Surface and borehole ground-penetrating-radar developments

TL;DR: The specific aspects of borehole radar are discussed and recent developments to become more sensitive to orientation and to exploit the supplementary information in different components in polarimetric uses of radar data are described.

Abstract: During the past 80 years, ground-penetrating radar (GPR) has evolved from a skeptically received glacier sounder to a full multicomponent 3D volume-imaging and characterization device. The tool can be calibrated to allow for quantitative estimates of physical properties such as water content. Because of its high resolution, GPR is a valuable tool for quantifying subsurface heterogeneity, and its ability to see nonmetallic and metallic objects makes it a useful mapping tool to detect, localize, and characterize buried objects. No tool solves all problems; so to determine whether GPR is appropriate for a given problem, studying the reasons for failure can provide an understanding of the basics, which in turn can help determine whether GPR is appropriate for a given problem. We discuss the specific aspects of borehole radar and describe recent developments to become more sensitiveto orientation and to exploit the supplementary information in different components in polarimetric uses of radar data. Multicomponent GPR data contain more diverse geometric information than single-channel data, and this is exploited in developed dedicated imaging algorithms. The evolution of these imaging schemes is discussed for ground-coupled and air-coupled antennas. For air-coupled antennas, the measured radiated wavefield can be used as the basis for the wavefield extrapolator in linear-inversion schemes with an imaging condition, which eliminates the source-time function and corrects for the measured radiation pattern. A handheld GPR system coupled with a metal detector is ready for routine use in mine fields. Recent advances in modeling, tomography, and full-waveform inversion, as well as Green's function extraction through correlation and deconvolution, show much promise in this field.

Summary

INTRODUCTION

• Ground-penetrating radar ͑GPR͒ -also known as georadar, subsurface radar, and ground-probing radar -is a geophysical method of obtaining information about the subsurface with extremely high resolution.
• GPR waves are sensitive to changes in the subsurface and to GPR data contrasts in electrical and magnetic properties; such changes can be detected, imaged, and characterized.
• It works well below the water table in clay-free freshwater environ-ments and through nonmineralogical clay ͑rock flour͒ to depths of 30 m.
• The consequences of antenna design and associated challenges are described.

PRINCIPLES OF GPR

• Every measurement assumes an underlying theoretical model.
• Without a theoretical model, a measurement result cannot be given meaning.
• Using GPR for subsurface applications therefore requires understanding how the EM waves that the authors use to obtain subsurface properties respond to changes in the subsurface.
• This does not preclude time-lapse measurements ͑Greenhouse et al., 1993͒ but only requires the system to change slowly ͑hours͒ compared to the time of measurement ͑milliseconds͒.
• A second direct consequence of the LTI system condition is that all time interactions are described by convolutions, and time can be transformed conveniently to frequency.

Electrical and magnetic material properties

• A homogeneous medium is shift invariant, meaning that only the distance between two points is relevant but absolute positions are not.
• For an anisotropic medium, the EM medium's property functions are tensors of rank two.
• Most rocks and soils are multicomponent fluid-filled porous media, and their electric and magnetic properties depend on the properties of the components and their specific mixtures and on the texture -and probably many other details.
• The ratio of the imaginary and real parts of the material property is known as the loss tangent because it represents an angle in the complex plane.
• At long wavelengths ͑low frequencies͒ compared to the size of the scattering target, quasi-static Rayleigh scattering occurs; at wavelengths comparable to the target size, resonance occurs; and at short wavelengths, optical scattering occurs.

Propagation and scattering

• Any antenna is made to optimize the transition of the EM wave, put into a cable by the signal generator, from the cable into the world with the least possible disturbance of the signal.
• The wavefield below ground travels through the earth materials with the speed of light in the material, and part of that wave directly travels to the receiving antenna ͑direct ground wave͒.
• Even with such systems, it is possible to rotate the antennas and exploit their polarization properties, e.g., to see rebar in concrete ͑to assess rebar condition͒ or to see past the rebar to ascertain concrete thickness.
• In the first case, the rebar is the target and the desired scattering object.
• As the interface becomes rough on the wavelength scale, the scattering becomes less specular and more diffuse.

GPR system and performance

• GPR has been deployed from the surface by hand or vehicle towed, in or between boreholes or tunnels, from aircraft, from satellites, and between planets.
• ‬R͒ represents two-way material attenuation losses; and R 4 is two-way geometric spreading loss ͑with an exponent that varies with target type; see Noon et al. ͓1998͔ for examples͒.
• The radar system puts energy into the transmitter antenna at a specified power and frequency spectrum, expecting a certain impedance match going into the antenna.
• It is difficult to calibrate ͑Oden et al., 2008͒ for ground-coupled antennas but relatively easy to calibrate for air-coupled antennas against a surface that should be smooth and horizontal at the wavelength scale, such as pavement ͑Maser and Scullion, 1992͒.
• To use a GPR quantitatively, this is where the authors must start making assumptions ͑Olhoeft, 2000͒.

Common assumptions, limitations, and consequences

• Many common assumptions are made in acquiring, processing, modeling, and interpreting GPR data.
• The magnetic properties are often assumed to be those of vacuum or free space.
• Interpreting velocity from hyperbolas is dangerous when other processes create patterns similar to hyperbolas ͑such as ice melt in permafrost around a hot pipeline or reflections from overhead wires or nearby cars͒.
• Ignoring antenna ground coupling will not give correct full-waveform modeling of details.
• Because of the way most antennas work, they radiate the wavefield in a wide beam and see off to the side as well as forward and aft, allowing the possibility of out-of-plane scattering from objects not directly under the antenna traverse ͑Olhoeft, 1994͒.

