www.elsevier.nlrlocaterjappgeo
Evaluation of GPR techniques for civil-engineering applications:
study on a test site
G. Grandjean
), J.C. Gourry, A. Bitri
BRGM, Direction de la Recherche, Departement Geophysique et Imagerie Geologique, AÕe. Claude Guillemin, BP 6009,
F-45060 Orleans Cedex 2, France
Received 29 October 1998; accepted 12 July 2000
Abstract
Ž .
Different ground-penetrating radar GPR techniques have been tested on the same site in order to establish the performance and reliability of this method when applied to civil-engineering problems. The Laboratoire Central des Ponts et
Ž .
Chaussees LCPC test site at Nantes, France, was selected because it includes most of the underground heterogeneities´
commonly found in urban contexts, such as pipes, small voids, etc. The GPR survey consisted in recording measurements in
Ž . Ž . Ž
tomographic surface to horizontal borehole measurements , monostatic 2D surface profiling and bistatic Common Mid
w x.
Point CMP modes above various buried heterogeneities. Different processing techniques were also performed, such as tomographic inversion, 2D and 3D migration, velocity analysis, as well as numerical simulations, the results of which can be
Ž .
summarized in three points. 1 Although the different filling materials of the site can be distinguished by velocity and attenuation tomography, the buried heterogeneities are more difficult to identify because of limited resolution related to
Ž .
angular aperture and Fresnel zone. 2 2D surface profiling can detect the different shallow heterogeneities, such as pipes and voids, down to a depth of several meters. Additional processing, such as forward modeling and attenuation curve analysis, provides more quantitative information related to the medium. A comparison between 2D and 3D migrated data
Ž .
highlights the error introduced when the structures are considered to be perfectly cylindrical. 3 CMP analysis gives relatively good estimations of vertical velocity contrasts when the medium is layered. A lithologic log can be derived assuming that the velocity changes are related to material variations.q2000 Elsevier Science B.V. All rights reserved.
Keywords: Geotechnics; Test site; Ground-penetrating radar; Velocity and attenuation tomography; Modeling
1. Introduction
The detection of underground heterogeneities us-ing non-destructive methods is a crucial problem in
)Corresponding author. Tel.:q33-2-38-64-34-75; fax:q
33-2-38-64-33-61.
Ž .
E-mail address: [email protected] G. Grandjean .
urban environments, especially for trenchless works. For example, unknown concrete house foundations or sandstone blocks located along the path of a drilling machine can cause major equipment damage and thus a loss of time and money. Geophysical methods, particularly the ground-penetrating radar
ŽGPR , can detect such superficial bodies with a.
relative efficiency depending on the field context, the dielectric properties of the host material and the
0926-9851r00r$ - see front matterq2000 Elsevier Science B.V. All rights reserved.
Ž .
nature and size of the bodies. The objective of this work, funded by the BRGM and the National Project on Trenchless Works, is to review the capabilities of GPR in urban environments for civil-engineering applications. We approached this problem by com-paring the results obtained at the same site using different survey configurations and different process-ing techniques.
The success of such work is mainly conditioned by the features of the site where data acquisition is carried out. Firstly, the site must be representative of the urban environment, which means that the proper-ties of the host materials and buried heterogeneiproper-ties must be consistent with those commonly found be-neath cities. Furthermore, the selected site must be well known and calibrated so as to be able validate the tested methods, i.e. the nature of the host mate-rial and the position of the buried heterogeneities must be precisely known. Finally, to ensure optimum data acquisition, the site must be easily accessible
Ž
and as free as possible from noise sources e.g.
.
electrical installations , trees, etc. By respecting these criteria, a good compromise should be reached be-tween reality and an idealized underground model. The geotechnical test site of the Laboratoire Central
Ž .
des Ponts et Chaussees LCPC at Nantes, France
´
ŽChazelas et al., 1997 was selected because it satis-.fies all these requirements.
Numerous studies describe efficient GPR tech-niques for detecting and imaging underground pipes,
Ž
voids, etc. Zeng and McMechan, 1997; Powers and
.
