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GPR FOR FAST PAVEMENT ASSESSMENT
May 2007
JHR 07-310 Project 00-2
Lanbo Liu
This research was sponsored by the Joint Highway Research Advisory Council (JHRAC) of the University of Connecticut and the Connecticut Department of Transportation and was carried out through the Connecticut Transportation Institute of the University of Connecticut. The contents of this report reflect the views of the authors who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the University of Connecticut or the Connecticut Department of Transportation. This report does not constitute a standard, specification, or regulation.
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1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No.
JHR 07-310 N/A 4. Title and Subtitle 5. Report Date
May 2007 6. Performing Organization Code
GPR for Fast Pavement Assessment
N/A 7. Author(s) 8. Performing Organization Report No.
Lanbo Liu JHR 07-310 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)
N/A 11. Contract or Grant No.
University of Connecticut Connecticut Transportation Institute Storrs, CT 06269-5202 N/A 12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered
FINAL 14. Sponsoring Agency Code
Connecticut Department of Transportation 280 West Street Rocky Hill, CT 06067-0207
N/A 15. Supplementary Notes
This study was conducted under the Connecticut Cooperative Highway Research Program (http://www.cti.uconn.edu/crp_home.html). 16. Abstract
This report summarizes the findings of Project JHRAC 00-2 for studying the fast assessment of road pavement with the ground penetrating radar (GPR). The report contains four parts. The first two on actual GPR data acquisition and analysis: one on laboratory measurements and one on field surveys. The last two parts examine the GPR signal forward modeling and signal data processing. We conducted laboratory tests of engineered materials using the RAMAC radar system with the 1-GHz antenna. The experiments used geotechnical fundamental measurements as the known parameters and correlated with the electromagnetic (EM) parameters obtained by GPR measurements. The fundamental parameters include thickness, density, aggregate material ratio, and air void ratio, etc. The GPR experiments test the materials to get the dielectric constant that directly determines EM wave velocity. Asphalt tests have been conducted on 30 asphalt specimens. The asphalt specimens produced at the Connecticut Advanced Pavement Laboratory have a dimension of 15 cm in diameter with 11.5 cm in height. Serving as the strong reflector to mark the travel time, an aluminum plate is placed underneath the specimen, to allow an easier identification of the time travel to and reflected back from the plate. The calculated EM wave velocity is about 131 m/microsecond for most dry asphalt specimens. The corresponding dielectric constant is ranging from 4 to 5. We have also tested the response of the asphalt specimens in different ambient states (dry, saturated with water, and frozen). GPR data using the 1-GHz antenna were collected several times on a then-newly paved road segment on the Depot Campus of the University of Connecticut (UConn) under different meteorological conditions. The GPR data clearly showed signature changes of the asphalt response between dry and water-saturated conditions. The radar wave velocity reduced about 5% when the asphalt was water-saturated (after heavy rain, collected in the morning of September 20, 2000). This change makes a relative clearer identification. Meanwhile, the reflectivity increased 60%, making the reflection from the bottom of the base of the asphalt layer much more visible. To theoretically understand the effect of a thin dielectric layer (such as the hot mixed asphalt pavement) on radar signal propagation, a finite difference time domain (FDTD) forward modeling algorithm was developed. The simulation clearly demonstrated the wave guide effect of this surface thin layer. This simulation can be used as guidance for developing multi-channel GPR systems. To improve the resolution and preserve the penetration, if high-and low-frequency surveys are conducted simultaneously over the same road segment, it is possible to extrapolate the high frequency signal to a deeper depth numerically through a digital signal processing algorithm known as extrapolation with deterministic deconvolution (EDD) and consequently gain a higher resolution to a greater depth.
17. Key Words 18. Distribution Statement
ground penetrating radar (GPR), non-destructive testing, pavement assessment, GPR antenna, surface coupling antenna, horn antenna, dielectric permittivity, electromagnetic wave velocity, finite difference time domain method, wave guide
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Acknowledgments
This work is sponsored by Connecticut Department of Transportation under Project JHRAC
00-2, “GPR for Fast Pavement Assessment: Experimental Tests.” The GPR equipment used in
acquiring the laboratory and field data was partly funded by the National Science Foundation
(NSF). The PI thanks Prof. Jack Stephens and Mr. James Mahoney for their assistance in
conducting the laboratory experiments, and Prof. Gregory Frantz for helping with sample
preparation.
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Table of Contents
Title Page i
Technical Report Documentation Page ii
Acknowledgments iii
Modern Metric Conversion Factors iv
Table of Contents v
1. Introduction 1
2. GPR laboratory tests of asphalt specimens in three states 2
2.1 Introduction 3
2.2 Laboratory measurements 4
2.3 Calculations of EM wave velocity and dielectric constant 7
2.4 Results discussion 10
2.5 Conclusions 15
3. GPR surveys on paved road for moisture content assessment 17
3.1 Introduction 17
3.2 Practical limitations on radar wave velocity measurements 18
3.3 Field measurements 19
3.4 Results discussion 21
3.5 Conclusions 22
4. Numerical modeling of GPR surveys over dielectric thin layers 23
4.1 Introduction 23
4.2 Summary of major features of guided wave propagation 25
4.3 GPR wide-offset field observations 29
4.4. Numerical simulations of TE and TM modes for field GPR data 30
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4.5 Results discussion 31
4.6 Conclusions 36
5. Mathematical treatment to improve the resolution and penetration 37
5.1 Introduction 37
5.2 Extrapolation by deterministic deconvolution 39
5.3 Applications to synthetic data 42
5.4 Applications to field GPR data 49
5.5 Conclusions 53
6. Conclusions and future work 54
6.1 A general summary 54
6.2 Future work 54
Disclaimer 55
References 56
Appendix: A list of publications on GPR authored by the PI and his research group 68
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1. Introduction
A fast, economical, and accurate means of assessment of road pavement conditions, at both
the network and project levels, is of great significance to highway management and
maintenance. The emerging ground penetrating radar (GPR) technology has a natural application
as a supplementary device for other road survey techniques such as the road video and infrared
surveys. GPR can be used to identify valuable parameters that cannot be obtained from a visual
evaluation of the road surface. These parameters include pavement-layer thickness and,
potentially, damaged, or deteriorated subsurface areas. Moreover, it would be possible to obtain
an more accurate characterization of the pavement structure by combining the data provided by
such a non-destructive testing (NDT) system with that supplied by destructive testing (coring
and sampling). Over the last decade, these potential benefits have prompted transportation
agencies and private industry in North America, Europe, and some developing countries, to start
incorporating GPR technology into pavement-assessment engineering practice. However, the
most challenging aspects for using GPR are, inevitably, the precise identification of subsurface
targets and the fast reduction of a huge amount of data into a form that is readily interpretable to
highway engineers.
To solve these problems, automatic acquisition and interpretation of GPR data for pavement
assessment has recently attracted tremendous attention and research efforts. As a preparation
phase for future research on the application of GPR techniques for pavement and bridge
assessment, the Principal Investigator (PI) of this project conducted a feasibility investigation on
state-of-the-art use of ground penetrating radar to rapid pavement assessment (Liu, 1998).
This report summarizes the major research results conducted by Project JHRAC 00-2 in 6
chapters. As an overall introduction, this chapter lays out the structure of the report. Chapter 2
reports the results on GPR laboratory testing results conducted in the Connecticut Advanced
Pavement Laboratory (CAP Lab). Chapter 3 summarizes the major findings of GPR field tests
over a low traffic volume road over a long period of time under different meteorological
conditions. Chapter 4 reports a piece of theoretical work on numerical simulation of the GPR
response to a surface thin layer of dielectric materials. Chapter 5 presents a digital processing
algorithm to improve the resolution of GPR signals and preserve the penetration depth. Finally,
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Chapter 6 provides an overall summarization and makes recommendations for using GPR as an
engineering tool for pavement assessment in the future.
2. GPR laboratory tests of asphalt specimens in three states
There are two major purposes for using ground penetrating radar (GPR) field survey in
pavement assessment. The first is for determining the thickness of the asphalt pavement; and the
second is for detecting subsurface deterioration. Determination of thickness needs to know the
velocity of radar waves, and deterioration between layers involves reflectivity of radar wave at the
interfaces. Both velocity and reflectivity are determined by the dielectric constant of the asphalt
pavement. This section of the report discusses the dielectric constant determination of asphalt
specimens in laboratory-controlled conditions. The experiment results may provide certain degree
of constraints for interpreting GPR field data for seeking thickness variation and subsurface
deterioration.
A series of laboratory experiments was conducted to determine the dielectric constant of hot
mix asphalt (HMA) pavement specimens in dry, water-saturated, and frozen states. We used the
RAMAC GPR system with the 1-GHz ground coupled antenna to measure the travel times for the
direct and reflected waves to calculate the radar wave velocity and dielectric constants of 30
specimens. Our major conclusions are: (1) In general, radar wave travels fastest in the asphalt
specimens under dry condition and slowest in water-saturated condition. When the water-saturated
specimens are frozen, radar wave velocity increases again to some degree, but slower than that in
dry condition; (2) Radar wave velocity increases slightly with the increase of void ratio for dry
samples. In contrast, it decreases significantly through water-saturated samples as their void content
increased. Correspondingly, the dielectric constant decreases noticeably with an increasing void
ratio in dry conditions, and increases appreciably in saturated conditions, in the range of void ratio
from 0.57% to 6%; (3) The changes of EM velocity and resulting dielectric constant for dry,
saturated, and frozen conditions can be reasonably predicted by the complex refractive index model
(CRIM) for porous media; (4) Variations in EM velocity and resulting dielectric constant with
respect to asphalt binder content implies that a lower value in asphalt binder content corresponds
with a higher void ratio; and (5) For a particular HMA specimen with a given void ratio, the
observed variations in EM velocity and resulting dielectric constant can be attributed to the changes
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in moisture content under different physical states.
2.1. Introduction
One of the most important factors affecting the life span and deformation of the HMA
pavements is the void content expressed by the void ratio (Saarenketo, 1997). Void ratio denotes
the volumetric fraction of void (or pore) space relative to aggregate and asphalt binder of a
pavement. The void ratio is important because void space could be filled with air, water, ice, or any
fractional combination of these three depending on the temperature environment. Each of these
three void materials has different mechanical properties which may influence the HMA’s overall
strength, durability, and stability. For example, the presence of water in void space can significantly
change the shear modulus of an HMA pavement. In contrast, the presence of ice in the voids will
effectively change an HMA’s bulk modulus. Moreover, freeze-thaw processes lower the tensile
strength of an HMA pavement and facilitate tensile failure (cracks). Clearly, the amount of
moisture penetrating into an HMA pavement, whether from above or below, depends on the
HMA’s void ratio and connectivity, and can have detrimental effects on the durability of that
pavement. In the last decade, ground-penetrating radar (GPR) has emerged as one of the most
widely used non-destructive testing tools in assessing HMA pavements (Saarenketo, 1992; al-Qadi,
1992; Davis et al., 1994; Maser, 1996; Liu, 1998; Saarenketo and Scullion, 2000).
