United States
Environmental Protection
Agency
Office of Research and
Development
Washington, DC 20460
EPA/600/R-92/089
May 1992
> ffc'
A Study to
Determine the
Feasibility of Using a
Ground-Penetrating
Radar for More Effective
Remediation of Subsurface
Contamination
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EPA/600/R-92/089
May 1992
o
A STUDY TO DETERMINE THE FEASIBILITY OF USING
A GROUND-PENETRATING RADAR FOR MORE EFFECTIVE
REMEDIATION OF SUBSURFACE CONTAMINATION
by
Dennis G. Douglas, Alan A. Bums, Charles L. Rino, Joseph W. Maresca, Jr.
Vista Research, Inc.
Mountain View, California 94042
Contract No. 68-03-3409
Project Officer
James Yezzi
Superfund Technology Demonstration Division
Risk Reduction Engineering Laboratory
Edison, New Jersey 08837
RISK REDUCTION ENGINEERING LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
This material has been funded wholly or in part by the United States Environmental Pro-
tection Agency under Contract 68-C9-0033 to Foster Wheeler Enviresponse, Inc. It has been
subject to the Agency's peer and administrative review, and it has been approved for publication
as an EPA document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
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FOREWORD
Today's rapidly developing and changing technologies and industrial products frequently
carry with them the increased generation of materials that, if improperly dealt with, can threaten
both public health and the environment. The U.S. Environmental Protection Agency is charged
by Congress with protecting the nation's land, air, and water resources. Under a mandate of
national environmental laws, the agency strives to formulate and implement actions leading to a
compatible balance between human activities and the ability of natural systems to support and
nurture life. These laws direct the EPA to perform research to define our environmental prob-
lems, measure the impacts, and search for solutions.
The Risk Reduction Engineering Laboratory is responsible for planning, implementing,
and managing research, development, and demonstration programs to provide an authoritative,
defensible engineering basis in support of the policies, programs, and regulations of the EPA
with respect to drinking water, wastewater, pesticides, toxic substances, solid and hazardous
wastes, and Superfund-related activities. This publication is one of the products of that research
and provides a vital communication link between the researcher and the user community.
This publication describes a research project that investigated the application of advanced
radar systems to detecting contaminants present in soil and groundwater. Ground-penetrating
radar, in combination with sophisticated data-processing techniques, was found to be a viable
means not only of detecting the contaminant substance and defining its extent but also of distin-
guishing this substance from natural subsurface features.
Risk Reduction Engineering Laboratory
E. Timothy Oppelt, Director
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ABSTRACT
Remediation of toxic spills is often costly and entails cumbersome procedures. The tradi-
tional method is to drill core samples in the area where the contaminant is thought to be present
and then analyze these in a laboratory. The denser the sampling grid, the more effective it is;
unfortunately, it is also more expensive to implement and more damaging to the environment A
nonintrusive method of detecting subsurface contamination, therefore, would be highly desirable.
Toward this end, the use of ground-penetrating radar (GPR) to locate and map subsurface con-
tamination was investigated. If GPR proves effective, it can be combined with conventional
methods to ensure better placement of drilling sites and to reduce the number of samples
necessary. The objective of this work was to assess the capability of GPR to identify natural
subsurface features, detect man-made objects buried in the soil, and both detect and define the
extent of contaminated soil or groundwater.
Several conclusions emerged from this study. The technology for the envisioned GPR
already exists. In terms of hardware, it was found that a radar system with a very high figure of
merit is required if the system is to operate effectively in all three generic subsurface environ-
ments modeled in this study. (These three environments contain the subsurface features that are
representative of seven out of ten "common cases," as defined by EPA, found at remediation
sites.) In terms of signal processing, it was found that for typical GPR systems synthetic-
aperture-radar (SAR) processing is required; this conclusion was based on three reasons: (1) bet-
ter horizontal resolution is achieved with SAR processing; (2) SAR processing allows the system
to operate at lower frequencies and thus achieve deeper penetration; and (3) SAR processing
reduces ambient noise, which improves the detection and identification capabilities of GPR.
It is recommended that simple proof-of-principle experiments be undertaken to validate the
models developed in this study. To the extent that the experiments prove successful, GPR may
become a significant tool in rapidly identifying and cost-effectively remediating subsurface con-
tamination.
This report was submitted in fulfillment of Contract No. 68-C9-0033 by Vista Research,
Inc., under the sponsorship of the U. S. Environmental protection Agency. This report covers a
period from December 12,1990, to May 20,1991; work was completed as of May 13, 1991.
IV
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TABLE OF CONTENTS
Disclaimer ii
Foreword iii
Abstract iv
List of Figures vii
List of Tables ix
Acknowledgments x
1 Introduction 1
1.1.1 Current Remediation Practices and Problems 1
1.1.2 Application of Ground-Penetrating Radar to Remediation 1
1.1.3 Report Organization 3
1.2 Objectives and Approach 5
1.2.1 Objectives 5
1.2.2 Technical Approach 5
2 Conclusions 7
3 Recommendations 10
4 Radars and Radar Signal Processing 12
4.1 Radar Fundamentals 12
4.2 Ground-Penetrating Radars 17
4.3 Short-Pulse and Synthetic-Pulse Radars 23
4.4 Real- and Synthetic-Aperture Signal Processing 24
5 Radar Figure of Merit 27
5.1 Introduction 27
5.2 Figure-of-Merit Derivation 27
5.2.1 Short-Pulse Radars 27
5.2.2 Synthetic-Pulse GPRs 29
5.3 Figures of Merit for Typical Radars 30
5.4 Processing-Gain Contribution to Figure of Merit 32
5.5 Environmental Contributions to Figure of Merit 34
5.6 Section Summary 35
6 Soil Characteristics, Soil Model, and Soil Geometries 36
6.1 Classification and Distribution of Soil Types 36
6.2 Characteristics of Soils and Contaminants 38
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6.3 Modeled Soil and Contamination Geometries 40
6.4 Dielectric Properties of Soils and Soil Mixtures 43
6.5 Section Summary 44
7 Detection Strategies 45
7.1 Introduction 45
7.2 Summary of Strategies 46
7.3 Model IB Strategy: Reflection from a Contaminant/Water Interface in Soil 47
7.4 Model IA Strategy: Reflection from a Thin Layer of Contaminant Sandwiched
between Layers of "Dry" and Wet Soil 49
7.5 Model II Strategy: Volume Scattering from Soils 56
7.6 Model II Strategy: Deducing Changes in the Local Average Refractive Index ... 65
7.7 Section Summary 66
8 Radar System Design 68
9 Numerical Analytic Model 72
9.1 Introduction 72
9.2 The INS Model 73
9.3 Signal Processing 76
9.4 Representative Examples 77
References 94
Appendices
A. Real Signals, Analytic Signals, and Complex Envelopes A-l
B. Calculations of Dielectric Constant, Conductivity, and Attenuation Coefficient
for Various Soils and a Petroleum Contaminant B-l
C. Modified Booker-Gordon Scattering Formula C-l
D. Correlation Function for Soil Variability Model D-l
VI
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LIST OF FIGURES
4.1 Block diagram of a generic radar 13
4.2 Examples of radar displays 15
4.3 Typical GPR pulse waveform 18
4.4 Block diagram of a short-pulse GPR 19
4.5 Example of a typical conventional GPR output display 21
4.6 GPR pulse intensity and hard-limited output 22
4.7 Short-pulse and synthetic-pulse radar waveforms: (a) a short-pulse radar trans-
mits a short burst of nearly sinusoidal signals; (b) a Fourier transform gives a
"spectrum" of the waveform; (c) a synthetic pulse transmits the spectrum in a
series of sinusoidal signals over the range of frequencies; (d) a Fourier transform
gives the effective waveform 24
4.8 Block diagram of a synthetic pulse radar system 25
6.1 Triangular Classification Chart for soil 37
6.2 Distribution of soil deposits 38
6.3 Models of subsurface conditions. In Model IA (a), the contaminant floats on the
water table; in Model IB (b) there is a gradual transition from wet to dry, but the
immiscibility of the contaminant with water causes a boundary to form at some
point; in Model II (c) the contaminant forms a plume that travels downward 42
7.1 Profiles of dielectric constant vs. depth: (a) distinct water table, and
(b) indistinct water table 50
7.2 Incident vs. reflected signal 52
7.3 Real part, imaginary part, and magnitude of the reflection coefficient vs. layer
thickness of a contaminant-saturated layer sandwiched between dry and water-
saturated soils (30% porosity and 0.03 S/m water conductivity 53
7.4 19?r(OI /(r(t)\ and 13r(r)| /I r(OI vs- laver thickness for a contaminant-saturated
layer sandwiched between dry and water-saturated soils (30% porosity and
0.03 S/m water conductivity) 54
7.5 |
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9.2 Processed returns for Q=140-dB GPR in perspective with 60-dB logarithmic
display 81
9.3 Unprocessed simulated returns for Q=l 60-dB GPR. Point targets are located at
10-m and 30-m depths 82
9.4 Processed returns for Q=180-dB GPR. Upper target is visible 83
9.5 Unprocessed returns for Q=180-dB GPR. Point targets are located at 10-m and
30-m depths 84
9.6 Processed returns for Q=180-dB GPR. Both targets are visible 85
9.7 Unprocessed returns for Q=190-dB GPR 86
9.8 Processed returns for Q=190-dB GPR 87
9.9 Unprocessed returns for Q=220-dB GPR 88
9.10 Processed returns for Q=220-dB GPR. Processing sidelobes are visible for target
at 10m 89
9.11 Unprocessed returns for Q=220-dB GPR with two closely spaced targets at 10-m
and 15-m depths 90
9.12 Processed returns for Q=220-dB GPR with closely spaced targets 91
9.13 Unprocessed returns for Q=220-dB GPR illuminating a wedge of randomly
located scatterers 92
9.14 Processed returns from Q=220-dB GPR illuminating wedge 93
Vlll
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LIST OF TABLES
5.1 Specifications for a "Typical" Commercially Available GPR 31
6.1 Electromagnetic Characteristics for Common Geologic Materials 39
6.2 Dielectric Constants of Typical Contaminant Materials 40
7.1 Detection Strategy Summary 46
7.2 Plane-Interface Complex Reflection Coefficient at 100 MHz 49
7.3 e^, < (e,. - I)2 >, and < t? > vs. Porosity and Mixture Type 60
7.4 63 and < % > for a Mixture of Rocks and 30% Porosity Soil 60
7.5 Minimum Q vs. d 62
7.6 e^ and e^ < t? > for d = 2.5 cm, 7 = 10 cm Stones in Various Soils 63
7.7 Backscatter Quantities for Solid Particles Imbedded in Dry, Low-Loss, 30%-Po-
rosity Soil at 10-m Depth (Tobs = 3000 s) 64
8.1 Values of Q^,, Necessary to Detect Various Targets in Various Environments
with SNR of 10 dB 70
9.1 Model Parameters 75
IX
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ACKNOWLEDGMENTS
This research report was prepared by Vista Research, Inc., for the U.S. Environmental Pro-
tection Agency's (EPA's) Risk Reduction Engineering Laboratory (RREL) on Contract No.
68-C9-0033. James J. Yezzi of the Releases Control Branch was the Technical Program Monitor
on the Work Assignment for EPA/RREL. Technical review was provided by Mr. Yezzi and by
Anthony N. Tafuri, Section Chief, Releases Control Branch. The authors would also like to
acknowledge Foster Wheeler Enviresponse, Inc., for their support during the project. This docu-
ment was edited by Monique Seibei and prepared for publication by Pamela Webster.
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Section 1
INTRODUCTION
1.1 Background
1.1.1 Current Remediation Practices and Problems
Remediation of a petroleum or chemical release from an underground storage tank (or a
hazardous waste storage site) requires that the horizontal and vertical extent of the contaminated
soil and groundwater region be located and quantified. This is traditionally accomplished by
preparing a plan to define drill sites, taking core samples at the planned sites, and then analyzing
the cores at a laboratory. A map based upon the contamination found in the samples is then
prepared, and is used to guide the cleanup operation. Since drilling and analysis operations can
be costly, it is desirable to minimize the number of samples while still preparing an adequate
map of the contaminated area.
Reducing the number of corings taken per unit area, while reducing cost, generally leads to
undersampling of the site. Concentrating a given number of corings in a limited area, while
increasing the sample density, presumes knowledge about the location and spatial extent of
contaminated areas. Further, since there is usually little geological information available about
the contaminated sites, even a fine sampling does not ensure that the contaminated areas will be
found. This is because fracture regions and fissures can channel liquid contaminants away from
the spill (or release) site. Thus, any point-sampling scheme is potentially flawed.
A substantial reduction in the number of core samples could be achieved if better tools
were available with which to prepare a drilling plan. These tools would create a "map" of the
subsurface features, with nearly continuous spatial coverage. Advanced ground-penetrating
radar (GPR) is one such tool that may offer the performance necessary to create these maps.
Such a system could be used in conjunction with conventional core-and-analyze techniques to
substantially improve remediation efficiency.
1.1.2 Application of Ground-Penetrating Radar to Remediation
The Risk Reduction Engineering Laboratory (RREL) of the Environmental Protection
Agency (EPA) has investigated the feasibility of using remote sensing techniques for a variety of
subsurface detection problems. For example, acoustic emission techniques have been used to
detect the failure of earthen structures such as dams, embankments, and so on [1]. The RREL
has also examined the feasibility of using acoustic sounding techniques, but problems were
encountered in efficiently coupling the transmitted pulse to the ground. Recently, the RREL
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investigated the use of 17 different remote sensing techniques for the detection of buried
containers [2]; this effort entailed an extensive literature search and a field evaluation of four of
the remote sensing systems. One of these systems was a short-pulse GPR; this system had
advantages over the other three methods examined (a metal detector, an electromagnetic
induction system, and a magnetometer) because it could detect both metallic and nonmetallic
buried containers.
RREL also evaluated the potential of continuous-wave (CW) and short-pulse GPR
techniques for mapping subsurface features [3]. Only limited success was achieved with the CW
system; however, as noted by Koerner and Lord in this work, further improvements to the
electronics and signal processing would be required before any definitive conclusions could be
made about the capability of the CW measurement approach.1 Better success was achieved with
the more conventional short-pulse GPR, but again the authors pointed out similar shortcomings
in the system used in the evaluation.
GPRs have been proposed repeatedly for applications involving sensing or mapping the
location (or likely location) of underground contaminants. Some experimental evidence of the
successful use of GPR for this purpose has been presented. However, this evidence is largely
anecdotal and lacks quantitative support. Thus, those positive results appear as special cases that
cannot be extrapolated to general situations. This deficiency arises from the lack of a
quantitative model for the effect of contaminants on those properties of soils that affect GPR
performance and, hence, GPR performance specifications. The work described below will show
that the lack of success in these prior programs can be largely ascribed to use (or considerations)
of radars whose performance levels are insufficient for the task and to a need for much more
intensive data processing.
While the literature indicates that radar measurement systems may have the potential to
improve remediation efforts, such potential has yet to be realized. Three key elements are
lacking in the radar studies: (1) a quantitative model of the effect of contaminants on the
radar-relevant properties of soils, (2) understanding and "matching" the radar characteristics to
the environment and the target(s) to be detected so as to get the best possible signals, and (3)
developing the signal-processing methods to take best advantage of the signals returned from the
subsurface scatterers.
1 In principle, the CW system was capable of excellent performance; its main deficiency was that an inadequate
number of discrete CW frequencies were available for use. It will be seen later that a multiple-tone CW system with
a large number of frequencies constitutes a "synthetic-pulse" radar, which offers a potential performance greatly
exceeding that of a conventional, short-pulse GPR.
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This report describes the results of a program whose purpose was to examine potential
radar designs and signal-processing concepts in terms of estimated radar performance in various
soil conditions and stratigraphy, with various moisture levels, and with various objects and
contaminants. The design elements incluued radar parameters (e.g., center frequency,
bandwidth, power, receiver sensitivity, dwell time, and so on) and signal processing concepts
(real aperture and synthetic aperture) that would allow researchers to "match" the soil and
detection targets (objects and contamination materials). Matching the radar design to the
environment is important since the performance of a ground-penetrating radar is related to the
environment in which it must operate. Generally, the lower the frequency and the higher the
power, the better the penetration of the electromagnetic wave into the soil. However, lower
frequencies will result in poorer spatial resolution. Thus, an optimum balance is sought; this
work seeks to determine that "optimum" design.2
1.1.3 Report Organization
Section 1 of this report gives some background information on ground-penetrating radar
and describes the objectives of the work assignment reported here; it also outlines the technical
approach taken to accomplish the objectives.
Section 2 provides the conclusions resulting from the technical work, and highlights the
key technical findings of each of the task elements.
Section 3 recommends that a "proof-of-principle" experiment be conducted to confirm and
validate the findings of this work assignment; Section 3 also summarizes the rationale for this
recommendation based upon the findings reported in this work.
Section 4 of the report introduces the technical effort with a brief discussion of
ground-penetrating radars and how they compare to ordinary "air-path" radars. This section
describes the key differences between a "real-pulse" radar and a "synthetic-pulse" radar—the two
types of radars considered in this work. The section also includes a brief discussion of
real-aperture and synthetic-aperture (coherent) signal processing—the two signal processing
methods discussed in this work.
Section 5 of the report introduces and develops the concept of a "figure of merit," Q, that
expresses the performance of the GPR radar system (radar plus signal processing plus
environment) in terms of a single number. After this concept has been developed, Qs for
existing real-pulse and synthetic-pulse radars are calculated based upon information provided by
the manufacturers; the effect of processing gain is discussed; and the environmental
2 In the context of the work described here, "optimum" refers to the best balance of radar designs from among those
considered, in the context of a given set of environmental parameters (soils and targets).
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contributions in Q are defined in terms of the radar cross section of the scatterers in the
environment. This section shows that the potential performance of synthetic-pulse radars is
40 dB to 60 dB greater than that of real-pulse radars.
Section 6 describes the soil modeling work performed in support of the radar design
objective. This section summarizes the classification of soil types and the broad distribution of
these soils throughout the United States, and then discusses the electromagnetic characteristics of
various soils and some likely contaminant materials. Following this, two basic
soil/contamination geometries are introduced. These two geometries, which can be used to
represent a wide variety of possible subsurface conditions, are used as the basis for the detection
strategies, presented in Section 7.
In Section 7, Q and the soil models are brought together. Here, a Qmin is determined as the
minimum value of radar Q necessary to detect various types of contamination in various
geometries, for various signal processing schemes. The section addresses the issues of particle
size and moisture content and how they relate to the detection problem, as well as the
contamination geometry. Section 7 will show that to detect a contaminant layer at a depth of 10
m in moderately dry, moderately fine-particle soils, a Q of about 160 to 180 is needed—a Q that
can be achieved with a real-pulse radar and coherent processing. To detect a contaminant plume
at 10 m in this same soil, however, a radar with a Q of 200 to 220 is required; this Q can be
achieved with a synthetic pulse radar and coherent processing.
Section 8 describes the design of the radar, drawing on the results of the previous sections.
The radar design, defined in terms of Q, is heavily dependent upon the environment in which it
must operate and the targets it must detect in that environment. A table is presented that
summarizes the required Q for a variety of soil environments, targets and target depths.
Section 9 provides a description of and the results obtained from a numerical model that
was developed to estimate GPR radar propagation and scattering in any desired scenario, and to
provide displayed examples of radar output for various spatial sampling schemes. The data in
this section complement that of Section 7 and graphically illustrate the need for high-<2 radars
and coherent processing techniques for tasks that entail the detection of low-cross-section targets
in difficult environments.
Some of the key reference material used during the performance of this work assignment is
listed at the back. In addition, there are four appendices that describe particular aspects of the
work in Sections 6 and 7.
