pipes results in field components that are ori- ented both parallel and orthogonal to the long
axis of the pipe. The reflected and transmitted fields for thin pipes are related by the following
Ž .
relationships Daniels et al., 1988 :
yi k r
S S
e
x x x y
E s E ysinu cosu
s t
ž
S S
r
y x y y
= cosu
9
Ž .
sinu E
e
yi k r s
s S y S
Ž .
ž
y y x x
ž
E 2 r
t
=sin2u y S sin
2
u q S cos
2
u 10
Ž .
x y y x
where E and and E are the scattered and
s t
transmitted fields, respectively, and u is the angle between the long axis of the transmit
dipole and the long axis of the cylinder. For linear targets S
and S are small compared
x y y x
to other components and thus E
e
yi k r s
s S y S
sin2u 11
Ž .
Ž .
y y x x
ž
E 2 r
t
The ratio E rE is maximized when u s 458 for
s t
both dielectric and conductive pipes and thus crossed-dipole antennas at 458 with respect to
cylinders represent the best antenna geometry to Ž
. image cylinders Fig. 2c .
4. Linear polarization and scattering from pipes physical model examples
To test the applicability of the analytical Ž
Ž . Ž
. .
solutions Eqs. 12 – 23 and Fig. 6 , data were
Ž . Fig. 6. Backscattering widths as a function of radius a ,
Ž . normalized by the wavelength
l of the incident field. Solid lines represent TM polarization and dashed lines
Ž . represent TE polarization. a TM backscattering widths
are greater than TE backscattering widths for most metallic Ž .
cylinders. b TE backscattering widths are greater than TM backscattering widths for small diameter, high
Ž . impedance, dielectric cylinders.
c TM backscattering
widths are greater than TE backscattering widths for small diameter, low impedance, dielectric cylinders.
Fig. 7. Geometry of bow-tie antenna elements for 500 Ž
. MHz air multi-component antenna. The antenna consists
Ž .
of four transmitting elements T1, T2, T3, T4 and two Ž
. receiving elements R1, R2 . The figure is drawn to scale.
recorded in a sand test pit using a Geophysical Ž
. Survey Systems GSSI bow-tie, multi-compo-
nent antenna having a center frequency of 500 Ž
. Ž .
MHz in air Fig. 7 . The antenna consisted of
two receiving elements and four transmitting Ž
elements eight different transmitting–receiving .
combinations that were used to record the data. Fig. 8 is a plot of the amplitude spectrum
obtained by taking the Fourier transform of both co-pole and cross-pole traces with no pipes
present. The soil interface influences current distribution and impedance of GPR antennas by
an amount determined by the antenna design and the electromagnetic properties of the ground.
A soil interface causes the antenna to radiate at
Ž .
lower frequencies 270 MHz peak on interface Ž
. than in an air whole-space 500 MHz peak .
The amplitude spectrum varies smoothly as a Ž
function of frequency no nulls at a given fre- .
quency and is approximately Gaussian in shape. A large polarization mismatch with cross-pole
Ž antennas is observed in Fig. 8 co-pole larger
. amplitude than cross-pole for all frequencies
because each frequency is linearly polarized. Constant polarization for all frequencies is a
Ž desirable feature of dipole antennas de Jongh et
. al., 1998 . While time-domain impulse radar
Ž .
Ž .
Fig. 8. Amplitude spectrum for co-pole solid and cross-pole dashed traces for an antenna located on the soil interface with no buried pipes. The amplitude spectrum varies smoothly as a function of frequency and is approximately Gaussian in
shape with a peak frequency of 270 MHz. The strong polarization mismatch for cross-pole antennas results in larger co-pole amplitudes for all frequencies because each frequency is linearly polarized.
radiates a pulse composed of many frequencies Ž
. Fig. 8 , the frequencies centered about 270
MHz have the largest amplitudes and are the most significant for determining the response
observed in field data. To illustrate the above concepts, data were
recorded over plastic and metal pipes with sur- vey directions normal to the long axis of the
pipes and at 158, 308, and 458 angles to the long axis of the pipes. Long pipes were used to avoid
resonance and edge effects. Pipes of varying radii were used to demonstrate the most signifi-
cant features observed in the analytic solutions. Fig. 9 shows the results of data recorded over a
0.0032 m radius copper pipe buried at a depth of 0.46 m and having a length of 3.05 m. A soil
permittivity probe, described by Caldecott et al. Ž
. 1985 and operating at 40 and 60 MHz fre-
quencies gave relative permittivity values of 4 near the surface and graded to a permittivity of
7 at a depth of 0.6 m. The peak 270 MHz frequency has a nominal wavelength of 0.42 m
and thus the copper pipe with a radius of 0.0032 m yields a radius-to-wavelength ratio of 0.008.
