Evaluation of GPR techniques for civil-engineering ...directory.umm.ac.id/Data Elmu/jurnal/J-a/Journal Of Applied Geophys… · The deformation of the pulse, i.e. time delay and amplitude

Ž .Journal of Applied Geophysics 45 2000 141–156www.elsevier.nlrlocaterjappgeo

Evaluation of GPR techniques for civil-engineering applications:study on a test site

G. Grandjean), J.C. Gourry, A. BitriBRGM, 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 theperformance 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 . Žtomographic surface to horizontal borehole measurements , monostatic 2D surface profiling and bistatic Common Midw 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 beŽ .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 toŽ .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 curveanalysis, 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 givesrelatively good estimations of vertical velocity contrasts when the medium is layered. A lithologic log can be derivedassuming that the velocity changes are related to material variations. q 2000 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: q33-2-38-64-33-61.

Ž .E-mail address: [email protected] G. Grandjean .

urban environments, especially for trenchless works.For example, unknown concrete house foundationsor sandstone blocks located along the path of adrilling machine can cause major equipment damageand thus a loss of time and money. Geophysicalmethods, particularly the ground-penetrating radarŽ .GPR , can detect such superficial bodies with arelative efficiency depending on the field context, thedielectric properties of the host material and the

0926-9851r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0926-9851 00 00021-5

( )G. Grandjean et al.rJournal of Applied Geophysics 45 2000 141–156142

nature and size of the bodies. The objective of thiswork, funded by the BRGM and the National Projecton Trenchless Works, is to review the capabilities ofGPR in urban environments for civil-engineeringapplications. We approached this problem by com-paring the results obtained at the same site usingdifferent survey configurations and different process-ing techniques.

The success of such work is mainly conditionedby the features of the site where data acquisition iscarried out. Firstly, the site must be representative ofthe urban environment, which means that the proper-ties of the host materials and buried heterogeneitiesmust be consistent with those commonly found be-neath cities. Furthermore, the selected site must bewell known and calibrated so as to be able validatethe tested methods, i.e. the nature of the host mate-rial and the position of the buried heterogeneitiesmust be precisely known. Finally, to ensure optimumdata acquisition, the site must be easily accessible

Žand 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´Ž .Chazelas 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,

Žvoids, 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 togetherunder the same field conditions. In view of this, wepresent here the results of three different experimentssystematically tested and compared at the same testsite. The first experiment consisted in tomographicmeasurements from the surface to a horizontal bore-hole, and was dedicated to estimating the velocityand attenuation fields across the site. The second wasa series of monostatic 2D surface profiling aboveeach known buried heterogeneity and recorded usingdifferent antenna frequencies, complemented by 3Dcoverage 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, 2Dr3Dmigration plus forward modeling, and velocity analy-sis on the CMPs, which led to the definition of themost appropriate technique for imaging each objectand characterizing the dielectric behavior of eachhost material.

After a description of the LCPC test site, aninventory of the different survey configurations usedand the associated results are presented, followed bya discussion concerning the contribution of eachacquisition 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 geophysicalŽ .measurements Chazelas et al., 1997 composed of a

pit of dimensions 26=20=4 m, divided into fivecompartments filled with different host materials.Fig. 1 is a sketch of the site showing its maincharacteristics. Compartments 1, 3, 4 and 5 arerespectively filled with silt, limestone sand, crushedgneiss with a grain size from 14 to 20 mm, andcrushed gneiss with a grain size from 0.1 to 20 mm.Compartment 2 is horizontally layered with thesefour materials. Several types of object are buried in

Žthe different compartments: polystyrene steps com-.partment 1 , iron pipes and PVC pipes filled withŽ .water or air compartments 1, 3, 4, and 5 , stones

Ž .and large limestone blocks 3, 4, and 5 and aŽ .masonry and an iron girder 5 .