Olhoeft, 1996; Tong, 1993; Annan et al., 1990 . However, because each technique is generally con-sidered individually in a specific context, it is diffi-cult to compare reliability when applied together under the same field conditions. In view of this, we present here the results of three different experiments systematically tested and compared at the same test site. The first experiment consisted in tomographic measurements from the surface to a horizontal bore-hole, and was dedicated to estimating the velocity and attenuation fields across the site. The second was a series of monostatic 2D surface profiling above each known buried heterogeneity and recorded using different antenna frequencies, complemented by 3D coverage over a specific area. Finally, bistatic
Com-Ž .
mon Mid Point CMP measurements in the sub-horizontally layered part of the site constituted the
third experiment. To guarantee the quality of inter-pretations, we tested different processing techniques, such as velocity and attenuation inversion, 2Dr3D migration plus forward modeling, and velocity analy-sis on the CMPs, which led to the definition of the most appropriate technique for imaging each object and characterizing the dielectric behavior of each host material.
After a description of the LCPC test site, an inventory of the different survey configurations used and the associated results are presented, followed by a discussion concerning the contribution of each acquisition and processing technique to imaging un-derground heterogeneities.
2. Field measurements and processing
2.1. The LCPC test site
In 1996, LCPC built a test site for geophysical
Ž .
measurements Chazelas et al., 1997 composed of a pit of dimensions 26=20=4 m, divided into five compartments filled with different host materials. Fig. 1 is a sketch of the site showing its main characteristics. Compartments 1, 3, 4 and 5 are respectively filled with silt, limestone sand, crushed gneiss with a grain size from 14 to 20 mm, and crushed gneiss with a grain size from 0.1 to 20 mm. Compartment 2 is horizontally layered with these four materials. Several types of object are buried in
Ž
the different compartments: polystyrene steps
com-.
partment 1 , iron pipes and PVC pipes filled with
Ž .
water or air compartments 1, 3, 4, and 5 , stones
Ž .
and large limestone blocks 3, 4, and 5 and a
Ž .
masonry and an iron girder 5 .
Ž
Depending on the type of host material silt,
.
limestone, gneiss , the grain size distribution and the
Ž .
Ž .
Fig. 1. Schematic diagram of the LCPC test site from Chazelas et al., 1997 . The five compartments, labeled 1 to 5, contain different host
Ž . Ž . Ž . Ž . Ž . Ž .
materials see legend and different buried objects, such as pipes E1 to E9 , voids D , blocks B , masonry M and stones S .
2.2. Surface–borehole tomography
Ž .
As described by Leggett et al. 1993 for seismic
Ž .
imaging, and by Olsson et al. 1992 , Valle and
Ž . Ž .
Zanzi 1997 , and Vasco et al. 1997 for GPR,
tomographic methods consist of inverting the ob-served radar wave travel times or amplitudes to determine the spatial distribution of velocity or atten-uation fields. Observed travel times and amplitudes are those measured after the radar wave has traveled
Ž .
Fig. 2. Schematic cross-section of the LCPC test site corresponding to the tomographic plane a , source–receiver geometry. The straight
Ž .
through the medium to be studied, from the transmit-ter to the receiver antenna.
In our configuration, a 100-MHz transmitter was displaced at the surface of the site according to the horizontal borehole direction, while the 100 MHz
Ž .
receiver was displaced inside the borehole Fig. 1 . Both antenna positions were spaced 0.5 m apart, producing 490 transmitter–receiver pairs for the ex-periment. The tomographic plane dimensions reach 27 m long by 4.5 m height, crossing perpendicularly
Ž .
the different compartments Fig. 2 .
The deformation of the pulse, i.e. time delay and amplitude decreasing, depends on the velocity and attenuation of the medium, and is a function of the path adopted by the radar wave between the trans-mitter and the receiver antennas. By picking the time of the earlier signal and its corresponding amplitude, one can relate each antenna position to these travel time and amplitude values. These data are then inverted according to the technique proposed by
Ž .
Jackson and Tweeton 1994 , where an iterative scheme is used to recover the velocity and attenua-tion fields.
Observed travel time t results from the sum along the ray path l of the product between the elementary portion of ray d l and the slowness p, taken as the reverse of the local velocity value.
ts
H
p l d lŽ .
Ž .
1l
For a large number of observations, a matrix notation can be used to express the slowness field P
vs. the travel times T and the partial derivative D matrices.
PsDy1T
Ž .
2Ž .
Eq. 2 is resolved using an Algebraic
Reconstruc-Ž .
tion Technique ART to reduce computation time
Ž .
and improve stability Mason, 1981 . As mentioned
Ž .
by Hollender 1999 , the interaction between the antenna and the medium is a crucial point in GPR attenuation tomography because the interactions be-tween the antenna and the soil affect the transmitted signal in amplitude and frequency. In our approach, where only amplitude effects are studied, we will correct the observed signals for antenna radiation pattern and coupling effects. The radiation pattern correction is estimated according to the work of
Ž .