A rapid and reliable estimation of the void ratio of an HMA pavement is necessary to
understand the role of moisture content in HMA durability and stability. Conventionally, HMA
void ratio and moisture content have been assessed by direct excavation or drill sampling, or by
radioactive methods (Saarenketo, 1997), which are costly and invasive. In this context, if a robust
relationship between radar wave velocity, void ratio and moisture content can be established; non-
destructive testing using GPR can be an efficient complementary tool for HMA pavement
assessment.
GPR has been used in the field to determine subsurface soil moisture content below highway
pavement (Topp et al., 1980; Greaves et al., 1996; Berktold et al., 1998; al Hagrey and Muller,
2000; Charlton, 2000; Redman et al., 2002). In laboratory experiments, Saarenketo (1998) reported
the effects of water in determining the dielectric permittivity of clay and silty soils. Saarenketo and
Scullion (2000) reported the relationship between void content and dielectric constant for dry HMA
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samples. Their studies resulted in the development of vehicles that can be used to assess pavement
properties of a newly placed mat by combining some GPR with infrared sensing technology with
the calibration from coring. Shang and Umana (1999) studied the dielectric constant and relaxation
time of asphalt pavement materials. In this paper, we are reporting the laboratory results of GPR on
prepared HMA specimens in three distinctive states (dry, water-saturated and frozen).
Using a radar system with 1-GHz antenna we tested HMA pavement materials in the CAP Lab
at the University of Connecticut. The experiments correlated the dielectric constant obtained by
GPR measurement with aggregate material composition, and void ratio of HMA specimens under
dry, water-saturated, and frozen states. Our objectives were to (1) determine the dielectric
properties of the asphalt specimens; (2) correlate the dielectric constants with void ratio and asphalt
binder content ratio; and (3) elucidate the evolution of the dielectric constant with respect to
simulated environmental states (dry, saturated and frozen).. These results can be used as a baseline
for GPR field surveys over road pavements in real world conditions, as well as for quality control
of pavement compaction assessment using radioactive methods.
2.2. Laboratory measurements
We tested 30 HMA specimens in dry, water-saturated, and frozen conditions. These cylindrical
asphalt specimens were produced at the CAP Lab using the applicable AASHTO standard at the
time TP4 for the fabrication of Superpave gyratory specimens. They are 15 cm in diameter, about
11.3 cm in height, and are composed of the same aggregate source materials. The GPR antenna was
set on top of a specimen, which, in turn, was set on a metal (aluminum) plate to gain total reflection
(Figure 2.1). The use of a metal plate facilitates an easy identification of the reflected waves by
providing perfect reflectivity.
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HMA
air waveT R
H
air
metal plate
ground wave
reflectedwave
D
Figure 2.1. This figure depicts the EM wave's general paths as it travels through the specimen. Idealized near-surface, near-field propagation paths along the interface of the air and an HMA pavement layer (or HMA specimen) with a thickness of H. T: the location of the transmitter; R: the location of the receiver. The separation of T and R is D. The air wave travels from T to R above the surface at the fastest velocity c0 (speed of light). The ground wave travels from T to R below the surface at a velocity of c0/√εr. where εr is the dielectric constant of the HMA. The reflected wave has a longer ray path: it hits the HMA-base (here a metal-plate) interface, and then is reflected to the receiver.
The experimental setup for testing the specimens in saturated condition is shown in Figure 2.2.
Figure 2.2. GPR measurement setup for a test on the water-saturated HMA specimen using the 1-GHz antenna in the CAP Lab, University of Connecticut.
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The asphalt binder grade (nomenclature for the binder grade is PG 64-28) used for producing
these specimens is identical for all samples. The asphalt binder content (AC %) in any one
specimen is given in terms of weight percentage. The samples consist of a range of proportions of
aggregates to form a void ratio that varies from 0.57% to 6.0%. The parameters of these 30
specimens are listed in Table 2.1.
The EM wave velocity of these newly produced HMA specimens were first tested in dry state.
Each specimen was then submerged into tap water in a sealed container and vacuum pumped, such
as is done for the Gmm (the max theoretical density of HMA test) to extract the air for 10 minutes to
reach water saturation. The samples were then submerged in a water tank to hold water-saturated
status until testing. These saturated specimens were measured with the 1-GHz GPR again to get the
water-saturated velocity. After this, the specimens were immediately refrigerated with a constant
temperature of –18 ºC for 20 hours to reach a frozen state. (Specifications for classic pavement
freezing-thawing experiments request the specimen to be frozen no less than 18 hours in one
freezing-thawing cycle). Finally, the frozen specimen was tested by the same procedure as was
done in dry conditions to get the EM velocity in frozen states. All tests were conducted at room
temperature in a time period as short as possible to prevent pore water dripping or thawing. For one
specimen under a given state, 10 GPR measurements were taken. The average of the 10
measurements on the reflected wave travel time was used to calculate the EM wave velocity for
that state.
Table 2.1 Basic parameters of the HMA specimens used in GPR laboratory experiments
Specimen Label
Height (cm)
Volume (cm3)
Dry Weight
(g)
Surface wet Weight
(g)
Submerged Weight (g)
10-min. vacuum
Weight (g)
Gmm (g/cm3)
AC (%)
Void Ratio (%)
A 11.31 1998.647 5062.8 5064.8 3095.8 5070.7 2.589 6.4 0.72 B 11.27 1991.578 5062.2 5066.4 3098.2 5067.2 2.589 6.4 0.57 C 11.25 1988.044 5054.1 5055.5 3092.2 5059.6 2.589 6.4 0.59 D 11.31 1998.647 5066.9 5070.6 3102.3 5082.6 2.626 5.4 2.02 E 11.26 1989.811 5008.9 5015.4 3055.3 5039.8 2.609 5.9 2.05 F 11.33 2002.181 5045.1 5051.7 3086.5 5063.4 2.609 5.9 1.57 G 11.41 2016.318 5053.8 5058.2 3093.1 5065.3 2.609 5.9 1.43 H 11.32 2000.414 5023.7 5029.9 3066.1 5063.3 2.626 5.4 2.63 I 11.36 2007.482 5062.5 5068.2 3086.6 5104.4 2.626 5.4 2.63
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J 11.43 2019.852 5046.0 5054.5 3059.0 5116.0 2.626 5.4 3.79 K 11.51 2033.99 5036.8 5046.5 3079.7 5112.8 2.626 5.4 4.06 L 11.38 2011.017 5050.1 5062.7 3079.3 5105.7 2.626 5.4 2.92 M 11.35 2005.715 5058.7 5062.0 3093.6 5077.1 2.609 5.9 1.56 N 11.31 1998.647 5046.7 5050.8 3078.5 5077.1 2.609 5.9 1.85 O 11.36 2007.482 5073.7 5075.3 3097.8 5083.3 2.589 6.4 0.96 P 11.33 2002.181 5082.7 5084.4 3105.2 5089.6 2.589 6.4 0.85 Q 11.35 2005.715 5085.6 5087.0 3104.6 5093.3 2.589 6.4 0.94 R 11.11 1963.304 5010.9 5015.9 3092.0 5035.3 2.665 4.8 2.30 S 11.18 1975.674 5066.6 5055.4 3134.1 5078.7 2.665 4.8 1.87 T 11.07 1956.235 4997.2 5001.9 3085.4 5008.2 2.638 5.3 1.16 U 11.30 1996.88 5023.6 5039.7 3088.0 5068.3 2.661 4.6 2.92 V 11.24 1986.277 5023.4 5039.7 3088.0 5068.3 2.661 4.6 2.35 X 11.48 2028.688 4987.2 5000.2 3060.1 5099.5 2.71 4.0 6.00 Y 11.32 2000.414 5000.2 5005.7 3064.1 5067.7 2.71 4.0 5.50 Z 11.52 2035.757 5019.2 5044.2 3072.2 5109.2 2.71 4.0 5.78
AA 11.30 1996.88 5041.2 5044.3 3052.6 5052.1 2.637 5.5 1.18 AB 11.42 2018.085 5129.8 5135.6 3160.7 5154.0 2.637 5.5 1.54 AC 11.26 1989.811 5029.9 5039.5 3072.8 5061.7 2.637 5.5 1.46 AD 11.20 1979.208 5000.3 5005.6 3079.1 5030.2 2.645 5.1 1.89 AE 11.19 1977.441 5056.7 5061.0 3048.2 5073.4 2.645 5.1 1.35
* mmG is the maximum theoretical specific gravity.
2.3. Calculations of EM wave velocity and dielectric constant
We make three justifiable assumptions about the electromagnetic parameters of an HMA to
simplify the EM velocity calculation. The first is that velocity does not depend on the magnetic
permeability because the asphalt binder and most crushed stones used for making pavement
aggregates are essentially non-magnetic. Second, most of the minerals composing the aggregates,
such as quartz, mica, and feldspar, are good insulators. The asphalt binder can also be regarded as
insulation material. Since the void ratio of an HMA is small, even when the voids are fully
saturated with fresh water, the conductivity is still very small. This fact warrants us the third
assumption, that the imaginary part of the dielectric permittivity can be considered negligible.
Therefore, EM wave velocity only depends on the real part of the dielectric permittivity.
The electromagnetic (EM) velocity v can be measured in a number of ways. The easiest way is
to measure the time difference between the direct air wave traveling in air and the ground wave
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traveling in the HMA (Figure 2.1). Unfortunately, for a near-offset (the separation distance between
the transmitter and the receiver is very short) survey, the arrival time difference is very small and
hard to measure accurately. Another way is the reflection method, in which the travel time
difference for the direct and reflected waves is the fundamental information for computing EM
wave velocity. As shown in Figure 2.1, the thickness of an HMA is comparable to GPR transmitter-
receiver separation. Taking this into account v was calculated by:
20
22
)(4
ttHDv
Δ++
=, (2.1)
where D is the separation between the transmitter and receiver; H is the thickness of the specimen;
t0 is the direct air wave travel time to the receiver, and �t is the time difference between the reflected
wave from the underlying metal plate and the direct air wave. All parameters on the right-hand side
of Eq. (2.1) are measurable in terms of either geometry or time. For example, the transmitter-
receiver separation is 0.1 m for the 1-GHz ground-coupled antenna of RAMAC/GPR manufactured
by MALA Geoscience, Inc., which was used in this study. The reason for choosing the ground-
coupled antenna is due to its smaller foot-print than the air-coupled horn antenna that is more
suitable for measuring the asphalt specimens with a diameter of 15 cm. The air-coupled horn
antenna has the advantage of rapid data acquisition that we do not need in this project for
measuring asphalt specimens in lab, but its larger foot print is definitely a disadvantage for
measuring small-sized asphalt specimens.
As argued before, due to the justified simplification, the velocity depends only on the real
part of the relative dielectric permittivity (the dielectric constant) through
2
222
vcorcv o
rr
o == εε ,
(2.2)
where �r is the dielectric constant; and co is the electromagnetic wave velocity in vacuum.