ŽDepending on the type of host material silt,.limestone, gneiss , the grain size distribution and the

Ž .buried object pipe, void, block, stone, etc. , theGPR signals acquired will vary because they areaffected by lithology, granulometry and the presenceof diffractors. In addition, the nature and dimensionof host materials and buried objects make this siterepresentative of true civil-engineering contexts. Fur-thermore, as LCPC positioned with high precision allthe objects and the limits of each compartment dur-ing the construction of the site, geophysical anoma-lies can be correlated to them without doubt.

( )G. Grandjean et al.rJournal of Applied Geophysics 45 2000 141–156 143

Ž .Fig. 1. Schematic diagram of the LCPC test site from Chazelas et al., 1997 . The five compartments, labeled 1 to 5, contain different hostŽ . 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 seismicŽ .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 todetermine the spatial distribution of velocity or atten-uation fields. Observed travel times and amplitudesare 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 straightŽ .lines connect source–receiver pairs used in the crosswell experiment b .


through the medium to be studied, from the transmit-ter to the receiver antenna.

In our configuration, a 100-MHz transmitter wasdisplaced at the surface of the site according to thehorizontal 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 reach27 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 andattenuation of the medium, and is a function of thepath adopted by the radar wave between the trans-mitter and the receiver antennas. By picking the timeof the earlier signal and its corresponding amplitude,one can relate each antenna position to these traveltime and amplitude values. These data are theninverted according to the technique proposed by

Ž .Jackson and Tweeton 1994 , where an iterativescheme is used to recover the velocity and attenua-tion fields.

Observed travel time t results from the sum alongthe ray path l of the product between the elementaryportion of ray d l and the slowness p, taken as thereverse of the local velocity value.

ts p l d l 1Ž . Ž .Hl

For a large number of observations, a matrixnotation can be used to express the slowness field P

vs. the travel times T and the partial derivative Dmatrices.

PsDy1 T 2Ž .Ž .Eq. 2 is resolved using an Algebraic Reconstruc-

Ž .tion Technique ART to reduce computation timeŽ .and improve stability Mason, 1981 . As mentioned

Ž .by Hollender 1999 , the interaction between theantenna and the medium is a crucial point in GPRattenuation tomography because the interactions be-tween the antenna and the soil affect the transmittedsignal in amplitude and frequency. In our approach,where only amplitude effects are studied, we willcorrect the observed signals for antenna radiationpattern and coupling effects. The radiation patterncorrection 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 measuredamplitudes A of the transmitted signal are theninverted assuming the following relation:

eya l

AsA D u ,f D u ,f 3Ž . Ž . Ž .0 T T R R l

Ž .Where D u ,f is the radiation pattern correctionfor a ray with azimuth f and elevation u from the

Ž . Ž .vertical, with f , u and f , u being azimuthsT T R R

and elevations of the ray at the transmitter and thereceiver, respectively. Parameter a refers to theattenuation factor and l is the travel path of the radar

Ž .wave. To calculate the a parameter, Eq. 3 islinearized using a decimal logarithmic conversion:

y20 log Aq20 log D u ,f D u ,f 20 log lq20 log AŽ . Ž .Ž .T T E E 0sa l. 4Ž .

20 log e

Ž .As Eq. 4 is linear with regard to a and r, theleft-hand term can be estimated for each transmis-

sion measurement so that:

y20 log Aq20 log D u ,f D u ,f y20 log lq20 log AŽ . Ž .Ž .T T E E 0s a l d l. 5Ž . Ž .H

20 log e l


Ž . Ž .Eq. 5 now has the same form as Eq. 1 and cantherefore be resolved using the algorithm alreadydescribed for travel time inversion. The parametriza-tion used to discretize the velocity field consisted in108 by 16 squared cells. Computations were per-

Žformed using MIGRATOM software Jackson and.Tweeton, 1994 based on an ART scheme and using

either straight or curved ray geometries. AccordingŽ .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 .velocity tomogram using curved rays c , and attenuation tomogram d . The black circles indicate the antenna positions. See Fig. 1 for

legend.


Žwave 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 thefollowing three iterations to see whether conver-gence improved. Two more iterations were run usingcurved rays before the model diverged. Fig. 3c and dshows respectively the velocity and attenuation dis-tributions on a longitudinal cross-section of the site.

