zero crossings between the model and the data align better, the original processing depth esti-
mate is adjusted from 0.34 to 0.36 m.
5. Estimating the soil density and water con- tent
The main wavelet being reflected by the pipe also has some character beyond that of the ideal
Ricker wavelet. In particular, the wavelet has one up-going peak and two down-going peaks,
with the ideal Ricker wavelet showing the two down-going peaks to be the same amplitude.
However, the recorded data show the two down-going peaks to have different amplitudes.
Ž This is caused by frequency dependence
or .
dispersion in the electromagnetic properties that control the velocity and attenuation of propaga-
Ž .
tion Olhoeft, 1998a . The Cole–Cole parame- ters in Fig. 10 are adjusted to match this ampli-
tude difference, changing the shape of the model wavelet to better fit the recorded data. In the
process, the zero crossing match requires an- other depth adjustment to 0.37 m. The depth to
the pipe has now been determined to a high accuracy, and the model result agrees remark-
Ž .
ably well with the known depth 0.37 m to the top of the pipe. The remainder of the wiggles in
the field data are caused by radio frequency Ž
noise and should not be modeled this is deter- mined by looking at the texture and patterns in
. the 2D radar image in the earlier figures .
Frequency dependences in geological materi- als are dominantly caused by dielectric relax-
ation processes related to the presence of water, and to a lesser extent by magnetic relaxation
processes related to the presence of iron bearing minerals, and a variety of scattering processes
Ž
. Olhoeft and Capron, 1994; Olhoeft, 1998a .
Assuming all of the frequency dependence comes from the presence of water, the model
fitted Cole–Cole parameters indicate the re- quirement of about 1 or 2 water by volume
in the soil between the antennas and the pipe to cause the required dispersion and subsequent
change in wavelet shape. The Bruggeman–
Ž Hanai–Sen volumetric mixing formula Sen et
Fig. 10. Further improving the model fit over Fig. 9 by including the effects of a frequency dependent complex dielectric permittivity.
. al., 1981; Olhoeft, 1987 may be used to con-
vert the dielectric permittivity into bulk density, giving a volume average density of 1.89 grcm
3
, 28 porosity sand equivalent soil between the
antennas and the pipe, right over the pipe through the trenching disturbed soil. These val-
ues are consistent with laboratory measurements
Ž on soil samples from the site
Olhoeft and .
Capron, 1993 and on the measured variation of frequency dependence with moisture content in
Ž soils
Kutrubes, 1986; Olhoeft, 1981, 1987; .
Canan, 1999 . These values are typically mea- sured in situ for soils using time domain reflec-
Ž .
tometry O’Connor and Dowding, 1999 , which requires pushing probes into the ground, but
have been derived here noninvasively from ground penetrating radar data.
The processing and modeling just performed require a few minutes played like a video game
on a 32-bit laptop computer. They have yielded Ž
considerable information about the pipe loca- .
Ž tion, size and depth and the soil density and
. water content . The processing, modeling, and
Ž .
display figure generation were all done with Ž
. the
GRORADAR
e software Olhoeft, 1998b .
6. Discussion