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Figure 2.3. An example of raw waveform of GPR surveys over a dry asphalt specimen which was placed on an aluminum plate. The arrow with letter D indicates the arrival of the direct wave, while the arrow with letter R indicates the arrival of the reflected wave from the aluminum plate. The wave trains in the later times are multiple reflections irrelevant to travel time estimation.
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Figure 2.4. Variations of EM wave velocity (a) and the dielectric constant (b) as a function of the void ratio obtained from GPR measurements of 30 HMA specimens for dry (Vd and Ed, with blue symbols and lines), water-saturated (Vw and Ew, with magenta symbols and lines), and frozen (Vz and Ez, with yellow symbols and lines) conditions.
EM wave velocity and the dielectric constant were calculated by this approach for all of the 30
pavement specimens. A typical time domain radar record is shown in Figure 2.3. The results of EM
velocity and the inferred dielectric constant as functions of the void ratio are shown in Figure 2.4
and discussed in detail in the next section.
2.4. Results discussion
To the first order, the results (Figure 2.4) clearly show that the zero-void velocity is about
130 m/�s and the zero-void dielectric constant is about 5.3. It implies that the HMA specimens
are good dielectric materials and quite transparent in an electromagnetic sense. When the void
ratio becomes larger, the EM velocity spreads out among dry, water-saturated, and frozen
conditions up to a value of 13% of the reference velocity (130 m/�s) when the void ratio is 6%.
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The corresponding changes in the dielectric constant reach as large as 25%.
The CRIM model
For analyzing the EM velocity in a porous medium like an HMA, a good approximation for a
hybrid material model is a solid skeleton containing void space, with the void filled with two
kinds of fluid. A dielectric model formulation commonly used is the complex refraction index
model (CRIM) (e.g., Robert, 1998; al Hagrey and Muller, 2000):
agwb nSnSnn )1()1( −+−+= φφφ , (2.3)
where n=√�r is the refractive index, and sub-indices b, w, g, and a represent bulk, water,
aggregate, and air, respectively. Also, ��is the porosity, and S is the water saturation. The
porosity ���is related to the void ratio e through
ee+
=1
φ . (2.4)
In the low porosity regime (less than 7%), the porosity and void ratio are not significantly
distinguished from each other. We applied the CRIM model to analyze the observed velocity and
dielectric constant by using the following parameters. Because the dielectric constant is about
5.5-6.5 for aggregates and 2.6-2.8 for asphalt binder (Saarenketo, 1997), and the asphalt content
(AC%) is only about 5% of the total weight of a specimen, the effective dielectric constant of 5.3
was used for the solid matrix (aggregates bonded by asphalt binder). The dielectric constant is 81
for fresh water, 3.17 for fresh water ice (Arcone, 1984), and 1 for air. Replacing na by ni, the
refractive index of ice, Eq. (2.3) was used again to compute the bulk dielectric constant for voids
filled with ice-water mix. Using these values, the modeling results for the case of air-water mix
filling the void space are shown in Figure 2.5. The modeling results for the case of ice-water
mix filling the voids are shown in Figure 2.6.
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1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) (b)
Porosity (%)Porosity (%)
Velo
city
(m/μ
s)
Die
lect
ricC
onst
ant
Figure 2.5. Prediction of EM wave velocity (a) and dielectric constant (b) variations as a function of porosity for water saturation changes from 0 to 1 by the CRIM model. The value of 0.80 best fits the observed results (Figure 2.4); it implies that the water-saturation reached about 80% after 10-min air-stripping pumping.
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
(a) (b)Porosity (%)Porosity (%)
Velo
city
(m/μ
s)
Die
lect
ricC
onst
ant
Figure 2.6. The CRIM predicted EM wave velocity (a) and dielectric constant (b) as a function of porosity for the ice-water mix case. In this case, the void space is filled with only ice and water, no air. Water saturation changes from 0 to 1 correspond to 100% frozen to unfrozen. The curve of water saturation of 0.2 best fits the observed results in frozen conditions (Figure 2.4); it implies that 20% of the pore water is still unfrozen after 20-hours freezing in a refrigerator.
The CRIM model appears to sufficiently interpret the observed results for the dry and water-
saturated conditions. When the void ratio increases, the velocity increases slightly for dry
conditions and decreases significantly for water-saturated conditions. This is simply due to the
fact that a larger fraction of air filling the voids leads to higher velocity, and a larger fraction of
pore water leads to lower velocity. The curve of S=0.8 may best fit the observed results for
water-saturated conditions. This implies that the pores of the HMA specimens were 80%
saturated by water, and 20% filled with air (Figure 2.5). This indicates that the 10 minutes of air-
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stripping pumping in the vacuum process we used to prepare saturated samples were not long
enough to reach ideal 100% saturation. In frozen conditions, the CRIM model also predicts that
velocity should increase with increase of the void ratio, if there is less than about 15% void
space filled with water (Figure 2.5a). Actually, the observed trend for the frozen condition
(Figure 2.4) slightly decreases with increase of the void ratio, and implies that there is about
20% of the pore water remaining unfrozen or being thawed when we took the GPR
measurements.
Void ratio-asphalt content correlation
The relationships between the observed EM velocity and resulting dielectric constant with
respect to the asphalt content were also studied (Figure 2.7). The variation trends are opposite to
variations of the velocity and dielectric constant with respect to the void ratio (Figure 2.4). The
EM velocity and resulting dielectric constant for the dry and frozen conditions do not change at
all with variation in asphalt content: the asphalt bitumen is only less than 6.5 % in an HMA
specimen, and so has little effect upon the bulk dielectric constant. An inverse correlation was
also found between the void ratio and the asphalt content (Figure 2.8). This observed inverse
correlation implies that lower asphalt content may lead to a larger void ratio. Therefore, the
amount of asphalt binder applied to an HMA plays a significant role in optimizing void ratio to
construct a durable and stable road surface.
Moisture content predicted by the Topp model
Based on our fitting for the saturated condition, the moisture content varies from zero to
5.6% when the void ratio changes from zero to 7%, with 80% saturation. The EM velocity drops
from 130 m/�s to 113 m/�s (Figure 2.4a). According to the model (Figure 2.9) given by Topp et
al (1980) the moisture content is related with the dielectric constant through
362422 103.4105.51092.2103.5 rrrv εεεθ −−−− ×+×−×+×−= . (2.5)
Using the velocity-dielectric constant relationship given by Eq. (2.2), for the same range in
velocity changes, the predicted moisture content increase by the Topp model is about 4.2%.
Apparently, the observed trend agrees with the Topp model reasonably well; the Topp model
slightly under-estimated the moisture changes.
14
Figure 2.7. EM wave velocity (a) and dielectric constant (b) variations for 30 HMA specimens as a function of asphalt binder content (AC%) in dry (Vd and Ed, with blue symbols and lines), water-saturated (Vw and Ew, with magenta symbols and lines), and frozen (Vz and Ez, with yellow symbols and lines) conditions.
15
AC = -0.3958VR + 6.3132R2 = 0.6503
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
0.00 2.00 4.00 6.00
Void Ratio (%)
Asp
halt
Con
tent
(%)
Figure 2.8. Correlation of void ratio and asphalt content extracted from 30 HMA specimens.
(a) (b)
Velocity (m/μs) Dielectric Constant
Moi
stur
eC
onte
nt(%
)
Moi
stur
eC
onte
nt(%
)
Figure 2.9. An empirical prediction (Topp et al., 1980) of the moisture content variations as functions of EM wave velocity (a), and the bulk dielectric constant (b).
2.5. Conclusions
The major conclusions from these experiments are (1) The EM wave velocity increases slightly
with the increase of void ratio for dry HMA specimens. In contrast, it decreases significantly by
increasing void ratio in water-saturated conditions. Correspondingly, with the increase of the void
ratio, the dielectric constant decreased slightly when the samples were dry, and increased
16
appreciably when the samples were water-saturated. (2) The changes of EM velocity and resulting
dielectric constant for dry, water-saturated, and frozen conditions can be sufficiently predicted by
the CRIM model for porous media. (3) A comparison of the observed and predicted EM velocity
and resulting dielectric constant variations in water-saturated conditions implies that some HMA
specimens did not reach full saturation when the GPR measurements were taken. (4) The observed
change of EM velocity and resulting dielectric constant in frozen conditions implies that water in
the HMA specimens were not completely frozen when the GPR measurements were taken. (5) The
variations in EM velocity and resulting dielectric constant with respect to asphalt binder content
ratio imply that low asphalt content corresponds with a high void ratio, so that in the lower end of
asphalt content EM velocity has the maximum fluctuation among different conditions. (6) The
observed variation in EM velocity and resulting dielectric constant was essentially affected by the
changes in moisture content, as predicted by the Topp model. With more GPR and other direct
measurements, GPR may prove to be an efficient way to non-destructively detect void ratio,
moisture content, and degree of pore water freezing for road pavements. This is of special interest
to engineers who are responsible for road inspection and maintenance in cold regions.
17
3. GPR surveys on paved road for moisture content assessment
A series measurement using the 1-GHz direct contact antenna was conducted on a segment
of low-volume traffic road on the Depot Campus of the University of Connecticut. The objective
of this measurement is to observe the difference of GPR signature on the meteorological effect
over different seasons, and to correlate the testing results obtained from the laboratory
experiment over the HMA specimens in three conditions described in the last chapter.
3.1. Introduction
As discussed in the introduction of the last chapter, sufficient durability and stability are the
two most wanted features for pavement using hot mix asphalt (HMA). The void ratio is one of
the key factors affecting the durability and stability of an HMA pavement. The reason of the
void ratio’s importance is obvious: void space could be filled with air, water, or ice (frozen
water), or any fractional combination of all of them in a low-temperature environment. This is of
particular importance in the New England area where freezing and thawing is the major player in
pavement degradation and deterioration. Each of these three constituents has different
mechanical properties. Thus, the presence of different amount of void constituents significantly
affects the overall physical behavior of an HMA pavement, in turn, influences the HMA’s
durability and stability. For example, the presence of water in void space, quantified by the
moisture content, can significantly change the shear modulus of an HMA pavement. In contrast,
the presence of frozen water (ice) in the voids will effectively change an HMA’s bulk modulus.
Moreover, the freezing-thawing process lowers the tensile strength of an HMA pavement and
facilitates tensile failure (cracks). Clearly, moisture penetrating into an HMA pavement, whether
from above or below, can have detrimental effects on the durability of that pavement. Reliable
estimation of the moisture content in an HMA pavement is the first step for thorough
understanding of the void-filling materials’ role in HMA’s durability and stability.
Conventionally, the information of an HMA’ void ratio and moisture content were assessed by
direct excavation method, like drilling samples, and radioactive methods in recent years
(Saarenketo, 1997). In this chapter a series of field experiments on correlating the moisture
content, and EM wave velocity for a given road segment whose void ratio is assumed to be
constant is discussed in details. The field data acquired over an entire annual cycle in spring,
summer, fall and winter are presented and compared to link the GPR velocity and the void-
18
filling materials.