Arcone 1995; Appendix . The antenna coupling cor-rection is introduced in the reference amplitude A0
Ž .
as described in Olsson et al. 1992 . The measured amplitudes A of the transmitted signal are then inverted assuming the following relation:
eyal
AsA D0
Ž
uT,fT. Ž
D uR,fR.
Ž .
3 lŽ .
Where D u,f is the radiation pattern correction for a ray with azimuth f and elevation u from the
Ž . Ž .
vertical, with fT,uT and fR,uR being azimuths and elevations of the ray at the transmitter and the receiver, respectively. Parameter a refers to the attenuation factor and l is the travel path of the radar
Ž .
wave. To calculate the a parameter, Eq. 3 is linearized using a decimal logarithmic conversion:
y20 log Aq20 log D
Ž
u ,f. Ž
D u ,f.
20 log lq20 log A left-hand term can be estimated for eachtransmis-sion measurement so that:
y20 log Aq20 log D
Ž
u ,f. Ž
D u ,f.
y20 log lq20 log AŽ
T T E E 0.
s
H
aŽ .
l d l.Ž .
5Ž . Ž .
Eq. 5 now has the same form as Eq. 1 and can therefore be resolved using the algorithm already described for travel time inversion. The parametriza-tion used to discretize the velocity field consisted in 108 by 16 squared cells. Computations were
per-Ž
formed using MIGRATOM software Jackson and
.
Tweeton, 1994 based on an ART scheme and using either straight or curved ray geometries. According
Ž .
to the proposition of Ivansson 1987 for avoiding ray bending complications, the path of the radar
Ž . Ž .
Fig. 3. Schematic cross-section of the LCPC test site corresponding to the tomographic plane a , velocity tomogram using straight rays b ,
Ž . Ž .
Ž
wave was first approximated to straight rays Fig.
.
3b and convergence was reached after seven
itera-Ž .
tions. We then used curved rays Fig. 3c for the following three iterations to see whether conver-gence improved. Two more iterations were run using curved rays before the model diverged. Fig. 3c and d shows respectively the velocity and attenuation dis-tributions on a longitudinal cross-section of the site. The different compartments can be distinguished on the velocity and attenuation tomograms. The av-eraged values of inverted velocity for compartments 1, 3, 4 and 5 are respectively estimated at 0.09, 0.12, 0.17 and 0.12 mrns. Similarly, the averaged attenua-tion values are estimated respectively at 9.5, 4.3, 2.6
Ž .
and 6.9 dBrm Table 1 . Compartments 3 and 5 are
Ž .
characterized by mean velocity 0.12 mrns and
Ž .
attenuation 4.3–6.9 dBrm values compared to compartments 1 and 4 that are filled with highly
Ž .
contrasted materials: high attenuation 9.5 dBrm
Ž .
and low velocity 0.09 mrns for compartment 1,
Ž .
and low attenuation 2.6 dBrm and high velocity
Ž0.17 mrns for compartment 4. This indicates that.
various kinds of material can be identified from velocity and attenuation tomograms, provided that their nature and granulometry show a sufficient con-trast.
Concerning the buried objects, no discernible sig-nal can be related to a specific target. Although some visible anomalies can be related to certain objects
ŽD, B1, B2, M , this is not the case for other signals. Že.g. a1, a2 . This difficulty to relate velocity and.
attenuation anomalies to buried objects can have two origins. The first one involves artifacts generated by errors when determining time zero, picking events or
Ž .
computing ray path geometry Hollender, 1999 . The other is related to resolution limits and uniqueness in tomography. This problem, examined in Williamson
Ž1991 , Williamson and Worthington. Ž1993. and
Ž .
Rector and Washbourne 1994 , can be due to pro-jection truncation, limited angular aperture or Fresnel zone dimensions. According to Rector and
Wash-Ž .
bourne 1994 , projection truncation can explain the resolution drop in the left and right extremities of the tomograms. Elsewhere, a limitation of the angular aperture defined by the geometry of the tomographic device can alter the spatial resolution. These authors state that the aperture-related resolution is approxi-mately equal to the Fresnel zone when:
y2
lrRs 58.8 tan
Ž
DF.
where l is the wavelength, R is the raypath length andDF is the angular aperture. In our case, where l
Table 1
Ž . Ž .
