Linking soil properties to permittivity data: Beyond ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Linking soil properties to permittivity data: Beyond the Complex Refractive Index Model
Author:Alessandro Brovelli <> (Dipartimento di Scienze dell'Ambiente e del Territorio, University of Milano-Bicocca)
Giorgio Cassiani <> (Dipartimento di Scienze Geologiche e Geotecnologie, University of Milano-Bicocca)
Presenter:Alessandro Brovelli <> (Dipartimento di Scienze dell'Ambiente e del Territorio, University of Milano-Bicocca)
Date: 2006-06-18     Track: Special Sessions     Session: Hydrogeophysical data fusion

The availability of reliable constitutive models linking the bulk electric properties of porous media to their inner structure is a key requirement for useful quantitative applications of non invasive methods. In this paper we focus on the use of dielectric measurements for (time-lapse) monitoring of fluid saturation changes in porous materials, e.g. via Time Domain Reflectometry (TDR) or ground penetrating radar (GPR). A number of empirical, semi-empirical and theoretical relationships have been proposed, linking the bulk dielectric constant with volumetric water content. Among the most popular are mixing models that involve some form of weighted average of the dielectric constants of the components. One such model, named CRIM (complex refractive index model) or LR (Lichteneker-Rother) has found extensive application in recent years. In this paper we first analyze the characteristics of the CRIM by means of theoretical considerations, thus drawing a link between the CRIM and the well known Archie’s law used for the analysis of DC resistivity in porous media. Next, we use pore-scale modelling and experimental results to show other characteristics of the CRIM, and in particular the dependence of its parameters on dielectric properties of the components, as well as on porosity. We then proceed to assess the robustness of the identification of CRIM parameters in presence of synthetic data error, thus concluding that CRIM parameters cannot, in general, be independently identified on the basis of bulk dielectric constant versus moisture content data. A novel theoretical model for the dielectric response of saturated porous media is proposed in the second section. The new constitutive relationship incorporates the theoretical link with Archie’s law as well as a combination of the well established Hashin and Shtrikman bounds. The proposed model is shown to be able to match both experimental and pore-scale modelling data with no use of ad-hoc fitting parameters.