3.2. Practical limitations on radar wave velocity measurements
For GPR measurements, the sampling rate is usually set to be about 10 times of the signal’s
central frequency. For example, the sampling frequency is 10.142 GHz for using the 1-GHz
antenna to collect data presented in this chapter. It is equivalent to a time domain sampling
interval of dt=0.0986 ns. For a trace or scan contains 480 samples, the total time window is
about 47.3 ns. For the 1-GHz monostatic antenna, the separation of the transmitter and the
receiver is fixed at 0.1 m. Thus, the difference in travel time of the air wave and the ground wave
is only
nscD
cD
cD
ttt rr
ag 434.0)13.5(3.01.0)1(
000
=−≅−=−=−=Δ εε
where tg and ta are the travel time of the ground wave, and the air wave, respectively. D is the
transmitter-receiver separation distance; co is the light speed in the air, and �r is the dielectric
constant of the HMA pavement. Given the typical nominal values for all the quantities involved,
the time difference value of 0.434 ns is about 4.4 sample intervals using the aforementioned
sampling rate. Moreover, the amplitude of the ground wave is √�r times large than the air wave
(Arcone, 1984). This is why the quantity of √�r is also known as the refraction index.
Meanwhile, the difference in travel times of the direct ground wave and the reflected wave (see
Figure 2.1) is
nsDHDcc
Dc
HDttt rrr
gr 9485.0)1.01.041.0(3.03.5)4(
)4( 222222
=−×+≅−+=−−+
=−=Δεεε
where tr is the travel time of the reflected wave from the pavement-base interface, and H is the
thickness of the pavement layer. This value of travel time difference is about 9.6 sample
intervals when using the same sampling rate mentioned above. The finite length of a source
19
impulse is another factor to mask accurate identification of wave phase arrivals. In the ideal
nominal case, the period of a GPR source wavelet with a central frequency of 1GHz is 1 ns. This
is equivalent to 10 samples in time domain. Antenna-ground coupling effect always shifts the
signal significantly to a lower frequency; the exact value depends on the electromagnetic
properties of the ground. This effect makes the period of the source wavelet even longer.
Clearly, identification of the arriving times of different wave types is the first step and
fundamental request to use GPR technique in pavement assessment correctly and fruitfully. It is
not a trivial task.
In the field data, the relative velocity changes associated with rainwater wetting in the HMA
can be up to 3-5%. This corresponds to 2-3 sample intervals’ change in GPR travel times. By
applying the Topp model (Topp, et al., 1980), this range in velocity variation suggests a moisture
change of 0.8-1.4%, and corresponds to the saturation change of 10-20% in an HMA with 7%
void ratio.
3.3. Field measurements
GPR surveys with the 1-GHz antenna were repeatedly carried out on an HMA paved, low
traffic volume road segment on the University of Connecticut’s Depot Campus on August 26,
2000, September 20, 2000, and May 21, 2002. The surveys were conducted along the edge of the
travel way, relatively close to the old highly distress pavement. The total length of this segment
under test is 23 meters. The spatial sampling interval of GPR scans (the distance between 2
adjacent time traces) is 0.05m; there are 450-460 scans in a GPR profile. Figure 3.1 shows the
typical survey setup. The field data clearly show the interface of the HMA pavement and the
base (Figure 3.2). The thickness of the HMA pavement layer varies from 0.05m in one end of the
survey profile, to 0.18 m in the other. The GPR profile shown as Figure 3.2a was acquired on
August 26, 2000, and the one shown as Figure 3.2b was acquired in the morning of September
20, 2000, after an overnight heavy rain. Though the surface of the asphalt layer might be
completely saturated with water, due to rapid run-off, the water table might not have significant
changes and was well beyond the detection depth of 1-GHz GPR, thus irrelevant to the GPR
surveys conducted at this site. Finally, Figure 3.2c shows the GPR profile surveyed on the same
segment on May 21, 2002. There was no rainfall directly before that date. Obviously, the
20
pavement-base interface was enhanced and became more continuous in the GPR profile when
the condition changes from dry to water-saturated. The reflectivity at this interface increased by
60%, as indicated by the amplitude changes in the single traces extracted at the horizontal
position x=18 m shown at the right side of the GPR profiles (indicated by the arrow points red
ellipse about 3 nanoseconds in travel time).
Figure 3.1. GPR field survey with the 1-GHz antenna on a newly HMA paved road segment on the University of Connecticut’s Depot Campus on August 26, 2000.
21
strong reflection
(c) May 21, 2002
(b) September 20, 2000 after rain
(a) August 26, 2000
Trav
elTi
me
(ns)
Trav
elTi
me
(ns)
Trav
elTi
me
(ns)
Figure 3.2. GPR profile acquired with the 1-GHz antenna on the HMA paved road segment shown in Figure 3.1. (a) data acquired on August 26, 2000; (b) data acquired on September 20, 2000 after overnight rain; (c) data acquired on May 21, 2002. The single traces for each survey date on the right are located at the distance of 18 meters in the profile. The reflectivity at the bottom of the pavement for September 20, 2000 was significantly increased (the red ellipse) implying strong presence of water in the base.
3.4. Results discussion
Careful examination of the reflector position of the pavement-base interface reveals a delay
of 2-3 sample intervals in the GPR profile in water-saturated conditions (Figure 3.2b), when
compared with GPR survey in dry conditions as shown in Figure 3.2a. This is equivalent to a
velocity change of 0.003-0.006 m/ns, about 2-5% relative change of a nominal dry velocity of
0.13 m/ns for the dry HMA pavement. By applying the Topp model, this variation range in
22
velocity implies a moisture content change of 0.8-1.4 %, and corresponds to a saturation change
of 10-20%, by using the CRIM model, in an HMA with 7% void ratio, a nominal value for HMA
pavement in natural conditions. Nevertheless, there is no direct measurement (e.g., coring) to
verify or validate these estimations. More coordinated work should be done in the future to make
this indirect method improve its applicability for road pavement assessment.
From the GPR profile we can see that it is still hard to accurately delineate the bottom of the
pavement layer. This is mainly due to that the period of the GPR signal generated by the 1-GHz
antenna is still too long. The wavelet of the direct wave masked the reflection from the pavement
bottom. In the future, an antenna with higher frequency (1.5 to 2 GHz) would be a better choice
for it will generate a shorter period wavelet and therefore with a higher resolution.
3.5. Conclusions
Field experiments using the 1-GHz GPR were conducted to study the effects of water content
on EM velocity and resulting dielectric constant under natural meteorological conditions. The
main conclusions are: (1) The changes of EM velocity and resulting dielectric constant for dry
and water-saturated conditions can be interpreted by the Topp model for accounting for the
water content variations. (2) The detected velocity change caused by rain water wetting results in
GPR signals velocity change of 0.003-0.006 m/ns, suggests the moisture content changes on the
order of 0.8-1.4% using the Topp model. Using GPR to determine subsurface moisture content
has been a sustainable interest in geology and geophysics (Berktold, et al., 1998; Charlton, 2000;
Greaves, et al., 1996; Haslund and Nost, 1998) at a larger scale than highway pavement. With
finer sampling intervals in time domain and an established baseline (obtained from direct depth
control, or repeated GPR surveys), GPR should also be capable to provide an efficient way to
detect moisture content variation, and pore water freezing for the purpose of HMA pavement
assessment.
23
4. Numerical modeling of GPR surveys over dielectric thin layers
The asphalt pavement is a typical dielectric thin layer for GPR surveys. Though monostatic
reflection mode survey is the most economical way to carry out GPR data acquisition, GPR
moveout survey, i.e., GPR data were acquired while the transmitter-receiver separation is
changing from short to wider distance, may reveal more information regarding subsurface
conditions. This chapter assesses GPR moveout survey performance in different near-surface
geological stratigraphy and different antenna orientations using 2-dimensional (2D) finite
difference time domain (FDTD) numerical simulations of field data. We first treat the simple
cases of radar pulses propagating along (a) the interface between two half-spaces (air/ice); and
(b) an ice thin layer wave-guide (air/ice/water) between two half-spaces. We then simulate four
more complex cases combining two radiation polarizations (TM and TE), and two geological
settings: a sandy/gravelly half-space overlain by a silty/clayey layer, and a silty/clayey half-
space overlain by a sandy/gravelly layer. Both cases are represented through different dielectric
constants. The results show that (1) more EM energy is radiated as an air wave for the TM mode,
and more EM energy will be sent into the ground when the TE mode is used, regardless of
stratigraphic sequence. (2) Where a gravelly sandy half-space overlain by a silty/clayey layer,
more EM energy will be trapped in the silty/clayey layer as the guided ground wave. (3) When
the TE mode is used there is much less air radiation for the case of silt overlying gravel than that
of silty/clayey half-space overlain by a gravel/sand layer. (4) For the stratigraphic sequence of a
sandy/gravelly half-space overlain by a silty/clayey layer, the TE mode fundamentally contains
only a ground wave, and the TM mode essentially contains only air wave energy. This implies
that for this case a far more complete separation of the air wave and the ground wave can be
reached. (5) Dispersion of phase and group velocities of the guided ground wave will be well
developed for the TE mode. These simulations imply that antenna polarization mode is an
important factor when using moveout surveys to study subsurface electromagnetic properties.
4.1. Introduction
The electromagnetic properties of the uppermost 5-10 meters of the solid earth play the most
important role when probing the earth with the electromagnetic devices like ground penetrating
radar (GPR). For many cases, the near-surface environment can be idealized as a dielectric thin
layer overlaying a half-space with different electromagnetic properties. The system of asphalt
24
pavement and the underlying sub-base makes a perfect example in the geotechnical world
(Saarenketo, 1997; Saarenketo and Scullion 2000). An ice sheet or soil layer forms other
examples (Arcone, 1984; Arcone et al., 2003). Though the thickness scale of these examples
appears to be quite different, for electromagnetic sounding purposes, they all can be viewed as a
wave-guide for electromagnetic probing at suitable, corresponding frequency ranges. When
performing varying-offset moveout GPR surveys of such strata, highly dispersive guided-wave
propagation can result, making analysis of the electromagnetic structure of the earth difficult.
Here we examine the nature of this propagation with theoretical simulations, which are powerful
and economical alternatives to field experiments, especially for environments in which real data
acquisition is prohibited or too expensive. Moreover, numerical simulation assists designing of
data acquisition geometry and procedures to make observations more effective and productive,
and allows many stratigraphic combinations to be tested.
Annan (1973) systematically summarized the mathematical development in electromagnetic
interferometry in a near-surface environment. He used complex integrals (e.g., Brekhovskikh,
1960) and normal mode analysis (e.g., Budden, 1961). Existing laboratory and field observations
(e.g., Rossiter et al., 1973; Annan et al., 1975; Arcone, 1984; Arcone et al., 1998) indicate that the
ground wave can be manifested by modal propagation over several tens of meters at lower
frequencies (100 MHz or less) when wide angle offset soundings are performed to measure ground
wave speeds. Nevertheless, small scale, natural near-surface layering can severely limit this path,
as we will see here.