Averaged wave parameters V: velocity; a: attenuation , dielectric parameters K : relative permittivity; Q: quality factor and GPR
Ž .
performance parameters P: wave penetration; r: wave resolution estimated from the different GPR techniques A, B and C carried out in
Ž .
compartments 1 to 5. A Velocity and attenuation values averaged for each node of the tomographic planes belonging to a specific
Ž . Ž .
compartment. B Wave parameters averaged from the 12 forward models for the 900, 500 and 300 MHz frequencies. C Velocity values averaged from the 13 NMO analyses. For parameters strongly dependent on frequency, extreme values for 300 and 900 MHz frequencies are indicated
Compartment 1: Silt 3: Limestone sand 4: Gneiss 14r20 5: Gneiss 0r20
( )A Surface borehole tomography
Ž .
r300 – 900 MHz m 0.15–0.03 0.14–0.03 0.23–0.06 0.16–0.04
( )C CMP analysis
Ž .
is comprised between 0.9 and 1.7 m, the Fresnel zone can be considered as the main limiting factor in terms of spatial resolution.
2.3. 2D surface profiling
This field experiment consisted in 12 surface GPR profiles located above the buried objects. They were devoted to analysing the diffracted signal in the classical minimum-offset configuration with 300, 500 and 900 MHz centered frequency antennas. The profiles were processed using the software Radar
Ž
Unix developed at the BRGM Grandjean and
Du-.
rand, 1999 according to the processing flow se-quence:
v spatial re-sampling of scans along the antenna
displacement axis to correct for velocity variations of the antenna during displacement;
v recovering amplitudes vs. time with an adaptive
gain function to correct for geometrical spreading and attenuation;
v coherence and frequency filtering according to the
observed amplitude spectrum to improve the signal to noise ratio;
v static corrections to remove topographic effects;
Ž .
Fig. 4. Schematic plan showing the location of profile 6 in compartment 3 of the LCPC test site a , and radar sections along profile 6 at 300
Ž . Ž . Ž . Ž .
v migration to correctly position the objects, the
migration velocities being calculated from the diffraction hyperbolas curvature.
As an example, Fig. 4 shows three typical pro-cessed sections before migration corresponding to
Ž .
profile 6 Fig. 4a , and recorded respectively with
Ž . Ž . Ž .
300 Fig. 4b , 500 Fig. 4c , and 900 MHz Fig. 4d antennas. These sections show reflected and diffracted signals in response to the different objects located in compartment 3: the lateral limit of the pit
Ž .P , a void D and different kinds of pipes E1–E9 .Ž . Ž .
In particular, these sections illustrate the variations in the maximum depth of penetration and resolution with frequency. The radar wave penetrates down to the bottom of the pit with the 300 and 500 MHz antennas, as its reflection can be observed at about 85 ns, whereas with the 900 MHz antenna, the wave is entirely attenuated at about 50 ns. Taking the velocities calculated from the transmission measure-ments, the corresponding penetration depths can be estimated at around 4.5 and 2 m for the 300–500 and 900 MHz antennas, respectively. Similarly, the sig-nal resolution, which we define here as a quarter of the ratio between the velocity and nominal frequency of the returned signal, can be estimated from these
Ž .
sections. For example, on profile 6 Fig. 4 , the resolution increases from 0.03 to 0.14 m when con-sidering 900 and 500 MHz antennas. Other GPR sections were similarly analysed in order to estimate
Ž .
such parameters Table 1 .
In addition, 53 parallel profiles, with a 10-cm spacing along the y-axis, were carried out with the 900 MHz antenna in compartment 4 so as to obtain a 3D data cube measuring 22=5.2 m. To reduce the volume of data without degrading the quality, data were resampled with inter-scans of 2 and 10 cm along the y- and x-axes, respectively, meaning that the final 3D data set was composed of 1101=53 scans. This experiment was performed in order to highlight the out-of-plane signals produced by side
Ž .
echoes, already described by Olhoeft 1994 . The study area is known to present longitudinal hetero-geneities — such as pipes — along the y-axis. If these are perfectly cylindrical, the out-of-plane sig-nals would be insignificant, and thus, the migrated
Ž .
and non-migrated sections in the y,t plane identi-cal.
