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 
, magnetic permeability 
, and electrical conductivity 
. Dielectric permittivity is a complex function having real and imaginary components. The real portion of dielectric permittivity is usually expressed as dielectric constant 
, 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 
10 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 
and relative magnetic permeability 
. The effect of magnetic permeability on GPR response is negligible for materials with a relative magnetic permeability value of = 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 (
measured at 100 MHz) of common earth materials.
| Material | from Davis and Annan, 1989 | from 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 
, 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.
Kansas Geological Survey
Web version December 3, 2001
http://www.kgs.ku.edu/Current/2001/martinez/martinez2.html
email:lbrosius@kgs.ku.edu