slows and attenuates the incident radiation. This process
with other studies of loess in the southern United States
is dispersive, which means that different frequencies
(Rodbell et al. 1997), which show a predominant
within the incident wavelets propagate at different speeds
amount of quartz, and also with studies of loess in inte-
rior Alaska (Pw 1955).
and attenuation rates (Stratton 1941, Brillouin 1960, and
Feynman et al. 1964).
Values of εst are directly related to the water content
DIELECTRIC THEORY
for nonmineralogic clays and silts (Topp et al. 1980)
and generally equal εs* for f < 600 MHz. Above about
We present the theory of radiowave propagation in
600 MHz, laboratory investigations (Hoekstra and
soils in this section in order to provide a basis for mod-
Doyle 1971, Hoekstra and Delaney 1974) show that
eling the GPR propagation at JPG later. The discussion
the adsorbed water on the particle surfaces of the clay
pertains to engineering-grade silt- and clay-size soils,
fraction (Tice et al. 1982) strongly influences the
but of little clay mineralogy so that it applies to the
dielectric properties. The adsorption process lowers both
soils at JPG. The radar detectability of a subsurface tar-
the high dielectric constant (81) of the normally free
get strongly depends on the radiowave speed, v, and
water and also the free water relaxation frequency (22
attenuation rate, β, of the burial soil. The speed deter-
GHz) to about 13 GHz. Values of εoo are generally
mines the shape of the antenna beamwidth. β deter-
related to the dry soil density, range from about 2.5 to
3.5, and equal εs* at frequencies above about 100,000
mines how deep the radiowaves will penetrate and
return to the surface with enough strength to be detected.
MHz. For soils of JPG and the radar frequencies used,
σ was large enough to also influence attenuation
These quantities are related to the relative complex per-
mittivity of soil, εs*, such that
because it determines how much of the radiowave
energy will be converted into conduction currents.
v = c/Real (εs*1/2)
The resulting values of εs* for silty and clay-rich
(1)
soils at frequencies above about 100 MHz provide high
values of β and wave speeds lower than would be
and
expected for sandy soils with the same volumetric
(
)
β dB / m = 20 log expiω / c Imag εs *1/2
water content. The β values (a quantitative discussion
is given later) increase as f approaches, and then
(2)
attenuation rates caused by the geometric spreading of
the radiation energy. At frequencies below about 1000
c = 3 108 m/s is the wavespeed in free space. The
MHz, the real part, ε′ = εst, often referred to as the
quantity εs* is determined by the Debye relaxation
dielectric constant, determines the wave speed v through
permittivity (Debye 1929), εrel, and a contribution
the relation
from the very-low-frequency soil conductivity, σ
v = c/ε′1/2
(Siemens/m, or S/m), such that
(5)
εs* = εrel iσ/ωε0
(3)
for a variety of frozen and unfrozen silts and
(nonmineralogic) clays (Hoekstra and Delaney 1974,
where
Topp et al. 1980, Delaney and Arcone 1984).
εrel = εoo + (εst εoo)/(1 + i f/frel).
(4)
EQUIPMENT AND METHODS
ε0 is the dielectric permittivity of free space (a con-
Radar system
tive soil permittivity, εoo is the very-high-frequency
We used the GSSI (Geophysical Survey Systems,
value, f = 2πω is the wave frequency in hertz (Hz), or
Inc.) SIR system model 2 and models 3207 (100 MHz),
frequency component for a radar wavelet, and frel is
5103 (300 MHz), and 101C (600 MHz) antenna trans-
ducers. We used the control unit to set the time range
mines the dipole moment density induced in a material
(in nanoseconds, ns) for the echo traces, the data ac-
by a passing wave. The quantity frel is a characteristic
quisition rate (48 or 64 traces/s), the sampling density
frequency above which the induced dipoles no longer
(512 samples per trace), trace sample density (16-bit),
stay in phase with the incident radiowave. These
and time variable gain (TVG) for the traces. We cali-
dipoles then generate interference, which effectively
brated our settings with the antennas set over targets
3
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