Fig. 5 shows two vertical sections through the
Ž .
data cube with no migration Fig. 5a , 2D migration
Ž . Ž .
in the x,t plane Fig. 4b , and 3D migration in the
Žx, y,t volume Fig. 5c . Fig. 5d indicates the loca-. Ž .
tion of the two sections and that of the buried objects. Analysis of these sections, particularly for the two signals enhanced by white arrows, reveals a remarkable difference depending on whether 2D or 3D migration was performed, with 3D migration offering a better focused signal than 2D migration.
Fig. 5. Schematic block-diagram of compartment 4 showing the buried objects and the vertical sections used to analyse the 3D
Ž .
data cube d . Vertical sections through the 3D data cube without
Ž . Ž . Ž .
migration a , with 2D migration of the x,t plane b , and with
Ž . Ž . Ž .
3D migrations of the x,t and y,t planes c . The arrows
Ž . Ž .
This confirms the existence of out-of-plane signals, a phenomenon that is observed every time a GPR
profile crosses a structure that is not perfectly cylin-drical, which is most often the case.
Ž . Ž .
Fig. 6. CMP gather recorded along the x-axis at a y-distance of 13 m a , with the corresponding semblance diagram b , and interval
Ž . Ž .
velocity curve c . Interval velocity curves calculated for all the CMPs were superposed onto the interpolated velocity field d . Migrated
Ž .
2.4. CMP measurements
CMPs were recorded in compartment 2, which is composed of seven horizontal layers of the different materials. The bistatic acquisition device consisted of two antennas that were moved symmetrically apart from a central point. The resulting data set — CMP gathers — is composed of a series of scans with the same CMP, and recorded with increasing transmit-ter–receiver offsets. This measurement configuration is used to estimate velocity variations with depth by
Ž .
applying the appropriate Normal Move Out NMO
Ž
corrections to each scan Fisher et al., 1992; Tillard
.
and Dubois, 1995; Greaves et al., 1996 . In our case, this operation was repeated so as to obtain 13 differ-ent CMPs distributed along the x-axis with measure-ments realized for each using 500 MHz antennas every 0.2 m with offsets ranging from 0.4 to 5 m. Fig. 6a shows an example of a CMP gather. NMO
Ž .
analyses were processed using Eq. 6 , giving the expression of the time correctionDt as a function of velocity V and offset x:
1r2 2
x
Dtst 1
ž
yV t2 2/
.Ž .
6The appropriate velocity law was then estimated
Ž
from the semblance diagram, calculated with Neidel
.
and Taner, 1971 :
2
For each CMP, the corresponding semblance
dia-Ž . Ž .
gram Fig. 6b was calculated from Eq. 7 giving the best velocity law found from the NMO correc-tions. These velocities were then converted to
inter-Ž .
val velocities Fig. 6c according to the Dix equation
ŽDix, 1955 . Depending on the CMP gather, the.
number of constant velocity layers varies from five to seven, and depending on the layer considered, the interval velocity ranges from 0.07 to 0.17 mrns. Lateral velocity variations are observed within lay-ers. Two principal causes can be proposed, the first involving the processing sequence and essentially due to errors introduced when picking velocities as
maxima of semblance diagrams, and the second re-lating to lateral velocity variations due to the differ-ential compaction of materials constituting each layer. In order to image appropriately the monostatic sec-tion recorded in compartment 2, a smoothed velocity field was computed from previous velocity analyses
ŽFig. 6d . A correlation between borehole informa-.
Ž .
tion and the migrated section Fig. 6e indicated that most of the reflections are related to dielectric con-trasts due to lithology.
Because the materials in compartment 2 are the same as those used to fill the other compartments, the CMP averaged velocities and those calculated from the tomograms or estimated from the 2D pro-files are compared in Table 1.
3. Synthesis and discussion
We shall now compare and discuss the data recorded at the LCPC test site using the different GPR acquisition techniques and the results obtained from the various types of processing. After a synthe-sis concerning radar wave penetration, resolution, velocity and attenuation for each sounded material, we will consider the effective contribution of GPR applied to civil-engineering auscultation.
3.1. On penetration and resolution
The GPR profiles in Fig. 4 show reflections from
Ž .
the boundaries of the test site P , and some
diffrac-Ž . Ž .
tions from a void D or pipes E1–E9 buried in compartment 3. The frequency effect of the source is clearly illustrated in terms of penetration and resolu-tion.