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1.2 Objectives and Approach
1.2.1 Objectives
The objective of the work reported here is to determine the circumstances under which a
GPR can be used for more effective remediation of a release of petroleum or other chemical
substances into the soil and groundwater. In particular, the goal is to determine whether a radar
with appropriate signal processing can achieve significantly better performance against
remediation targets (soils and contaminants) than prior results have shown and whether such a
radar warrants a number of proof-of-principle and demonstration-measurement programs. In this
context, "more effective remediation" means a reduction of, or better placement of, monitoring
wells required for initiating, tracking, and verifying remediation. To realize a substantial
improvement over conventional monitoring techniques, it is necessary to show that a radar
system can be used to: (a) rapidly develop accurate maps of the main features of the subsurface
topography with sufficient resolution to improve the placement of monitoring wells and reduce
their number, and (b) develop maps of subsurface objects and contaminated regions.
This objective entails radar design and trade-off studies to "match" the radar configuration
and signal processing to the resolution, sensitivity, and depth penetration necessary for the radar
to "see" the subsurface features and detect contaminated regions.
1.2.2 Technical Approach
Prior work ([4], [5],and [6], for example) has shown that the propagation of
electromagnetic energy through soils is determined by the frequency of the propagating wave
and the electrical properties of the propagation medium, in particular the dielectric permittivity.
(The dielectric permittivity is used to calculate the complex dielectric constant, complex
reflection coefficient, loss tangent, and attenuation coefficient). Thus, before the performance of
various ground-penetrating-radar and processing designs can be assessed, the properties of the
medium in which the radar waves will propagate must be determined. Accordingly, the
approach selected for this work initially concentrated on finding a suitable soil model—one that
could express the electrical properties of soils over the range of frequencies of interest.
After a suitable soil model was located and implemented, two additional
radar-performance models were developed that used the soil model as a source for input
parameters. One model developed was analytical; this model examined radar performance using
the radar equation as the starting point. A second, numerical, model was also developed. This
model calculated and visualized the radar processes as seen in (x, depth) "slices" through the
soil. In addition to creating visual examples of the radar processes for both real-aperture and
synthetic-aperture radars, the numerical model allows the consequences of various spatial
sampling schemes to be explored. These two models calculate and (in the case of the numerical
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model, visualize) radar performance in terms of engineering units—watts, radar cross section,
time, meters, and so on—units that are both meaningful and essential to a quantitative
understanding of how various configurations might be expected to perform in different
conditions.
An assessment of radar performance in situations representative of actual sources,
contaminants, and hydrogeology requires that these conditions be somehow presented to the
radar modeling codes. To this end, three soil-contamination geometries were developed in this
work. These three geometries can be configured to comprehend seven of the ten
hydrogeological/contaminant scenarios posed by the EPA as "...common combinations of
sources, contaminants, [and] hydrogeology" [7].3 These three geometries were used to represent
various generic conditions. Assessment of the performance of the radars and signal-processing
methods was accomplished by comparing the outputs of the analytical and numerical models for
various types of radars and their characteristics and for real- and synthetic-aperture
signal-processing methods, and for various combinations of soil, moisture content, and
contaminant configuration.
While an assessment can be made based upon relative performance, a complete assessment
of a selected design must include one or more detection strategies, that is, estimates of how the
radar data are used to detect the selected targets (objects and/or contaminants), and estimates of
how well the system would work in various environmental conditions. To this end, this work
also included the development and evaluation of the detection strategies necessary for successful
utilization of the best design resulting from the analytical and numerical models.
3 Leaks over two connected aquifers, over crystalline fractured rock, and over karst terrain are not presently
incorporated into Vista Research's model.
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Section 2
CONCLUSIONS
The objective of this study was to determine under what circumstances and with what
configuration a ground-penetrating radar can be used for more effective remediation of release of
petroleum or other chemical substances into the soil and groundwater. In the pursuit of this
objective, several radar-system alternatives were considered—each of which was based upon
existing, and therefore, achievable, technology. The system realization has both hardware and
software (i.e., signal processing) alternatives.
The consideration of alternative designs for the radar system required the development of a
"figure of merit," which was derived from fundamental and well-founded radar design principles
and which encompassed hardware and software considerations. This work considered the
relative performance of several existing radar designs: a typical short-pulse radar, a short-pulse
radar with higher transmitter power, and a synthetic-pulse radar. The results of this work
showed that, although the short-pulse and synthetic-pulse radars were mathematically equivalent,
the synthetic-pulse radar offered 40 to 60 dB better performance than the short-pulse radar
because the former could transmit far greater power per spectral line than the latter.
Furthermore, the results of this stage showed that, while the improved performance offered by
the synthetic-pulse system was not often needed for the usual "hard-target" GPR applications,
such improvements are essential for the detection of small changes in dielectric constant such as
would be expected in a situation where a small region (or thin layer) of contamination was
encountered.
Two signal-processing methods were also included in this stage of the work: real-aperture
and synthetic-aperture (SAR) processing. The results of this work showed that
synthetic-aperture (coherent) processing offered a significant advantage for remediation
applications over the usual incoherent processing because such processing, while
computation-intensive, afforded a higher effective of signal-to-noise ratio and reduced clutter
from adjacent reflections. To detect modest levels of most common contaminants, at depths of
10 to 15 m, and in moderately conducting soils, it was estimated that a combined
radar-processing figure of merit of 200 to 220 dB is necessary. Considering the current radar
technology, it was determined that this level of figure of merit could only be achieved by
combining a synthetic-pulse radar with synthetic-aperture processing. It was also determined
that one can obtain an additional processing gain of 35 dB by using a 3000-s observation time to
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collect data from a three-dimensional volume and then SAR-processing these data; the figure of
merit could thus be effectively increased by 35 dB, which would mean better performance of the
GPR in detecting the desired target.
As part of the radar design assessment task, a numerical model was developed that could
illustrate the nature of radar returns from various modeled soils and geometries, and show the
processing gains of different signal-processing methods. To support this effort, a model was
developed that described the electrical characteristics of soils and of various potential
contaminant materials at radar frequencies from about 20 MHz to about 200 MHz. This work
determined that, for the radar frequencies considered, the dielectric constant and attenuation
coefficient associated with these soils (with the exception of wet clays and ionic (salt-laden) silts
and sands) were not fundamental obstacles to the propagation of radar energy through the
medium. Further, this work showed that, for the range of radar frequencies most suitable to
radar energy penetration to a working-goal-depth of about 10 m (in nominal soil conditions),
consistent with the bandwidth necessary for adequate resolution, the dielectric constants and
attenuation coefficients were nearly constant over the spectral range.
The second stage of the work entailed the development of useful geological and
contamination geometries that could describe various contamination layers and plumes. These
geometries were needed so that the performance of the radar designs could be tested against the
modeled electrical characteristics of the bulk materials. This work led to the development of
three essential geometries that represented seven of the ten "common cases" of remediation
configurations described by the EPA.
One important outgrowth of this work was that it became clear that a "typical" remediation
site suitable for a baseline test could not easily be defined, because the soil properties, moisture
content, and contamination environment differed dramatically at each of the sites described in
the literature. An almost limitless combination of factors could be ascribed; this made the radar
design assessment difficult because not every combination could be addressed. To deal with this
lack of a "typical site," a generic soil condition (comprised of a sand-clay mixture) was selected.
The assessment work entailed adding various moisture and contaminant contributions to this soil
mix, appropriate to the geometry considered. This "soil" is roughly equivalent to the "synthetic
soil matrix" (SSM) developed by the EPA as representative of Superfund sites [8,9].
The numerical model allowed the effects of various spatial sampling schemes to be
examined. This model showed that, with the incoherent signal processing usually applied to
GPR data, the wide beamwidths associated with GPRs created a confusing display of the
subsurface environment; these results were consistent with the images usually created by
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commercial GPRs. The numerical model also showed that when synthetic-aperture processing
was used, the background noise in the radar images was reduced and discrete scatterers in the
radar field of view were tightly localized.
A significant portion of the design assessment task addressed various detection strategies.
That is, given a radar and a geometry, this work sought to identify key strategies that could be
used to deduce the presence (or lack) of contamination in the subsurface returns from the
processed data. This was a central effort in the work (after the basic feasibility of using
synthetic-pulse radar and SAR processing for remediation support had been established). This
work resulted in two novel findings. First, it appears that for contaminants with low dielectric
constants (which includes most non-ionic materials), there can be large contrasts in volumetric
scattering (up to 7 dB) between contaminated and uncontaminated regions. Such contrast ratios
are well within the detection range for a system with a high figure of merit, such as the
synthetic-pulse radar with SAR processing designed in this work assignment. Second, it was
determined that a thin layer of contaminant "floating" on the water table will produce a
measurable signal if the layer is more than a few centimeters thick; the appearance of such a
signal at some point in a survey would indicate the presence of contaminant there. However, the
nature of this signal is such that it might be difficult to distinguish it from a local change in the
depth of the water table, so its overall utility is questionable, even though it is surprisingly
strong. On the other hand, thicker layers will produce a strong and distinctive signal. Strong
signals will also be produced if abrupt transitions are induced at the boundaries between a
lighter, immiscible contaminant and a water table with gradually increasing saturation. It is
shown that volumes of pure fine and very fine soil particles (such as found in silts and clays) can
greatly degrade the performance of a GPR. These soils are usually found with some fraction of
larger imbedded particles such as sand grains. The analytical model has determined that the
presence of these larger particles facilitates the detection of contaminated regions.
-------
Section 3
RECOMMENDATIONS
This work assignment has shown that, for the environments and contamination geometries
modeled here, a radar with a high figure of merit combined with coherent signal processing can
detect contamination under a wide range of conditions. Such a radar can be achieved with
existing technology.
The scope of the work accomplished here, however, represented an idealized soil
environment and did not comprehend a largely inhomogeneous propagation medium. In an
extreme case, this type of soil environment can lead to poor estimates of the radar propagation
velocity, which limits the ability of the coherent processing to properly "register" the scatterers.
It can also lead to an increase in the radar clutter field, which decreases the otherwise achievable
signal-to-noise ratio. On the other hand, the detection of contaminants is facilitated by the
presence of small irregularities in an otherwise "pure" soil as a result of the increased volume
scattering that occurs.
While the results of the work assignment showed two-dimensional coherent processing
(surface distance, depth) was necessary to detect, deep, low-contrast targets, important
performance gains could be achieved using three-dimensional techniques (surface area, depth).
This type of data collection (and processing) will be necessary in order to enhance weak targets
in a cluttered environment, and it is essential to provide a vehicle for "intelligent,"
understandable displays.
Thus, while the results of this work indicate that ground-penetrating radar is likely to be
useful in improving remediation work under many circumstances, they are based on modeled
data and cannot be considered conclusive. While modeling of environments is possible in
principle, such work would not (because of the clutter) realistically or economically model any
particular environment. Therefore, unless an experiment is performed to test and validate the
models and the findings resulting from this work, the use of GPR for remediation purposes will
remain an unanswered question.
It is recommended that an experimental program be conducted, using a synthetic-pulse
radar combined with synthetic-aperture signal processing. It is recommended that the initial
experiments be "proof-of-principle" measurements. The objective of these initial experiments
would be to calibrate a GPR in terms of figure of merit and other needed parameters, and to
collect a limited set of subsurface data at a quantified site so that the findings of this work could
10
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be validated and the use of high-figure-of-merit radars in real environments might be better
understood. It is further recommended that in the initial experiments data be collected and
coherently processed three-dimensionally.
To the extent the proof-of-principle is successful and confirms the potential fov using radar
in remediation work, an expanded measurement and demonstration program could be
undertaken.
11
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Section 4
RADARS AND RADAR SIGNAL PROCESSING
The object of the work reported here is to determine if a ground-penetrating radar can be
used to detect subsurface contamination. Thus, radar concepts and radar signal-processing
techniques are inseparably intertwined with the electromagnetic properties of soil and
contaminants. While it is not the purpose of this report to provide an exposition in the area of
radars and signal-processing methods, some tutorial information about radars and radar signal
processing may be desirable as a background for the more detailed descriptions provided later.
Therefore, this section of the report provides a brief overview of some essential radar and signal
processing concepts.
4.1 Radar Fundamentals
RADAR is an acronym for RAdio Detection And Ranging. A radar operates by radiating
electromagnetic energy and detecting the echo returned from objects that reflect the incident
energy. The amount of energy reflected from electrically nonconducting, or weakly conducting,
objects (e.g., rocks, plastic pipes, etc.) is related to the differences between the dielectric
constant of the object and the dielectric constant of the surrounding medium. A metallic,
conducting object (such as a drum or pipe) is usually a better reflector than a nonconducting one.
The radiated energy of a radar (the transmit waveform) is usually a short pulse or series of pulses,
but some specialized radars use other types of waveforms.
The character of the detected echo can provide information about the reflecting object(s)
[10]. For example, the distance to the reflecting object(s) can be determined by measuring the
time delay between transmission and echo reception and multiplying by the speed of propagation
of the electromagnetic energy. Or, the amplitude of an echo signal can be used to gain
information about the scattering properties of the target object, or object's size, if the radar
system is calibrated and if it has sufficient range resolution. In a coherent radar system, the
phase of the detected echo can provide information such as the speed of the target (actually, the
vector component of velocity directed towards the radar), or its scattering properties. A high
degree of coherence means that the relative timing and frequency of the radar signals are well
controlled or measured (to a small fraction of the period of the radar center frequency);
coherence is an essential requirement for synthetic-aperture radar and synthetic-pulse radar
signal processing.
12
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A block diagram of the basic parts of a generic radar system appears in Figure 4.1. In this
radar, the oscillator is used as the basic frequency reference, and the waveform generator acts to
gate the oscillator signal on and off to form pulses. The clock is used to control the timing of the
signals; that is, the width of the pulse, the pulse repetition frequency (prf) (i.e., the temporal
spacing between successive pulses), and so on. The power amplifier boosts the low-level
voltages from the oscillator/waveforming circuits to high levels for transmission. The T/R
switch serves to isolate the transmitter section of the radar from the receiver, since a powerful
signal injected into a sensitive receiver could damage or introduce non-linear saturation effects in
the sensitive front end of the receiver.4 In most cases, the radar antenna is built with significant
directionality (or high gain or narrow beamwidth), so that the radar has the ability to resolve
targets in angle, or has angular resolution. A notable exception to this is the case of a synthetic
aperture radar, where the antenna is often physically small to achieve a wide beamwidth, and
directionality is obtained through movement of the antenna. Signal processing is used to focus
the number of wide beams into a single tightly focused beam, as described in a later section.
ANTENNA
Figure 4.1. Block diagram of a generic radar.
The receiver section of a simple radar is usually comprised of a low-noise amplifier,
followed by a mixer, followed by amplification and display. The echo signal returned to the
radar is greatly reduced in amplitude compared to the strength of the transmitted signal. This is
due to three main factors. First, beam spreading the causes the power density of the transmitted
pulse to decrease as it propagates away from the radar. Second, the target intercepts and then
scatters back only a fraction of the energy incident on it. Finally, the receiving antenna
intercepts only part of that scattered energy. In addition to these factors, the propagating
medium itself can absorb some of the energy propagating in both directions (in air this path
attenuation loss is generally small, but for a ground-penetrating radar the attenuation can be very
high). Furthermore, the antenna itself is not 100% efficient in radiating (and receiving), since
4 Directional couplers, or separate but closely spaced transmitting and receiving antennas, are sometimes used
instead of a T/R switch.
13
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some energy is absorbed in the antenna itself and some is reflected away. Thus, to pick up the
returned echo, the radar's receiver must be very sensitive. Furthermore, the receiver must be
low-noise so that the echo signals are not dominated by the internal "electronic" noise in the
receiver.
As the echoes are returned to the antenna, they are amplified and mixed with signals from
(or derived from) the reference oscillator to create an intermediate frequency; then they are
detected to recover the time series of the echo(es). In a more complex radar, the mixer and
detector might be replaced by a coherent detector that senses the phase relationship between the
transmitted and received signals, thus providing the complex or quadrature components of the
echo(es). The coherent signals can provide information about the radial velocity of the echo(es)
by means of the temporal Doppler frequency shift, and other useful information, as described
below.
There are many different types of displays for radar information. The simplest is the
A-scan, illustrated in Figure 4.2a, where the time series of the returning echoes are individually
shown on a cathode ray tube (CRT), for example. By saving the echoes and displaying a series
of them displaced vertically or laterally, &B-scan (or waterfall) display can be created, such as is
illustrated in Figure 4.2b.5 If the radar antenna rotates, the A-scan data can be saved and
displayed on radial lines corresponding to the pointing angle of the radar antenna. If the
amplitude of the echo is represented by the intensity of the corresponding displayed point, a PPl
display is created, as illustrated in Figure 4.2c; this is the most common display format for
search-and-track radars. (It is noted that data from ground-penetrating radar are usually
displayed in an intensity-modulated version of the B-scan format).
Radar echoes are usually measured in time, from the time of transmit to the time the echo
is received. The distance between the radar and the echoing object is determined from the range
equation
* = '/£]• (4-!)
5 In traditional GPR work, this display is often referred to as a "wiggle" plot.
14
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o
o
LLJ
t
TIME
(a)
SCAN NUMBER
1
2 §
O J
0.
,/v n
TIME
(b)
(c)
Figure 4.2. Examples of radar displays.
15
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where R is the distance to the echo, At is the time difference between the transmitted and
received signals, and cp is the speed of propagation of the radar energy in the medium. The
range resolution of a radar system is determined by the spectral bandwidth, B, of the
system—wide-band systems imply short-duration pulses and thus better resolution or ability to
separate two closely spaced echoes. That is, the range resolution is related to the pulse width,
At (= 1/5), according to
(4.2)
For example, a radar with an effective pulse duration of 10 ns requires a bandwidth of
100 MHz. In air, its resolution is 1.5 m (4.5 ft). In soil, it will be about half that, or about
0.75 m (2 ft). Note that a recording bandwidth of about 100 MHz would be required to capture
the radar signals.
The radar principle has been applied to systems operating at a wide range of frequencies,
from high-frequency (HF) radars that operate at a few megahertz to laser radars that operate at
optical frequencies. While radar was originally developed as a military tool to detect and track
aircraft and ships, it has established itself as an important instrument in civilian areas such as
environmental monitoring (weather radar) and law enforcement (speed radars). Radar is also
establishing itself in civil engineering, where it is being used for nondestructive testing, fault
location, and other applications.
There are literally dozens of variations on the basic radar theme described above. Most of
these variations serve to optimize radar performance for a particular mission or objective. Each
of these variations may include coherent and incoherent radars, encompass numerous transmit
waveforms (e.g., simple pulse, chirped pulse, CW, and others) and antenna configurations
(e.g., steerable antennas, phased arrays, synthetic arrays, and so on), and each may utilize a
variety of signal-processing techniques appropriate to the mission. Some are designed for the
detection of motion or temporal change; others are designed for the precise measurement of
range and angle. Still others are designed to quickly search or examine broad volumes of space.
Some designs are best suited for airborne or space applications.
When one considers the essential requirements for a ground-penetrating radar, most of the
specialized radar types can be eliminated, leaving the basic pulse radar. In ground-
penetrating radar, the basic pulse radar is commonly referred to as a short-pulse radar, implying
that the radar has a wide bandwidth. Another type of ground-penetrating radar is the
synthetic-pulse radar. While these two radars are mathematically equivalent, the differences in
the way the equivalent temporal transmit waveforms are formed lead to significant
implementation and performance differences. Conventional, short-pulse GPRs and
synthetic-pulse GPRs are discussed and contrasted in Section 4.3.
16
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4.2 Ground-Penetrating Radars
Radars have traditionally been used to search for (and track) air-, sea-, space-, or
land-based targets from ground-based, airborne, and space-based platforms. In these
applications, the propagation medium is air (or vacuum) and the propagation velocity is
essentially constant at 3 x 108 m/s (air density fluctuations can affect radar signals to some
degree). However, since electromagnetic waves can penetrate rock and soil to varying degrees,
the system can become a ground-penetrating radar. There are, however, significant differences
between GPRs and free-space radars in terms of both propagation and echoing characteristics.