This chapter investigates the wave-guide effects of a surface layer on electromagnetic wave
propagation using the finite difference time domain (FDTD) simulation technique. We first
present FDTD simulation results for half-space cases to demonstrate the physical fidelity of
FDTD numerical simulation. Then we treat the modal propagation case of a thin layer of ice
between two half-spaces (air, and water). Finally, the results of electromagnetic wave
propagation in TE and TM modes at pulse central frequencies of 400 and 65 MHz are discussed.
We simulated field data acquired from Fort Richardson, Alaska (AK) (a lower dielectric constant
sandy gravel half-space overlain by a higher dielectric constant sandy silt layer), and Hanover,
New Hampshire (NH) (a sandy silt half-space overlain by sandy gravel layer). The field data and
synthetic results were analyzed with time-frequency analysis with instantaneous parameters to
25
extract guided-wave group velocity dispersion characteristics. We conclude that the simulation
results reasonably resemble fundamental wave propagation features in the field data and are
helpful to interpret field observations.
4.2. Summary of major features of guided wave propagation
We first define TE and TM modes used in this chapter (Figure 4.1). The TE mode is the
‘transverse-electric mode with respect to the x-direction, which is the direction of the GPR profile,
and can be expressed by the 2-dimensional Maxwell’s equation with in-plane magnetic field
components Hx, and Hy and out-of-plane electric field component Ez such that
,
,
,
zszxyz
zy
zx
EJy
Hx
Ht
Ex
Et
HyE
tH
σε
μ
μ
−−∂∂
−∂∂
=∂∂
∂∂
=∂
∂∂∂
−=∂∂
(4.1)
where ���� and � are dielectric permittivity, magnetic permeability, and electrical conductivity,
respectively; and Jsz is an electrical current source function in the z-direction. This case is
equivalent to the TMz mode (the transverse-magnetic mode with respect to the z-direction) as
defined in another convention, for example, by Taflove and Hagness (2000). Similarly, the TM
mode is the ‘transverse magnetic mode with respect to the x-axis’ that has in-plane electric field
and transverse magnetic field expressed by the 2D Maxwell’s equation in TM mode such that
,
,
,
szyxz
yzy
xzx
Mx
Ey
Et
H
Ex
Ht
E
Ey
Ht
E
−∂∂
−∂∂
=∂∂
−∂∂
−=∂∂
−∂∂
=∂∂
μ
σε
σε
(4.2)
where Msz is a magnetic dipole source function in the z-direction. GPR data can be acquired in
either a TE or TM mode, as depicted in Figure 4.1. We adopted a right-hand coordinate system
with the x-direction as the strike of the GPR profile, the y-direction is vertical and downward, and
the z-direction is perpendicular to the plane coinciding with the GPR profile. By using 2D
26
modeling we assume there are no variation in both material properties and electromagnetic fields in
the z-direction. Horizontally polarized antennas with the parallel configuration facing each other
communicate TE waves (upper panel of Figure 4.1); whereas horizontally polarized antennas with a
serial configuration communicate TM waves (lower panel of Figure 4.1).
Figure 4.1. Sketch of TE and TM modes with corresponding antenna orientations. The positivex-direction is that of wave propagation from the transmitter to the receiver; along the GPRprofile. The y-axis is vertical downward; and the z-direction is perpendicular to the x-y plane, in accordance with the right-hand-rule.
As indicated by Annan (1973), the propagation of radar waves along the interface between two
dielectric half-spaces (e.g., air and the ground) can be idealized by four types of propagation
(Figure 4.2). Wave A is the fundamental spherical air wave propagates through the air at the free-
space velocity c; wave B is the counterpart of A in the ground known as the ground wave. If the
ground is homogeneous with refractive index, n (n=√�), then ground wave B propagates at the
velocity of c/n and is n times stronger than the air wave. These two waves are matched at the air-
ground interface by two other waves in order to maintain field continuity across the boundary. In
air, wave C is an evanescent wave (also known as the inhomogeneous wave) that decays
exponentially with height (see Figure 4.3) and propagates horizontally at the speed c/n to match the
ground wave B. In the ground, wave D, known as the head wave (also named as surface wave, or
27
lateral wave), propagates downward at the critical angle )/1(sin 1 nc−=θ with a planar phase front,
but with a horizontal velocity of c to match the air wave A. In the near field, waves B and D are
indistinguishable. The two waves are well separated with increasing propagation distance into the
far field.
Figure 4.2. Idealized near-surface, near field propagation paths along the interface of the freespace and a dielectric half-space (ground) for a TE mode antenna orientation ((a), modifiedfrom Annan, 1973). S: the location of the TE mode source; A: the wavefront of the air wave; B: the wavefront of the ground wave; C: representation of the inhomogeneous evanescent airwave matching the ground wave B; and D: the wavefront of the head wave (or the so-called lateral wave) in the ground matching the spherical air wave; θc: the critical angle. The snapshot at the time of 25 ns after the firing of the TE source from FDTD simulation (b)clearly shows the different paths illustrated in (a). The modeling was carried out at theinterface of the free space and a dielectric half-space with dielectric constant of 3.17 (for freshwater ice). The source is a Ricker wavelet with central frequency of 200 MHz. The fastdecay of the evanescent wave C with respect to height above the ground is illustrated in Fig.3. Note the reversal of phases between the air wave (leading half-cycle is blue) and the ground wave (leading half-cycle is red).
The situation can change radically when the ground is layered. Depending on the relative values
of refractive index n of each layer, guided modes can propagate in the layers and either vastly
extend or vastly limit the range of the ground wave. To illustrate this a thin layer of ice between the
28
Figure 4.3. (a) Time domain synthetic records of the Ez electric field along x-axis at the surface; (b) The amplitudes of the Ez electric field at different elevation at elapsed time of 25 ns. Theevanescent wave decays exponentially with increasing elevation above the surface, and is in phase with the ground wave below the surface; whereas the air wave and the ground wave haveopposite phases. The total length of the profile is 19.25 m (350 x 0.055m).
Figure 4.4. The FDTD time domain wide-angle offset simulation of the Ez electric field for the TE mode generated by a 200-MHz Ricker wavelet and received on the surface of a 40-cm thick ice layer of an air-ice-water system. Note the continual excitation of refracted air waves.
29
free half-space and the half-space of water was simulated with FDTD. Figure 4.4 presents the
FDTD synthetic wide-angle reflection and refraction (WARR) GPR profile of the Ez field for a
TE mode generated by a 200-MHz Ricker wavelet recorded along the surface of a 40-cm thick
ice layer of an air-ice-water system. The ice layer has a dielectric constant of 3.17 and the cold,
fresh water has a dielectric constant of 87. The profile shows shingling associated with wave
mode dispersion and simulates field data presented by Arcone (1984, Figure 10) for a lake ice
cover in mid-winter.
4.3. GPR wide-offset field observations
Wide offset GPR surveys were conducted at two sites with path lengths up to tens of meters,
and with a quasi-infinite medium to eliminate the reflections that occur from lateral boundaries
(e.g., walls) in scale models. The first site is on Fort Richardson, near Anchorage, Alaska, where a
surface layer of wet, sandy silt with an average thickness of about 34 cm has a slower speed than
the underlying drier strata of sands and gravel (Arcone et al., 2003). The second site is in Hanover,
New Hampshire, where a thin layer of drier, gravelly sand that varies from 16 to 20 cm in thickness
overlies sandy silt of glacial Lake Hitchcock. At each site we established a profile test line along
which we dug several holes to aid profile interpretation. At the Hanover site we used 400-MHz
antennas to acquire wide-angle, variable offset profiles (upper panel of Figure 4.5) and an 800-
MHz antenna set to record reflection profiles (antennas at constant separation, lower panel of
Figure 4.5). The wide-angle profiles allow us to look at the modes propagating in the layer; while
the reflection profile allows us to interpret stratigraphic structure of the ground. At Fort Richardson,
we acquired a 100-MHz wide-angle reflection and refraction (WARR) profile in TE mode (shown
later in Figure 4.8a). At each site our structural studies include documentation of layer depth,
general sediment type, water content, and mineralogy in order to determine what attenuation
mechanisms may be present. In addition, GPR reflection profiles compensated for the difficulty of
complete excavation in order to document near surface layering.
30
Figure 4.5. Varying offset, 400-MHz Wide-angle (top) and constant-offset, 800-MHz reflection (bottom) profiles recorded along a single test line in Hanover, NH. Left panel of the wide-angle offset profiles is acquired in TE mode and the right panel is in TM mode with transmitter placed at the 0-m distance of the reflection profile. Arrow indicates the reflection from the bottom of the wave-guide layer. Dielectric constant of lower layer was interpreted from hyperbolic diffraction, that of upper layer from direct observation of depth, and the time delays.
4.4. Numerical simulations of TE and TM modes for field GPR data
Our numerical simulation algorithm adapts the finite difference time domain (FDTD) method
(e.g., Taflove and Hagness, 2000), based on Yee’s original staggered grid (Yee, 1966), with a
perfectly matched layer as the absorption boundary condition to truncate outbound waves
(Berenger, 1994). Based upon the field observations the electromagnetic parameters for soil
materials and stratigraphic geometry at the two sites are listed in Table 4.1. Since the main concern
is the generation and propagation of the guided ground wave caused by the surface layer, sub-strata
were simplified as a uniform half-space with constant electromagnetic properties. The conductivity
values were measured directly at Fort Richardson (Arcone and Delaney, 2002) and are estimated at
Hanover. The quantity h in Table 4.1 is layer thickness.
31
Table 4.1. Electromagnetic material properties and stratigraphy at the two sites under study
Site Fort Richardson site, AK Hanover site, NH
Free space � =1.0, � =0.0 S/m � =1.0, � =0.0 S/m
Surface layer � = 22.7, � = 0.0005 S/m
h =0.34 m
� = 8.0, � = 0.0004 S/m
h =0.20 m
Sub-strata � = 10.6, ��= 0.0002 S/m �= 12.0, � = 0.002 S/m
For all materials the relative magnetic permeability is equal to unity. We used a central
frequency of 400 MHz for the source wavelet for both Hanover and Fort Richardson sites to
carry out FDTD simulations in TE and TM modes; and also a 65 MHz source wavelet
propagating in TE mode for Fort Richardson for comparison with existing WARR GPR data.
The 400-MHz, variable offset GPR simulated syntheses for the two sites at Hanover, NH and
Fort Richardson, AK are shown in Figure 4.6. The time step in the simulation is 0.0667 ns, a
value that sufficiently satisfies the Courant stability condition (Taflove and Hagness, 2000). The
total time window is 100 ns. Figs. 6a and 6c present the transverse horizontal electric component
Ez for the TE mode; while Figure 4.6b and 6d present the in-plane, horizontal electric field Ex for
the TM mode. With similar arrangement, the wave field snapshots for different modes and
different geological stratigraphies are shown as Figure 4.7. Each panel contains the snapshot at
13.33 ns elapsed time for the corresponding electric field and magnetic field.