BOREHOLE GPR

• Borehole GPR operates in a single borehole, between two boreholes ͑crosshole GPR͒, from a borehole to the surface ͑vertical radar profile͒, or from a borehole to a mine tunnel.
• In each situation, the surrounding conditions of the antennas are very different from those of surface GPR antennas.
• Fundamental studies on the behavior of antennas in cylindrical structures, which can be used for designing borehole radar antennas, can be found in King and Smith ͑1981͒,.

Surface and borehole GPR developments 75A107

• Quite different from those in free space.
• The borehole-antenna radiation patterns and the received signal forms are important for understanding the radar system.
• Because the host rock is heterogeneous, the radiation patterns are difficult to measure in situ.
• This can lead to large errors in velocity estimates based on such arrivals because it is assumed they are recorded at the feed points ͑Irving and Knight, 2005͒.
• These realistic models include cy-lindrical geometries, general dispersive models, and proper representations of borehole antennas.

Physical limitations and challenges

• The authors use lower frequencies compared to conventional surface-based GPR to achieve a larger penetration range.
• The diameter of the borehole is typically less than one-tenth of the wavelength of the radar signal.
• Directional borehole radar antennas have been developed to meet this need ͑Lytle et al., 1979͒.
• The antennas must be rotated mechanically, which makes the system complicated.
• An Adcock array ͑Adcock, 1959͒ composed of multiple parallel dipole antennas can measure the phase differences between antennas to achieve the desired signal directivity.

Radar polarimetry

• An EM wave has two orthogonal components spanning the plane perpendicular to the propagation direction.
• And radar polarimetry measures not only the amplitude of the scattered wave but also scattering mechanisms of targets.
• As noted earlier, EM waves are described by vector fields, and the components of these vectors contain information about the 3D objects that scatter the wave.
• The scattering depends on the frequency bandwidth; therefore, the authors also must select the operation-frequency bandwidth.
• Figure 4 shows an FDTD simulation of scattering from a subsurface fracture model with a rough surface.

Surface and borehole GPR developments 75A109

• The model in Figure 4a has a thin fracture with a flat surface, whereas the model in Figure 4b has a thick fracture with a rough surface.
• The plots on the left show the vertically polarized wave, which has the same polarization as the incident wave.
• A flat surface causes only a copolarized reflected wave, but a rough surface causes co-and cross-polarized reflected waves.
• Many techniques have been proposed for analyzing polarimetric radar information; ␣-entropy classification is one such technique ͑Cloude and Pottier, 1997͒ that has been applied to polarimetric borehole radar data.
• A zero angle means surface scattering in the geometric optics limit ͑specular reflection͒.

Crosshole data imaging and inversion

• Tomographic techniques are among the most popular imaging schemes used for crosshole geophysical measurements.
• For these applications, the authors are interested in imaging approaches as alternatives to tomography that can be applied to crosshole borehole radar data ͑Zhou and Sato, 2004; Takahashi and Sato, 2006͒.
• If the host rock is relatively resistive, EM attenuation is small and signal-processing techniques used in seismic signal processing are quite useful for borehole radar.
• The borehole separation was 20 m, and the depth of the cavity was more than 70 m.
• Then reverse-time migration is applied to the same data set using the full waveform, and the image shown in Figure 6b is obtained.

Ground-coupled antennas

• To detect subsurface objects in GPR data collected at the surface, it is usually sufficient to measure and interpret the data in real time.
• This can all be done in real time, and data acquisition can be carried out in the fastest possible way.
• This velocity can be estimated from the diffraction pattern in fixed-offset GPR data when it is clearly visible in the data and the object is present in an approximately homogeneous embedding.
• In cases where the scattering amplitudes are small compared to the direct waves or interface reflections, or when the shape of the scattering object becomes of vital importance, as in buried antipersonnel land mines, it is important to have high fidelity in antenna location and orientation information, antenna directivity, and subsurface wave velocity distribution.
• The subscripts ␣ and ␤ represent the orientation of the receiving and the transmitting antennas, respectively.

Air-launched antennas and accounting for antenna effects

• To circumvent problems with antenna impedance matching the ground, air-launched antennas can be used.
• When they are at sufficient height above the ground, the electric field that is emitted can be regarded as independent from the subsurface.
• Schematic representation of the model for multicomponent total-field imaging.

GPR and dual sensors for humanitarian demining

• Humanitarian demining is a very important and urgent issue not only in mineaffected countries but all over the world.
• These metal detectors can detect metal pieces weighing less than 10 mg contained in plastic antipersonnel mines located down to 20 cm below the surface.
• For a handheld system, the sensor must be compact.
• Because of very strong clutter from the ground surface and inhomogeneous soil in the GPR data, the combined use of GPR with a metal detector is advantageous.

Handheld GPR system

• ALIS has a few unique features that other dual sensors do not have.
• The SFCW radar system for ALIS was achieved using a compact handheld vector network analyzer ͑VNA͒, developed by Tohoku University.
• The calibration data can also be stored in the memory of the VNA, and the output data can be calibrated by using the stored data.
• This impulse GPR system generates a short pulse of approximately 200 ps, which covers frequencies ranging from virtual DC to a few gigahertz.
• The antennas are combined in the sensor head with a coil sensor acting as the metal detector.

Sensor-tracking system

• The most unique feature of ALIS is its sensor-tracking function.
• During operation, the sensor operator can observe the metal-detector-response image along with a picture of the ground surface on a display.
• Signal processing requires antenna-position information, and GPR imaging is impossible in conventional handheld GPR and dual sensors because the trajectory of the sensor is unknown in a handheld system.
• ALIS uses a CCD camera fixed on the handle of the sensor head for sensor tracking, which can be found on the handle shown in Figure 9a .
• The dots indicate the positions where ALIS acquired GPR and metal-detector data along with the sensor positions.

