Kansas Geological Survey, Current Research in Earth Sciences, Bulletin 247, part 1
Modeling Dielectric-constant Values of Geologic Materials: An Aid to Ground-penetrating Radar Data Collection and Interpretation

Table 3. Summary of dielectric mixing model categories (adapted from Knoll, 1996).

Category	Method	Types	Advantages	Disadvantages	References
Effective medium	Compute dielectric properties by successive substitutions	Bruggeman- Hanai-Sen (BHS)	-Accurate for known geometries	- Cumbersome to implement - Need to choose number of components, initial material, and order and shape of replacement material	Sen et al., 1981; Ulaby et al., 1986
Empirical and semi-empirical	Mathematical functional relationship between dielectric and other measurable properties	Logarithmic; Polynomial	-Easy to develop quantitative relationships -Able to handle complex materials in models	-There may be no physical justification for the relationship -Valid only for the specific data used to develop the relationship and may not be applicable to other data sets	Dobson et al., 1985; Olhoeft and Strangway, 1975; Topp et al., 1980; Wang and Schmugge, 1980
Phenomenological	Relate frequency dependent behavior to characteristic relaxation times	Cole-Cole; Debye	-Do not need component properties or geometrical relationships	-Dependent on frequency-specific parameters	Powers, 1997; Ulaby et al., 1986; Wang, 1980
Volumetric	Relate bulk dielectric properties of a mixture to the dielectric properties of its constituents	Complex Refractive Index (CRIM); Arithmetic average; Harmonic average; Lichetenecker-Rother; Time-Propagation (TP)	-Volumetric data relatively easy to obtain	-Do not account for micro-geometry of components -Do not account for electrochemical interaction between components	Alharthi and Lange, 1987; Birchak et al., 1974; Brown, 1956; Knoll, 1996; Lange, 1983; Lichetenecker and Rother, 1937; Roth et al., 1990; Wharton et al., 1980