For a GPR the propagation medium has a strong influence on the radar signals; it is usually
highly variable from one location to another and generally inhomogeneous at every location. In
particular, soils contain varying degrees of water and ionic materials that strongly affect the
propagation and attenuation of the electromagnetic wave. Generally, the speed of propagation of
the radar signals will be much slower for GPRs than for free-space radars; if the propagation
medium is inhomogeneous, the propagation speed will vary with position. These media are also
sometimes dispersive, so the propagation speed varies with the radar frequency (even across the
bandwidth of the radar).
GPRs generally differ from conventional radars in several significant ways. First, they
need to operate at short range and with high resolution, both of which imply a wide bandwidth
(or a short pulse length). Second, the attenuation of electromagnetic waves in the ground
generally increases substantially as the center frequency of the radar is raised, thus making
low-frequency operation more desirable. GPRs thus tend to have remarkably high ratios of
bandwidth to center frequency, or a high fractional bandwidth (fractional bandwidths of GPRs
often exceed unity, and the concept of a "center frequency" can itself become fuzzy). Figure 4.3
illustrates some features of a typical GPR pulse, which here is one and one-half "carrier" cycles
long. Special techniques have been developed over the last two decades to generate the required
wideband signals; these technologies have led to the successful commercial use of GPRs. Figure
4.4 shows a block diagram of a typical short-pulse GPR.
17
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100 MHz center freq/100 MHz BW
I
I-
CD
-z.
LLJ
or
r-
co
LJJ
LJJ
DC
-0.4 -
-0.8 -
-1.2
10
TIME - ns
Figure 4.3. Typical GPR pulse waveform.
Perhaps the most distinguishing feature (and limiting factor) of a GPR is the antenna.
Clearly, GPR antennas must themselves have wideband capabilities. They need to be in intimate
contact with the ground to avoid reverberations due to signals reflecting back and forth between
the surface and the antenna.6 For the same reason, the transmission line coupling the transmitter
to its antenna must be as short as possible to minimize reverberations due to impedance
mismatches at either end. Waveguide transmission lines are also to be avoided because they are
dispersive and have limited bandwidths. Multi-element and large antennas are generally ruled
out because (1) there will be unacceptable differential delays between the arrival times of the
radar pulses at the individual elements, (2) they require the use of long transmission lines, and
(3) it would be difficult to move such an antenna around. Consequently, GPRs characteristically
6 This is a problem for airborne GPR systems, which are used when rapid surveys under difficult or immediately
dangerous conditions are required. Besides being costly, airborne GPRs incur a sizable system penalty due to poor
transmission through the air/ground interface (which can be avoided in non-airborne GPRs by designing the
antennas to operate efficiently when in contact with the ground). Reverberation has been a problem for
helicopter-borne systems under low-altitude flight conditions. (Airborne GPRs are not, in trie present analysis,
under consideration for remediation purposes.)
18
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OSCILLATOR
TIMING
SYSTEM
1
A/D
COMPUTER
SYSTEM
t
DATA
STORAGE
^ DATA
""" ANALYSIS 1
\
SUBSURFACE
MAPS
POWER
SUPPLY
~ *"
PULSE
GENERATOR
TRANSMIT
ANTENNA
SIGNAL
CONDITIONER
-*-
RECEIVER SY
AMPLIFIER
STEM
RECEIVE
ANTENNA
TRANSMITTING
SYSTEM
RECEIVING
SYSTEM
Figure 4.4. Block diagram of a short-pulse GPR.
have small antennas and hence little directionality. In addition, the customary GPR antenna must
couple the radar power into (and out of) the soil as efficiently as possible while minimizing
radiation into the surrounding air to avoid contaminating the radar signal with unwanted echoes
from above-ground objects and structures.
Considerable effort has been expended to develop optimum GPR antennas. Because it is
small and affords a wide bandwidth, the most common type is a "bow-tie" dipole antenna
(similar to those used for UHF TV reception—which is also a wideband application) that has
been placed in a metal cavity loaded with lossy material. These lossy materials act to impede
radiation into the air and to improve the coupling into the ground. To avoid using a transmission
line, the transmitter is usually integrated into the antenna. Typically, the transmitter itself is
merely a narrow-pulse generator. In this configuration, the transmitting antenna itself becomes
19
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the device that most strongly determines the radar-pulse duration and shape. The strength of the
transmitted pulse is determined by the amount of power that can be switched rapidly. Typical
short-pulse radars are limited to pulse energies of microjoules.
To avoid using a T/R switch, which would excessively compromise the transmitter
performance in GPR applications, separate receiving antennas are employed. Conventional
short-pulse GPRs also usually dispense with the mixing and intermediate-frequency
amplification stages. Rather, the entire received signal (carrier plus modulation) is directly
displayed, recorded, or sampled and digitized. Consequently, GPRs are intrinsically coherent
radars; this feature lends GPRs to processing that requires coherence (e.g., SAR processing).
Older GPRs (and, still, most commercially available ones) employ sampling oscilloscope
technology to stretch the time duration of the echo-vs.-time delay (or range) to the point where it
can be handled by a practical recording system. In this technique, a single sample is taken per
radar pulse, and subsequent samples are taken at progressively later times with respect to the
start of the transmitted pulse to build up a complete radar sweep. A large number of transmitted
pulses are necessary to complete a single sweep. Time-dilation factors of 1000 are not
uncommon; this, for example, would reduce the recording bandwidth requirement from
100 MHz to 100 kHz. The downside is that the radar energy is used inefficiently (which reduces
its "figure of merit"). Recently, fast transient digitizers have become available; these digitizers
can capture an entire radar sweep per pulse. Although such digitizers would greatly improve the
effective performance of a GPR, this work was unable to identify any commercially available
GPR that currently uses them.
As might be expected, GPR displays are also somewhat unconventional in traditional radar
terms. The typical GPR output consists of a hard-limited, intensity-modulated plot of the echo
strength vs. range. A typical output is illustrated in Figure 4.5 [11]. Very little signal processing
is normally done, which accounts for the seemingly complex, busy, and difficult-to-comprehend
nature of these plots. Expert interpretation is often required before one can understand this type
of display.7
7 It is likely that this situation grew out of the high cost and unavailability in field environments of the computing
power needed to adequately process the data, not from a lack of understanding. Most GPR applications involve
locating discrete objects in real time, which normally does not require sophisticated processing. Rather, a trained
operator manipulates the radar to achieve the desired result. For the present remediation application, however,
sophisticated processing is essential.
20
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45 feet
1.5' -•
Depth
(Time)
Figure 4.5. Example of a typical conventional GPR output display.
Much of the apparent complexity of GPR displays comes from the low directionality of the
usual GPR antennas. Echoes from underground objects are received over a sizeable span of
radar locations, which gives rise to the hyperbolic arcs regularly seen in GPR output displays.
That is, radar energy reflected from a specific underground point is not well localized in the
display. Another artifact typically seen comes from the fact that the data presented are
essentially raw. This results in the banded appearance of echoes in typical GPR displays. As
described above in connection with Figure 4.3, a typical radar signal consists of a pulse-like
envelope on a carrier waveform. The amplitude and phase of the envelope carries the
information. For standard GPR radars, there are sufficient cycles of carrier present to make a
clear and unambiguous estimation of the envelope. For short-pulse (wideband) signals, on the
21
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other hand, the envelope cannot be easily obtained electronically, and instead, substantial
computation is necessary to mathematically recover the envelope, as discussed in Appendix A.
GPR manufacturers have taken the expedient of presenting the magnitude of the real signal.
While this approach is certainly easy to implement, and more or less preserves the outline of the
envelope, it also retains the internal structure of the GPR signal. Thus, a
one-and-one-half-cycle-long GPR signal, for example, has approximately three peaks and would
appear in a display as three wide, dark bands with narrower light bands in between, as illustrated
in Figure 4.6. A complex, "squiggly" plot is produced when many targets are present. Multiple
reflections, such as between a buried object and the surface, further confuse the raw picture.
Besides merely confusing the eye, these artifacts are clutter that hide the desired information.
100 MHz center freq/100 MHz BW
LU
DC
H
C/)
III
>
LU
DC
THRESHOLD
DETECTED OUTPUT
FOR T = 0.25
-0.2
10
TIME - ns
Figure 4.6. GPR pulse intensity and hard-limited output.
It was noted at the beginning of this section that the strength of an echo is related to the
difference in dielectric constant between the target and the medium. For ground-penetrating
radars, the differences in dielectric constant between contaminants and soils with varying
features may be small. Therefore, unlike the traditional free-space radars and their targets, a
GPR used to improve remediation effectiveness may not directly sense a contaminant "target"
22
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and separate these returns from the weak echoes caused by the surrounding soil. Rather,
inhomogeneous soils (varying particulates, rocks, other objects, and so on) can return strong
clutter fields that compete with the desired target, whose echoes may be weak. (Buried objects
such as pipes, barrels, tanks, and so on, however, may produce strong returns with respect to the
clutter.) Thus, while there are few conceptual differences between GPRs and free-space radars,
the data returned by these systems may be much different and may entail different signal
processing in order to extract the desired information.
4.3 Short-Pulse and Synthetic-Pulse Radars
A repetitive pulse signal such as that produced by a conventional GPR has a waveform and
spectral magnitude similar to that shown in Figures 4.7a and 4.7b. The spectrum consists of a
series of narrow lines separated by the prf. Its overall extent is roughly the reciprocal of the
individual pulse duration, and the width of the individual spectral lines is roughly the reciprocal
of the duration of the pulse train.
Since the temporal and spectral representations are a Fourier transform pair, they are
entirely equivalent. Either one is a complete description of the signal. Consequently, it is
possible to start by generating a spectrum of discrete electromagnetic tones, or lines, and add
them together to synthesize a pulse train. Figures 4.7c and 4.7d show the direction of the
process. The line spacing determines the effective prf, the overall span of the tones (or their total
number) establishes the pulse width, and each line has a (narrow) bandwidth determined by its
duration.8 This scheme, of course, requires that the timing, or phase, of each line be carefully
controlled.
While the short-pulse and synthetic-pulse radars are mathematically equivalent, the
advantage of the latter results from the recognition that the lines do not have to be transmitted at
the same time to produce, mathematically, the same result. Thus, each line can be transmitted
sequentially at relatively high power without saturating the electronics. Synthesis is done after
echo reception, by a computer, which is relatively indifferent to dynamic range. Of course,
careful timing is necessary to synthesize the pulse train, and care must be taken to appropriately
sample the received signals. Weak echoes are temporally superimposed upon a large signal due
to leakage of the transmitted tone into the receiver and to echoes from the surface and from
near-surface features. Clever schemes have been implemented to deal with this issue. Such
schemes, combined with the long time it takes to sequentially transmit all the tones, reduce the
figure of merit of synthetic-pulse GPR systems; nevertheless, the advantage gained by the
synthesis process outweighs the disadvantage. It will be seen that synthetic-pulse GPRs not only
8 Details of these relationships are presented in Section 5.
23
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do better than conventional short-pulse radars, they enable exploitation of a potentially powerful
contaminant detection strategy not previously contemplated. A block diagram of a typical
synthetic-pulse radar is illustrated in Figure 4.8.
TIME
(a)
time
FREQUENCY
(b)
PRF
(TRANSMITTED WAVEFORM)
(SPECTRUM)
FREQUENCY
PRF
(C)
TIME
(d)
f
(TRANSMITTED TONES)
time
(INVERSE SPECTRUM)
Figure 4.7. Short-pulse and synthetic-pulse radar waveforms: (a) a short-pulse radar transmits a short burst of
nearly sinusoidal signals; (b) a Fourier transform gives a "spectrum" of the waveform; (c) a synthetic pulse transmits
the spectrum in a series of sinusoidal signals over the range of frequencies; (d) a Fourier transform gives the
effective waveform.
4.4 Real- and Synthetic-Aperture Signal Processing
The distinction between real- and synthetic-aperture radars is quite analogous to that
between short- and synthetic-pulse waveforms. A narrow-beam, real-aperture antenna is many rf
wavelengths wide, and, if the phasing across the aperture is done properly, instantaneously forms
the beam much the same way the components of a wide spectrum add coherently to form a
narrow pulse. There is an equivalent Fourier-transform relationship between the spatial signal
across the aperture and the beam, and, analogously, the angular beamwidth is roughly the
reciprocal of the effective aperture width measured in rf wavelengths.
24
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1 SIGNAL
CONDITIONER
]
i
AMPLIFIER
RECEIVING
SYSTEM
TRANSMIT
ANTENNA
RECEIVE
ANTENNA
TRANSMITTING
SYSTEM
RECEIVING
SYSTEM
Figure 4.8. Block diagram of a synthetic-pulse radar system.
Just as it is possible to synthesize a narrow pulse by sampling in the spectral domain, it is
possible to synthesize a narrow beam by sampling in the spatial domain, by moving a small
antenna across the span of the aperture desired for synthesis. Again, careful phasing and
sampling are necessary. Various means of synthesizing apertures (i.e., SAR processing),
including computer processing, have been developed. SAR systems are usually employed from
airborne platforms, although the principles can be applied to GPR applications. Skolnik [10] and
Brown and Porcello [12] provide excellent, in-depth descriptions of SAR systems.
25
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GPR applications add another degree of complexity to the SAR picture because of the
wide spectral extent of the signals. As will be discussed in Section 5, however, SAR processing
can dramatically improve the performance of a radar. It is necessary to SAR-process each
frequency in the spectrum when the fractional bandwidth is large.9 This process is described in
Section 9. In this GPR remediation application, it is necessary to use SAR processing to localize
the echoes and thus clean up the output display.
9 An alternative and completely equivalent approach, called "time-migration," can be applied. Here, the processing
is done by shifting and summing signals sampled in the time domain at each small-antenna position. Actually, since
it turns out to be more efficient to accomplish the mathematical operations in the frequency domain (due to the FFT
algorithm), migration is actually usually accomplished by first spectrally transforming the data from the time to the
frequency domain. "Migration" is a term borrowed by GPR workers from its seismic-exploration analogue.
26
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Section 5
RADAR FIGURE OF MERIT
5.1 Introduction
Different GPR configurations and specifications often make it difficult to make
comparative evaluations between units. Some means of comparing the sensitivities or
performance of different radars and types of radars is needed. Here, a "figure of merit" is
developed to quantify radar performance.
5.2 Figure-of- Merit Derivation
5.2.1 Short-Pulse Radars
The starting point is the radar equation, which gives the received power, Pr, in terms of
various radar and external (environmental) parameters:
_
R~
where
PR is the transmitted radar power,
GT is the transmitter antenna gain,
GR is the receiver antenna gain ( =GT -GR=G, when the same antenna (or identical antennas)
are used for transmitting and receiving),
A, is the rf wavelength,
Grcs is the target radar cross section (res),
a is the attenuation coefficient, and
R is the effective target range in the medium (soil).
This expression is strictly true only for a narrowband radar; in general one needs to account for
the frequency variations of all the parameters. For these purposes, however, the expression
suffices.
The power received by the radar competes with additive noise, PN, which is given by
These new parameters are:
27
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Fs, the system noise factor,
k, the Boltzmann constant (1.38 x 10~23 J/°K)
ro, the reference temperature (290°K), and
BN, the system noise bandwidth.
GPRs usually coherently add or average a large number of pulses to improve the
signal-to-noise ratio (SNR). If m pulses are added, the SNR is
PR
™P~-
"N
Thus the SNR becomes
The first factor on the right embodies the radar- specific parameters, and is defined as the figure
of merit:
(5.3)
^ }
Q is thus the average power output of the radar transmitter divided by the noise spectral
density of the receiver. The larger Q is, the smaller the subsurface feature change detectable by
the GPR. Note that Q has units of Watts/( Watts/Hz), or seconds.
At this point it is necessary to make a distinction between GPRs that use
sampling-oscilloscope technology and those that use transient digitizers. For the former, a single
sample is taken per transmitted pulse, and the range at which the sample is made is gradually
increased until an entire range "sweep" is made. In this case the effective prf is
true prf
prf number of samples per sweep
More advanced (and expensive) pulsed GPRs record all the relevant range cells from each pulse
(or sweep) at once, which can substantially increase ^ and Q.
For a pulsed radar, optimum SNR is obtained under matched-filter conditions, where the
pulse length is related to the noise bandwidth according to
At.-L.
BN
Noting that the resultant factor iPTG2 in the expression for Q is just the total radiated energy in a
pulse, ET, we have
28
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<5-4)
This says that Q is proportional to the product of the sweep rate (the effective pulse repetition
rate) and the energy per transmitted pulse.
If the pulse-length/bandwidth matched condition is not met, a bandwidth correction factor,
CB (where CB > 1) is introduced as a multiplicative factor on Fs, which proportionally reduces Q.
It is assumed that all the radars under consideration have been designed for optimum operation,
so that CB ~ 1 .
5.2.2 Synthetic-Pulse GPRs
The figure -of -merit conclusions discussed in Section 5.2.1 also apply to synthetic -pulse
GPRs. It is necessary only to find and use the appropriate values for the pulse energy and
effective prf . A synthetic -pulse radar operates by sequentially transmitting a series of quasi-CW
signals (tones), recording a single (complex) number characterizing the entire echo return at each
frequency (tone), and transforming the array of numbers into the time domain, as discussed in
Section 9.
The n tones separated in frequency by A/. Each tone is AT s long and has power Pn. Then
the overall bandwidth and duration of the signal train a single sweep are, respectively,
B = anAf
and
The factor a accounts for spectral weighting.
Range resolution is determined by the effective pulse length, which is approximately the
reciprocal of the overall bandwidth, or
B anbf'
and the (maximum) effective prf or sweep rate is
f =- = —.
J prf -TT AT
In a properly designed synthetic-pulse GPR, the signal is reorganized so that the transmitted
energy during a sweep, ET, comes out almost all at once, during the pulse duration interval, T.
Then the effective transmitted power is
ET is the product of the average power per tone times the total sweep duration,
29
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and Ea is the average energy per tone,
F -F
E.--ET.
In addition, the incremental noise bandwidth should be arranged to be roughly the reciprocal of
the duration of individual tones, or
so the weighted total effective noise bandwidth will be
10
Putting these parameters into the expression for the figure of merit, one obtains1
AF£a ,0 AFEa
e=^T2-5xl° X^T' <5'5)
The large advantage, in terms of potential sensitivity, of synthetic -pulse radars over
conventional GPRs is associated with the energy per sweep parameter. The associated penalty is
cost and more complex and lengthy processing.
5.3 Figures of Merit for Typical Radars
One typical commercially available conventional GPR has a maximum sweep rate of
fprf = 256 Hz and a radiated pulse energy of 88 pW (Table 5.1). The receiver noise figure has not
been stated; however, it can be safely assumed that it is on the order of 15 dB, which is typical
for high-dynamic-range, gain-controlled preamplifiers. Then, the calculated Q will be in the
3.2 x 1012 - 1.6 x 1014 s range, or 120 - 140 dB relative to 1 s. These values are consistent with
the Q given for another manufacturer's radar — one with greater transmit power (see the inset in
Table 5.1).
It is worth noting that the lowest frequency system has the best intrinsic sensitivity, and
also experiences the least absorption. Theoretically, lower frequencies imply a penalty in spatial
resolution, but this is probably not an important issue since the probable detection strategies are
to sense subtle changes in (1) the volume scattering coefficient, (2) reflection from interfaces,
and (3) bulk refraction. That is, exquisite range resolution is not a requirement for those
strategies.