While this radius-to-wavelength ratio is only for a single frequency, most of the energy radiated
from the antenna is composed of frequencies that have TM polarization scattering widths
greater than TE polarization scattering widths Ž
. Figs. 3 and 6a . Fig. 9 demonstrates that this is
Ž .
the case with the TM component T2R1 much Ž
. greater than the TE component T1R2 . Cross-
Ž .
pole components T2R2 and T3R1 yield maxi- mum values when the dipole antennas are ori-
ented at 458 to the long axis of the cylinder, as Ž . Ž
. described by Eqs. 9 – 11 . No difference be-
tween cross-pole configurations would be ex- pected with ideal antennas over homogeneous
soils or at a 458 survey angle for co-pole config- urations. Coupling between the four transmit-
ting elements and two receiving elements, in addition to small construction and alignment
differences, results in a slightly different an- tenna response between the two cross-pole
Ž
. Ž
. T2R2 and T3R1 and co-pole T2R1 and T1R2
configurations. Heterogeneities in the soil also
Fig. 9. GPR survey normal and at 158, 308, 458 to the long axis of a copper pipe buried at a depth of 0.46 m, having a
radius of 0.0032 m, and a length of 3.05 m. A 270 MHz center frequency antenna on soil with a relative permittiv-
ity of 7 has a nominal wavelength of 0.42 m and thus the copper pipe yields a radius-to-wavelength of 0.008. Figs. 3
and 6a suggest that this small radius-to-wavelength ratio
Ž .
results in larger TM scattering widths T2R1 Fig. 7 than Ž
. TE scattering widths T1R2 Fig. 7 . Cross-pole compo-
Ž .
nents T2R2 and T3R1 yield maximum values when the dipole antennas are oriented at 458 to the long axis of the
Ž . Ž .
pipe as described by Eqs. 9 – 11 .
produce differences due to the antenna element offsets.
Data were also recorded over metal and plas- tic pipes, having a radius of 0.0381 m, a length
of 3.66 m, and buried at a depth of 0.61 m. A 270 MHz antenna yields a nominal radius-to-
wavelength ratio of approximately 0.09. Figs. 3 and 6a suggest similar backscattering widths for
TM and TE polarizations for metallic pipes
having this radius-to-wavelength ratio. In con- trast to the thin metal pipes, Fig. 10 demon-
Ž .
strates that the TM polarization T2R1 is only Ž
. slightly larger than the TE polarization T1R2 ,
as predicted from analytic solutions. Cross-pole Ž
. components T2R2 and T3R1 still yield maxi-
mum values when the dipole antennas are ori- ented at 458 to the long axis of the metal pipe,
as in the thin metallic pipe case. In contrast to
Fig. 10. GPR survey normal and at 158, 308, 458 to the long axis of a steel pipe buried at a depth of 0.61 m,
having a radius of 0.0381 m, and a length of 3.66 m. A 270 MHz center frequency antenna yields a nominal radius
to wavelength ratio of approximately 0.09. Unlike the thin pipe, Figs. 3 and 6a suggest similar TM and TE scattering
widths for metallic pipes having this radius-to-wavelength
Ž .
ratio. In this figure, the TM T2R1 polarization is only Ž
. slightly brighter than the TE polarization T1R2 , as pre-
Ž .
dicted. Cross-pole components T2R2 and T3R1 still yield maximum values when the dipole antennas are oriented at
458 to the long axis of the pipe, as in the thin pipe case. Fig. 11. GPR survey normal and at 158, 308, 458 to the
long axis of a PVC pipe buried at a depth of 0.61 m, having a radius of 0.0381 m, and a length of 3.66 m. A
270 MHz center frequency antenna yields a nominal radius to wavelength ratio of approximately 0.09. Figs. 4 and 6b
suggest larger backscattering widths for TE compared to TM, given this radius-to-wavelength ratio. This figure
verifies that the TE polarization is greater than the TM
Ž .
polarization. Cross-pole components T2R2 and T3R1
still yield maximum values, as in the metallic pipe case, when the crossed-dipole antennas are oriented at 458 to the
long axis of the pipe.
metal pipes, Fig. 11 demonstrates that the TE Ž
. polarization T1R2 is larger than the TM polar-
Ž .
ization T2R1 , as predicted from analytic solu- Ž
. tions. Cross-pole components T2R2 and T3R1
still yield maximum values when the dipole antennas are oriented at 458 to the long axis of
the plastic pipe, as in the metallic pipe case.
5. Conclusions
