, for most of the moisture range, the logarithmic Lichtenecker's 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 Lichtenecker's 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, ε s, and it permits the estimation of ε s in volcanic soils from dry soil samples packed in air, where previous estimates (developed for mineral soils) failed to do so.