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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--page 2 of 13

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Ground-penetrating radar (GPR) is a geophysical technique, similar to seismic reflection, that uses electromagnetic (EM), rather than acoustic, waves to image the shallow subsurface (Ulriksen, 1982; Davis and Annan, 1989; Daniels, 1996). GPR has been used to aid in geologic (e.g., Pratt and Miall, 1993; Liner and Liner, 1995; McMechan et al., 1998), hydrologic (e.g., Annan et al., 1991; Knoll and Clement, 1999), engineering (e.g., Botelho et al., 1998), archeological (e.g., Dolphin et al., 1978), and petroleum (Knight and Endres, 1990) investigations.

GPR operates in the electrical conduction wavelength region of the electromagnetic spectrum. Whereas seismic response is a function of acoustic properties, GPR response is a function of the electromagnetic properties: dielectric permittivity epsilon, magnetic permeability mu, and electrical conductivity sigma. Dielectric permittivity is a complex function having real and imaginary components. The real portion of dielectric permittivity is usually expressed as dielectric constant epilson, subscript r, which is the ratio of the electric-field storage capacity of a material to that of free space. The imaginary portion of dielectric permittivity is usually expressed as dielectric loss, which represents attenuation and dispersion. Dielectric loss is negligible if the conductivity of a material is low, less than approximately10 milliSiemens/meter (mS/m), as it is for many geologic materials. Thus, dielectric constant is typically the primary component of dielectric permittivity. Magnetic permeability, the magnetic field divided by the magnetic field strength, is the product of the permeability of free space Mu, subscript 0 and relative magnetic permeability Mu, subscript r. The effect of magnetic permeability on GPR response is negligible for materials with a relative magnetic permeability value of Mu, subscript r = 1, which is the value for most sedimentary materials. Dielectric permittivity, magnetic permeability, and electric conductivity are frequency dependent and behave differently over various frequency ranges (Powers, 1997). Dielectric constant generally decreases with increasing frequency, while conductivity and dielectric loss increase with increasing frequency. However, their behavior is relatively consistent over the typical GPR antenna frequency range of 25-1,500 MHz.

Dielectric constant is a critical GPR parameter because it controls the propagation velocity of electromagnetic waves through a material and the reflection coefficients at interfaces, as well as affecting the vertical and horizontal imaging resolution. Therefore, knowing dielectric-constant values of materials helps in planning GPR surveys and in better understanding and interpreting GPR images.

Measured dielectric-constant values for various rocks and minerals may be found in the literature (e.g., Davis and Annan, 1989; Daniels, 1996; Olhoeft, 1989; Schon, 1996; Ulaby et al., 1990). Reported bulk dielectric-constant values of common earth materials are presented in table 1, and reported dielectric-constant values of common minerals and fluids are presented in table 2. These data are broadly useful; however, bulk dielectric constants of rocks and sediments actually reflect complex mixtures of materials and architectures that vary from one rock lithology to the next. In rocks and sediments, dielectric properties are primarily a function of mineralogy, porosity, water saturation, frequency, and depending on the rock lithology, component geometries, and electrochemical interactions (Knight and Endres, 1990; Knoll, 1996). Variations in each of these parameters can significantly change bulk dielectric constants. Dielectric mixing modeling is a forward-modeling technique that provides a basis for predicting expected bulk dielectric-constant values based on specific input parameters. Numerous dielectric-constant mixing models have been proposed, and all fall within four broad categories: effective medium, empirical and semi-empirical, phenomenological, and volumetric (Knoll, 1996) (table 3).

Table 1. Bulk dielectric constants (epsilon, subscript r measured at 100 MHz) of common earth materials.

Materialfrom Davis and Annan, 1989from Daniels, 1996
Air 1 1
Distilled water 80  
Fresh water 80 81
Sea water 80  
Fresh water ice 3-4 4
Sea water ice   4-8
Snow   8-12
Permafrost   4-8
Sand, dry 3-5 4-6
Sand, wet 20-30 10-30
Sandstone, dry   2-3
Sandstone, wet   5-10
Limestone 4-8  
Limestone, dry   7
Limestone wet   8
Shales 5-15  
Shale, wet   6-9
Silts 5-30  
Clays 5-40  
Clay, dry   2-6
Clay, wet   15-40
Soil, sandy dry   4-6
Soil, sandy wet   15-30
Soil, loamy dry   4-6
Soil, loamy wet   10-20
Soil, clayey dry   4-6
Soil, clayey wet   10-15
Coal, dry   3.5
Coal, wet   8
Granite 4-6  
Granite, dry   5
Granite, wet   7
Salt, dry 5-6 4-7

Table 2. Dielectric constants of common minerals and fluids. Note: These values are for specific minerals and fluids from specific study sites. Minerals and fluids taken from other sites may have slightly different dielectric constant values or may exhibit dielectric anisotropy.

Material Dielectric constant Frequency (MHz) Source
Acetone 20.9 1 Lucius et al., 1989
Albite 7.0 1 Olhoeft, 1989
Air 1.0 1 Lucius et al., 1989
Benzene 2.3 1 Lucius et al., 1989
Calcite 6.4 1 Olhoeft, 1989
Calcite 7.8-8.5 Radio Keller, 1989
Carbon tetrachloride 2.2 1 Lucius et al., 1989
Chloroform 4.8 1 Lucius et al., 1989
Cyclohexane 2.0 1 Lucius et al., 1989
Ethylene glycol 38.7 1 Lucius et al., 1989
Gypsum 6.5 750 Martinez and Byrnes, 1999
Halite 5.9 1 Olhoeft, 1989
Ice 3.4 1 Olhoeft, 1989
Kaolinite 11.8 1 Olhoeft, 1989
Methanol 33.6 1 Lucius et al., 1989
Mica 6.4 750 Martinez and Byrnes, 1999
Montmorillonite 210 1 Olhoeft, 1989
Olivine 7.2 1 Olhoeft, 1989
Orthoclase 5.6 1 Olhoeft, 1989
Pyroxene 8.5 1 Olhoeft, 1989
Quartz 4.5 1 Olhoeft, 1989
Tetrachloroethene 2.3 1 Lucius et al., 1989
Trichloroethene 3.4 1 Lucius et al., 1989
Water 80 1 Lucius et al., 1989

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; Knoll, 1996; Lange, 1983; Lichtenecker and Rother, 1931; Roth et al., 1990; Wharton et al., 1980

This paper provides a brief discussion of dielectric-constant mixing models, a general review of the important equations governing GPR response, and presents an application of Time-Propagation (TP) dielectric mixing modeling to predict reflection coefficients, reflection travel-times, and imaging resolution. Three examples illustrate TP modeling of sandstones and carbonates, and the relationship between dielectric constant and porosity phi, mineralogy (Xm), water saturation (Sw), fluid-rock electrochemical interaction, and hydraulic permeability (k). A downloadable Excel 97 workbook containing interactive worksheets involving TP modeling and reflection coefficient and two-way travel time modeling is included as appendix A.

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Kansas Geological Survey
Web version December 3, 2001