Imaging

• As discussed, one of the advantages of GPR is the ease of understanding and interpreting acquired data sets.
• Unfortunately, buried antipersonnel mines are very difficult to detect in GPR data because of strong clutter.
• Soil does not contain gravel or other solid objects; therefore, this GPR image principally represents moisture heterogeneity.
• The authors can define clutter as radar signals reflected from objects that are not their targets.
• Figure 12a is the raw data, and Figure 12b is the Kirchhoff migration image.

Evaluation tests in mine-affected countries

• International organizations such as the International Test and Evaluation Program for Humanitarian Demining ͑ITEP͒ are conducting sensor evaluation tests for humanitarian demining under controlled conditions.
• They also provide technical information on tested sensors to end users.
• ALIS has been tested in some mine-affected countries, including Afghanistan ͑Sato, 2005͒, Egypt, Croatia ͑Sato, 2009͒, and Cambodia.
• The metal detector found 1193 objects; but with ALIS, the deminers were able to judge 484 of them as possible mines and 709 as metal fragments.
• This meant that 709 out of 1193 points ͑about 60%͒ did not have to be prodded, reducing the time of demining operations drastically.

PRESENT AND FUTURE DEVELOPMENTS

• The international regulatory environment For many years, GPR could be used without specific limitations enforced by governments.
• GPR is now regulated in parts of the world as an ultrawide-band ͑UWB͒ device ͑Taylor, 1995; Olhoeft, 1999; Paulino et al., 2008͒ with specific power, frequency, and usage limitations.
• Regulatory offices are the U. S. Federal Communications Commission ͑FCC͒ and the European Telecommunications Standards Institute ͑ETSI͒.
• In the United States, the FCC defines GPR as "Afield disturbance sensor that is designed to operate only when in contact with, or within one meter of, the ground for the purpose of detecting or obtaining the images of buried objects or determining the physical properties within the ground.
• The energy from the GPR is intentionally directed down into.

Modeling, tomography, and full-waveform inversion methods

• With increased computer power, it has become standard to run numerical 3D models for many different GPR applications ͑e.g., Teixeira et al., 1998͒.
• Current FDTD provides full-value GPR modeling tools.
• Modern implementations include the possibility of modeling realistic antennas ͑Lampe et al., 2003; Warren and Giannopoulos, 2009͒ and magnetic losses in the materials ͑Cassidy and Millington, 2009͒.
• Multioffset data have been used in AVO inversion to estimate thin-bed properties ͑e.g., Deparis and Garambois, 2009͒.

Crosscorrelation and deconvolution methods for obtaining GPR responses

• The theory of extracting the Green's function from correlations of recorded field fluctuations has become known as seismic interferometry ͑Schuster, 2009͒.
• Retrieving the electric-field impulse response ͑Green's function͒ between two points from correlations of thermal-noise measurements was established by Rytov and colleagues in the 1950s.
• An example of this application for surface GPR can be found in Hanafy and Schuster ͑2007͒ and for borehole GPR in Liu and He ͑2007͒.
• Interferometry by crosscorrelation can be performed trace by trace, and there are no restrictions on the subsurface heterogeneity; but for all practical purposes, the conductivity should be small.
• The desired spectral width of the impulse-reflection response can be larger than is available in the recorded data, and this cannot be reconstructed.

CONCLUSIONS

• For many applications, the detection problem requires only recording and interpreting data.
• Full nonlinear inversion has been developed for monostatic GPR data using a 1D earth model.
• In borehole radar, new developments include directional borehole radar, which uses optical electric-field sensors to produce high-quality data because the passive sensors minimize the total metal content in the receiver array, resulting in good phase characteristics.
• The use of handheld GPR applied to humanitarian demining has been one of the successful developments of modern radar technology.
• Attention has shifted from imaging and linear inversion and tomography to full-waveform nonlinear inversion and tomography.

Figures

Figure 4 shows an FDTD simulation of scattering from a subsurace fracture model with a rough surface. A vertical electric-dipole