10 Note that the weighting factor, a, divides out in this expression.
30
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Table 5.1. Specifications for a "Typical" Commercially Available GPR
Parameter Value
Antenna Impedance 240 Q
Pulse to Antenna 100 V
Radiation Efficiency 35%
Applied Peak Power 41.7 W
Radiated Peak Power 14.6 W
Radiated Average Power 2.63 mW
Center Frequency (CF) 80 MHz
Pulse Duration 6 nS
Radiated Pulse Energy 88 pJ
Bandwidth (BW) 170 MHz
Fractional Bandwidth (BW/CF) 2.1
"Another Radar"
Q=155dB
Pulse to Antenna = 400 V
In the course of this work assignment, several GPR manufacturers were contacted. One
manufacturer stated that his company has special-order transducers in the "two-kilowatt" range,
or about 17 to 20 dB stronger. These would boost the figure of merit to the vicinity of 140 to
160 dB re 1 s. However, the manufacturer seemed reluctant to provide details about this radar,
and it is unclear from his information whether such parameters as the prf and noise factor are
unaffected; thus, it may not be possible to achieve all of the theoretical improvement implied by
the power increase.
Substantial improvement is possible with the transient digitizer approach. The commercial
system used as an example in Table 5.1 takes up to 1024 samples per sweep at a maximum prf of
256 kHz, so its effective prf is only about 250 Hz. A hypothetical system that has the same
hardware but that uses a transient digitizer could in principle operate at the maximum prf and
thus attain a figure of merit in the 150 to 170 dB re 1 s range.
A Q of 190 dB re 1 s may be possible if both higher power and a transient digitizer are
used. This may represent the practical limit of short-pulse GPR technology.
Only one synthetic-pulse GPR is known to exist. This system is a prototype developed in
the 1970s for the Bureau of Mines [13]. Its characteristics are not well quantified, so it would be
necessary to make several assumptions here to estimate its Q value. It is claimed that the power
per tone is 5 W and that there can be as many as 1401 tones extending from 20 to 160 MHz
(140-MHz raw bandwidth and 80-MHz center frequency). In terms of spectrum it appears to be
similar to conventional systems, and it evidently uses standard GPR antennas. For this analysis,
it is assumed that the system has a 25% overall radiation efficiency, spectral weighting
equivalent to the short-pulse radar system, and a 15-dB system noise factor. Here, A/ (min) is
100 kHz, so there are 1401 tones. It is further assumed that Ar = lOfis, which is the minimum
31
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possible (it would take 14 ms to complete a sweep, fory = 70 Hz). The average energy per
tone will be £a = 0.25 x5xl4xlO~3 = 17.5mJ and the potential figure of merit for the prototype
synthetic-pulse will be Q = 1.4 x 1022 s, or about 220 dB re 1 s.
This synthetic -pulse GPR, however, dwells far longer on each tone than is theoretically
allowed, and evidently does not approach optimum performance. It is likely that the Q for this
system is actually on the order of 200 dB. Nevertheless, it is far superior to standard GPRs in
terms of Q.
This analysis shows that the performance of the 80-MHz synthetic -pulse GPR is about 60
dB better than the performance of the standard 80-MHz short -pulse GPR, and appears to be
roughly equivalent to a hypothetical high-power short-pulse GPR system that uses a transient
digitizer. Clearly, synthetic -pulse GPRs offer a tremendous potential advantage over
conventional GPRs.
5.4 Processing-Gain Contribution to Figure of Merit
Tohs, which is the middle factor in the basic expression for SNR (Eq. (5.2)), embodies all of
the processing gain. It is merely the total effective time that a GPR "looks" at a target, including
all the time spent at locations where contributions to SAR processing are gathered. In principle,
due to the intrinsic stationarity of the situation, a GPR can continue recording data in one
location and achieve an arbitrarily large SNR. However, a GPR must move across the surface at
a useful rate, a factor that limits the dwell time. Suppose that A/ is the along-track resolution
requirement and v is the radar velocity. Then the dwell time is Al/v and the number of pulses
averaged is
In general, it is difficult to make a specific choice for Tohs because of the variability of the
environmental situation. A high-<2 GPR operating in a low-loss environment can afford a short
dwell time. Conversely, a high-loss environment can be at least partly compensated for by
moving the GPR very slowly. Then, the cost of doing a remediation survey becomes an issue,
and a trade-off assessment appropriate to each site needs to be done. (Such a study was beyond
the scope of the present work.) For the purposes of this study and this report, a 1-s observation
time has been arbitrarily chosen.
However, an order-of-magnitude estimate of a practical value for Tohs can be made. This
estimate is based on SAR-processing considerations. Focused-SAR processing can achieve a
linear resolution approximately equal to half the dimension of the real aperture of the antenna.
Since the aperture size, D, of the small antennas required for GPR work are approximately a
half-wavelength (D = A/2)) at the center frequency, the achievable resolution is about res = A/4,
32
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where A, is the wavelength in the soil. For the nominal center frequency of 100 MHz and soil
dielectric constants in the 3 to 10 range, the theoretical resolution ranges from 0.25 to 0.4 m
(i.e., about 1 ft). In order to achieve that resolution, however, the length of the synthetic aperture
(i.e., the distance the real antenna needs to be moved) must be at least
where R is the range (or depth to the point being reconstructed). For example, measurements
need to be made over a 20-m (65-ft) span to maximally reconstruct features at 10-m depth; at
30-m depth, the required span rises to 60 m (200 ft).11 Furthermore, to avoid grating lobes, the
field must be sampled rather densely. Sampling-theory considerations indicate that a new
sample needs to be made at quarter-wavelength spacings. Thus the number of samples required
is
A'
GPR SAR sampling needs to be done over a two-dimensional space, however, so the
number of samples needed to reconstruct one subsurface point is
2 (8/?Y
m=n =^J.
The area is A = L*ff = (2R)2, and the time required to cover this area is the coherent observation
time:
16/?2
11 Signal loss due to geometrical spreading and, especially, soil attenuation is likely to prevent the achievement of
the full aperture width required for maximal reconstruction, particularly at greater depths. Furthermore, note that the
formulas presented in this section generally imply that more samples will be required in soils with a high dielectric
constant (since X, appears in the denominators). The putative benefit of the cost of collecting and dealing with more
samples is higher subsurface resolution. However, soils with high-dielectric constants contain more water and have
higher losses in general, and achieving full benefit is unlikely. It may thus be desirable to forgo the processing
required to obtain the full theoretical resolution. For example, processing data from an e = 20 soil at the same
resolution as an e = 3 soil by reducing the span would speed the survey up by a factor of V20/3 = 2.6.
33
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The observation time can be quite large. For example, at 100 MHz in e = 3 soil and
R = 10 m, and a reasonable speed of 0.3 m/s (1 fps), Tohs is nominally about 3000 s (50 min).
This would produce 35-dB processing gain compared to Tohs = 1 s.12
To sample a subsurface area uniformly (e.g., A), the GPR must be moved over a larger
surface area, given by (\JA+2R)2. Then the number of samples necessary to reconstruct an area
is
The limiting value applies for large areas. For large areas, the total necessary search time
approaches
T = V2-
""-^ Xv'
Suppose, as in the example used above, that reconstruction to a depth of 10 m is desired.
Then, the time required to survey a lOOxlOO-m area (about two acres) is about 8 h. This appears
to be a reasonable and rather good rate.
5.5 Environmental Contributions to Figure of Merit
The third term in the expression for SNR (Eq. (5.2)) contains the environmental factors.
For unity SNR,
(4n)3R4
Thus, the minimum detectable radar cross section is
(mint _ SNR I M ^ '. ; I ,5-
mm(Qj( X2 ' P ^
For an 80-MHz system with Q = 220 dB re 1 s operating in a medium with 1-dB attenuation per
meter and a relative dielectric constant of 20,l3 the minimum detectable res at 10-m depth for
10 dB SNR is 3 x 10~12 m2. In comparison, the standard system can detect an res of 3 x 10" m2
under the same conditions. A Q = 190 dB system (one with high-power pulse plus transient
digitization) system could detect an res of 3 x 10~9 m2.
To put this in perspective, consider the detectability of a plane interface between dielectric
media. The effective res of such an interface is approximately
12 Every subsurface point reconstructed would benefit by this amount of gain.
13 This is a moderately conducting (0.03 S/m) soil with a 50% void fraction fully saturated with water (i.e., a fairly
difficult situation).
34
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where r is the reflection coefficient of a plane interface between dielectric 1 above and dielectric
2 below:
I •
This approximation applies in the case of small differences in dielectric constant. For the
Q - 220 dB re 1 s system under the above conditions, the minimum detectable reflection
coefficient will be about 1 x 10"8. A reflection coefficient of 1 x 10"8 corresponds to a relative
change in dielectric constant, Ae/e, of 4 x lO'8. In principle, the standard system could detect a
sharp boundary between layers with a dielectric change of 4 x 10 , or 0.01%.
5.6 Section Summary
It was shown above that the performance of a GPR radar system, including the radar
hardware and the signal processing, in the environment, can be expressed in terms of a single
number, Q, the figure of merit. Q can be used to compare the performance of various hardware
items.
If the formula for Q is inverted, the Q required to detect various contaminants in various
environmental geometries can be calculated. The concept of Q and the calculation of the
required Q for various configurations of environmental geometries are used throughout the
remainder of this report.
An important element in this section is the contribution SAR processing can make to the
remediation effort. SAR, and particularly three-dimensional SAR processing, can increase a
radar's Q by as much as 20 to 40 dB.
35
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Section 6
SOIL CHARACTERISTICS, SOIL MODEL, AND SOIL GEOMETRIES
This section of the report describes the expected electromagnetic properties of the
environments that might be found at remediation sites—that is, how various soil materials are
distributed around the United States; how these soil types affect the propagation of radar energy
through the soil and reflections from the interface between layers; how the propagation and
reflection are affected by moisture in the soil; the effects of a water table; and the effects of
various contaminant materials in the medium.
6.1 Classification and Distribution of Soil Types
Soil materials can be classified according to the Triangular Classification Chart developed
by the U.S. Army Corps of Engineers [14]. This classification scheme, illustrated in Figure 6.1,
categorizes soils according to what percentage of three primary components they contain; these
components—clay, sand and silt—are categorized according to particle size. As will be shown
below, these various mixtures of coarse and fine particles have an effect on the propagation of
radar energy into the ground that depends upon the ratio of the mixture. Thus, an engineering
assessment of GPR performance must include a description of the soil mixture; a "clay-sand"
mixture was used for most of the analysis shown below.
Morey and Harrington [14] include a map that shows the distribution of various soil types
throughout the United States. This map, reproduced in Figure 6.2, can be used with the
Triangular Classification Chart (and the analysis in Sections 5 and 7) to broadly estimate how the
radars described in this report would work in various locations around the U.S. The
characteristics of most of the deposits are described as follows.
• Wind-Blown Deposits. These include both silt and sand; high concentrations of salts
exist in some portions of these deposits.
• Saprolite. This generally consists of massive clay. The contact with unweathered
bedrock is generally gradational.
• Coastal Plains Deposits. These are generally sand, silt, or clay. The water table is
high and swamps are numerous, particularly near the coast.
• Desert Deposits. These are generally dry sand, silt, or clay. Caliche may be present in
some areas.
36
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100
100
yCL\Y-SU.
SIZE LIMITS
SAND -- 2.0 TO 0.05 mm
SILT - 0.05 TO 0.005 mm
CLAY -- LESS THAN 0.005 mm
40 60 80 100
PERCENT SILT
Figure 6.1. Triangular Classification Chart for soil.
• Basin Deposits. These are generally dry silt and clay in low areas surrounded by sand
and gravel. Deposits and groundwater may be highly mineralized. Caliche is common
in some areas.
• Alluvium. Materials present are variable. The water table is high in many areas; it may
be highly mineralized.
• Lake Deposits. These are generally silt and clay. Deposits and groundwater may be
highly mineralized.
37
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TANA ~' - - j .'NORTH'DAKOTA A MINNESOTA • /
Lake deposits
[VI] Glacial deposits
|^2 Desert deposits
Wind-blown deposits
Basin deposits i—i
| I Deposits variable—generally thin
Coastal plain deposits .. . Umjt of g|adatjon
Figure 6.2. Distribution of soil deposits.
6.2 Characteristics of Soils and Contaminants
It was noted above that the speed of propagation of electromagnetic energy is determined
by the dielectric constant of the propagation medium, and that the absorption of the energy is
determined by the attenuation coefficient of the medium. It was also noted that for a GPR, the
effects of the soil can have a strong influence on the propagating energy, depending on the type
of soil and its constituents. The values of dielectric constant and attenuation coefficient vary
with the type of soil, its moisture content, its conductivity due to ionic materials (i.e., salts in the
soil), and the frequency of the electromagnetic energy. Table 6.1 lists typical values for the
dielectric constant and conductivity at 100 MHz for a number of common geologic materials.
This table also "ranks" the materials in terms of penetration depth at VHP (100-MHz)
frequencies.
38
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Soils generally consist of solid grains with relative dielectric constants in the 4.5 to 5.5
range and low conductivity, plus pores filled with variable amounts of air (relative dielectric
constant = 1) and water (relative dielectric constant = 80). Due to its large relative dielectric
constant, and possibly large conductivity, the amount of water present has a major effect on the
properties of the mixture.
Table 6.1. Electromagnetic Characteristics for Common Geologic Materials [11]
Material
Air
Limestone (dry)
Granite (dry)
Sand (dry)
Bedded Salt
Freshwater Ice
Permafrost
Sand, Saturated
Freshwater
Silt, Saturated
Rich Agricultural Land
Clay, Saturated
Seawater
Approximate
Conductivity
-------
electrical conductivity of most of these materials is very low; they are essentially nonconducting.
It is noted for Tables 6.1 and 6.2 that the dielectric constants of geologic constituents (solid
grains, water, air) and contaminants are generally clearly separated.
Table 6.2. Dielectric Constants of Typical Contaminant Materials
Material
n-Pentane
n-Hexane
n-Octane
n-Decane
n-Dodecane
Carbon tetrachloride
Carbon disulfide
Methanol
Trichloroethylene
Chlorobenzene
Benzene
Toluene
Styrene
Nitrobenzene
e
1.84
1.89
1.95
1.99
2.014
2.238
2.641
32.63
3.4
5.708
2.284
2.438
2.43
34.82
6.3 Modeled Soil and Contamination Geometries
Models for subsurface conditions are essential for evaluating radar performance. Such
models need two parts: (1) a description of the disposition of the contaminant and (2) the effect
of a contaminant on radio frequency propagation properties. A review of the literature suggested
two fundamental situations, which depend primarily on the groundwater condition. For the
purposes of this work, these two basic configurations were termed Model I and Model II, and are
illustrated in Figure 6.3.
Model I postulates the presence of a water table, whether it is immediately detectable, as in
Model 1 A, or not, as in Model IB. Depending on its source, a contaminant will travel down
through drier soil to the water table or flow upwards to it. Because a major interest in this work
is petroleum contaminants, which are less dense than and immiscible with water, the main
feature of Model I is a layer, possibly thin, of contamination "floating" on the water table. It is
reasonable to expect that a sharp boundary will form between the contaminating substance and
the water. The radar system question thus becomes: how big an echo contrast is needed in order
for the contaminating substance to be detected by a GPR of a given performance (i.e., a given
figure of merit)?
40
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Model I is subdivided into two categories, based on the way water and contaminant
interact with the soil. In Model IA, the soil is granular so that there is little capillary action, and
is either mostly dry or virtually saturated; this results in sharp, detectable discontinuities at the
interface between two strata. In this case the water table itself would be seen by the GPR, and
the contamination would be revealed as a laterally localized change in reflection at the water
table. In Model IB, capillary action leads to gradual transitions from moist to saturated soils, as
illustrated by the gradual shading in Figure 6.3b. In this case, the soil's electrical properties also
vary slowly with depth, and such changes do not reflect radar pulses well (GPRs are often not
able to "see" the water table for this reason). Here, it is postulated that the immiscibility of the
contaminant and water will cause a boundary to form between them. There may be no distinct
upper surface to the contamination; in this case, contamination would be revealed by the
appearance of a laterally localized reflecting boundary. Note that a high-resolution GPR could in
principle distinguish between this situation and a local soil stratum, which has finite thickness.
Model I was implemented in a computer code that calculates the reflection coefficients of
dielectric boundaries and layers. It uses inputs from the bulk soil properties code described in
Section 6.4, written to calculate the electrical properties of various soil/water/contaminant
mixtures.
Note that Model I also addresses the situation in which the soil is nowhere saturated
(i.e., where there is no water table) but where there is a relatively impermeable layer such as clay
below. Then the contaminant will form a layer on the surface of the impermeable medium,
which can be detected as described above.
Model II addresses the situation in which there is no water table or impermeable layer to
impede the downward spread of contaminant. Here, there is a bottomless "plume" of
contamination, which is considered to diffuse laterally as it proceeds from the source. (See
Figure 6.3c.) The plume itself does not produce any detectable radar signal, since scattering can
only come from sufficiently abrupt discontinuities in the electrical properties. Thus an
alternative detection strategy is necessary.
In the scenario depicted in Model II, the presence of the contaminant changes the
scattering from subsurface features; it may be possible to take advantage of this change, which is
itself a detectable feature. Small changes in soil density or porosity and the presence of discrete
scatterers such as rocks and pebbles will produce a "clutter" background. The strength of this
background signal depends on the dielectric properties of the medium, which are strongly
controlled by the liquid content (be it water or contaminant). Because the dielectric constant of
water is about 80, while that of petroleum products is about 2 (see Tables 6.1 and 6.2), the
replacement of pore water with contaminant will have a large effect on the electrical properties
of the medium and hence on the clutter level. Adding contaminant to dry soil will increase the
41
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^??ra^«™^«^w«w«?«JJ?«$
ground level
soil medium
a)
ntarnination
water table
ro u n d level
$oil medium
b)
ground level
coRtam ination
plume
soil medium
C)
water table
Figure 6.3. Models of subsurface conditions. In Model IA (a), the contaminant floats on the water table; in Model
IB (b) there is a gradual transition from wet to dry, but the immiscibility of the contaminant with water causes a
boundary to form at some point; in Model n (c) the contaminant forms a plume that travels downward.
42
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overall dielectric constant and replacing water with contaminant will decrease it. The expected
effect of contaminants in this case is to suppress the clutter. Reported occurrences of this
scenario have shown a complete washout of the clutter level in the contaminated region.
Model II was implemented as a change in the volume scattering coefficient that depends
on contaminant level. As implemented in the model, the "plume" is a simple cone. The goal
was to obtain estimates of the amount of contamination that could be detected for a given GPR
figure of merit.
A review of the two models shows that, given their parameters, they can be used to
represent seven of the ten cases described by Walther et al. [7] as being common at remediation
sites.
6.4 Dielectric Properties of Soils and Soil Mixtures
To reliably calculate the strengths of radar echoes returned from subsurface layers,
boundaries, and irregularities, there must be a means of calculating changes in the dielectric
properties of the soil when contaminated material is present. The soil model chosen for this
work was written to implement the Bruggeman-Hanai-Sen (BHS) formula [6], which describes
the soil as various interdispersed media (particles, liquid water/contaminant, air). According to
the BHS formula, which was extended from the Hanai-Bruggeman-Wagner theory [16], the
parameters of a two-phase heterogeneous dielectric soil with complex dielectric constants are
related through the expression
i * *\ ( * \|/3
(£,„-£)£,
= —; r — , (6.1)
(em-ej)(ve )
where
e* = the complex dielectric constant of the mixture,
£*„ = the complex dielectric constant of the "matrix" material (e.g., soil grains),
ej = the complex dielectric constant of the "disperse" phase (e.g., air or water), and
()> = the volume fraction of the dispersed phase (e.g., porosity).
The exponent value of one-third comes from an assumption that the dispersed phase behaves
electrostatically in the same way as it does for small spheres.
To obtain e*, it is necessary to solve a cubic polynomial equation with complex parameters.