4.5. Results discussion
When there is total reflection at the interfaces there is no loss of energy other than that due to
geometric spreading of the waves, and the propagation is thus modal. This occurs when the upper
and lower layers have higher wave speeds than the waveguide layer (e.g., Fort Richardson site).
The total reflection occurs at a critical angle �c = sin-1 (n1/nm), where m is either 0 (for air) or 2 (for
sub-strata). For the opposite case where n0 or n2 is greater than n1, transmission occurs through the
interface and energy is continually lost during propagation. For example, FDTD simulations
predict that a much stronger TE guided ground wave occurs at Fort Richardson site (Figure 4.6c)
32
than at the Hanover site (Figure 4.6a) where total reflection does not occur on the bottom interface
of the thin layer. For the TM mode, FDTD simulations also predict that a much stronger guided
wave travels at a group velocity between that of the air wave and the ground wave, with a relatively
low attenuation rate, in the low-velocity thin layer (the Fort Richardson case, Figure 4.6d) than in
the Hanover site wave guide (Figure 4.6b). It is clear from Figure 4.7 that the TE mode generates
more ground waves; whereas the TM model generates more air waves, with a stronger head wave
matched in the thin layer, regardless of near-surface stratigraphic sequence. For the TE mode, at the
same elapsed time, the case of sandy layer overlaying silty sub-strata (Hanover, NH) has a larger
propagating range, while the case of a silty layer overlaying gravelly sub-strata has more electric
energy being trapped in the surface thin layer.
(a) (b)
(c) (d)
Fig. 4.6. Simulated 400-MHz wide-angle GPR profiles of (a) the Ez component in the TE mode; (b) the Ex component in the TM mode, for the Hanover site; and (c) the Ez component in the TE mode and (d) the Ex component in the TM mode, for the case of Fort Richardson site.
33
Figure 4.7. The simulated 400-MHz GPR wave propagation snapshot in (a) TE mode and (b) TMmode at time step 200 (elapsed time of 13.33 ns) for the Hanover site, and in (c) TE mode and(d) TM mode for the Fort Richardson site.
Where the upper layer is electrically thin (comparable to an in-situ wavelength or shorter) and
34
has a faster speed than the lower sub-strata, such as a drier soil over a wetter soil (e.g., the case in
Hanover, NH), or an ice layer over water (Figure 4.4), or a frozen soil over thawed soil, wave
energy continually transmits into the lower layer at a rate that can only be predicted by full wave
modal theory.
Theory and observations (Annan et al., 1975; Hoeskstra and Delaney, 1974, Arcone and
Delaney, 2002) have proved that when the upper thin layer has a slower speed than the sub-strata,
modes will propagate at angles beyond the critical angle for both interfaces and the upper thin layer
becomes a refractive waveguide, just like an optical fiber. This occurs when a wetter soil overlies a
drier soil, or when an unfrozen soil sits on top of permafrost, or bedrock. This is clearly shown by
the field observations and FDTD numerical simulation as shown in Figure 4.8. The shingling of the
waveforms is clearly associated with dispersive propagation velocity. The numerical simulation
(Figure 4.8b) qualitatively resembles the observation shown in the field WARR profile. More
quantitative analysis to exploit the data for more propagation characteristics using the instantaneous
amplitude and the instantaneous frequency (Taner et al., 1979; Barnes, 1991; Liu and Oristaglio,
1998) is shown in Figure 4.9. In Figure 4.9a the distribution of the instantaneous amplitude is
shown as a function of the corresponding instantaneous frequency at the same travel time and
location. The distribution should, and does resemble the Fourier transform (FT) results with a
central frequency of about 65 MHz. Much more data points are close to the central frequency,
which is not so apparent by using the FT method. Direct examination of the waveforms of Figure
4.8a shows lower frequency ground wave trains arrive before the higher frequency ones (Arcone et
al., 2003) to mark apparent velocity dispersion. Figure 4.9b gives a different view of the velocity
dispersion phenomenon by plotting the instantaneous amplitude as a function of the instantaneous
frequency and the group velocity. This is similar to the technique used by Parra (1996). The group
velocity was inferred from the phase velocity (determined by the phase travel time and receiver
location). Though the velocity is obviously dispersive, no clear Airy phase (Arcone, 1984) can be
identified based on this analysis. This may possibly be caused by the silty surface layer being too
thin, or, the bandwidth of the GPR signal being not wide enough.
35
Figure 4.8. The observed 100-MHz WARR GPR profile in TE mode at Fort Richardson, Alaska(a); and the corresponding FDTD simulated synthesis with a source impulse of Ricker wavelet at65-MHz central frequency (b). The field data were generated by nominally rated “100-MHz” antenna, whose ground-loaded value determined from near-field coupling was 65 MHz (after Arcone et al., 2003).
Figure 4.9. (a) Amplitude spectrum extracted from the instantaneous parameter analysis of the65-MHz Fort Richardson WARR data. It resembles the spectral analysis given by conventionalFourier transform with the central frequency at about 65 MHz; (b) Dispersion relationship derived by the instantaneous parameter analysis from 65-MHz field data. The wave propagation is dispersive with obvious frequency dependency, but no obvious Airy phase can be found. Thefrequency-velocity-amplitude technique used here follows Parra (1996).
36
4.6. Conclusions
Using finite difference time domain technique we have modeled four cases: a combination of 2
situations of geology (a gravelly sandy half-space overlain by a sandy silt layer, and a sandy silt
half-space overlain by gravelly sand half-space) and 2 transverse modes of antenna radiation (TM
and TE). The main conclusions are summarized as follows.
More EM energy is radiated as an air wave for the TM mode; and more EM energy will be sent
into the ground for the TE mode, regardless of geological setting (Figure 4.6). Meanwhile, in a
geological setting where a lower � gravelly sand half-space is overlain by a higher � sandy silt layer
(the case of Fort Richardson), more EM energy will be trapped in the sandy silt layer as a TE mode
in the ground wave guide and very little energy will occur as air radiation, when compared with the
same radiation mode in the case of a higher � sandy silt half-space overlain by a layer of lower �
gravelly sand. For the geological setting of a lower � gravelly sand half-space overlain by a higher �
sandy silt layer, the TE mode mainly contains a ground wave and the TM mode mainly contains air
wave energy, which is traveling at a phase velocity of c and a lower group velocity, as evidenced by
the apparent shingling of the energy arrivals (Figure 4.6d). This implies that for this case a far more
complete and long lasting separation of the air wave and the ground wave can be reached.
It appears that for this common case of an electrically thin drier layer over wetter sediments
that both TE and TM waves are highly suppressed when compared with the case of a thin wetter
layer over drier and coarser sediments (e.g., Fort Richardson), especially for TM waves. For
higher frequency antennas, the guided ground wave modes may propagate better, but then strong
attenuation properties (water relaxation and scattering) intrinsic to the layer itself will also
become a factor in suppressing the ground modes. These properties will also be a factor for
thicker layers, which will offer more path length.
37
5. Mathematical treatment to improve the resolution and penetration
At a given location if both high- and low-frequency GPR data were available, a synthetic
GPR image with deep-penetration and high-resolution can be reconstructed by a signal
processing procedure known as extrapolation with deterministic deconvolution (EDD). There are
two fundamental assumptions to make EDD work. First, the correlation (a transfer function or
filtering function) between the high- and low-frequency data at one location can be
deterministically extracted. Second, this transfer function is spatially stationary so that it can be
applied to another location. Based on the principle of applying EDD to seismic data, which is for
generating the synthetic well logs from surface seismic data, we have extended EDD treatment
to GPR data for the purpose of recovering the high-resolution contents at greater depths. The
compensation of the frequency-dependent absorption loss is based on the constant Q model. This
chapter presents the preliminary test results with numerical synthetic time records. EDD with the
synthetic data appears to be promising. More tests need to be done before EDD can be routinely
applied to GPR field data. For a successful application of EDD to real world data, a careful pre-
processing of the field data is far more critical than the EDD algorithm itself.
5.1. Introduction
The tradeoff between penetration and resolution of a given radar pulse is a well-known
phenomenon to the GPR user community. It is trivial to honor the fact that objects far away
cannot be seen as clearly as those closer to an observer. Likewise, GPR images become blurry or
lose resolution at greater depths, this is caused by the fact that the high-frequency content of the
signal suffers more severe loss than low-frequency content. However, it has always been
desirable that GPR have the ability to detect targets at greater depths and with higher resolution.
In general, it is hard to obtain a subsurface image with deep-penetration and high-resolution
simultaneously. However, if both high- and low-frequency data were acquired at the same
location, we may be able to take the advantages of the relative deeper penetration of the low-
frequency signal and the relatively higher resolution of the high-frequency signal. By taking
advantage of the deep penetration of the low-frequency data and the higher resolution of the
high-frequency data simultaneously, it was a common practice in the last two decades to patch
the high-frequency GPR profile with shorter time window at shallow depth onto the low-
38
frequency GPR profile with longer time window. Clearly, the desire to get deep-penetration and
high-resolution simultaneously can hardly be fulfilled with any rigidly configured physical
approach. The only possible solution is seeing if digital signal processing techniques can lend us
some help.
Deterministic deconvolution was originally used to increase signal resolution in seismic
exploration (Oldenburg, et al., 1981; Treitel and Lines, 1982) then adopted to enhance GPR
reflection profiles (Xia, et al., 2004). Digital signal analysis recognizes the low- and high-
frequency GPR responses at a particular location as the convolutions of the low- and high-
frequency source wavelets with the material properties (medium imperfection shown as
attenuation and impedance contrast shown as reflectivity), respectively (Liu and Oristaglio,
1998; Treitel and Robinson, 1966; Liu, et al., 1998). If both low- and high-frequency responses
at a shallower (for surface GPR) or closer (for borehole radar) location and low-frequency
response for deeper or farther locations are available, one can infer the high-frequency response
at the deeper or farther locations. The information about the high-frequency response for the
deeper/farther locations is extrapolated by extending the relationship of high- and low-
frequency correspondence at shallower parts into greater depths. In certain circumstances, this
extension can be achieved through the extrapolation by deterministic deconvolution (EDD), as
has been down in the treatment of seismic data (Zhou, et al., 2001).
The procedure is explained in detail in the following sections with mathematical derivations
at the first, followed by applying EDD to both synthetic and field data to verify the effectiveness
of this method. The examples showed that EDD has restored some high frequency contents in
later times (greater depth). However, EDD is more effective at improving the resolution of
synthetic data than the real field GPR data, simply because synthetic data is noise-free and real-
world field data contains random noise caused by variety of sources and system errors due to
differences in system response for antennae working at different central frequencies. This
chapter concludes with a discussion on future research for this topic.