Figure 10. a GPR and meta located at the

Full text

Surface and borehole ground-penetrating-radar developments
Evert Slob
1
, Motoyuki Sato
2
, and Gary Olhoeft
3
ABSTRACT
During the past 80 years, ground-penetrating radar 共GPR兲 has
evolved from a skeptically received glacier sounder to a full mul-
ticomponent 3D volume-imaging and characterization device.
The tool can be calibrated to allow for quantitative estimates of
physical properties such as water content. Because of its high res-
olution, GPR is a valuable tool for quantifying subsurface hetero-
geneity, and its ability to see nonmetallic and metallic objects
makes it a useful mapping tool to detect, localize, and character-
ize buried objects. No tool solves all problems; so to determine
whether GPR is appropriate for a given problem, studying the
reasons for failure can provide an understanding of the basics,
which in turn can help determine whether GPR is appropriate for
a given problem. We discuss the specific aspects of borehole ra-
dar and describe recent developments to become more sensitive
to orientation and to exploit the supplementary information in
different components in polarimetric uses of radar data. Multi-
component GPR data contain more diverse geometric informa-
tion than single-channel data, and this is exploited in developed
dedicated imaging algorithms. The evolution of these imaging
schemes is discussed for ground-coupled and air-coupled anten-
nas. For air-coupled antennas, the measured radiated wavefield
can be used as the basis for the wavefield extrapolator in linear-
inversion schemes with an imaging condition, which eliminates
the source-time function and corrects for the measured radiation
pattern. Ahandheld GPR system coupled with a metal detector is
ready for routine use in mine fields. Recent advances in model-
ing, tomography, and full-waveform inversion, as well as
Green’s function extraction through correlation and deconvolu-
tion, show much promise in this field.
INTRODUCTION
Ground-penetrating radar 共GPR兲 — also known as georadar, sub-
surface radar, and ground-probing radar — is a geophysical method
of obtaining information about the subsurface with extremely high
resolution. Several comprehensive textbooks discuss the technique
共Conyers and Goodman, 1997; Bristow and Jol, 2003; Daniels,
2004; Jol, 2009兲.
GPR waves are sensitive to changes in the subsurface and to GPR
data contrasts in electrical and magnetic properties; such changes
can be detected, imaged, and characterized. GPR’s high frequency
makes it insensitive to electrochemical reactions seen at lower fre-
quencies, but the resulting high resolution makes it sensitive to phys-
ics and geometry, texture, and structure, which are very useful in un-
derstanding and describing heterogeneity 共Olhoeft, 1991a, 1991b兲.
Its depth of penetration ranges from 5400 m in polar ice to less than
1 m in wet bentonite clay, with typical ranges of 10–30 m in sand. It
works well below the water table in clay-free freshwater environ-
ments and through nonmineralogical clay 共rock flour兲 to depths of
30 m.
GPR is one of the few techniques sensitive to changes in water and
nonmetallic materials, and it has a still-increasing number of appli-
cations. Instead of writing an historic overview, which has been done
by Annan 共2002, 2005兲, we provide an overview of the applications
that have been developed over the years. Surface and borehole GPR
have found applications in glacier 共Stern, 1929兲 and polar ice
共Bailey et al., 1964; Robin et al., 1969兲 mapping; aquifer character-
ization and hydrogeology 共Barringer, 1965; Beres and Haeni, 1991兲;
planetary exploration on Mars and the moon 共Simmons et al., 1972兲;
salt exploration 共Thierbach, 1974; Mundry et al., 1978兲; coal mining
共Cook, 1977兲; geotechnical, hydrological, and environmental prob-
lems 共Benson, 1979; Owen and Suhler, 1982; Sandness and Kim-
ball, 1982兲; detecting thawing zones in permafrost areas 共Olhoeft,
1980兲; mine-efficiency improvements 共Nickel et al., 1983; Niva et
al., 1988兲; pavement and railroad ballast problems 共Rodeick, 1984;
Maser, 1986;
Olhoeft et al., 2004兲; archaeology 共Vaughan, 1986; Be-
Manuscript received by the Editor 14 January 2010; revised manuscript received 8 June 2010; published online 14 September 2010.
1
Delft Technical University, Department of Geotechnology, Delft, The Netherlands. E-mail: e.c.slob@tudelft.nl.
2
Tohoku University, Center for Northeast Asian Studies, Sendai, Japan. E-mail: sato@cneas.tohoku.ac.jp.
3
Colorado School of Mines, Department of Geophysics, Golden, Colorado, U.S.A. E-mail: golhoeft@mines.edu.
© 2010 Society of Exploration Geophysicists. All rights reserved.
GEOPHYSICS, VOL. 75, NO. 5 共SEPTEMBER-OCTOBER 2010兲; P. 75A103–75A120, 12 FIGS.
10.1190/1.3480619
75A103
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van, 1991兲; fracture mapping 共Olsson et al., 1985; Holloway et al.,
1986; Grasmueck, 1996兲; agriculture 共Collins and Doolittle, 1987;
Allred et al., 2008兲; geomorphology 共Leatherman, 1987兲; tunnel de-
tection 共Greenfield, 1988; Olhoeft, 1988兲; stratigraphy and sedimen-
tology 共Hsi-Tien, 1989; Davis and Annan, 1989; Schenk et al.,
1993兲; subsurface utility mapping 共Liu and Shen, 1991兲; land-mine
and unexploded ordnance 共UXO兲 detection 共Olhoeft et al., 1994兲;
and forensics investigations 共Owsley, 1995兲. The references listed
here cite some early work or refer to reference books and by no
