Ž .
Journal of Applied Geophysics 45 2000 111–125 www.elsevier.nlrlocaterjappgeo
Ground penetrating radar polarization and scattering from cylinders
Stanley J. Radzevicius , Jeffrey J. Daniels
Department of Geological Sciences, The Ohio State UniÕersity, 125 South OÕal Mall, Columbus, OH 43210-1308 USA Received 18 October 1999; accepted 10 July 2000
Abstract
Ž .
Ground penetrating radar GPR polarization is an important consideration when designing a GPR survey and is useful to constrain the size, shape, orientation, and electrical properties of buried objects. The polarization of the signal measured by
the receive antenna is a function of the polarization of the transmit antenna and scattering properties of subsurface targets. Circular cylinders represent important environmental and engineering targets such as buried pipes, wires, and rebar. The
backscattered fields from cylinders may be strongly depolarized depending on the orientation of the cylinder relative to the antennas, the electrical properties of the cylinders, and the radius of the cylinder compared to the incident wavelength. These
polarization dependent scattering properties have important implications for target detection, survey design, and data interpretation.
As the radius-to-wavelength ratio of metal and plastic pipes decreases, the backscattering properties become more polarization dependent. When using linearly polarized dipole antennas, metallic pipes and low impedance dielectric pipes are
best imaged with the long axis of the dipole antennas oriented parallel to the long axis of the pipes. High impedance, dielectric pipes, are best imaged with the long axis of the dipoles oriented orthogonal to the long axis of the pipes. q 2000
Elsevier Science B.V. All rights reserved.
Keywords: Ground penetrating radar; Polarization; Cylinders
1. Introduction
Ž .
Ground penetrating radar GPR is a common geophysical technique for investigating the shal-
Ž low subsurface Annan and Davis, 1989; Ol-
hoeft, 1992; Peters et al., 1994; Daniels et al., .
1998 . The vector nature of the GPR electro-
Corresponding author. E-mail address: radzevgeology.ohio-state.edu
Ž .
S.J. Radzevicius .
magnetic field, commonly referred to as polar- Ž
ization, is described Beckman, 1968; Born and .
Wolf, 1980; Mott, 1986; Balanis, 1989 and is largely ignored by interpreters of GPR data.
Ž .
Investigations by Roberts 1994 and Roberts Ž
. and Daniels 1996, 1997 have demonstrated the
potential of using the polarization characteristics of GPR for defining the size, shape, orientation,
and material properties of buried objects.
This paper describes polarization and cylin- der scattering theory and concepts relevant for
the GPR practitioner. Analytic solutions and
0926-9851r00r - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž
. PII: S 0 9 2 6 - 9 8 5 1 0 0 0 0 0 2 3 - 9
GPR data examples over buried pipes of vary- ing radii are used to illustrate polarization con-
cepts and verify the applicability of theory to commercial dipole antennas and physical mod-
els. This manuscript also describes which dipole antenna configurations will result in optimal
survey design, depending on whether the targets of interest are metallic or plastic pipes.
2. Polarization
The electromagnetic field at a given point in space, at a given time, has both a magnitude and
a direction, and thus is described by vectors. As the electromagnetic wave propagates, the orien-
tation and magnitude of these vectors change as a function of time. Polarization describes the
magnitude and direction of the electromagnetic field as a function of time and space. When the
Ž time varying EM fields vary sinusoidally time
. harmonic , polarization may be classified as
linear, circular, or elliptical. If the vector that describes the electric field as a function of time
is always directed along a straight line, the field is said to be linearly polarized. If the vector
sweeps out a circle, it is referred to as circular polarization. Both are special cases of elliptical
polarization, in which the electric field traces out an ellipse. An arbitrary electromagnetic field
can be described by three orthogonal basis vec- tors. Since the electric and magnetic fields are
orthogonal to the direction of propagation, if we choose one of the basis vectors in the direction
of propagation, the electric field can be decom- posed into two orthogonal basis vectors. The
electric field of a wave traveling in the z direc- tion can be described by two orthogonal compo-
Ž .
nents as given by Balanis 1989 : E
z ,t s E e
ya z
cos v t y b z y f
Ž .
Ž .
x x 0
x
and E
z ,t s E e
ya z
cos v t y b z y f 1
Ž .
Ž .
Ž .
y y0
y
where a represents the attenuation constant, b the phase constant, v the angular frequency, f
the phase, and E and E
are the maximum
x 0 y 0
amplitudes of the E and E components, re-
x y
spectively. 2.1. Linear polarization
For a wave to have linear polarization, the time-phase difference between the two compo-
nents must be D
f s f y f s np n s 0,1,2,3, . . .
2
Ž .
y x
2.2. Circular polarization Circular polarization is achieved only when
the magnitudes of the components are the same and the time-phase differences are multiples of
pr2.
E s E
x y
and 1
D f s f y f s
q 2 n p 3
Ž .
y x
ž
2 Ž
. where q and y refer to clockwise CW or
Ž .
counterclockwise CCW rotation. n s 0, 1, 2, 3, . . .
2.3. Elliptical polarization Elliptical polarization is achieved only when
the time-phase difference between the two com- ponents are odd multiples of pr2 and their
magnitudes are not the same or when the time- phase difference between the components are
not equal to multiples of pr2, regardless of their magnitudes.
Case 1: E E
x y
and 1
D f s f y f s
q 2 n p 4
Ž .
y x
ž
2 n s 0, 1, 2, 3, . . . ,where q and y refer to CW
or CCW rotation.
Case 2: np
D f s f y f
n s 0,1,2,3, . . .
y x
2 5
Ž .
D f 0 for CW Df - 0 for CCW.
Pipes and other objects scatter energy prefer- entially, depending on the incident polarization.
The polarization and orientation of the transmit antenna is thus important to ensure sufficient
energy is scattered from subsurface targets to allow measurement by the receive antenna.
Preferential scattering may result in depolariza- tion of the incident field. Depolarization occurs
when the amplitude or phase of the incident
Ž Ž ..
field components Eq. 1 are modified such
that the scattered field results in a different polarization. The ability of the receive antenna
to measure these scattered fields is determined not only by the power of the scattered fields,
but also by the polarization match between the scattered fields and the receive antenna. The
polarization of the field incident on the receive antenna is determined by the polarization of the
field radiated by the transmit antenna and the degree of depolarization experienced by scatter-
ing from subsurface objects. It is thus important to understand the polarization properties of GPR
antennas and scattering from subsurface objects.
Most commercial GPR antennas are dipole or bow-tie antennas that radiate linearly polarized
energy with the majority of the radiated electric field oriented along the long axis of the dipole
or bow-tie. For a description of dipole fields
Ž .
over a half-space, consult Annan 1973 , Annan Ž
. Ž
. et al.
1975 , Arcone 1995 , Engheta et al.
Ž .
Ž .
1982 , Smith 1984
and Radzevicius et al. Ž
. 2000b . A complete polarization mismatch us-
ing dipole antennas results when the scattered field and polarization of the receive antenna are
Ž Ž ..
both linearly polarized Eq. 2 and oriented at
right angles to each other. For example, rotating ideal dipole antennas orthogonal to each other
Ž .
crossed-dipoles results in a complete polariza- tion mismatch. Spiral, or other circularly polar-
ized antennas, are also used for pipe detection. A complete polarization mismatch using circu-
larly polarized antennas results when the scat- tered field and receive antenna are both circu-
Ž Ž ..
larly polarized Eq. 3 , but have electric fields Ž
with opposite rotation directions left and right .
circular .
3. Normal incidence plane wave scattering by circular cylinders fundamental theory and