A computer program was written to set up the problem with soil parameters (porosity, type of
fluid (water or contaminant), and fluid saturation level) and solve the cubic equation. Note that a
cubic equation has three roots. Identification of the correct root was sometimes difficult, because
occasionally more than one was physically permitted.
43
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Multi-phase mixtures, such as soil particles/water/air, are dealt with by repeated
application of this formula. Care must be taken to correctly identify which phase is the
"disperse" one and which is the "matrix." The approach chosen here was to first consider
particles dispersed in the fluid and then consider air-filled voids dispersed in the moist mixture.
Input quantities for the model are the total void fraction, the fraction of the total voids filled with
fluid, and the conductivity of the void water. A full range of values for these parameters can be
accepted. Either sand particles or clay particles can be specified; these differ in their intrinsic
conductivities. Test cases using this code along with reasonable input values produce a range of
outputs that agree well with measured soil properties and confirm the expected effects of
contaminant. Note that by adjusting the model coefficients for "sand," a wide variety of
common geological materials can be modeled, including limestone, shales, silts, granite, and so
on.
Examples of calculations of the dielectric constant, conductivity and the attenuation
coefficient for various soils and a petroleum contaminant are given in Appendix B. The plots in
this appendix show the value of the electromagnetic parameters as a function of radar frequency,
from 10 MHz to 200 MHz, for liquid fractions of 0%, 30%, 60%, and 100%.
6.5 Section Summary
Soil types vary widely across the United States. Soil composition (particle type,
homogeneity, particle size and distribution of sizes, moisture content, and the presence of ionic
materials in the soil) has a dramatic impact on the way a radar wave will propagate in the soil.
To address these issues, a bulk soil model was developed that allowed the electromagnetic
properties of the soil to be estimated as a function of radar frequency. This model was then used
to calculate radar propagation and scattering for two essential geometries.
44
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Section 7
DETECTION STRATEGIES
7.1 Introduction
Section 5 introduced three basic models for the effects of contamination on the soil under
different circumstance (e.g., interaction of a contaminant with the water table). It appears that
these three models can cover all of the circumstances that appeared to produce changes in
subsurface electromagnetic properties amenable to exploitation by a GPR. Here, possible
strategies for using a GPR successfully under the different circumstances are explored. For the
purpose of this discussion, the GPR is a synthetic-aperture radar, since system SAR/migration
processing is essential in this application.
The discussion in this section has been limited primarily to the issue of whether or not
there is a detectable signal against noise. This is fat fundamental starting point, because without
the expectation of a measurable signal in the first place there would be no hope of using a GPR
even if clutter and subsurface variability were not issues. Although those are critical issues, it is
too extensive a subject to attack here and is one which, in any event, cannot be addressed
seriously without experimental efforts. Since no two areas are geologically identical, each
presents a different problem. SAR processing is an essential step toward reducing clutter due to
discrete objects and localizing the energy scattered from a given underground volume.
Here, it is assumed that the "contamination" is a low-loss organic compound or mixture
that has a dielectric constant of 2 (see Table 6.2). Petroleum, gasoline, and their constituents, for
example, fall in this class. The results could be extended to other classes; however, it would be
tedious and would require extensive effort to cover all possible cases and combinations, and the
results would not affect the basic conclusions already drawn here.
The effects of contamination on radar scattering can be subtle. High-sensitivity
synthetic-aperture GPRs, extensive, high-order data processing, and improved displays will be
needed to achieve success. These three elements have been lacking in previous efforts to use
GPR for contaminant mitigation, and thus, although GPRs have been touted for decades as tools
for remediation, they have not really been used for this purpose. Much of the GPR work in this
area seems to have been done as an ad hoc aside.
An evidently novel and exciting theoretical finding developed here is that there can often
be surprisingly strong contrasts between the volumetric scattering from contaminated and
non-contaminated soils. This effect may provide the best method for tracking contamination.
45
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Our mathematical modeling shows that it will usually require a very sensitive GPR to detect this
contrast. Although there have been reports of conventional GPRs detecting the contrast,
modeling analyses show that such radars cannot, in general, do the job. Another novel prediction
developed here is that a thin layer of contaminant (only centimeters thick) will produce a
detectable signature. However, it is questionable whether this signature could be exploited
successfully, since it is primarily manifested as a time delay and could thus easily be confused
with variations in the distance between the GPR and the reflecting layer (i.e., between the surface
and the water table).
7.2 Summary of Strategies
Three strategies were developed for detecting contaminants. They are based on the three
models that depict underground conditions.14 The strategies are discussed in detail below, and
are summarized in Table 7.1.
Table 7.1. Detection Strategy Summary
Model
Identifier
I-A
I-B
II -."
Expected
Is There a Phenomenon
Is There a Significant (Produced by
Water Table Water Table an Immiscible
Influence? Echo? Contaminant)
Yes Yes Changes
Interface
Reflection
Signature
Yes No Forms a
Reflecting Layer
or Interface
No No (1) Changes the
Volume
Reflection
Coefficient
(2) Changes the Bulk
Refractive Index
Detection
Strategy
Look for
Specific Lateral
Changes in the
Plane-Layer
Reflection
Coefficient
Look for the
Appearance of
Plane-Interface
Reflections
Look for
Contiguous
Changes in
Background
Echo Contrast
Look for Changes
in Propagation
Velocity
Method
Map the
Plane-Layer
Reflection
Signature
Map Plane
Interface
Reflections
Measure and
Map the
Spatially
Averaged
Volume res
Map the
(Adaptive)
SAR Migration
Parameter
Clearly, Models IA and IB focus on a light contaminant floating on water. As noted in
Section 6, the situation in Model IA is very similar to that of a contaminant resting on a
relatively impermeable layer, such as rock or clay, and thus also applies to such a situation.
14 It was previously noted that these three models were distilled from a larger set, and in fact cover most "common
cases" (7 of 10) at remediation sites [7].
46
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There are two basic issues. First, is there sufficient radar sensitivity to detect the echo
contrasts? Second, will the variations in underground geology mask the echo contrasts due to
contaminants? Presumably, the first question can easily be answered. The second issue,
however, is so site-specific that only an estimate of the lower bound of detectability can bt made
here. >
A subsidiary matter related to the second issue involves SAR processing. Perhaps the most
important aspect of SAR is to localize energy scattered from large discrete objects. However,
SAR does not do this perfectly, and sidelobes are generated. Thus there may be a varying
apparent clutter level due to the sidelobes of migrated echoes from discrete buried objects.
Results from the numerical analytic studies described in Section 9 show that post-migration
sidelobe levels for a point scatterer are 30 to 40 dB below the peak. Another effect that needs to
be considered is the possibility of scattering from above-ground objects.
7.3 Model IB Strategy: Reflection from a Contaminant/Water Interface in Soil
This situation, in which strong reflections will invariably be created, will be considered
first because it is probably the easiest to deal with. Because they are immiscible, it is postulated
that contaminant will displace pore water and induce a discontinuity between soil saturated with
contaminant and the same soil saturated with water. A distinct boundary will be produced only
in the region of the contaminant pool. The only significant variable is the void fraction.
A special approach needs to be taken to calculate the effective res of a plane layer or
interface. Normally, the res is defined for finite objects with plane-wave illumination (i.e., for an
infinitely distant transmitter), but in this case it is necessary to deal with large, nearby scatterers.
It can be shown that the effective res of an infinite plane interface is approximately
<5p = \r\2nR\
where r is the plane- wave reflection coefficient and R is the distance to the interface. Normally,
the range to an object is irrelevant to its res. Here, the increase in res with range is interpreted as
the result of expansion of the effective scattering area with range. The scattering region is
roughly defined by the first Fresnel zone radius, which also defines the approximate lateral
extent over which the interface needs to appear "plane." The radius of the Fresnel zone for
backscatter is
The rf wavelength, X, is measured in the soil, and is thus shorter than its free-space value by the
factor lA/e^. For wavelengths on the order of 1 to 2 m and ranges between 3 and 30 m, F is in
the 1- to 6-m interval. If it is larger than this, a plane interface will appear to be "infinite." What
this says is that points on the surface that are quite distant from the geometrical point of
47
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reflection do not contribute much to the total signal. On the other hand, a radar pulse reflected
from a "facet" smaller than the Fresnel zone will be weaker than it might otherwise be. Thus, the
diameter of the contaminant pool must be as least as big as about 2F to achieve the full res value.
This approximation for the res involves using the plane-wave reflection coefficient for
dielectric interfaces at normal incidence instead of the true boundary condition, which depends
on the off-axis angle of incidence. This approximation is justified by the relatively weak
dependence on the incidence angle, the relatively small variation of the angle of incidence over
the span of the Fresnel zone, and the large uncertainties in the actual subsurface environments,
which do not justify highly precise predictions. The plane-wave reflection coefficient at normal
incidence for a plane interface between media 1 and 2 is
Z.-Z,
r = •
where the Zs are the (complex) wave impedances in the two media. For low-loss dielectric
media, this reduces to the formula used in Section 5.5,
^
Table 7.2 lists values for the reflection coefficient for a plane boundary between soils of
various void fractions saturated with contaminant (e = 2) and saturated with water of various
conductivities. These values were actually calculated as a special case (i.e., zero-thickness) of
the method described above.
It is assumed here that all facets are sufficiently flat over distances that are large compared
to the Fresnel zone, so that the interfaces can be considered to be effectively infinite. The only
remaining factor, then, is the reflection coefficient. It was noted in Section 5.5 that the minimum
detectable reflection coefficient (at 10 dB SNR) was \r\ = 1 x 10"8 for a Q = 220 dB re 1 s
synthetic -pulse GPR operating against a soil with 1 dB/m attenuation. For a standard GPR
system with Q = 140 dB re 1 s, the magnitude of the minimum detectable reflection coefficient
was 1 x lO^1. Here, the goal is to determine what this means in terms of the layer parameters, the
most important of which is its thickness, d.
The reflection coefficients are also weak functions of frequency. Their magnitudes tend to
decrease slightly with increasing frequency and their phases approach 180° more closely. Even
in the most extreme case (50% porosity, 0.3 S/m conductivity), the magnitude of the reflection
coefficient varies only 13% between 10 and 500 MHz and its phase changes by only 4.3°. In the
50- to 150-MHz band most likely to be employed by GPRs in this application, the magnitude and
phase change only 7% and 1.3°, respectively.
48
-------
Table 7.2. Plane-Interface Complex Reflection Coefficient at 100 MHz
Porosity
30%
40%
50%
Water Conductivity - s/m
0.01
0.303Z179.80
0.402Z179.80
0.495Z179.80
0.03
0.305Z179.50
0.403Z 179.4°
0.496Z 179.4°
0.1
0.305Z 178.4°
0.405Z178.30
0.498Z178.80
0.3
0.314Z176.30
0.417Z176.00
0.514Z175.80
It is apparent that the porosity controls the magnitude of the reflection coefficient but has
little effect on its phase angle. On the other hand, conductivity changes slightly alter both the
phase angle and the magnitude, although the effect is weak. The complex reflection coefficient
of an interface between lossless dielectrics is purely real. Loss in the lower (water-saturated)
medium introduces a finite imaginary component. However, the magnitude of the imaginary
part of the complex reflection coefficient is mores than 20 dB lower than that of the real
component. It would be virtually impossible to detect it.
The main point here is that an interface formed between contaminant- and water-
saturated regions will produce very strong reflections. Virtually any GPR should be able to
detect it under reasonable conditions.
A less-dense contaminant will displace water downwards. Consequently, the region above
the contaminant should be relatively dry and thus have low attenuation. This condition would
enhance the visibility of such regions.
7.4 Model IA Strategy: Reflection from a Thin Layer of Contaminant Sandwiched between
Layers of "Dry" and Wet Soil
In this case the presence of a distinct water table is postulated. "Distinct" means that the
transition from "dry" to saturated appears abrupt to a radar pulse. Generally in order for this
transition to be detectable, it must occur within a distance that is short compared to the rf
wavelength, say 10%. Such situations evidently occur in coarse-grained soils where capillarity is
not a strong factor. A light contaminant would be expected to pool and form a thin layer floating
on the water table [17]. The solid lines in Figures 7.la and 7.1b illustrate how, in the case of a
distinct water table, the depth profile of the dielectric constant might change between clean and
contaminated regions.
49
-------
10
15
_ WATER
TABLE
- NO CONTAMINANT PRESENT
- CONTAMINANT PRESENT
WATER
"TABLE
- NO CONTAMINANT PRESENT
- CONTAMINANT PRESENT
(a) (b)
Figure 7.1. Profiles of dielectric constant vs. depth: (a) distinct water table, and (b) indistinct water table.
A similar situation arises when a high-density contaminant falls toward a relatively
impervious stratum that produces a radar echo. The strategy in either case is to detect the
signatures of changes between the reflection properties of the interface where there is no
contaminant and where contaminant has pooled.
The concern (and the thrust of this analysis) is with detecting thin layers. Detecting thick
layers appears to present no challenge because the echoes from each of the two interfaces will be
time-resolved and strong, so that multiple reflections will be seen as a decaying train of
reverberating echoes.
Plane-wave reflection at normal incidence is assumed. The reflection coefficient of a layer
sandwiched between dissimilar media can then be easily computed from transmission-line
impedance theory. This approach accounts for all the multiple reflection between the two
interfaces, which leads to reverberation phenomena that would be noticeable, in the case of a
thick layer of contaminant, as a series of discrete repetitive echoes. Consider the situation
depicted in Figure 7.2, where a plane layer of thickness d and relative dielectric constant £^ is
between infinite media with e, and £3. All three media may have complex dielectric constants.
The reflection coefficient may also be a complex number. It is referenced to the top surface of
the first interface. The effect of the intermediate layer and lower medium can be lumped into an
equivalent "input impedance," Z,. Then, the reflection coefficient is
50
-------
where t|, is the (complex) wave impedance of the upper medium.15 Z,, in turn, is
l+r'exp(-2y2d)
Z'=Tl2l-r'exp(-2Y2J)'
where T|2 and y2 are respectively the impedance and propagation constant in the layer.16 Finally,
r' is the reflection coefficient between media 2 and 3 considered alone, or
As this set of formulas is rather complicated, a computer program was written to the calculate
numerical values for | r\ under various conditions. It calls subroutines derived from the earlier
programs developed to provide values for the soil dielectric constants.
For a thin layer, where 2yd « 1, and where the soil dielectric constants have negligible
imaginary components (i.e., have low losses), a simple analytic form is possible:
r =
This formula has the general form
r=rr(l+jf/fc),
where rr is the reflection coefficient if there is no intermediate layer and fc is a "cutoff
frequency.
Figures 7.3 through 7.6 present some typical results. This example is for a 30%-porosity
soil and an operating frequency of 100 MHz, which is approximately in the middle of what
seems to be the optimum band for this GPR application.17 Consistent with Model IA precepts,
this example involves a layer saturated with er = 2 contamination sandwiched between dry soil
and water-saturated soil. In this example the water has a moderate conductivity of 0.03 S/m.
15 The wave impedance is given by
11
where Zg is the impedance of free space (377 ohms).
16 The propagation constant is
y
where £<, = 2rc/A.is the free space wavenumber and / = V- 1-
17 The 50- to 150-MHz band appears to provide the best balance between penetration, which favors low
frequencies, and resolution, which improves at shorter wavelengths. For this application, high resolution does not
seem to be necessary, and may actually be disadvantageous.
51
-------
INCIDENT
SIGNAL
REFLECTED
SIGNAL
r
t
Figure 7.2. Incident vs. reflected signal.
The main effect for layer thicknesses in the 1- to 10-cm interval is a large increase in the
imaginary part of the reflection coefficient. The real part of r and its magnitude stay relatively
constant. For thin layers, then, the appropriate detection strategy here is to process and inspect
data associated with reflections from the water table so as to look for an imaginary component to
r. It appears that contaminant layers only a few centimeters thick might be detectable.
Note that because the magnitude of the reflection coefficient is much larger than the
minimum detectable level and is only slightly affected by the contaminant, the layer will produce
strong echoes (for wideband GPRs) that should be easily detectable under most circumstances
and to relatively great depths. A prerequisite of Model IA is that there be relatively dry soil
above the contaminant layer, because of the presence of a distinct water table and the tendency
of low-density contamination to displace water and dry the soil. Thus, low rf propagation loss is
expected above the layer.
Neither changes in soil porosity nor conductivity affect this low rf propagation loss
significantly. Increased porosity enhances the overall magnitude of the reflection coefficient but
has little effect on the ratio of the imaginary part of r to its magnitude. This ratio tends to remain
relatively constant for a given layer thickness. The reason is that porosity has a small effect on
the dielectric constant of the layer because the dielectric constant of the contaminant is relatively
close to that of the soil particles. The increased magnitude of r with porosity is due to the
increased differences of £r between layers. Conductivity effects are minor because it only affects
the reflection at the f^/E^ interface. Not only is the effect of conductivity small there (as can be
52
-------
seen in the results presented in Table 7.2), but the intervening layer tends to shield changes.
Almost by definition, the layer itself has very low conductivity (and hence loss) because it is
saturated with contaminant and contains a negligible amount of water.
Dry/Oil/Water Sat 30% VoWs-0.03 S/m
LLJ
O
LLJ
O
O
z:
O
h-
o
LJJ
DC
0.4
0.2
-0.4
Re r(t)
Im r(t)
0.02 0.04 0.06 0.08
LAYER THICKNESS - m
0.1
Figure 7.3. Real part, imaginary part, and magnitude of the reflection coefficient vs. layer thickness of a
contaminant-saturated layer sandwiched between dry and water-saturated soils (30% porosity and 0.03 S/m water
conductivity.
As might be expected, changing the operating frequency in the case of thin layers has a
nearly proportional effect on the relative strength of the imaginary component of r. Figure 7.5
illustrates this. The imaginary part of r arises from multiple reflections and interference between
the two interfaces, which become larger relative to the period of an rf cycle as the frequency
increases. Eventually, as the frequency increases or the layer gets thicker, cyclical interference
phenomena appear. Note that the behavior in Figure 7.6 fairly closely follows the
r = rc(l +jf/fc) behavior predicted for thin layers.
The emphasis here has been on the detectability of thin layers, since they are apparently
both more likely to occur and harder to detect. Thick layers will produce strong, reverberating
echoes that would be relatively easy to detect.
53
-------
Dry/Oil/Water Sat 30% VoWs-0.03 S/m
o
<
DC
0.02 0.04 0.06 0.08
LAYER THICKNESS - m
0.1
Figure 7.4. |9?r(f)|/|r(r)| and |3r(r)|/|r(OI vs. layer thickness for a contaminant-saturated layer sandwiched
between dry and water-saturated soils (30% porosity and 0.03 S/m water conductivity).
The final consideration is how to detect the presence of a significant imaginary component
of r. Information on r is contained in the GPR output signal. Although this signal is real, it is
convenient to treat it as being the real part of a complex, "analytic" signal. The imaginary part of
the signal, or echo from the layer, can be obtained directly if the GPR employs a quadrature
detection system (the only GPR known to do this directly is the existing synthetic-pulse GPR).
For the more common type of GPR, which directly digitizes the entire real signal, the alternative
is to compute the imaginary part using a Hilbert transform (Appendix A). It would not be
necessary to compute the Hilbert transform of the entire GPR sweep; only the part of the echo
from the water table interface needs to be analyzed because it is the signature of that feature
which is needed.
In the time domain, a GPR output signal is actually the convolution of the transmitted
radar pulse with a function that describes the scattering medium. For reflection from a plane
interface in non-dispersive media, this simplifies to convolution with a delta function, so that the
received signal is a delayed, reduced-in-magnitude replica of the transmitted signal. In the
frequency domain, this convolution corresponds to multiplication by a function
54
-------
Dry/Oil/Water Sat 30% VokJs-0.03 S/m
1 -
<
cc
0.02
0.04
0.06
0.08
0.1
LAYER THICKNESS - m
Figure 7.5. 1 9?r (t )| /( r (0)| , 1 3r (f)| /| r (0)| , and | r (r)| /) r (0)| vs. layer thickness for a contaminant-saturated layer
sandwiched between dry and water-saturated soils (30% porosity and 0.03 S/m water conductivity).