means are a full account of all activities.
The fact that GPR works so well in the above-mentioned applica-
tions is because of the wave-propagation nature of GPR in combina-
tion with its sensitivity to changes in electromagnetic 共EM兲 material
properties — particularly to changes in the presence of water. Many
applications of GPR are detection applications, where minimal sig-
nal processing is required and interpretation can be carried out on the
recorded data from which the low-frequency content is filtered out
共dewow兲. For applications where some quantification is desired
共burial depth, size and orientation of object, moisture content, etc.兲,
imaging and/or inversion is necessary. One of the earliest theoretical
developments is presented in Annan 共1973兲. Modeling, imaging and
tomography, and inversion of GPR data are active fields of research.
Because GPR relies on wave propagation, many methods that have
been developed for seismic exploration have been adapted 共because
GPR and seismic have important differences兲 and used for GPR 共Liu
and Shen, 1991; Fisher et al., 1992a; Goodman, 1994; Witten et al.,
1994兲. Specific applications require that data be recorded close to a
deep target, and this is achieved using GPR in or between boreholes.
Our paper starts with a section on the principles of GPR where the
material properties to which electromagnetic waves are sensitive are
discussed, followed by a brief discussion on propagation and scatter-
ing effects and a simple rule for estimating system performance.
Special attention is given to borehole GPR because of the physical
limitation of a borehole. The consequences of antenna design and as-
sociated challenges are described. This is followed by discussions
on polarimetric use of borehole GPR and dedicated imaging and in-
version methods for crosshole data. The developments that have led
to migration and linear-inversion algorithms dedicated to EM waves
are discussed, and imaging GPR data from ground- and air-coupled
acquisition configurations is described. We treat one case study,
choosing the humanitarian demining application of GPR because it
is recent and has been developed to the level where it can be used
routinely. The section on present and future developments briefly
describes the current regulatory environment under which GPR
must be used as well as new developments in modeling, inversion,
tomography, and data-driven methods for extracting Green’s func-
tion and redatuming GPR sources.
PRINCIPLES OF GPR
Every measurement assumes an underlying theoretical model.
Without a theoretical model, a measurement result cannot be given
meaning. Using GPR for subsurface applications therefore requires
understanding how the EM waves that we use to obtain subsurface
properties respond to changes in the subsurface. Because the used
field strengths cause small enough disturbances relative to the exist-
ing equilibrium field, the subsurface responds linearly to the radar
wave. We also assume the subsurface does not change in time over
the duration of a single measurement. Because of these two condi-
tions, subsurface GPR applications are investigations on a linear,
time-invariant 共LTI兲 system. Hence, all measurements can be under-
stood from linear-system theory, and all operations that we apply are
filters that can be understood from filter theory. This does not pre-
clude time-lapse measurements 共Greenhouse et al., 1993兲 but only
requires the system to change slowly 共hours兲 compared to the time of
measurement 共milliseconds兲.
As a direct consequence of the LTI system condition, the mea-
sured field strengths are linearly proportional to the applied source
strengths, and medium property functions are independent of the
amplitude of the applied fields and sources. They may depend on
time relative to a reference-time instant, usually chosen as the time
when the transmitter is switched on. This allows for modeling all
kinds of time-relaxation phenomena, which can be formulated math-
ematically by writing the medium property that shows time relax-
ation as a time-convolution operator — a notion going back to Boltz-
mann 共1876兲. A second direct consequence of the LTI system condi-
tion is that all time interactions are described by convolutions, and
time can be transformed conveniently to frequency. The advantage
of such a transformation is that time convolutions of two time-de-
pendent functions transform to products of these frequency-depen-
dent functions in the frequency domain, and the time-derivative op-
erator is reduced to an algebraic factor.
Electrical and magnetic material properties
If a medium’s property function is a constant, the medium is said
to be homogeneous; if it varies as a function of position in space, it is
said to be heterogeneous or inhomogeneous. A homogeneous medi-
um is shift invariant, meaning that only the distance between two
points is relevant but absolute positions are not. For such media, a
spatial Fourier transformation can be carried out with similar bene-
fits as for the time-Fourier transformation. If a medium’s property
function does not depend on orientation, the medium is said to be
isotropic, whereas an anisotropic medium has a property function
that is orientation dependent.
For an anisotropic medium, the EM medium’s property functions
are tensors of rank two. Generally, we use a macroscopic model