In order to estimate the penetration and resolution of radar waves according to the physical character-istics of the different compartments, we tried to match observed GPR profiles with those calculated by forward modeling. The advantage of this method is the full integration of the wave propagation phe-nomena. The modeling principle, taken from Bitri
Ž .
parame-ters are explicitly introduced in the numerical grid as the relative permittivity:
´0
Ks ,
´void
and the quality factor:
1 v´X
Ž .
vQs s Y ,
tand sqv´
Ž .
vŽ .
taken as the reverse of the loss tangent Bano, 1996 . It was demonstrated in these studies that the medium parameters are respectively associated to propagation parameters, namely velocity, attenuation and wave dispersion. As suggested by Turner and Siggins
Ž1994 , the approximation of a constant Q attenua-.
tion model leads to consider the Q values as valid only in a restricted frequency bandwidth. Conse-quently, identical models calculated with very differ-ent frequency bandwidths should not be comparable. A trial and error match of the modeled and observed sections was performed to estimate these quantities
characterizing the materials composing the site. The position and nature of the buried objects was known and imposed in these models.
The section presented in Fig. 4c was modeled according to the dielectric models presented in Fig. 7a and b; the corresponding synthetic section is presented in Fig. 7c. The dielectric models were adjusted so that the curvature of the hyperbolas and the limit of GPR signal penetration respected Fig. 4c, indicating a good estimation of the wave velocity and attenuation. This procedure was repeated for all the GPR profiles. The values of the K and Q parameters attributed to the different media of the compartments, and the related parameters for the extreme 300 and 900 MHz frequencies are presented in Table 1.
The response to the heterogeneities also merits analysis because this depends on resolution com-pared to size. When objects are sufficiently large
Ž .
compared to wavelength e.g. blocks, voids, etc. , their interpretation is facilitated because the reflected signal contains complete information about their
Ž . Ž .
Fig. 7. Relative permittivity a , and Q factor distribution b used to model the 2D 500 MHz GPR profile recorded in compartment 3
Žcompare with Fig. 3c , and the computed synthetic section c . The method for estimating velocity from hyperbola curvature and the limit. Ž . Ž
of penetration are indicated. Pspit limit reflection; Dsvoid diffraction; E1–E9sdiffraction of three sets of pipes E1–E4–E7,
.
shape. On the contrary, when objects are too small compared to wavelength, they are difficult to identify because diffraction phenomena occur, causing com-plex interactions between the wave and the objects. Consequently, no major difference was observed be-tween the GPR signature for the cables and the small pipes, except for the pipe containing water. In this
Ž .
case Fig. 4c , pipe diameter is 4 cm, with pipe E1 made of metal iron and pipes E2 and E3 made of PVC containing water and air, respectively. The GPR responses to pipes E1 and E2 show one and two hyperbolas, respectively. For E1, the observed signal represents diffraction of the wave on the metallic pipe, whereas for E2, echoes from the top and bottom of the pipe are observed, which occurs
Ž .
when the medium inside the pipe water in this case has a sufficiently low velocity to separate the two echoes of the returned signal. In comparison, the signal of pipe E3 containing air shows a different pattern because the velocity through air is higher, thus rendering the two echoes mixed and indis-cernible.
3.2. OnÕelocity and attenuation
The velocity values obtained from surface–bore-hole tomography, 2D profiling and CMP analysis are summarized in Table 1. For each compartment of the site, the deviation between the velocity values esti-mated from the three considered techniques is only a few centimeters per nanosecond, which indicates coherent results and a good reliability for each method. However, local heterogeneities in the medium can produce a dispersion of the attenuation and velocity values, leading to some difficulties in recovering the main structures. For example, Fig. 6d and e shows the complexity involved in correlating the information derived from interval velocity curves with the a piori known velocity layers. The high
Ž .
velocity value 0.15–0.17 mrns observed for com-partment 4 using the different techniques could be explained by the high porosity of the gneiss at B 14r20 mm. The effective characteristics of this ma-terial, considered as a mixture of bulk rock and air, can be approached by a simple Lichtenecker’s law
ŽOlhoeft, 1980 :.
KsKx1Kx2. . . Kxi
Ž .
81 2 i
where K) is the effective permittivity, and K and i
x the permittivity and volume fraction of the ithi
medium, respectively. Assuming that bulk gneiss
Ž
permittivity is that of compartment 5 6.9 — gneiss
.
at B 0r20 mm and thus low porosity , that air
) Ž
permittivity is 1, and that K s3 i.e. the
permittiv-. Ž .
ity measured in compartment 4 , Eq. 8 gives a porosity for compartment 4 of about 0.3, which is in good agreement with the sample measurements.