= r0 = rr exp{-;27i:/(T0 + AT)} .
Here, t0 is the macroscopic delay due to propagation to the layer and back and AT is a
perturbation, which could be caused by a small change in range or delay. For small
perturbations, 27r,/AT« 1, so
-J2"f*o, , .-, r» \
r0 = rre (1 -;2ic/At),
which is the same form as reflection from a sandwiched layer. Indeed, for a thin, relatively
low-loss layer,
AT = 2^^-^
2"V0
-Tl3
£3-62
ATn = - ATO ,
£,-£,
where ATO is the additional time delay if the range to the water table is increased by a distance
equal to the thickness of the layer. Thus, the effect of a localized, thin layer is qualitatively the
same as a local increase of depth of the water table. It would be difficult to distinguish between
the presence of a layer and a local drop in the level of the water table.
55
-------
o
DC
DC
O
LU
Q
0.6
0.4
0.2
30% pores, t = 5 cm, sigma = 0.03 S/m
|Re r(f)|
|lm r/Re r|
40 80
FREQUENCY-MHz
120
160
Figure 7.6. Magnitude of the real part of r and the ratio of the imaginary to real parts vs. frequency (30% porosity,
5-cm thickness, and 0.03 S/m water conductivity).
However, from a remediation standpoint, one would naturally look for low places in the
water table because that is where contamination would be expected to collect. This analysis
shows that any contamination filling low spots on the water table will at least not suppress the
effect. The key to detecting thin layers of contamination floating on the water table may be S AR
processing, because it acts to automatically remove macroscopic phase shifts due to propagation
as well as concentrating the signal from the specular reflection point.
7.5 Model II Strategy: Volume Scattering from Soils
The idea here is that small density variations in the soil due to pebbles, rocks, different
grain sizes, and even the pores between and inside the grains will produce some level of volume
scattering. It is well established that a medium with a spatially varying dielectric constant (or
refractive index) will scatter rf energy. It is postulated that contaminant will displace air or water
in the pores and thus alter the strength of the dielectric constant variations.
56
-------
To start with, we need a model for the scattering from a spatially randomly varying
medium. Perhaps the simplest of these leads to the Booker-Gordon formula for the backscatter
per unit volume due to statistically homogeneous and isotropic refractive-index (or dielectric
constant) fluctuations:18
27i(l
Here, k = 271/A. is the rf wavenumber in (average background) medium, and / is the correlation
distance of dielectric constant fluctuations in the medium. This medium is assumed to have an
exponential correlation function; for example,
It will be seen that the magnitude of / is about the same as the average grain size. There are
some other assumptions. First, the correlation distance / is to be much smaller than the size of
the scattering volume. Second,
(£,. -!)£/« 1 .
This expression essentially says that the rf field inside a grain is to be the same as the one
outside; it thus puts a restriction on the product of grain size and relative dielectric change. In
addition, there is a much more severe assumption that Aer = (er - 1) itself should be small
compared to unity. Although it turns out that this last assumption (i.e., that < Ae2 > can be small)
is often reasonably well justified for dry and contaminated soils in a statistical sense, it is not true
for soils with significant amounts of water. Furthermore, the approximation is not generally
satisfied at a more fundamental level of the electromagnetic problem. In addition,
weak-scattering theory is being applied to a situation where strong scattering may occur. Thus it
must be recognized that the numerical results presented are approximate and in some cases may
be correct only to an order of magnitude. These approximations are justified by the intrinsically
great uncertainties in soil properties, the immediate need to obtain even order-of-magnitude
estimates, and the fact that such estimates are adequate for comparing different GPRs.
However, it appears that a simple extension of the Booker-Gordon theory will produce a
better approximation than the formula presented above over a wider range of dielectric constant
18 If the mean value of the fluctuations relative to the surrounding medium is unity, and the fluctuations are weak,
so that Ae = 4Aw , where n is the refractive index, this expression takes on its more familiar form:
57
-------
fluctuations. The modified Booker-Gordon scattering formula is presented in Appendix C. The
new expression for the backscatter per unit volume is:
where
For small < Ae2. >, this provides the same predictions as the standard Booker-Gordon formula. It
is more conservative for large values of Aer.
The next step is to relate the correlation function to soil properties. A simple,
two-constituent soil model with different dielectric properties will be used. As one proceeds
along an imaginary line through the soil, the local dielectric constant will jump back and forth at
random points between the two dielectric values. One example is solid rocks and pebbles
imbedded in smaller-grained material. At the other extreme one can imagine an essentially
homogeneous soil of fine particles with some void fraction. The primary difference between the
two is in the correlation distance.
This model is an example of one of the classic "random telegraph" waveforms, where the
signal jumps randomly between values y, and y2 at an average rate ^. The number of jumps in an
interval are assumed to follow the Poisson probability law. It is a straightforward matter to show
that the corresponding correlation function is in fact exponential (Appendix D):
Now, the relationship between soil conditions and the model parameters must be
determined. One required parameter is the correlation distance, /. To estimate this, suppose that
there are m particles of interest per unit volume and that the average particle size is d. Then the
volume fraction occupied by the particles will be
, —3
(p = ma ,
the number of shifts per unit length will be
->,k"3
r ~ T «/3 _ 2V
and the correlation distance will be
,=_LSJ_
2C~4"3
58
-------
The correlation distance can also be expressed in terms of the average distance between
particles, s. The number of particles per unit volume is approximately
m= \7
Consequently,
and
= 4'
These expressions are thought to be reasonably accurate so long as § is not too large (()> < 0.5).
The other required parameter is the variance of fluctuations. Suppose that a fraction (|) of
the soil has an effective refractive index erl and the rest has er2. Then, approximately,
.1/3
and
For the case of a soil consisting of small grains with e, and voids with £3, the soil porosity is
given by (1 - (j>). Table 7.3 lists some representative values for < (er - I)2 > and <£?> for three
mixtures of soil and void material (i.e., air, water, and contaminant) at three porosities. Also
included in Table 7.3 are the corresponding values of the dielectric constant of the medium, eave,
which are obtained independently from the soil mix dielectric properties calculation. These
examples are intended to illustrate the range of magnitudes of these quantities. Intermediate
levels of saturation will produce intermediate values of these parameters. As anticipated, using
the modified Booker-Gordon formula produces similar values for < (er - I)2 > and < ^2 >, and
hence the predicted scattering strength, except when the dielectric changes are large, as when
water is added, where the modified form predicts a significantly lower backscatter level. Note
that there is a rather strong sensitivity to the presence of contaminant.
Similar values of < £,2 > can be expected for other mixes, such as rocks and pebbles
imbedded in soils. For example, consider a mixture consisting of = 5% rocks (e = 4.5)
59
-------
Table 7.3. Em, < (e, - I)2 >, and < ^ > vs. Porosity and Mixture Type
£„, <(er-l)2> <^2> Porosity •< 1 -)
30% 40% 50%
Mixture Soil Grains (e=4.5) 3.0 0.27 0.25 2.6 0.51 0.39 2.2 0.94 0.57
-Air(e=l)
Soil Grains (e=4.5) 10.4 5.5 0.92 14.2 3.9 1.2 19.5 2.5 1.3
- Water (e=81)
Soil Grains (e=4.5) 3.7 0.067 0.070 3.4 0.11 0.11 3.2 0.16 0.14
-Contaminant (e=2)
imbedded in dry soil that itself has 30% porosity, which has a dielectric constant £sollma = 3.0.
Here, < %2 >= 0.068. Table 7.4 summarizes the changes if the soil becomes saturated with water
or contaminant. These changes should produce a detectable contrast between dry, wet, and
contaminated mixtures. As expected, the presence of contaminants is revealed by a reduction in
scattering, which would appear as a blank region in a picture of the underground environment.
Table 7.4. EJ and < ^ > for a Mixture of Rocks and 30% Porosity Soil
Mixture
5% Rocks/95% Dry Soil
5% Rocks/95% Water-Saturated Soil
5% Rocks/95% Contaminant-Saturated Soil
"
3.0
10.4
3.7
0.068
0.18
0.013
It is expected that the rf wavelength will usually be significantly larger than the correlation
distance. In that case, the radar cross section per unit volume becomes
The strong dependence on / mirrors our expectation that a soil consisting of rocks and pebbles
imbedded in dirt will be a much stronger scarterer than small grains and voids. After inserting
the values for / and < ^2 >, one obtains
128
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the order of one-quarter wavelength. The range resolution is determined by the pulse length, and
is typically about three-quarters of the center-frequency wavelength for the wideband GPRs.
Thus the minimum scattering volume is on the order of
^ = 0.15^ = (A/2)3
(here, A, is the wavelength in the ground). The res is thus
^min ~ P rain
where A,0 is the free-space center-frequency wavelength.19
These considerations show that contamination could produce detectable changes in volume
scattering. But first it must be determined whether there is sufficient scattering to produce a
detectable echo at all. The lower limit is scattering from the intrinsic graininess of the soil. Soils
containing a distribution of pebbles, gravel, stones, etc., will presumably yield larger volumetric
scattering.20
The next task is to ascertain the radar sensitivity required to detect volume backscatter
from the intrinsic graininess of the soil. Table 7.5 lists values at 100 MHz for the res and
minimum value of Q needed to detect volume scattering at 10-m depth in low-loss (dry) soil with
a 1-s observing time duration vs. the mean particle diameter. The soil is assumed to be
homogeneous with 30% porosity, and has an average dielectric constant of 3.0. Table 7.5 shows
that it would not be possible to detect the intrinsic scattering due to soil graininess with a
conventional GPR (e.g., with Q = 140 dB re Is) unless the soil were very coarse (i.e., made up of
stones bigger than 10 cm) or the observing time was much greater than 1 s. The implication is
that an advanced synthetic -pulse GPR would be needed in order for this detection strategy to be
considered a possibility.
19 Note that this formula does not apply for small values of <)>, which is the case for mixtures with widely spaced
scatterers. The requirement that the correlation distance be small compared to both the scattering volume and rf
wavelength imposes the condition
20 Note that a distinction is being made between a more or less homogeneous distribution of scatterers that occupy a
multiplicity of resolution volumes and widely spaced, isolated scatterers. The former produce a relatively smooth
picture, whereas the latter, after SAR migration, are distinctly resolved. With this detection strategy, one looks for
relatively slow changes in background level that are due to contaminants. Individual scatterers are a nuisance (a
major aspect of the SAR processing is to localize their influence).
61
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Table 7.5. Minimum Q vs. d
d (mm)
0.01
0.1
1
10
100
o(m2)
i x ur16
1 x 1Q-'3
1 x KT10
1 x 1Q-7
IxKT*
Qmin(dBrels)
260
230
200
170
140
Gmin(dB)(Tobs = 3000s)
225
195
165
135
105
Adding water or contaminant to the soil changes the picture. As seen in Table 7.3, when
the 30%-porosity soil used in this example is saturated with water, < ^2 > increases by about a
factor of 4; furthermore, eave rises from 3.0 to 10.4, so the res, which is proportional to
\n t-2
E-«<$ >>
increases by 8 dB. However, according to the soil dielectric properties calculation, if the added
water has moderately high conductivity (a = 0.03 s/m), the attenuation becomes 0.4 dB/m at 100
MHz, or 8 dB for 10-m depth. Thus, this increased attenuation nearly counteracts all of the res
increase due to the water. Higher values of water conductivity or soil porosity will greatly
increase the losses and reduce detectability.
Contaminants will generally reduce the res. For example, saturating the soil in this
example with contaminant will cause the res to drop by 4 to 5 dB. This contrast should be big
enough to provide a good opportunity to detect contaminant-soaked soils. Another important
point discovered here is that scattering from fairly small-scale graininess is in principle
detectable with an advanced (synthetic-pulse/SAR), high-<2 GPR.
Imbedded pebbles, rocks, etc., lead to soil conditions that usually produce much greater
radar signal than the intrinsic graininess. For example, consider a mixture consisting of d =
2.5-cm stones, whose average spacing is s = 10 cm, imbedded in the 30%-porosity soil. Here,
E, = 4.5,
/ = d = 2.5 cm,
' = 0.0156,
and
<^2>= 0.046.
For this mixture, the calculated res at 100 MHz is about a = 1.3 x 10~5 m2. Thus, adding 5% rock
will raise the scattering level by more than 110 dB above the intrinsic scattering from silty soil
62
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with (d = 10 urn) grains. A standard GPR with a Q = 140 dB re 1 s would just be on the verge of
seeing this enhanced scatter under the conditions used in the example (i.e., dry, low-loss soil).
Increased losses, of course, will reduce the visibility.
Table 7.6 shows what happens in this example when the soil part of the mixture contains
water or contaminant instead of being dry. Listed there is the average dielectric constant of the
background medium plus the value of the quantity
C<^2>,
which is proportional to the res. For a water-saturated 30%-porosity soil, the predicted res rises
to 3 x 10~5 m2; with contaminant saturation, it drops to 2 x 10"6 m2. There will be about a 6- to
7-dB contrast between dry and contaminant-saturated soil in this example, somewhat larger than
the 4- to 5-dB contrast produced in scattering from the fine-scale graininess. Clearly, the
presence of larger particles can dominate the volumetric scattering and enhance the volume
scattering contrast produced by contaminants. However, volumetric scattering contrasts are
generally subtle, which implies that careful and extensive spatial averaging would be needed to
bring out the desired features.
Table 7.6. Emf and e^2 < £? > for d = 2.5 cm, s = 10 cm Stones in Various Soils
Soil Condition
Porosity of Soil Component
30%
Dry
10% Water
30% Water
60% Water
100% Water
10% Contamination
30% Contamination
60% Contamination
100% Contamination
3.00
3.38
4.35
6.35
10.4
3.12
3.25
3.45
3.71
0.080
0.041
0.00061
0.066
0.39
0.066
0.052
0.035
0.019
50%
2.22
2.75
4.25
8.24
19.5
2.34
2.52
2.79
3.16
0.22
0.11
0.0017
0.21
1.18
0.19
0.15
0.11
0.060
Table 7.6 also illustrates another phenomenon. Under partial water saturation the
dielectric constant of the soil-plus-water component can match that of the rocks, which makes
the rocks invisible to the GPR. However, no amount of contaminant can produce this effect.
Thus, regions where contaminant displaces soil moisture will become visible to a GPR.
Table 7.7 lists various quantities, including the minimum required Q to just detect
(SNR=1) this scattering at 10-m depth in dry, low-loss soil and a 1-s total observation time.
Operation in other soils can be readily scaled from these numbers. In no case would a standard
GPR be able to detect the scattering.
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Table 7.7. Backscatter Quantities for Solid Particles Imbedded in Dry, Low-Loss, 30%-Porosity Soil at 10-m Depth
(T,^ 3000s)
4>
-------
Note that the lateral dimension of the minimum scattering volume is on the order of 50 to
100 cm, depending on the average soil dielectric constant and operating frequency. Since this is
probably much smaller than the plume dimension, it is possible to obtain processing gain by
spatially averaging the migrated echoes. Essentially, it is desirable to process the data
three-dimensionally through filters matched to expected plume characteristics. Another useful
strategy might be to increase the effective scattering volume by reducing the radar bandwidth
(i.e., increasing the pulse width) and restricting the SAR aperture. These trade-offs should also
be looked at.
Also note that the radar cross sections per unit volume are generally very small in these
examples. This means that additional propagation loss due to scattering will be negligible and
multiple scattering will not be important.
In conclusion, it appears that contaminants can produce detectable changes in volume
scattering if a high-Q radar is used. The remaining question is whether these changes are
masked by natural variations in volume scattering that are on the same scale as those found in
the plume.
7.6 Model II Strategy: Deducing Changes in the Local Average Refractive Index
SAR processing requires the dielectric constant of the soil as an input. As this parameter is
unknown, it is necessary to estimate it somehow. One way is to use the radar data themselves.
One vendor, for example, has an analysis program that permits the operator to manually
superimpose a computer-generated hyperbola on a data display and adjust it to match observed
features due to discrete scatterers. The computer-generated hyperbola incorporates the dielectric
constant. It is then used to migrate the data over the field. This is successful to the extent that
the dielectric constant remains uniform over the field. Otherwise, the hyperbolas change shape
and/or deviate from hyperbolic form altogether.
This suggests that localized changes of the dielectric constant could be detected by
(1) adaptively changing the migration parameter over the field or (2) quantifying the mismatch
between the "average" hyperbolas and the local curves. Of course, to do this in a "traditional"
way would require a sprinkling of strong discrete scatterers throughout the field both above and
below the suspected contamination region. However, as shown above, the volumetric scattering
even from uniform soils is detectable with high-2 radars. It may be possible to devise a test of
migration quality of volumetric scattering or find out how much perturbation of the local
dielectric constant is required to achieve a sharp migration "focus" of small-scale variations of
the volumetric scatter level.
65
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7.7 Section Summary
The impact of these strategies on the required radar performance can now be assessed.
Several new and interesting findings have come out of the work described in this section. These
relate to the strategies associated with Models IA and n.
First, it appears that when the contaminant has a low dielectric constant there are fairly
large contrasts (up to 7 dB) in volumetric scattering between contaminated and uncontaminated
regions. Most contaminants possess this electrical characteristic. Of course, the contaminant has
to be present in sufficient concentration to appreciably alter the electrical properties of the soil.
The intrinsic volumetric scattering from the soil itself can be detected if a sufficiently sensitive
GPR is used. (This is true of nearly all soils.) A GPR with significantly greater sensitivity than
provided by the standard commercial units is needed, unless the soil happens to have a lot of
large rocks in it. This finding evidently provides an explanation as to why GPRs have not been
generally employed for remediation and contaminant mapping, although there is some reported
experimental evidence that a contaminant having a low dielectric constant does suppress
volumetric scattering [17]. This analysis may be the first attempt to quantify both the effect of
the shifts in dielectric constant and the consequent requirements of the GPR.
Second, while the results for fine particles (silts and clays) would at first suggest that
unachievably high values of Q are necessary to detect Model II contamination, such high Q may
not really be required. This is because it is likely that fine materials have larger particles (sand,
pebbles, etc.) interspersed in the volume. The larger particles may thus contribute to detectable
levels of volume scattering contrasts.
Third, it was determined that a thin layer of contaminant "floating" on the water table will
produce a measurable signature if it is more than a few centimeters thick. The echo from the
water table will be modified in a distinctive fashion. Since the reflection coefficient of the water
table interface is generally very large, a GPR may not need a very high Q in order to detect this
change. Since the effect appears as a local increase in the depth of the water table, it may be
difficult to distinguish an apparent depth increase due to a thin contaminant layer from an actual
increase. However, from a remediation standpoint, depressions in the water table would be the
most likely places to look for contaminants.
Thick layers of contamination would be easier to distinguish because the changes produced
in the signature are on the same order as the echoes themselves. The only sensitivity issue is,
then, the desired depth of penetration, which is so soil-dependent and variable that it is
impossible to make a general statement about it except to say that more sensitivity is better.21
21 This advice is given with the caveat that if the GPR is too sensitive, clutter (especially from above-ground
reflections) can mask the desired signal.
66
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Lastly, we note that there are no particularly strong GPR requirements associated with the
Model IB strategy. A large reflection coefficient and resultant strong echo wiD be produced by
the formation of a contaminant/water interface. As with Model IA, more sensitivity is generally
better, since it permits a greater depth of penetration.
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Section 8
RADAR SYSTEM DESIGN
Radar system design begins with a specification of the externally determined operating
requirements, such as range coverage, resolution, search rate, and minimum detectable target
size. These specifications must be tempered by practical limits imposed by technology and cost.