wherein the electric current density, the electric displacement cur-
rent, and the magnetic flux density are proportional to the electric
and magnetic fields. We use subscript notation. A vector is written
with a lowercase Latin subscript to indicate the three vector compo-
nents; the summation convention applies to repeated subscripts. We
can write
J
k
共x,t兲⳱
冕
␶
⳱0
t
␴
kr
共x,
␶
兲E
r
共x,t ⳮ
␶
兲d
␶
,⇔
J
ˆ
k
共x,
␻
兲⳱
␴
ˆ
kr
共x,
␻
兲E
ˆ
r
共x,
␻
兲
D
k
共x,t兲⳱
冕
␶
⳱0
t
␧
kr
共x,
␶
兲E
r
共x,t ⳮ
␶
兲d
␶
,⇔
D
ˆ
k
共x,
␻
兲⳱ ␧
ˆ
kr
共x,
␻
兲E
ˆ
r
共x,
␻
兲,
75A104 Slob et al.
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B
p
共x,t兲⳱
冕
␶
⳱0
t
␮
pq
共x,
␶
兲H
q
共x,t ⳮ
␶
兲d
␶
,⇔
B
ˆ
p
共x,
␻
兲⳱
␮
ˆ
pq
共x,
␻
兲H
ˆ
q
共x,
␻
兲共1兲
where x, t denotes the position vector in 3D space and time, respec-
tively;
␻
⳱ 2
␲
f denotes radial frequency, with f being natural fre-
quency; J
k
, D
k
, and B
p
denote the time-domain vector components of
the electric-current density, the electric-displacement current, and
the magnetic-flux density, respectively; E
r
and H
q
denote the vector
components of the electric and magnetic field strengths; and
␴
kr
, ␧
kr
,
and
␮
pq
denote the tensor components of the electric conductivity,
the electric permittivity, and the magnetic permeability of the medi-
um, respectively. The quantities with the diacritical hats 共carets兲 are
the frequency-domain equivalents of the time-domain quantities.
The time-integration bounds in equation 1 show the causality condi-
tions satisfied by the fields and the medium’s property functions, for
which reason the quantities on the left-hand sides of the left column
in equation 1 are causal time functions as well.
The free-space parameters are defined as isotropic parameters and
have the subscript zero to denote free-space values:
␴
0
⳱ 0Sm
ⳮ1
,
␮
0
⳱ 4
␲
⫻10
ⳮ7
Hm
ⳮ1
, 共2兲
␧
0
⳱
1
␮
0
c
0
2
Fm
ⳮ1
.
The new parameter in the definition of the electric permittivity is the
free-space propagation velocity, which is given by c
0
⳱ 299,792,458 m/ s 共by definition兲. Most rocks and soils are multi-
component fluid-filled porous media, and their electric and magnetic
properties depend on the properties of the components and their spe-
cific mixtures and on the texture — and probably many other details.
How these dependencies can be understood is a topic of research in
itself; for EM parameters, we refer to texts by von Hippel 共1954兲,
Choy 共1999兲, Sihvola 共1999兲, and Milton 共2002兲. To understand the
EM parameters in terms of desired physical parameters is beyond the
scope of our paper, although it is important to note that whenever the
properties deviate from those of free space, they must become com-
plex quantities and frequency dependent and may become nonlinear
and hysteretic.
Assuming a homogeneous isotropic medium and wave-propaga-
tion factor exp共ⳮ ikR兲, where R is radial distance, the wavenumber
of propagation is a complex function of frequency given by 共Balanis,
1988兲
ik⳱ i
␻
冑
␧
ˆ
*
␮
ˆ
*
⳱
␣
Ⳮ
i
␻
c
, 共3兲
where ␧
ˆ
*
and
␮
ˆ
*
are the generalized complex electric permittivity
and magnetic permeability, respectively, and
␣
is the positive real
coefficient of attenuation that represents the part of the EM wave en-
ergy that is irreversibly converted into heat.
Mathematically, the conductivity can be incorporated in the per-
mittivity and expressed as a complex number ␧
ˆ
*
⳱ ␧
ˆ
ⳮ i
␴
ˆ
/
␻
⳱ ␧
0
共␧
⬘
ⳮ i␧
⬙
兲. We also express the magnetic permeability as a gen-
eral complex function
␮
ˆ
*
⳱
␮
0
共
␮
⬘
ⳮ i
␮
⬙
兲. The general expressions
for the attenuation coefficient and propagation velocity are then giv-
en by
␣
⳱
␻
c
0
冉
兩␧
⬘
␮
⬘
ⳮ ␧
⬙
␮
⬙
兩
2
冊
1/2
冋
冉
1Ⳮ
冉
␧
⬘
␮
⬙
Ⳮ ␧
⬙
␮
⬘
␧
⬘
␮
⬘
ⳮ ␧
⬙
␮
⬙
冊
2
冊
1/2
ⳮ sign共␧
⬘
␮
⬘
ⳮ ␧
⬙
␮
⬙
兲
册
1/2
c⳱ c
0
冉
2
兩␧
⬘
␮
⬘
ⳮ ␧
⬙
␮
⬙
兩
冊
1/2
冋
冉
1Ⳮ
冉
␧
⬘
␮
⬙
Ⳮ ␧
⬙
␮
⬘
␧
⬘
␮
⬘
ⳮ ␧
⬙
␮
⬙
冊
2
冊
1/2
Ⳮ sign共␧
⬘
␮
⬘
ⳮ ␧
⬙
␮
⬙
兲
册
ⳮ1/2
, 共4兲
and all square roots must be taken positive.
Frequency dependence is the result of the irreversible process of
converting EM wave energy into heat through conduction or relax-
ation processes or from scattering. Dielectric relaxation losses are
primarily caused by the presence of water 共von Hippel, 1954兲 and
can be enhanced by the presence of clay minerals 共Olhoeft, 1987兲.
The magnetic properties of iron oxides can cause GPR reflections
共van Dam and Schlager, 2000; van Dam et al., 2002兲. The ratio of the
imaginary and real parts of the material property is known as the loss
tangent because it represents an angle in the complex plane. Magnet-
ic and electric loss tangents can be computed as tan
␦
m
⳱
␮
⬙
/
␮
⬘
,
tan
␦
e
⳱ ␧
⬙
/ ␧
⬘
. Magnetic relaxation losses are caused by the pres-
ence of iron minerals, and both usually follow a Cole-Cole frequen-
cy dependence 共Olhoeft and Capron, 1994兲 with a slope of log loss
tangent versus log frequency between zero and Ⳳ1 . Electrical con-
duction losses always have a slope of ⳮ1 . Scattering losses always
have a slope much greater than one. Frequency dependence causes
the earth to act as a low-pass filter, altering pulse shape as well as am-
plitude with propagation distance 共sometimes called pulse broaden-
ing兲.
For most earth materials, the magnetic permeability can be taken
as the free-space value. Further simplification is obtained when we
assume the electric permittivity and conductivity have constant val-
ues and ␧
ˆ
*
⳱ ␧
0
共␧
⬘
ⳮ i
␴
/ 共
␻
␧
0
兲兲 and when we assume
␴

