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Bohling, Geoffrey C. / A ground penetrating radar study of water table elevation in a portion of Wisconsin's central sand plain
[DNR-050] (1988)

III. Radar theory and hydrogeological applications,   pp. 19-32 PDF (3.7 MB)


Page 20

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applications of GPR to hydrogeology also are discussed in this chapter.
B. Constitutive Parameters
In many applications earth materials can be treated as linear dielec-
trics, meaning that the vector volume density of electrical current and vec-
tor volume density of polarization are proportional to the applied electrical
field. The proportionality constant relating the vector volume density of
current to the electrical field is called the conductivity and is, in general, a
complex value, given by
o.=o-   +io''.                          (1)
The proportionality constant relating the vector volume density of polari-
zation to the electrical field is e - Ec where
E=f? +ii 1(2)
is the permittivity of the material and e0 =8.854 X 10-12 Farad/m is the
permittivity of free space. The relative permittivity, Er, is a dimensionless
parameter defined such that
E = er 60.                         (3)
The imaginary portion of the conductivity, ' ' , accounts for time lags in
conduction response of the material to a time-varying electrical field.
Similarly, c'  accounts for time lags in the polarization response of the
material (King and Smith, 1981).
In Maxwell's equations (which govern the propagation of elec-


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