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.

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 exp*i*ω / *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

(Siemens/m, or S/m), such that

(5)

εs* = εrel *i*σ/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*/*f*rel).

(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 *f*rel 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 *f*rel 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