Geoscience Reference
In-Depth Information
For the incident pulse at the air-soil interface, the reflection coefficient R is determined by the
contrast in relative dielectric permittivity (K) between the air (K = 1), and the soil (K = K s ):
=
+
1
1
K
K
R
(2 4.1)
s
s
It is assumed that the conductivity is sufficiently small to be ignored, that the surface is flat, and
that the soil properties are homogeneous. The above relationship can be rearranged to determine the
soil permittivity from a measured reflection coefficient. In practice, the GPR system is calibrated
with metal plate target with a known reflection coefficient of −1. The reflection coefficient can be
measured by calibrating the GPR system with a sufficiently large metal plate (dimensions > Fresnel
zone diameter) placed at the surface (Redman et al., 2002). The magnitude of the reflection coef-
ficient is the ratio of the amplitude A r of the reflected wavelet from the soil surface to the amplitude
A m of a wavelet measured at the same elevation over a metal plate target with a reflection coefficient
of −1. Using Equation (24.1), K s can be determined from the ratio of the amplitude of the wavelet (A r )
reflected from the surface and from the amplitude of the wavelet (A m ) reflected from a metal plate:
2
A
A
A
A
1
+
r
K
=
m
r
m
(24.2)
s
1
The soil water content θ is then estimated using a suitable mixing formula. For the data pre-
sented in this case study, the empirical relationship of Topp et al. (1980), was used:
42
63
θ=− +
0 053
.
0 0292
.
K
−× +×
55 10
.
K
43 10
.
K
s
(24.3)
s
s
24.3 SAMplInG volUMe
The electrical properties of the near surface, directly below the GPR antennas, determine the mea-
sured surface reflectivity. This region or sampling volume for the method can be roughly approxi-
mated by a vertical cylindrical zone extending from the surface to some defined sampling depth.
For GPR antennas at height h above the surface, with a wavelength λ in air at their center frequency,
the diameter D of the circular sampling zone at the surface (the Fresnel zone) is given by Equation
(24.4). For a 500 MHz center frequency GPR at a height of 1 m, the diameter D is ~1.1 m:
λ
2
D
= +
2
λ
h
(24.4)
4
The sampling depth is controlled by the subsurface EM attenuation and velocity. Numerical
modeling has shown that for a 500 MHz GPR system, this sampling depth is ~0.09 m for a wet soil
with a volumetric water content of 20 percent and ~0.18 m for a dry soil with a volumetric water
content of 5 percent (Redman et al., 2003). The sampling depth is inversely proportional to the cen-
ter frequency of the GPR system, allowing lower-frequency GPR antennas to sample more deeply.
24.4 fIeld MeASUReMentS
Using the methodology described previously, surface reflectivity measurements were collected over
a number of sites (Redman et al., 2002, 2003). These examples demonstrate the variability often
 
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