␻
␧
0
.
Then equation 4 reduces to
␣
⳱
Z
0
␴
2
冑
␧
⬘
, c⳱
c
0
冑
␧
⬘
, 共5兲
where Z
0
⳱
冑
␮
0
/ ␧
0
denotes the free-space plane-wave impedance.
The result in equation 5 is used by many people and is a good approx-
imation in applications where GPR works well.
Another derived parameter of interest is wavelength, defined as
␭
⳱ 2
␲
/ R共k兲⳱ c / f, where R共k兲 means the real part of k. Wave-
length is an important parameter for determining scattering proper-
ties and resolution. At long wavelengths 共low frequencies兲 com-
pared to the size of the scattering target, quasi-static Rayleigh scat-
tering occurs; at wavelengths comparable to the target size, reso-
nance occurs; and at short wavelengths, optical scattering occurs.
Propagation and scattering
Any antenna is made to optimize the transition of the EM wave,
put into a cable by the signal generator, from the cable into the world
with the least possible disturbance of the signal. A ground-coupled
GPR antenna is optimized to emit this wave into the ground. Once
the EM wave leaves the transmitter antenna, some part of the field
leaks through the air directly to the receiver antenna 共direct airwave兲
and is scattered from nearby above-ground objects 共despite possible
Surface and borehole GPR developments 75A105
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attempts to shield the antenna兲. The wavefield above and below
ground may travel between the antennas by multiple paths. The
above-ground wavefield will travel with the speed of light in air,
which is known, is always faster than in the ground, and thus is easily
recognized in multioffset data or in fixed-offset data when it occurs
as a hyperbolic event. The wavefield below ground travels through
the earth materials with the speed of light in the material, and part of
that wave directly travels to the receiving antenna 共direct ground
wave兲.
On its propagation path, the wavefield amplitude decreases by
geometric spreading and material-attenuation losses. At some point,
the wavefield is scattered in the form of reflection, refraction, or dif-
fraction because the wave encounters a change in electric or magnet-
ic properties. A fraction of the wavefield is returned to the receiver;
path-loss considerations similar to those from the transmitter apply
here as well. The total effect of changes in amplitude from material
losses is the result of energy loss by surface scattering at interfaces,
by volume scattering from inhomogeneous materials, and by expo-
nential thermal-conversion losses from electrical conduction and
from dielectric and magnetic relaxation processes in the material
volume through which the wavefield passes along the paths from the
transmitter to the scattering object and back to the receiver. These
losses vary along different paths, and the frequency, angular orienta-
tion, and polarization dependencies can be used to identify the type
of loss.
The fraction of the EM wavefield that is returned to the radar sys-
tem from the subsurface scattering object is determined by the con-
trast in electric and magnetic properties at an interface between an
object and its embedding media. For objects large relative to the
wavelength, this is commonly given by the single-interface Fresnel
reflection coefficient 共Balanis, 1988兲, which has special cases for
layers that are thin compared to the apparent wavelength 共Tsang et
al., 1985兲 and that have cross-sectional areas that are small com-
pared to the wavelength. Snell’s law describes the amount of energy
transmitted through or reflected from a contrasting interface as a
function of incidence angle; it varies with polarization. For dissipa-
tive media, the angles are complex 共Balanis, 1988兲.
The polarization of an EM wave and the type of polarization inci-
dent on a contrasting interface, the high aspect ratio of an object
共wire or fracture兲, or a periodic pattern in a sedimentary sequence
also determines the amount and direction of wave scattering. These
dependencies are described by the Stokes matrix 共van Zyl and
Ulaby, 1990兲. Several commercial radar systems separate transmit-
ter from receiver antennas or provide antennas at different orienta-
tions inside one antenna box. With such systems, full-polarization
data can be recorded. Many other commercial radar systems do not
offer all possible transmitter-receiver polarization combinations and
usually only offer linear copolarized electric-field antennas. Howev-
er, even with such systems, it is possible to rotate the antennas and
exploit their polarization properties, e.g., to see rebar in concrete 共to
assess rebar condition兲 or to see past the rebar to ascertain concrete
thickness. In the first case, the rebar is the target and the desired scat-
tering object. In the second case, the bottom of the concrete is the de-
sired target, and the rebar is clutter or the undesired scattering object.
Aflat, smooth interface, relative to the wavelength, will scatter the
incident wave energy without changing the energy shape 共without
changing the antenna pattern; Ulaby et al., 1982兲. This is known as
specular reflection. As the interface becomes rough on the wave-
length scale, the scattering becomes less specular and more diffuse.
This is like going from a mirror to frosted glass, only on a larger
scale. In GPR, a typical example is a water table that appears rough
with a thick capillary fringe in finer-grained materials or smooth
with a thin capillary fringe in coarser materials. Another example is
with gasoline or oil floating on the water table, changing surface ten-
sion and wettability to smooth the capillary fringe. If this occurs in a
volume that is otherwise isotropic and homogeneous for energy
propagating through it, the situation is like the difference between a
frozen ice cube that is clear versus a snowball that looks white and
translucent from light scattering. Such scattering creates wave-
length- 共or frequency-兲 dependent losses because the energy is not
scattered in a useful direction, where “useful” means the energy
comes back to the receiver. However, this frequency dependence be-
comes a diagnostic of the scale of the scatter objects 共such as the cap-
illary fringe or rocks buried as road fill兲, and the depolarization may
indicate texture 共paleoriver channels seen by space shuttle radar un-
der sands in the western Sahara; Schaber et al., 1986兲.
GPR system and performance
GPR has been deployed from the surface by hand or vehicle
towed, in or between boreholes or tunnels, from aircraft, from satel-
lites, and between planets. It is sometimes used to look through
walls, e.g., to detect people. GPR operates by emitting radiofre-
quency EM energy as a short-pulse or swept frequency from a trans-
mitter antenna. The energy is coupled into the ground from the trans-
mitting antenna, and some fraction of the energy returns to the same
antenna 共monostatic兲 or a separate receiving antenna 共bistatic兲. The
properties of the radar system determine what happens to the signal
getting to the transmitter and back from the receiver; but between the
transmitter and receiver antennas, it is controlled by the geometry of
the antennas and the properties of the ground, including coupling
and buried-object 共target兲 responses. This latter is described by the
radar equation, which in one form is 共Noon et al., 1998兲
G
Tx
C
Tx
G
Rx
C
Rx
P
S
⳱
共4
␲
兲
3
R
4
␭
␽
exp共ⳮ 4
␣
R兲
, 共6兲
where the radar-system parameters are on the left-hand side and the
ground and target parameters are on the right. The values G
Tx
, C
Tx
,
G
Rx
, C
Rx
, and P
S
are, respectively, the transmit and receive antennas’