39
5.2. Extrapolation by deterministic deconvolution
Subsurface structure responses to the impinging radar source are recorded by the receiving
antenna as time-domain traces. And these recorded responses R(t) can be regarded as the
convolution among the GPR source signal wavelet W(t), the subsurface structures S(t), in terms
of the reflectivity, and the material’s intrinsic attenuation A(t). Given this simple analytic model,
the recorded responses Rl(t) for the low- frequency, and Rh(t) for the high-frequency, can be
expressed as the convolutions of the source wavelet Wl(t) and Wh(t) and the material structure
S(t), respectively, and Al(t) and Ah(t), the material’s attenuation properties for low- and high-
frequency GPR signal, respectively, in the following two equations:
)()(*)()()()(*)()(tAtStWtR
tAtStWtR
hhh
lll
∗=∗= (5.1)
where the asterisk symbol ‘*’ denotes convolution. The structure function, S(t), is the same for
both high- and low-frequency signals anywhere in the subsurface. Combining the two equations
in eq. (5.1), S(t) cancels out and we end up with a direct relationship between Rl(t) and Rh(t)
)()()( tRtGtR lh ∗= (5.2)
where G(t) is the lump-sum transfer function that defined as the ratio of the convolutions
between the source wavelet and attenuation for the high- and low-frequency signals;
)()()()()(
tAtWtAtWtG
ll
hh
∗∗
= (5.3)
the attenuation operator can be simplified with a reasonable theoretical model which
characterizes the medium’s intrinsic attenuation property. One such model is the well-known
constant Q model (Liu, et al., 1998), which defines a linear dependence of the attenuation to
signal frequency, i.e., �=�0f, so the attenuation operator becomes:
ftt eetA 0)( αα −− ==
and the ratio of the attenuation operators for high- and low-frequency GPR signals is simply:
40
fttff
l
h eetAtA
lh Δ−−− == 00 )(
)()( αα
Thus, the lump-sum transfer function can be expressed as
ftft
l
h
ll
hh etgetWtW
tAtWtAtWtG Δ−Δ− ∗=∗=
∗∗
= 00 )()()(
)()()()()( αα (5.4)
where g(t) is the transfer function between the high- and the low-frequency source wavelets.
Apparently, g(t) was originally defined as the spectral ratio in frequency domain. It can also be
elucidated as the cross-correlation of the high- and low-frequency time sequences in time
domain by the following derivations. From eq. (5.2)
ftllh etRtgtRtGtR Δ−∗∗=∗= 0)()()()()( α (5.5)
It is straightforward to invert eq. (5.5) and get the transfer function g(t) by
)](),([)()( 0 tRtRdeconvetgtG lhft =∗= Δ−α (5.6)
where function deconv[Rh(t), Rl(t)] means de-convolving Rl(t) out of Rh(t) and
ftlh etRtRdeconvtg Δ∗= 0)](),([)( α (5.7)
Due to the assumed spatial invariability of g(t), the predicted high frequency signal response
at a different location, Rh2(t), can be obtained by convolving g(t) with the low frequency signal
response Rl2(t) measured at location 2. The mathematical expression can be described by
)()()( 22 tRtgtR lh ∗= (5.8)
With this process, the ‘extrapolated’ Rh2(t) has inherited both advantageous properties of the
different frequencies, high resolution and deep penetration. The inversion of g(t) is a
deconvolution that is a deterministic process (eq.(5.7)), such that the high frequency signal
response, Rh2(t), is extrapolated from the measured low frequency response, Rl2(t) (eq.(5.8)).
Therefore, this method is regarded as the extrapolation by deterministic deconvolution (EDD).
41
A simple and effective way to find g(t) is to use a linear optimum discrete-time filtering
method. This chapter uses the widely adapted Wiener filtering technique. The low-frequency
signal, Rl(t), can be regarded as the input, g(t) is the filter system and the filter response or
output is Rh(t), so that
k)-g(t(k)R = g(t)*(t)R = (t)RN
0kllh ∑
=
⋅ (5.9)
where N is the length of the discrete input signal. The principle of orthogonality (Haykin, 2002)
specifies the necessary and sufficient conditions for the optimum operation of the filter as
NitRigtRktREN
ilhl …==−⋅−− ∑
=
0,1,2,k ,0))]()()()(([0
(5.10)
where g(i) is the i-th coefficient in the impulse response of the optimum filter. Expanding this
equation and rearranging terms produces,
0,1,2,...Nk ),()()(0
=−=−⋅∑=
kpkirigN
i (5.11)
where )]()([)( itRktREkir ll −⋅−=− is the auto-correlation of the input; while
)]()([)( tRktREkp hl ⋅−=− is the cross-correlation between the filter input, Rl(t-k), and the
desired response, Rh(t), for a time step lag (k). Let R denote the N-by-N autocorrelation matrix
of Rl(t), and P denotes the cross-correlation vector between the input of the filter and the desired
output, simplifying eq. (5.11),
PgR =⋅ (5.12)
This is the so-called Wiener-Hopf equation (Haykin, 2002). The filter vector, g(t), can now be
readily calculated by the inverse of the matrix R times P,
PR g -1 ⋅= (5.13)
Using g(t) in eq. (5.8), we are able to calculate the high-frequency extrapolation at any location
given the low-frequency response at those locations.
The resolution enhancement using EDD is illustrated with a single trace of real GPR data
collected at one location using both high- and low-frequency records (Figure 5.1). The top panel
42
of Figure 5.1 is a snippet of 100-MHz GPR data, the low-frequency sequence, and the second
panel is the 400-MHz data, the high-frequency sequence. The recording time window for high-
frequency data is usually shorter than the low-frequency counterpart. The transfer function
derived from the records shown in the top two panels is presented as the third panel. Apparently,
the effective length of g(t) is limited by the length of the high-frequency data. The bottom panel
shows the EDD synthesis of the high-frequency record. Comparison of the EDD synthesis and
the original high-frequency data in the earlier time shows a reasonable agreement between these
two sequences. This agreement is the base to entrust the EDD extrapolation for later times
(corresponding to greater depth). The approach and effectiveness of EDD are further examined
in the following sections when it is applied to synthetic and real GPR data.
5.3. Applications to synthetic data
To test the effectiveness of EDD for improving GPR data resolution, synthetic time traces
are computed from a 2-dimensional (2D) finite-difference time-domain numerical modeling
technique (Liu and Arcone, 2003). A five layer model was created and a metal cylinder was
positioned in the center of the third layer (Figure 5.2). The model consists of 600 grid cells, 300
of which are in the horizontal or x-direction and 200 grid cells in the vertical or y-direction. All
the four sides of the model domain are bounded by an 8-grid cell thick perfectly match layer
(PML) absorption boundary (Berenger, 1994). All grid cells have a uniform size of 0.02 m on a
side. Thus, the modeled physical domain is 6m x 4m. The material properties of different layers,
from top to bottom, are:
1) A strip of air at the top of the model with the dielectric constant of vacuum and zero
conductivity (�r = 1, and ��= 0.0 S/m);
2) A 0.4 m thick surface layer with �r = 9, and ��= 0.0 S/m;
3) A 1.6-m thick dielectric layer with �r = 16, and ��= 0.0 S/m;
4) An electrically conductive cylinder (�r = 25, and ��= 107 S/m) with a radius of 0.5 m
centered in the third layer;
43
Figure 5.1. EDD illustration using a single trace from a piece of real data. From top to bottom: 1) the low- frequency record; 2) the high-frequency record; 3) the transfer function; and 4) the extrapolated high-frequency syntheses by EDD.
44
5) Another thin layer with the same thickness and property of Layer 2;
6) A dielectric half-space with the same material property of Layer 3.
Figure 5.2. The model used to generate the synthetic GPR time records for evaluating the EDD method. The dielectric constant of each layer is labeled as �� The unit of the conductivity � is Siemens per meter (S/m).
The synthetic time sequences are generated with a source impulse whose shape is a Ricker
wavelet with the central frequency of 100- and 400-MHz, respectively. A time step of 0.026667
nanoseconds (ns) is used for both high- and low-frequency time sequences, a value fulfills the
stability condition for FDTD modeling (Schroder and Scott, 2002) when the grid size is 0.02 m.
The time step adapted in the forward model is about 10 times shorter than the sampling rate used
in acquiring 400-MHz GPR field data. For example, the sampling frequency of 4141 MHz
corresponds to a sampling interval of 0.2415 ns. Thus, it is necessary to re-sample the synthetic
time traces to a longer time interval to reduce the redundancy and increase the efficiency of EDD
calculation. For the numerical modeling, the total simulated time is 66 ns (2500 time steps),
which allows enough time for the reflected waves from the bottom interface to travel back to the
receiving points at the air-ground surface. The sources and receivers were placed one grid above
the air-ground interface to mimic the monostatic reflection profiling. A total of 51 time traces
were generated with this model with a 0.4-m source-receiver separation. The profile extended 5
meters in the x-direction with 0.1-m spacing between two adjacent traces.
45
The evaluation of EDD was conducted following procedures described in Section II with
results shown in Figures 5.3, 5.4 and 5.5. The top panels of Figures 5.3, 5.4 and 5.5 are the
original low-frequency (100 MHz) records. The second panels are the original high-frequency
(400 MHz) records. The third panels are the calculated transfer function, g(t). Finally, the bottom
panels are the extrapolated high-frequency traces with EDD.
0 1 2 3 4 5
0
20
40
60
Low-frequency (100MHZ) records
Tim
e(n
s)
0 1 2 3 4 5
0
20
40
60
High-frequency (400MHZ) Records
Tim
e(n
s)
0 1 2 3 4 5
0
20
40
60
Transfer Functions
Tim
e(n
s)
0 1 2 3 4 5
0
20
40
60
High-frequency Syntheses by EDD
Distance (meter)
Tim
e(n
s)
Figure 5.3. The EDD extrapolation for the synthetic records generated with the model shown in Figure 5.2. From top to bottom: 1) the low- frequency record; 2) the high-frequency record; 3) the transfer function; and 4) the extrapolated high-frequency syntheses by EDD. The recording time windows are 66 ns for both high- and low-frequency synthetic data.
46
0 1 2 3 4 5
0
20
40
60
Low-frequency (100MHZ) recordsT
ime(
ns)
0 1 2 3 4 5
0
20
40
60
High-frequency (400MHZ) Records
Tim
e(n
s)
0 1 2 3 4 5
0
20
40
60
Transfer Functions
Tim
e(n
s)
0 1 2 3 4 5
0
20
40
60
EDD with only High-frequency Channel 11
Distance (meter)
Tim
e(n
s)
(by Ch. 11)
Figure 5.4. Same as Figure 5.3 with the exception of only trace No. 11 of the high-frequency record 400 MHz record is used for calculating the transfer function g(t) in EDD extrapolation.
47
0 1 2 3 4 5
0
20
40
60
Low-frequency (100MHZ) records
Tim
e(n
s)
0 1 2 3 4 5
0
20
40
60
High-frequency (400MHZ) Records
Tim
e(n
s)
0 1 2 3 4 5
0
20
40
60
Transfer Functions
Tim
e(n
s)
0 1 2 3 4 5
0
20
40
60
High-frequency Syntheses by EDD
Distance (meter)
Tim
e(n
s)
Figure 5.5. Same as Figure 5.3 with the exception of a shorter time window (45 ns) is used for the high-frequency 400 MHz record for calculating the transfer function g(t) in EDD extrapolation.