On the contrary, the values of attenuation factor estimated from the attenuation tomography and 2D profiling show a higher disparity, insofar as the former are systematically lower than that latter. Be-cause the surface–borehole and 2D surface surveys
Ž .
were carried out respectively with low 100 MHz
Ž .
and high 300, 500 and 900 MHz antennas, this disparity could result to the approximation
intro-Ž
duced in the constant Q attenuation model Turner
.
and Siggins, 1994 . This model assumes that Q, taken as the slope of the attenuation factor a vs. frequency, is constant for restricted frequency band-widths, but not for a wide range in frequency, for example 100 to 900 MHz. The increasing value of Q with frequency observed here has already been
de-Ž .
scribed by Powers and Olhoeft 1994 and Hollender
Ž .
and Tillard 1998 . This shows the limitations of the constant Q model and prevents representation of a material attenuation by a single parameter because it also depends on the frequency used.
In the case of the LCPC test site, the maximum depth of penetration and resolution vary respectively from 1 to 5 m and from a few centimeters to 0.25 m, depending on the considered frequency and the di-electric properties of the medium. The present study has demonstrated the potentiality of three different GPR techniques when applied to civil-engineering investigations, provided that the appropriate recom-mendations are respected.
v When boreholes are available, velocity and
at-tenuation tomography is suitable for estimating the dielectric properties of a medium. Heterogeneities can also be imaged provided that they are larger than the wavelength. The ray coverage and angular reso-lution used in the reconstruction algorithm must also be adapted.
v 2D surface profiling is best suited to quickly
to depth domain, out-of-plane signals generate arti-facts when the structures are not perfectly cylindri-cal. For advanced studies, modeling algorithms can be used to estimate dielectric properties of the medium and heterogeneities.
v For sub-horizontally layered media, CMP
pro-cessing by NMO analysis and semblance diagrams can be used to recover velocity variations with depth. This technique offers a resolution in relation to the frequency used. In our case, the 100 MHz signal has too large a wavelength to resolve the velocity layers, but the velocity distribution found gives a first ap-proximation of the medium properties.
Consequently, the GPR experiments carried out on the LCPC test site led us to consider the different capabilities of these techniques for civil-engineering sounding applications in urban environments. Al-though velocity and attenuation distributions can be efficiently recovered by surface–borehole tomogra-phy, boreholes are generally not available. In this case, velocity distribution with depth can be success-fully estimated from CMP measurements, provided that the medium is sub-horizontally layered. Monos-tatic 2D surface profiling is well adapted to quickly locating underground heterogeneities with a rela-tively high reliability and, provided that control by modeling is carried out, velocity and attenuation data can be approximately estimated.
4. Conclusion
In the framework of a study dedicated to estimat-ing the performance of GPR for civil-engineerestimat-ing applications, three sounding techniques were tested on the LCPC test site at Nantes, France: surface– borehole tomography, 2D surface profiling and CMP analysis.
After processing according to three techniques, the results are coherent in terms of velocity and attenuation values. Monostatic 2D surface profiling is the fastest and most reliable way of imaging sub-surface structures. Forward modeling can also be used to analyse this response in order to obtain more quantitative interpretations. In reality, the choice of the sounding technique depends on the kind of problem to be resolved and the field conditions. If boreholes are available, velocity and attenuation
tomography is suitable for estimating the dielectric properties of a medium. Heterogeneities can also be imaged depending on limitations due to aperture-re-lated resolution and Fresnel zone dimension. CMP analysis can be used to recover the velocity field if the substratum is sub-horizontally layered. This in-formation is then used to correctly image the monos-tatic sections. The performance of each technique is mainly conditioned by the material properties. In our case, depending on the kind of material sounded
Žsilt, limestone sand, gneiss with different grain size.
and the source frequency used, resolution and attenu-ation vary from a few centimeters to 0.25 m and from 2.5 to 45 dBrm, respectively. The penetration depth varies from approximately 1 to 5 m, making GPR a convenient tool for civil-engineering sound-ing applications.
Acknowledgements
This work was carried out with the support of BRGM and the National Project on Trenchless works. We would like to thank LCPC for letting us use the test site, and for the technical support during the acquisition campaign. We also thank Rowena Stead for careful editing of the final manuscript.
Appendix A. GPR modeling method
The starting point is a solution of Maxwell’s
Ž
equation in the frequency–wavenumber domain v,
.
k . This expression gives the electric field E gener-ated by a source locgener-ated at depth z, propagating upward through a homogeneous medium prior to
Ž
being recorded at the surface Bitri and Grandjean,
.