directional gains and coupling efficiencies and the radar-system per-
formance 共the ratio of mean transmitted power to the minimal de-
tectable signal兲;
␣
is attenuation in nepers/m;
␭
is wavelength in the
ground;
␽
is the scattering target cross section; R is the distance to
the target; exp共ⳮ
␣
R兲 represents two-way material attenuation loss-
es; and R
4
is two-way geometric spreading loss 共with an exponent
that varies with target type; see Noon et al. 关1998兴 for examples兲.
The radar system puts energy into the transmitter antenna at a
specified power and frequency spectrum, expecting a certain imped-
ance match going into the antenna. With most air-coupled antennas,
this expectation is usually met; but with ground-coupled antennas,
the properties of the ground may change the impedance match and
the efficiency of the transmitter 共the equivalent also occurs at the re-
ceiver兲 as the antennas move over changing ground conditions. This
change of impedance match contains useful information. It is diffi-
cult to calibrate 共Oden et al., 2008兲 for ground-coupled antennas but
relatively easy to calibrate for air-coupled antennas against a surface
that should be smooth and horizontal at the wavelength scale, such as
pavement 共Maser and Scullion, 1992兲. To use a GPR quantitatively,
this is where we must start making assumptions 共Olhoeft, 2000兲.
75A106 Slob et al.
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Horizontal and vertical resolutions are not the same for GPR, and
they vary with position and depth. Both are a function of wavelength
and geometry 共including depth兲. The vertical resolution is a function
of wavelength and scatterer size or layer thickness. It also depends
on signal-to-noise ratio 共S/N兲 and signal-to-clutter ratio. For pulse
radars, the vertical resolution is generally one-third to one-fourth of
the dominant wavelength with normal noise and clutter 共Yilmaz,
2001; Daniels, 2004兲. For frequency-domain GPR, it is given in
terms of the bandwidth used to determine the ability to distinguish
between 共resolve兲 two targets closely spaced in depth, and it is given
as the propagation velocity divided by the square root of two times
the bandwidth.
The Fresnel zone describes the circular region on an interface 共or
in an ellipsoidal volume for a scattering object兲 that coherently dif-
fracts or backscatters energy and thereby specifies resolution
共Smith, 1997; Yilmaz, 2001兲. The horizontal resolution is propor-
tional to the square root of the product of wavelength and depth
共Daniels, 2004兲. Wavelength should be understood as the wave-
length in the ground, including pulse broadening with propagation
distance. Horizontal resolution can be improved by migration,
which is described later. Vertical resolution can sometimes be im-
proved by deconvolution.
Common assumptions, limitations, and consequences
Many common assumptions are made in acquiring, processing,
modeling, and interpreting GPR data. Each assumption has limita-
tions with consequences that can lead to misinterpretation. The mag-
netic properties are often assumed to be those of vacuum or free
space. Because the product of magnetic permeability and permittivi-
ty determines velocity, depth will not be compromised; but if the per-
mittivity is then used to estimate water content, the water content
will be too high. Using only electric-field antennas will not let the
magnetic component be separated. If two high-contrast objects are
buried on top of each other, the topmost will shadow the lower one,
which can be dangerous when dealing with UXO. The geometry of
reflection from the top and bottom of a hollow plastic pipe may look
like two hyperbolas, misinterpreted as two separate objects. A syn-
cline may appear, as in seismic pitfalls 共Yilmaz, 2001兲, as a bow tie
masquerading as an object hyperbola. Interpreting velocity from hy-
perbolas is dangerous when other processes create patterns similar to
hyperbolas 共such as ice melt in permafrost around a hot pipeline or
reflections from overhead wires or nearby cars兲. Ignoring the anten-
na radiation pattern will not let geometric distortions be corrected
properly. Ignoring antenna ground coupling will not give correct
full-waveform modeling of details.
Although velocity can be measured by a variety of means 共Ol-
hoeft, 2000兲, it is often assumed based upon site conditions 共mea-
sured in one location and assumed to be useful for the whole site兲.
This is particularly dangerous with depth, such as above and below a
water table where depth to a pipe using only one velocity will result
in errors in depth estimates and increased excavation hazards. The
same thing can happen horizontally if moving from concrete to soil
changes not only velocity but also antenna coupling. With a multi-
layered earth, wave guides may appear along with multipathing and
can create errors in horizontal and vertical positions 共Sander et al.,
1992兲. Because of the way most antennas work, they radiate the
wavefield in a wide beam and see off to the side as well as forward
and aft, allowing the possibility of out-of-plane scattering from ob-
jects not directly under the antenna traverse 共Olhoeft, 1994兲. This is
advantageous when 3D data are collected covering an area, but it can
lead to pitfalls when interpreting 2D GPR data collected along a line.
In that case, ignoring the out-of-plane possibility and fitting hyper-
bolas to the resultant shape will give the wrong velocity, depth, and
location of the scattering object 共it is a different cross section
through a 3D hyperboloid兲. Errors are introduced in full-waveform
amplitude modeling when air-launched antennas are calibrated on a
sloped railroad ballast bed, assuming a horizontal surface, or on
gravel beds that are rough at the wavelength scale, assuming it is
smooth 共Olhoeft et al., 2004兲.
BOREHOLE GPR
Borehole GPR operates in a single borehole, between two bore-
holes 共crosshole GPR兲, from a borehole to the surface 共vertical radar
profile兲, or from a borehole to a mine tunnel. In each situation, the
surrounding conditions of the antennas are very different from those
of surface GPR antennas. Fundamental studies on the behavior of
antennas in cylindrical structures, which can be used for designing
borehole radar antennas, can be found in King and Smith 共1981兲,
Greenfield 共1988兲, and Sato and Thierbach 共1991兲. Schematics of a
borehole radar measurement in single- and crosshole modes are
shown in Figure 1. Because antennas in boreholes are strongly af-
fected by the surrounding medium, the antenna characteristics are
Reflection from
a point target
Point reflector
Direct wave
Direct wave
Reflected wave
Traveltime
Planar reflector
Depth
a
)
b)
Reflection from
a planar target
Figure 1. Schematic representation of borehole GPR measuring con-
figurations. 共a兲 Transmitter and receiver are set in the same borehole
in single-hole measurement, whereas 共b兲 in crosshole measurement,
they are set in separated boreholes.
Surface and borehole GPR developments 75A107
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Frequently asked questions

Q1. What have the authors contributed in "Urface and borehole ground-penetrating-radar developments" ?

No tool solves all problems ; so to determine whether GPR is appropriate for a given problem, studying the reasons for failure can provide an understanding of the basics, which in turn can help determine whether GPR is appropriate for a given problem. The authors discuss the specific aspects of borehole radar and describe recent developments to become more sensitive