48
Data in Figure 5.3 shows both the low- and high-frequency traces which are recorded with a
time window of 66 ns. Each pair of the low- and high-frequency traces at one location generates
one unique transfer function. A comparison of the EDD extrapolated high-frequency signal and
the original 400 MHz traces shows that the extrapolation works properly: the extrapolated and
the original simulated traces are literally identical, as they should be, since no extrapolation has
been conducted here at all. The high-frequency information is available in all space where low-
frequency information available. This step was designed to verify that the EDD algorithm can
work properly for a monostatic GPR profile.
To test algorithm’s capability of extrapolation in the lateral direction, we assumed that the
high-frequency 400 MHz data with the full length of the time window is available at only one
location, Trace No. 11. EDD was carried out by using g(t) calculated from Trace No. 11 alone
and applied to all locations on the low-frequency profile to get the extrapolated high-frequency
syntheses. The extrapolation result is shown in Figure 5.4. Obviously, by losing the correlation
constraints at all other locations, the image formed by the extrapolated traces is much more
smeared. Nevertheless, the dominant frequency of the traces is still high and close enough to the
original high-frequency record, and the reflection from the lower thin layer is clearly seen.
For surface GPR, extrapolation into greater depths is the main purpose to run EDD. We
tested the capability of EDD by shortening the window of the 400-MHz record to 40 ns then
carried out the EDD extrapolation again. The results are shown in Figure 5.5. Even with
truncated 400-MHz data, the EDD algorithm was still able to show the reflection from the thin
layer which is beyond the cut-off window for the 400-MHz data.
To examine how much high-frequency contents has been recovered, we turn to an
examination of the spectra from the original and EDD extrapolated high-frequency traces. The
comparison of the spectra from the EDD extrapolated syntheses and the original records
corresponding to the time domain records (Figure 5.5) are shown as Figure 5.6. It is clear that
EDD has recovered the high-frequency lose in deeper part effectively with the comparison of the
original high-frequency records (the second panel from the top) and the EDD extrapolated
syntheses (the bottom panel). From Figure 5.6 we can see that the peak value of the amplitude is
about 100 MHz in the spectra of the low-frequency records, while it is corresponding to about
49
400 MHz for the high-frequency records. As expected, the high-frequency records have a wider
frequency bandwidth than the low frequency records. The spectra of g(t) and EDD have
maximum amplitude at about 400 MHz. The spectra of the high-frequency syntheses by EDD
resembled the original simulated high-frequency records. This good agreement between the
original and EDD data can be explained by the fact the simulated synthetic data is noise-free and
has close cross-correlation at all the locations. The comparison of the four spectra plots show
that the extrapolated high-frequency records retained the same resolution as the original high-
frequency records.
5.4. Applications to field GPR data
For serving the ultimate objective of boosting up the resolution of the field GPR data, EDD
was further examined by being applied to a set of the 100-MHz and 400-MHz field data
collected in the town of New Milford, Connecticut, for highway engineering purposes (Liu,
2004). Both the 100- and 400-MHz data sets were collected along a single survey line with 10-
cm trace spacing. The soil at the site is very sandy/gravelly with a great depth of penetration.
Both data sets show a strong reflector at the two-way travel time 100 ns. The time window
length of the 100-MHz data is 400 ns (only 250 ns is used for EDD analysis), while the length
for the 400-MHz data is 105 ns. Figure 5.7 shows the original data and the EDD processing
results. Though the EDD extrapolation has not reached the level of effectiveness shown in the
synthetic data, it does catch the major features of the 100-MHz data beyond 105 ns and boost up
them to a shorter period (higher frequency).
50
0 1 2 3 4 5
0
200
400
600
800
Spectra of Low-frequency (100MHZ) records
Fre
qu
ency
(MH
z)
0 1 2 3 4 5
0
200
400
600
800
Spectra of High-frequency (400MHZ) Records
Fre
qu
ency
(MH
z)
0 1 2 3 4 5
0
200
400
600
800
Spectra of Transfer Functions
Fre
qu
ency
(MH
z)
0 1 2 3 4 5
0
200
400
600
800
Spectra of High-frequency Syntheses by EDD
Distance (meter)
Fre
qu
ency
(MH
z)
Figure 5.6. From top to bottom: the spectra of the 100-MHz records, 400-MHz records, the transfer function g(t), and the EDD extrapolated syntheses.
51
0 2 4 6 8 10 12 14 16
0
50
100
150
200
250
Low-frequency (100MHZ) recordsT
ime(
ns)
0 2 4 6 8 10 12 14 16
0
50
100
150
200
250
High-frequency (400MHZ) Records
Tim
e(n
s)
0 2 4 6 8 10 12 14 16
0
50
100
150
200
250
Transfer Functions
Tim
e(n
s)
0 2 4 6 8 10 12 14 16
0
50
100
150
200
250
Hi-frequency Syntheses by EDD
Distance (meter)
Tim
e(n
s)
Figure 5.7. EDD extrapolation of field data acquired at the New Milford, CT site (Liu, 2004).
52
0 2 4 6 8 10 12 14 16
0
100
200
300
400
500
Spectra of Low-frequency (100MHZ) records
Fre
qu
ency
(MH
z)
0 2 4 6 8 10 12 14 16
0
100
200
300
400
500
Spectra of High-frequency (400MHZ) Records
Fre
qu
ency
(MH
z)
0 2 4 6 8 10 12 14 16
0
100
200
300
400
500
Spectra of Transfer Functions
Fre
qu
ency
(MH
z)
0 2 4 6 8 10 12 14 16
0
100
200
300
400
500
Spectra of High-frequency Syntheses by EDD
Distance (meter)
Fre
qu
ency
(MH
z)
Figure 5.8. From top to bottom: the spectra of original 100-MHz and 400-MHz field data, the transfer function g(t), and the EDD extrapolated high-frequency Syntheses for the New Milford data set.
53
The comparison of the spectra for the field data are shown in Figure 5.8. The extrapolated
high-frequency syntheses by EDD have the same resolution as the original 400-MHz data. The
centroid of the spectra of the field data has a downshift to lower frequencies for both the 100-
and the 400-MHz data, and it is more obvious for the 400-MHz data. The coupling effect of the
antenna to the ground (Liu, et al., 1998; Zhou, et al., 2001) is the main cause for this shift. The
spectra in Figure 5.8 are relatively rough in comparison with the spectra shown in Figure 5.6,
due mainly to the existence of signal noise caused by real-world conditions. When comparing
with the application to the synthetic data (Figures 5.3 – 5.6), without surprise, the application to
the real field data shows a moderate success, caused mainly by the uncertainties and errors
existing in both the high- and low-frequency data from various sources. The degree of
correlation has been degraded.
5.5. Conclusions
In this chapter we described the extrapolation with deterministic deconvolution (EDD)
method to enhance signal resolution in later times for a GPR profile. The EDD approach has
been explained with the assistance of a number of examples using both synthetic and field GPR
data. Application of EDD to synthetic data demonstrates that it can work effectively as the
method designed for. The application of EDD to real GPR data achieved certain effectiveness
with moderate success. Apparently, we need carry out further theoretical development before
applying EDD to real field data. A sequence of carefully designed procedures of field data
acquisition and data pre-processing underlies the effectiveness of the EDD method.
54
6. Conclusions and Future Work
6.1 A general summary
This report presents a scope of research on GPR pavement assessment covering (1) the
laboratory experiments on HMA specimens in dry, water-saturated and frozen conditions; (2) a
series of GPR field measurements in different meteorological conditions for assessing the water
content in paved road; (3) a numerical simulation of GPR response to a surface dielectric thin
layer with the finite difference time domain method; and finally, (4) a digital signal processing
algorithm to improve the resolution of GPR signals. As a non-destructive testing tool for
pavement assessment, GPR proves an approach supplementary to the traditional direct and
impact engineering tests for HMA pavement properties.
With the combination of laboratory test results and field observations, GPR is capable of
providing indirect estimate on void ratio of the pavement as well as the state of pore fluid in the
voids. This information is critical for extending the durability and stability of HMA paved road,
especially when the information is in-situ, and real-time (or close to real-time). Calibration of
field data with laboratory test results of the HMA specimens with the same composition may
substantially improve the accuracy of pavement parameter estimations.
6.2 Future work
GPR technique for pavement assessment is becoming more and more mature in the last
several years. A number of commercially available systems have been emerging to the market.
Advancement in electronic and computer engineering technologies will continue the reduction of
GPR hardware cost. Numerous theoretical and analytical studies, including results presented in
this report, could be acting as the technical support for GPR pavement assessment in production
mode at both the project and network levels. Advances in hardware and software will make GPR
technique affordable to most state DOTs for paved road status monitoring at the network level
and quality assessment and control at project level. Close interactions among DOT laboratories,
project managers, and academic researchers will push the GPR technique to a new level of
engineering application and make it more attractive to pavement engineers. These interactions
55
can be hosted by state DOT laboratories or DOT sponsored pavement research centers in
academic institutions.
Disclaimer: The contents of this report reflect the views of the author who is responsible for
the facts and accuracy of the data presented herein. The contents do not necessarily reflect the
official views or policies of the Connecticut Department of Transportation or the Federal
Highway Administration. The report does not constitute a standard, specification, or regulation.
Neither the United State Government nor the State of Connecticut endorses products or
manufacturers. Trade marks or manufacturer names appear herein only because they are
considered essential to the objective of this document.
56
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Appendix: A list of publications on GPR authored by the PI and his research group
Arcone, S. A., P. Peapples, and L. Liu, Propagation of a ground-penetrating radar (GPR) pulse in
a thin-surface waveguide, Geophysics, 68, 1922-1933, 2003.
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fractures in crystalline bedrock, MS thesis, 163 pp. Department of Geology and Geophysics,
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Penetrating Radar Signals, MS Thesis, Department of Geology and Geophysics, University of
Connecticut, 82 pp., December 2004.
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ground penetrating radar signals, EOS, Trans. American Geophysical Union, Joint Assembly
Supplement, abstract no. NS22A-05, 85(176), JA275, 2004.
Liu, L., The ground penetrating radar (GPR) survey at the future site of the Lebanon Historical
Society Museum, Connecticut, Report to the Archaeology Research Specialists, Inc. 19pp,
1996.
Liu, L., State-of-the-art rapid non-destructive pavement assessment: Ground penetrating radar
(GPR) in monostatic mode, Report to the Joint Highway Research Advisory Council,
Connecticut Department of Transportation, 1998.
Liu, L., Detection of possible old buried graves in the Pickett District Cemetery with ground
penetrating radar (GPR) in New Milford, Connecticut, Technical Report to Connecticut
Department of Transportation, 23 pp., 2004.
Liu, L., Fracture characterization using borehole radar: Numerical modeling, Water, Air, and
Soil Pollution, 2006 (in press).
Liu, L., and S. Arcone, Propagation of radar pulses from a horizontal dipole in variable dielectric
ground: A numerical approach, Subsurface Sensing Technologies and Applications: An
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