1998 :
E k , k , z
Ž
s0,v.
sE k , k , z ,Ž
v.
eyi kzzŽ
A1.
x y x y
where k , k , and k are the wavenumbers in the x,x y z y and z direction, respectively, v is the angular frequency, and i is the imaginary unit in the complex
Ž .
space. Eq. A1 is associated to the dispersion equa-tion relating kz to k , kx y and k, defined as the wavenumber in the propagation direction:
2 2 2
k is generally a complex quantity ksbqia, where the real and imaginary parts refer respectively to the phase and attenuation factors, and depend on the dielectric properties of the medium according to the
Ž .
classical relation Ward and Hohmann, 1987 :
2
(
ks v ´myivms
Ž
A3.
where ´, m and s are respectively the complex dielectric permittivity, the magnetic permeability and the electric conductivity. To take into account the dispersion process in which dielectric parameters are dependent on frequency, a Q constant relaxation model can be used, as mentioned by Turner and
Ž .
Siggins 1994 . The dielectric permittivity becomes
ŽBano, 1996 :.
ny1
v ny1
´ v
Ž .
s´0ž /
Ž
yi.
Ž
A4.
v0
in which ´0 and v0 are two constants taken respec-tively as the reference permittivity and frequency. The index n is related to the quality or dissipation factor Q:
2 y1 v´X
Ž .
vns tan
Ž .
Q where Qs YŽ
A5.
p sqv´
Ž .
vŽ . Ž .
By combining Eqs. A3 and A4 k, which is now dependent on frequency:
Žny1.r2
Assuming that we define a reference velocity V0
as:
and the expressions of a and b becomes:
v p v
Because we only consider the monostatic mode, i.e. the transmitter at the same location as the re-ceiver, we can split the electric field E into its downgoing Ey and upgoing Eq components, and
state that:
E k , k , z
Ž
s0,v.
sEqŽ
k , k , z ,v.
eyi kzzŽ
A9a.
x y x y
provided that the phase velocity is divided by two. This assumption refers to the exploding source model
ŽClaerbout, 1985 . In the case of a ID medium,.
where variations of dielectric parameters are only observed along the z direction, we can express the above equation as:
E k , k , z
Ž
x y szyDz ,v.
sR k , k , z E
Ž
.
qŽ
k , k , z ,v.
eyi kzDzŽ
A9b.
x y x y
where Dz is the discretization step along z, and
Ž .
R k , k , zx y is the space Fourier transform of the medium impedance contrasts. Using a phase-shift
Ž .
method Gazdag, 1978 , the upgoing wave is con-volved to the R function from zszmax prior to being extrapolated upward to z–Dz until zs0.
Because the extrapolation in the Fourier domain
Ž .
demands a homogeneous medium in x, y,Dz lay-ers, two computational steps are needed. In a first instance, the medium properties are averaged in
lay-Ž .
ers x, y,Dz , so that the medium becomes
horizon-Ž . Ž .
tally stratified and Eqs. A9a and A9b can be applied. For that, the wavenumber kz m is calculated from the averaged medium properties ´m, sm and
mm. In a second instance, a correction term is applied
Ž .
to the extrapolated field in the x, y, z,v space to take into account the lateral variations of the medium. The exact correction term is:
2 2 2 2 2 2
i
Ž
'
kz mykxykyy'
kx y zykxyky.
Dze
Ž
A10.
where kx y z is the exact wavenumber calculated with non-averaged dielectric parameters. In view of the
Ž .
is approximated with a zero order Taylor expansion, giving the approximated correction term:
eiŽkm zykx y z.Dz.
Ž
A11.
Finally, the antenna spectral signature and its radiation pattern have to be taken into account. The antenna spectral content is integrated by multiplying the extrapolated field by the tapering function:
2
where vc and vN are respectively the centre and Nyquist angular frequencies, and Bv is the band-width. The term related to the 3D antenna pattern is
Ž .
then applied to E k , k , zx y s0,v according to ana-lytical solutions of a single element steady state
Ž .
dipole Arcone, 1995 :
cosusinw
where K is a constant related to the antenna, n is the
5
refraction index in the medium, the symbols and
H and define the parallel and normal planes with
respect to the antenna displacement, e and i sub-scripts refer to the external and internal field, respec-tively, with respect to the critical angle.
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