Invariably, there are compromises made to arrive at an optimum design. Here, there are only
two basic specifications, sensitivity and resolution. These determine the GPR configuration
(e.g., short pulse vs. synthetic pulse), center frequency, and bandwidth.
It is desirable to maximize resolution to the extent possible, which implies a system with a
fractional bandwidth near unity. Then only the center frequency remains to be specified. Due to
the extreme variability of the environment, a single "best" center frequency is difficult to specify.
Because of the large fractional bandwidth, the analysis approach is to consider frequency bands
spaced by half-decades. These trade-off analyses for a variety of conditions showed that a center
frequency near 100 MHz affords a reasonable and generally applicable compromise between
penetration depth and resolution. The 30-MHz band has lower attenuation, and thus permits
greater penetration, but has a SAR-processed resolution on the order of 2 to 3 m (6 to 10 ft),
which is probably inadequate. The 300-MHz band has good resolution (20 to 30 cm, or about
1 ft), but suffers high attenuation except under unusual circumstances. A further consideration
regarding resolution involves the blanking of the receiver during pulse transmission, which limits
the minimum range depth coverage.22 In the 30-MHz band, the pulse width will be about 33 ns,
so echoes from at least the first several meters (6 to 10 ft) into the ground will be lost. The
choice of operating frequency also affects sensitivity. There is somewhat more GPR power
generally available at lower frequencies, and this improves sensitivity. However, the volumetric
scattering res is proportional to the cube of the frequency, a fact that appears to favor higher
frequencies. However, since attenuation enters as an exponential factor that increases rapidly
with frequency, it will sooner or later dominate the advantage provided by improved res at higher
frequencies.
22 For short-pulse GPRs, there is also a time delay while the receiver recovers from overloading due to the powerful
transmitted pulse. This does not affect a synthetic-pulse GPR, which must be designed to operate in the continuous
presence of the transmitted tone.
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GPR sensitivity is determined primarily by the product of its figure of merit and the
observation time, Q x Tohs. The observation time is determined by the desired search rate, and
involves the cost of surveying a remediation site. That is, it will require a relatively long time to
survey a site with high losses and low intrinsic volumetric res compared to one where losses are
low and where there are many underground scatterers. This is because, for a site with high
losses, the GPR must move slowly in order to achieve a sufficient dwell time at each of its
locations. Once the res and range requirements are specified for a given soil condition and a
minimum search rate is stated, the minimum value for Q can be established.
As described above, a GPR design intended for remediation work is site-dependent, but in
general it must have the largest practically attainable value of Q. Table 8.1 bounds the problem
and list values of <2mjn for several scenarios; this table is intended to suggest the range of values
for Q min that would be required. The entries in this table show the value(s) of Qmin needed to
detect the radar scattering (with an SNR of lOdB) from four different "targets," in three different
soil environments, for targets located at four different depths. The targets in the table are: (1) a
long, 2-inch-diameter, conducting object such as a pipe,23 (2) a layer of contaminant above a
well-defined water table (Model I contamination), (3) a Model n contamination geometry with
0.1% by volume of imbedded 3 mm grains (which may be more representative of a "real" soil
than a pure, intrinsic soil [8,9], and (4) an intrinsic Model II geometry. The descriptions of the
"soils" in this table (sandy silt, silty sand, and clay) are based upon particle size, as shown in the
table; for all of the soils here, a 30% saturation is assumed. For each combination of soil, target,
and target depth, two values of Qmjn are given. The first value is the Qmin needed to detect that
scenario with a Tobs of 1 s; this was the Tobs used for most of the analysis described above. The
second value is the Qmin needed to detect that scenario with a 3000-second Tobs; this Tobs is a
likely value for surveying an area at a site and using three-dimensional coherent processing, as
discussed in Section 5.4. These values are approximate, and it should be noted that these values
represent the underlying detectability of structures that produce scattering; the strategies for
locating contamination depend on detecting changes in the echoes from these targets. Depending
on the "target" and soil, detectability ranges from "very easy" to "impossible." In general, high
attenuation severely limits GPR performance. High-Q (i.e., Q » 140 dB re Is) GPRs can access
a significantly greater span of possible soil conditions.
23 Perpendicular polarization of the electric field was assumed; while this was not discussed in the report,
perpendicular polarization will result in a weaker echo signal strength for the pipe than parallel polarization; thus the
polarization used here represents a "worst case" geometry.
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Table 8.1. Values of Q^ Necessary to Detect Various Targets in Various Environments with SNR of 10 dB
Depth - meters
Soil/Target
10
15
20
Sandy/silty soil, 30% saturation (particle size = 0.5 mm)
2-in.-diameter pipe-like object
Model I contamination
Model II contamination
-with 0.1% imbedded 3-mm grains
-with 0% imbedded 3-mm grains
Silty/sandy oil, 30% saturation (particle size = 0.05mm)
2-in.-diameter pipe-like object
Model I contamination
Model II contamination
-with 0.1% imbedded 3-mm grains
-with 0% imbedded 3-mm grains
95/60 105/70 110/75 115/80
60/25 70/35 75/40 80/45
150/115 160/125 170/135 175/140
180/145 195/160 200/165 205/170
100/65 115/80 125/90 135/100
65/30 80/45 90/55 100/65
155/120 170/135 180/145 190/155
215/180 235/200 245/210 255/220
Clay soil, 30% saturation (particle size = 0.005 mm)
2-in.-diameter pipe-like object
Model I contamination
Model II contamination
-with 0.1% imbedded 3-mm grains
-with 0% imbedded 3-mm grains
240/215
205/170
270/235
>300
>300
>300
>300
>300
>300
>300
>300
>300
>300
>300
>300
>300
One conclusion drawn from the GPR industry survey accomplished during the course of
this work is that the basic short-pulse GPR technology has essentially matured. There appears to
be little potential for significant further rf hardware development; that is tens of dBs
improvement in terms of antenna, pulse, receiver, and so on, are unlikely. Some incremental
improvement in power-bandwidth product may result from high-power optically triggered pulser
technology currently being developed.24 However, a 30-dB improvement in Q can be obtained
by replacing the "sampling-oscilloscope" method of recording the data with a transient digitizer
method. It was noted in Section 5.2.1 that a Q of perhaps 190 dB re 1 s could be achieved using
a high-power pulser and transient digitization. Such a radar could be assembled at the subsystem
24 Optical triggering also provides a benefit by eliminating stray radiation from cabling, since non-conducting
optical fibers can be used to connect the GPR head to the control and recording unit. For the same reason, optical
fibers are also used to carry the received signals. Note that in the Bureau of Mines synthetic-pulse GPR the original
coaxial cables have been replaced by optical fibers.
70
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level (i.e., by connecting a commercially available rf head and controller to an available
digitizer/recording system). For the application considered here, however, it is not considered
cost-effective to develop or build short-pulse GPR hardware at the subsystem level and below.
The status of synthetic-pulse GPR technology is somewhat different. There is only one
known prototype unit. As that unit employs older technology, there appears to be considerable
opportunity for improvement. According to its specified characteristics, it has a potential Q of
about 220 dB re 1 s. It is not well characterized, however, but it is believed that it actually has a
Q about two orders of magnitude less than its potential, or about 200 dB re 1 s. This unit
nevertheless appears to outperform short-pulse GPRs, and would be adequate for
proof-of-principle testing in appropriate soils. Further development of synthetic-pulse GPR
technology at both the subsystem and system level is indicated if a more generally useful system
is to be developed.
As noted above, the environment is a key factor in selecting a Q for the radar design. A
1988 EPA study described the types of soils found at various Superfund sites around the U.S.
[9,19]. This work found that, based upon a total of 151 samples (119 in the Eastern U.S., 32 in
the Western U.S.), 40% provided, no information on soil type, 30% were described at "sandy
clay," and 20% were described as "sandy." Only 10% of the samples were described as
"primarily clay." Thus, based upon this work, one could expect that most soils in areas where
radar might be used as a remediation tool would be "sandy clay" or "sandy." Thus, a design
choice Q of 220 dB re 1 s would be expected to meet the requirements as much as 90% of the
time.
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Section 9
Numerical Analytic Model
9.1 Introduction
In Section 7 detection strategies were presented for each of the contamination models
described in Section 6. As noted in Section 7, detection depends on radar sensitivity and the
environment in which the contaminated soil or water is imbedded. The sensitivity issue is easily
resolved within the context of the quality factor for and integration time for the particular radar
and the scattering characteristics of the contaminated region as dictated by the models developed
in Section 6. The primary purpose of the numerical analytic model is to demonstrate the
viability of the detection strategies under conditions more representative of real environments.
Only two generic types of scattering interactions are considered, namely, discrete
scattering and reflection. The simplest discrete scatter is an isotropic point source. The simplest
reflection occurs at a dielectric interface between two homogeneous media. With appropriate
distributions of the location and strength of these elemental scatterers, a wide variety of
contamination models can be simulated. A predictive geophysical model must accommodate
considerably more detail both in its constituent parts and their mutual scattering interactions;
nonetheless, the imbedded non-interacting scatterer (INS) model captures the essential elements
of a real scattering environment, and is therefore adequate for optimizing a GPR design and
evaluating its capabilities. The INS model, moreover, provides a tractable means of
demonstrating the improvements in detection that can be achieved by advanced signal
processing.
The numerical analytic model assumes that in the absence of scattering, the ground is a
lossy dielectric. Signal attenuation due to ohmic losses is the most severe problem that must be
overcome in designing an effective GPR for detection of soil contamination. Thus, the ability of
a radar to concentrate energy at depth is the primary figure of merit of the system. The radar
parameters that affect this figure of merit have been collected in a single parameter, as described
in Section 6; however, signals from a large number of radar locations can be processed
coherently to enhance the detectability of a localized scattering region. Matched-filter
processing of the combined GPR returns should provide a nearly optimum detection scheme for
weak localized scattering regions.
72
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Section 9.2 reviews the draws on the material in Sections 5 and 6 to describe the INS
model, which is specified in terms of a minimal set of radar, soil, and cross-section parameters.
The model is effectively calibrated so that for a given quality factor and integration time, the
output intensity has units of signal-plus-noise power normalized to the average noise power.
Thus, unity or zero dB corresponds to the average receiver noise level. By simulating the
echo-strength-vs.-depth profiles for a large number of adjacent receiver locations, one can
synthesize the "wiggle" display that is commonly used for GPR data presentation. It is more
convenient to present the data as contours of constant normalized signal-plus-noise power plotted
against ground distance and true depth. In this unprocessed display format, the detected GPR
echoes from discrete targets are smeared over hyperbolic arcs.
Section 9.3 describes a matched-filter processing procedure, which is effectively a near
optimum time-migration scheme that minimizes the deleterious effects of weak signal
contributions to the reconstruction at any subsurface point. One should think of the
reconstruction process as a point-by-point interrogation of each subsurface point for scattered
energy. The effective size of the interrogation point depends on the bandwidth of the radar and
the maximum separation of the receivers. The unambiguous region that can be interrogated
depends on the frequency separation or pulse repetition rate and the receiver spacing.
Unambiguous angle resolution requires a receiver separation of one half the minimum
wavelength in the medium. Similarly, the unambiguous depth is determined by the propagation
velocity times twice the reciprocal of the minimum frequency separation. The enhanced
detectability of processed radar returns is two-fold. The coherent integration reduces noise and
the resultant localization reduces clutter from adjacent targets.
Section 9.4 presents a number of examples that demonstrate these effects for representative
systems. The intent here is not to present an exhaustive case study but rather a few examples
that clearly illustrate the processing gain that can be used to advantage for remediation of
petroleum or chemical spills.
9.2 The INS Model
For a single scatterer at a distance rmn from receiver element n, the GPR signal generator
computes the return signal contribution as
~2Y<7""')+^,, (9.1)
where %„ is a gaussian random variable with variance 0^ and p(f) is a spectral weighting factor,
which will be described shortly. For reference,
, ( 2nf r—Y
Y = -(/orvU£) =- '—N^EO (9.2)
I v * r~ / i * " i v^
73
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as defined by the soil model described in Section 6.4. Thus, yr is the one-way loss factor, and
y, = 27T//C (/) is the propagation factor.
The depth-dependent return signal is the Fourier transform of Eq. (9.1), which is
implemented with an FFT algorithm as
vn(kAr ) = I vn(/;) exp { 2nijk/N}. (9.3)
;
The output is converted to distance units by using 5r = cV(25) with c0 the velocity of light at the
center frequency, and B the bandwidth. The pulse spectrum is scaled so that
I v „(£)=!. (9.4)
;
For a pulse with a real nonnegative frequency envelope, this ensures that the maximum value of
p(t ), the inverse Fourier transform of p(f), is unity. The frequency envelope implicitly absorbs
any weighting imposed to control range sidelobes.
To display the GPR model output in its simplest form, one plots
/>,,(£Ar) = |v,,(£Ar)|2. (9.5)
In the absence of frequency dispersion, it follows from Eq. (9.1) and Eq. (9.3) that
,r,.m}
, ,,.m ,
- rnm)/c0)CM |2 -^-~ - - + O2, . (9.6)
The angle brackets denote averaging, and the principal energy content of Pn lies within an
interval T. Eq. (9.6) summarizes the GPR output in arbitrary units. The strength factor Cm
implicitly contains all the system parameters as well as the strength of the scatterer. To calibrate
the model in real units, note that average power should have the form
(9.7)
at the peak of the peak of the transmitted pulse, which has been forced to be unity by Eq. (9.4).
The m factor implies a coherent integration of m independent returns to form the estimate. The
remaining terms are standard elements in the radar equation. To isolate the system factors from
environmental and operational factors, a GPR figure of merit has been defined:
where fprf is the pulse repetition frequency. Thus, m =fprfT where T is the dwell time. Here BN is
the noise bandwidth, which need not be equal to B, the frequency extent of the incident
waveform. The quality factor is a ratio of average received power to the total noise power at the
receiver output. In terms of the quality factor,
74
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"" (4jtrnm)4
where T represents the dwell time for the measurement. It is obviously more convenient to
express the total received power to total noise power ratio, namely
(9.9)
Thus, let
and
GN=I/JN. (9.12)
With Cm in Eq. (9.1) defined by Eq. (9.11), the detected intensity as defined by Eq. (9.5) is the
ratio of total received power to total noise power. With this definition, the predetection
integration or dwell time is accommodated effectively by scaling the receiver noise level. The
model parameters that need to be specified are summarized in Table 9.1.
Table 9.1. Model Parameters
Parameter Definition
Q Figure of Merit (seconds'1)
Tohs Dwell Time (seconds)
o7fj Radar cross section for m* scatterer (meters2)
fc Center frequency
&f Frequency step
N Number of frequencies (even) distributed about fc
fj=fc + (j- N/2 -1 )A/" j"1 frequency
\ = fjc(fc) In situ wavelength at center
There is considerable interest in a pulsed radar because it provides a comparatively
inexpensive way to get a lot of power into a short pulse. In the frequency domain, the pulse is
adequately represented by the gaussian form
p(f+fc) = A/Vrt?exp{-(rtT/)2}. (9.13)
With this definition of p(f), the pulse envelope has the gaussian form
/7(0 = exp{-(r/t)2}, (9.14)
which satisfies the normalization condition automatically. A typical system might run from 67
to 133 MHz with a center frequency of 100 MHz with T = 2/(nB).
75
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Modeling propagation and scattering in a dense, highly inhomogeneous medium is
currently one of the most challenging problems in electromagnetics and acoustics. Nonetheless,
it is possible to construct a simple model that captures the essential elements of the signal
environment in which a practical GPR must operate. The model is based on simplified physical
descriptions of contamination structures that preserve the dominant signal characteristics
although not their complete manifestation in a real radar environment. The resulting radar model
is adequate for GPR performance analysis, consistent with design efforts in this phase of the
work, but it is not intended for geophysical interpretation of the radar data.
In a homogeneous region of space, Eq. (9.1) effectively describes the backscattered
radiation from an isolated point source. Consider an aggregate model consisting of
non-interacting scatterers (NIS). It is recognized that the real propagation environment is much
more complicated than can be accommodated by the NIS model; however, the model can be
expanded in a straightforward manner to accommodate the ground contamination models
described above. For example, Model II can be simulated by a wedge- or cone-shaped region of
contamination that manifests itself by a randomly distributed collection of point scatterers.
Similarly, to model contaminant floating on a water table interface (Model I), a localized
reflecting layer can be introduced. In the GPR model, only the receivers very nearly overhead
see the reflection. To complete the model, white noise is added to the GPR signal.
9.3 Signal Processing
Coherent, synthetic aperture processing (also referred to as "time-migration" processing in
the case of a static target environment) is intuitively motivated by the hyperbolic spread of a
single point target return when observed from multiple GPR radar positions. It is clear, however,
that integrating the signal returns over hyperbolic signal space sectors is neither optimum nor
efficient. A more general procedure uses matched-filter principles; an estimate is made of the
contribution of the return signal from position r' that minimizes the effects of receiver noise.
This is achieved by matching the signal with a weighting function that emphasizes the strongest
returns. Thus,
o(r') =
*l —
exp{-2a;rj
(9.15)
where r'„ represents the distance from the nth receiver to the point r'. The reconstruction
assumes knowledge of the frequency-dependent attenuation and phase velocity in the medium,
which must be estimated. It should also be noted that the reconstruction is performed in the
temporal frequency domain. Thus, for a pulsed system, the return from each pulse is
discrete-Fourier-transformed to generate the frequency samples atfj. For a swept-frequency
system, the reconstruction proceeds directly.
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The matched-filter operation implied by Eq. (9.5) is applied for each subsurface point
within a region below the antenna array. For display purposes, a subsurface image can be
formed by computing
/X) =1 ^(r')exP{2Y/r^}r,t |2. (9.16)
The renormalization compensates the weighting that was introduced to minimize noise
contamination in the reconstruction. Thus, a point source is reconstructed at the level it would be
observed by an overhead receiver. If one further compensates for the signal spreading loss and
the attenuation due to absorption, the noise level will increase with depth. For detection
purposes, it may be best to accept the same average signal variation that is inherent in the
unprocessed displays. Once the processing algorithms have been tested on real data, techniques
can be developed to reproduce a fully compensated image to the limits of detection for the
particular system.
9.4 Representative Examples
To illustrate the detection capability implied by various systems that could be exploited for
GPR leak detection applications, we use a 100-MHz system with a 66-MHz bandwidth. In the
simulations this is implemented with 66 discrete frequencies separated by 1 MHz; however, as
noted Section 6, this is mathematically equivalent to a 15-ns pulsed system with a free-space
unambiguous range of 150 m. That is, the bandwidth primarily establishes the ability of the
system to resolve targets in range. The effectiveness of the particular system for GPR is dictated
mainly by the quality factor, which is also the primary driver in the cost of the system.
To provide a demanding but realistic propagation environment, the soil model used 100%
saturation, 30% void fraction, and 0.003 mhos conductivity, which is representative of saturated
silt soil. To address the detection issue in its simplest form, two isolated point targets, one above
the other, were inserted at depths of 5 and 30 m. Both scatterers have an equivalent res of -70 dB
relative to one square meter. This scattering level is representative of the equivalent cross
section of typical leak scenarios as discussed in Section 7. The simulations used 80 receiver
locations separated by 0.2 m, which provides unambiguous angle resolution at the center
frequency of the pulse. The detected radar data are displayed as contours of constant
signal-plus-noise intensity, as described above. Matched filter processing is then applied over a
40-by-40 point grid covering a 15-m swath below the receivers to a depth of 35 m. To
accommodate the large dynamic range of these processed data, a perspective plot of the
reconstructed intensity is used.
77
-------
Figure 9.1 shows the signals that exceed the average noise level for a Q=140 dB system of
the type that is routinely used to detect shallowly buried pipes. No evidence of the targets can be
seen. The matched-filtered data are shown in Figure 9.2. The origin of the coordinate system is
at -35-m depth and 0-m horizontal displacement. Thus, the left-hand edge of the plot represents
the signal at the surface. The vertical axis extends from -50 to 20 dB. The processed data do not
recover either of the targets at Q=140 dB. Figure 9.3 shows the same plot as Figure 9.1 for a
Q=160 dB system. Here one begins to see the hyperbolic band that is associated with a point
scatterer. The processed data shown in Figure 9.4 clearly resolve the upper scatterer. In the
unprocessed data the target returns are less than 10 dB above the noise level, whereas the
processed data provide about 20 dB of signal-to-noise improvement. Even so, the lower target
cannot be detected. It should also be noted that the noise fields for the simulations are identical.
This is convenient in that Figures 9.1 and 9.2 can be used to identify purely noise-induced
features or false alarms.
As shown in Figure 9.5, increasing the quality factor to 180 dB does not reveal the lower
target; however, when the processed data shown in Figure 9.6 to Figure 9.2 are compared, the
lower target begins to emerge above the noise level. Figure 9.7 shows the detected returns from
a Q=190 dB system, which is just beginning to "see" targets at a depth of 35 m. The processed
data shown in Figure 9.8 clearly reveal the lower target. Figures 9.9 and 9.10 show the
corresponding simulations for a Q=220 dB system. Here both targets are easily detected in the
raw data. The processed data, moreover, are beginning to show the azimuthal sidelobe structure
of the matched filter. Because of the complexity of the propagation environment, the sidelobe
structure and, to a lesser extent, azimuthal resolution vary with depth. Even so, matched-filter
processing will resolve scatterers with 30 to 40 dB of suppression of the returns from adjacent
scatterers. This is illustrated in Figures 9.11 and 9.12, which show the effect of moving the
lower scatterer to within 5 m of the upper scatterer.
The resolving capability of matched-filter processing is crucial because a real ground
environment will contain a variety of imbedded discrete scatterers; moreover, as discussed in
Section 7, random variations in the properties of the soil itself are a potential source of
backscatter. To simulate this type of environment within the context of the soil contamination
models that have been developed for this study, the researchers generated a wedge-shaped region
containing a large number of randomly located scatterers with -30-dB cross sections. At the
apex of the cone, a single scatterer with a -20-dB cross section was included for reference.
Figure 9.13 shows the detected signal plot. One sees a broadened hyperbolic region, which
suggests a collection of local scatterers, but the details of the configuration cannot be inferred
78
-------
directly. The processed data shown with a slightly different perspective from the previous plots
in Figure 9.14 clearly reveal both the scatterer at the apex and the wedge-shaped extent of the
scatterers.
All the reconstructions presented here used perfect knowledge of the average propagation
characteristics, whereas this would have to be estimated as part of the reconstruction for real
data. Thus, considerable work needs to be done to develop a viable but efficient processor for
real data. If the radar has appropriate sensitivity, however, the method holds considerable
promise for GPR remediation of underground leak and soil contamination detection.
79
-------
Pulse GPR Q=140 dB T=1 sec
o.o
-5.0
-10.0
-15.0
0.
0> -20.0
Q
-25.0
-30.0 -
-35-°
CONTOURS
A: 1.0E+00
0.0
5.0 10.0
Ground distance — m
15.0
20.0
Figure 9.1. Unprocessed simulated returns for Q=140-dB GPR. Point targets are located at 10-m and 30-m depths.
80
-------
THETA: 70. PHI: 130.
X: O.OOE+00 2.00E+01 5.13E-01 Y: -3.50E+01 O.OOE+00 8.97E-01
Z: 1.00E-05 1.00E+01 1.00E+00
Figure 9.2. Processed returns for Q=140-dB GPR in perspective with 60-dB logarithmic display.
81
-------
Pulse GPR 0=160 dB T=1 sec
5.0
10.0
Ground distance — m
15.0
CONTOURS
A: 1.0E+00
B: 1.0E+01
20.0
Figure 9.3. Unprocessed simulated returns for Q=160-dB GPR. Point targets are located at 10-m and 30-m depths.
82
-------
THETA: 70.
X: O.OOE+00
Z: 1 .OOE-05
PHI: 130.
2.00E+01 5.13E-01
1.00E+02 1.00E+01
Y: -3.50E+01 O.OOE+00 8.97E-01
Figure 9.4. Processed returns for Q=180-dB GPR. Upper target is visible.
83
-------
Pulse GPR Q=180 dB T=1 sec
-35..
•o°o
10.0
Ground distance — m
15.0
CONTOURS
A: 1.0E+00
B: 1.0£+01
20.0
Figure 9.5. Unprocessed returns for Q=180-dB GPR. Point targets are located at 10-m and 30-m depths.
84
-------
THETA: 70.
X: O.OOE+00
Z: 1.00E-05
PHI: 130.
2.00E+01 5.13E-01
1 .OOE+04 1 .OOE+03
Y: -3.50E+01 O.OOE+00 8.97E-01
Figure 9.6. Processed returns for Q=180-dB GPR. Both targets are visible.
85
-------
Pulse GPR Q=190 dB T=1 sec
-35,
5.0 10.0
Ground distance — m
15.0
CONTOURS
A: 1.0E+00
B: 1.0E-I-01
20.0
Figure 9.7. Unprocessed returns for Q=190-dB GPR.
86
-------
THETA: 70.
X: O.OOE+00
Z: 1 .OOE-05
PHI: 130.
2.00E+01 5.13E-01
1 .OOE+05 1 .OOE+04-
Y: -3.50E+01 O.OOE+00 8.97E-01
Figure 9.8. Processed returns for Q=190-dB GPR.
87
-------
Pulse GPR Q=220 dB T=1 sec
o.o
-5.0
-10.0
-15.0
Q.
o> -20.0
Q
-25.0
-30.0
-35.C
'
5.0 10.0
Ground distance
CONTOURS
A: 1.0E+00
B: 1.0£-f01
C: 1.0E+02
15.0
20.0
m
Figure 9.9. Unprocessed returns for Q=220-dB GPR.
-------
THETA: 70.
X: O.OOE+00
Z: 1.00E-04
PHI: 130.
2.00E+01 5.13E-01
1.00E+08 1.00E+07
Y: -3.50E+01 O.OOE+00 8.97E-01
Figure 9.10. Processed returns for Q=220-dB GPR. Processing sidelobes are visible for target at 10 m.
89
-------
Pulse GPR Q=220 dB T=1 sec
-35.
5.0 10.0
Ground distance — m
15.0
CONTOURS
A: 1.0E+00
B: 1.0C401
C: 1.0E+02
0: 1.0E+03
20.0
Figure 9.11. Unprocessed returns for Q=220-dB GPR with two closely spaced targets at 10-m and 15-m depths.
90
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TVIETA; 70.
X: O.OOE+00
Z: 1 .OOE-04
PHI: 130.
2.00E+01 5.13E-01
1.00E+08 1.00E+07
Y: -3.50E+01 O.OOE+00 8.97E-01
Figure 9.12. Processed returns for Q=220-dB GPR with closely spaced targets.
91
-------
Pulse GPR Q=124.8 dB T=1 sec
-35,
5.0
10.0
Ground distance — m
15.0
CONTOURS
A: 1.0E+00
B: 1.06+01
C: 1.0E+02
0: 1.0E+03
20.0
Figure 9.13. Unprocessed returns for Q=220-dB GPR illuminating a wedge of randomly located scatterers.
92
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THETA: 75.
X: O.OOE+00
Z: 1 .OOE-04
PHI: 120.
2.00E+01 5.13E-01
1 .OOE+05 1 .OOE+04
Y: -3.50E+01 O.OOE+00 8.97E-01
Figure 9.14. Processed returns from Q=220-dB GPR illuminating wedge.
93
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REFERENCES
1. R. M. Koemer and A. E. Lord, Jr., "Spill Alert Device for Earth Dam Failure Warning,"
Project Summary, EPA-600/S2-84-007, U.S. EPA Municipal Environmental Research
Laboratory, Cincinnati, Ohio (February 1984).
2. A. E. Lord, Jr., and R. M. Koemer, "Nondestructive Testing (NDT) Techniques to
Detect Contained Subsurface Hazardous Waste," EPA-600/S2-87-078, U.S. EPA
Hazardous Waste Engineering Research Laboratory, Cincinnati, Ohio (February 1988).
3. R. M. Koerner and A. E. Lord, Jr., "Microwave System for Locating Faults in
Hazardous Materials Dikes," EPA/600/S2-85-014, U.S. EPA Hazardous Waste
Engineering Research Laboratory, Cincinnati, Ohio (July 1986).
4. G. R. Olhoeft, "Tutorial: High Frequency Electrical Properties," Proceedings of the 3rd
International Conference on Ground Penetrating Radar, Open-File Report 90-414, U.S.
Geological Survey, Lakewood, Colorado (May 1990).
5. Peter Ulriksen, Application of Impulse Radar to Civil Engineering, Doctoral Thesis,
LUTVDG/(TVTG-1001)/1-175/1982, Lund University of Technology, Lund, Sweden
(1982).
6. S. K. Duke, "Calibration of Ground Penetrating Radar and Calculation of Attenuation
and Dielectric Permittivity Versus Depth," Report No. T-3920, Master's Thesis,
Colorado School of Mines, Golden, Colorado (13 June 1990).
7. E. G. Walther, A. M. Pitchford and G. R. Olhoeft, "A Strategy for Detecting Subsurface
Organic Contaminants," Proceedings of the NWWA/API Conference on Petroleum
Hydrocarbons and Organic Chemicals in Ground Water, Houston, Texas, National
Water Well Association (12-14 November 1986).
8. M. E. Tabak, W. Glynn and R. P. Traver, "Evaluation of EPA Soil Washing Technology
for Remediation at UST Sites," Camp Dresser & McKee, Inc. (no date).
9. Synthetic Soil Matrix (SSM-SARM) User's Manual, U.S. EPA Risk Reduction
Engineering Laboratory, Edison, New Jersey (December 1988).
10. M. I. Skolnik, ed., Radar Handbook, 2nd ed., McGraw-Hill Publishing Company, New
York, New York (1990).
11. D. V. Smith, "Propagation of Ground Penetrating Radar Signals in Soils," 2nd
International Symposium on Geotechnical Applications of Ground-Penetrating Radar,
University of Florida, Gainesville, Florida (10 March 1988).
12. W. M. Brown and L. J. Porcello, "An Introduction to Synthetic Aperture Radar," IEEE
Spectrum (September 1969).
13. R. C. Kemerait and J. N. Griffin, "Synthetic Pulse Radar," Proceeding of the 3rd
Technical Symposium on Tunnel Detection, Colorado School of Mines, Golden,
Colorado (12-15 January 1988).
14. R. M. Morey and W. S. Harrington, Jr., "Feasibility Study of Electromagnetic
Subsurface Profiling," Report No. EPA-R2-72-082, Office of Research and Monitoring,
U. S. Environmental Protection Agency, Washington, D.C. (October 1972).
94
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15. R. C. Weast, ed., CRC Handbook of Chemistry and Physics, 52nd ed., The Chemical
Rubber Co., Cleveland, Ohio (1972).
16. Darold Wobschall, "A Theory of the Complex Dielectric Permittivity of Soil Containing
Water: The Semidisperse Model," IEEE Trans, on Geosci. Elec., Vol. GE-15, No. 1
(January 1977).
17. G. R. Olhoeft, "Direct Detection of Hydrocarbon and Organic Chemicals with
Ground-Penetrating Radar and Complex Resistivity," Proceedings of the National Water
Well Association Conference on Petroleum Hydrocarbons and Organic Chemicals in
Ground Water, Houston, Texas (November 12-14, 1986).
18. CDM Report under Work Assignment 3-30 on the Variability of Soils at Superfund
Sites, Memo from Michael Borst, U.S. EPA, Soil and Material Engineering Section,
RGB Superfund Technology Demonstration Division, to Carolyn K. Offutt, U.S. EPA,
Special Projects Support Staff, Hazardous Site Control Division (28 February 1991).
19. P. Esposito, "Characterization of RCRA/CERCLA Sites with Contaminated Soil,"
Bruch, Hartman & Esposito, Inc., Cincinnati, Ohio, prepared for the EPA on Extractive
Treatment of Excavated Soil, Edison, New Jersey (1-2 December 1988).
95
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Appendix A
REAL SIGNALS, ANALYTIC SIGNALS, AND COMPLEX ENVELOPES
The Hilbert transform relates a real signal, x(t), to a complex "analytic" signal,
where
is the Hilbert transform of x(t) (0
X(f) f=0
^0
and
The analytic signal is also related to the quadrature and complex-envelope representations
of the real signal. In the former case, the real signal is written in terms of amplitude and phase
modulations:
= p (t) cos 2nf0t -q(t)sin 2itf0t .
a(t) is the real amplitude-modulation envelope of the signal. The quadrature components are
and
Next, the complex signal representation of the real signal is s(t), where
where 91 denotes the real part and
A-l
-------
u(t) is the complex envelope, which in turn is related to the quadrature components
according to:
The analytic signal can also be written in the "modulation/carrier" form:
sH(t) = uH(r)
For "narrow-band" signals,
A-2
-------
Appendix B
CALCULATIONS OF DIELECTRIC CONSTANT, CONDUCTIVITY,
AND ATTENUATION COEFFICIENT FOR VARIOUS SOILS
AND A PETROLEUM CONTAMINANT
soil, void Iraclion -05, water conductivity -003
100
frequency - Mhz
soil, void fraction -05, water conductivity - 0 03
100
frequency - Mhz
soil, vo«j fraction - 0 5. water conductivity - 0 03
100
frequency - Mhz
B-l
-------
soil, void fraction - 0 5. gas conductivity - 0 0
,.
-
1
LF-60*
t
frequency • Mhz
soil, void fraction -05. gas conductivity - 00
(S/m|
frequency - Mhz
soil, void fraction -05: gas conductivity - 0 0
a. 01 -
(dB/m|
_)_
//
1 ///
kl
1
— J—
|
10 100 10(
frequency - Mhz
B-2
-------
clay void fraction - 0 5, waier conductivity - 0 03
clay, void fraction -05; water conductivity - 0 03
100
frequency • Mhz
clay, void fraction -05; water conductivity - 0 03
(dB/m
100
frequency - Mhz
B-3
-------
clay, void fraction -05. gas conductivity « 00
0
!_._.
._!
tie-
qu«
1
nc
0
•y - Mhz
LF * 0%
LF - SCW
LF - 100-
.
'«
1
10
clay, vox) fraction - 0 5, gas conductivty «• 0 0
100
(requency - Mhz
clay, void fraction * 0 5; gas conductivity - 0 0
100
frequency - Mhz
B-4
-------
Appendix C
MODIFIED BOOKER-GORDON SCATTERING FORMULA
The Booker-Gordon formula is based on the Bom approximation, whereby the total
electric field in the medium is replaced by the incident field. In general, the backscatter cross
section is given by
afe = 47c|/(6,-6)|2,
where
• - k2 C -
/(o,-o) = -n (-6 x (6 x £(?'))} {Er(r')~
4 Jv
o is a unit vector to the receiving (and transmitting) point, k is the wave vector in the medium,
and £(r') is the total electric field in the medium. Under the Born approximation, the total field
is replaced by the (unit strength) incident field,
where I = -o is a unit vector in the incident propagation direction for backscatter. This leads to
the expression where the res is proportional to
<(er-l)2> = .
Now, because the characteristic dimensions (correlation length, grain size, etc.) of the soil
medium are taken to be small compared to the wavelength and isotropy is assumed, this suggests
using the Rayleigh approximation in place of the Born approximation. The Rayleigh
approximation is based on electrostatics, where the field inside a homogeneous sphere is known
to be uniform and given by
If this is used in place of the Born approximation, the factor < Ae^ > is replaced by
l) 3Ae,
For small values of Aer, this reduces to the Born approximation. Note that this formulation
applies equally well for complex e,. (i.e., lossy objects).
C-l
-------
Appendix D
CORRELATION FUNCTION FOR SOIL VARIABILITY MODEL
Let y be a random variable which can have two values, y, and y2, as described in the text.
The autocorrelation of a function/(y) is
Bfrj) = J J /(y,)/(y2)p(y,)p(y2| y];rj)dyldy2.
According to the Poisson probability law, the probability of having n shifts in a distance rd is
^ n\
Because y must shift between its two values, the conditional probability is
P(y2\ Virt = ^(0)5(y2 - y,) +/», (I)6(y2 + y,) +P. (2)6(y2 - y,) +.
= 5(y2 - y,) I P (n) + 5(v2 + y,) I /» (n).
nevett nodd
Thus
£ ^)^
«o^ J
2! 4! "- 3! 5!
In particular, if/(y) = y - < y >,
B =^~2^
D-l
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO
EPA/600/R-92/089
3. RECIPIENT'S ACCESSIOf*NO.
PB92-169 382
4. TITLE AND SUBTITLE
A Study to Determine the Feasibility of Using a
Ground-Penetrating Radar for More Effective Remediation
of Subsurface Contamination
5. REPORT DATE
May 1992
6. PERFORMING ORGANIZATION CODE
AUTHORIS) "
D.C. Douglas, A.A. Burns, C.L. Rino, J.W. Maresca, Jr.
Vista Research, Mountain View, CA 94042
8. PERFORMING ORGANIZATION REPORT NO.
PERFORMING ORGANIZATION NAME AND ADDRESS
Foster Wheeler Enviresponse, Inc.
Building 209, Bay F
Woodbridge Avenue
Edsion, New Jersey 08837
10. PROGRAM ELEMENT NO.
FRSV1A
11. CONTRACT/GRANT NO.
68-C9-0033
2. SPONSORING AGENCY NAME AND ADDRESS
Risk Reduction Engineering Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
Project Report/Project Summary
14. SPONSORING AGENCY CODE
EPA/600/14
15. SUPPLEMENTARY NOTES
Project Officer: James J. Yezzi, Jr.
Comm: (908) 321-6703
16. ABSTRACT
Remediation of hazardous material spills is often costly and entails cumbersome
procedures. The traditional method is to drill core samples in the area where the con-
taminant is thought to be present and then analyze these samples in a laboratory. The
denser the sampling grid, the more effective it is; unfortunately, it is also more
expensive to implement and more damaging to the environment. A nonintrusive method for
detecting subsurface contamination, therefore, would be highly desirable. Toward this
end, the capability of ground-penetrating radar (GPR) to identify natural subsurface
features, detect man-made objects buried in the soil, and both detect and define the
extent of contaminated soil or groundwater was assessed.
The study concluded that the technology for the envisioned GPR already exists. In
terms of hardware, it was found that a synthetic-pulse radar has the potential to operate
effectively in the three types of subsurface environments modeled in this study, environ-
ments representative of seven out of ten "common cases" found at remediation sites. In
terms of signal processing, it was found that synthetic-aperture-radar (SAR) processing
is preferable because better horizontal resolution can be achieved; the system can
operate at lower frequencies and thus can achieve deeper penetration; and most importantly
ambient noise is reduced. The study found that a high-performance radar, when combined
with SAR processing, match-filtering, and one of several detection strategies, can detect
even a thin layer of contaminant floating on the water table, and can distinguish the
acoustic returns from contaminant-saturated soil as opposed to those from water-saturated
soil. Simple proof-of-principle experiments were recommended to validate the models
developed in this study.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
synthetic aperture radar
subsurface investigation method
ground penetrating radar
mapping subsurface contamination
non-intrusive subsurface investigation
detecting subsurface contamination
electromagnetic subsufrace investigation
IB. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS {This Report/
Unclassified
21. NO. OF PAGES
115
20. SECURITY CLASS (Thupage>
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
D-2
*U.S COVIRNMENT PRINTING OFFICE- 1992-6te-00^16'4i
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