The different compartments can be distinguishedon the velocity and attenuation tomograms. The av-eraged values of inverted velocity for compartments1, 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 areŽ .characterized by mean velocity 0.12 mrns and

Ž .attenuation 4.3–6.9 dBrm values compared tocompartments 1 and 4 that are filled with highly

Ž .contrasted materials: high attenuation 9.5 dBrmŽ .and low velocity 0.09 mrns for compartment 1,

Ž .and low attenuation 2.6 dBrm and high velocityŽ .0.17 mrns for compartment 4. This indicates thatvarious kinds of material can be identified fromvelocity and attenuation tomograms, provided thattheir nature and granulometry show a sufficient con-trast.

Concerning the buried objects, no discernible sig-nal can be related to a specific target. Although somevisible anomalies can be related to certain objectsŽ .D, B1, B2, M , this is not the case for other signalsŽ .e.g. a1, a2 . This difficulty to relate velocity andattenuation anomalies to buried objects can have twoorigins. The first one involves artifacts generated byerrors when determining time zero, picking events or

Ž .computing ray path geometry Hollender, 1999 . Theother is related to resolution limits and uniqueness intomography. This problem, examined in WilliamsonŽ . Ž .1991 , Williamson and Worthington 1993 and

Ž .Rector and Washbourne 1994 , can be due to pro-jection truncation, limited angular aperture or Fresnelzone dimensions. According to Rector and Wash-

Ž .bourne 1994 , projection truncation can explain theresolution drop in the left and right extremities of thetomograms. Elsewhere, a limitation of the angularaperture defined by the geometry of the tomographicdevice can alter the spatial resolution. These authorsstate that the aperture-related resolution is approxi-mately equal to the Fresnel zone when:

y2lrRs 58.8 tan DFŽ .where l is the wavelength, R is the raypath lengthand DF is the angular aperture. In our case, where l

Table 1Ž . 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 inŽ .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 valuesaveraged from the 13 NMO analyses. For parameters strongly dependent on frequency, extreme values for 300 and 900 MHz frequenciesare indicated

Compartment 1: Silt 3: Limestone sand 4: Gneiss 14r20 5: Gneiss 0r20

( )A Surface borehole tomographyŽ .V mrns 0.09 0.12 0.17 0.12Ž .a dBrm 9.5 4.3 2.6 6.9

( )B 2D profilingK 13 6 3 5.5Q 7 20 30 7Ž .V mrns 0.07 0.12 0.17 0.13

Ž .a dBrm 15–45 6–20 1.5–4.5 9–27300 – 900 MHzŽ .P m 1.5–1 4.5–2 4.5–4.5 2.5–1.5300 – 900 MHzŽ .r m 0.15–0.03 0.14–0.03 0.23–0.06 0.16–0.04300 – 900 MHz

( )C CMP analysisŽ .V mrns – 0.10 0.15 0.10


is comprised between 0.9 and 1.7 m, the Fresnelzone can be considered as the main limiting factor interms of spatial resolution.

2.3. 2D surface profiling

This field experiment consisted in 12 surface GPRprofiles located above the buried objects. They weredevoted to analysing the diffracted signal in theclassical minimum-offset configuration with 300, 500and 900 MHz centered frequency antennas. Theprofiles were processed using the software Radar

ŽUnix developed at the BRGM Grandjean and Du-

.rand, 1999 according to the processing flow se-quence:

v spatial re-sampling of scans along the antennadisplacement axis to correct for velocity variationsof the antenna during displacement;

v recovering amplitudes vs. time with an adaptivegain function to correct for geometrical spreadingand attenuation;

v coherence and frequency filtering according to theobserved amplitude spectrum to improve the signalto 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 300Ž . Ž . Ž . Ž .MHz b , 500 MHz c , and 900 MHz d . Pspit limit; Dsvoid; E1–E9s three sets of pipes E1–E4–E7, E2–E5–E8, and E3–E6–E9

made respectively of iron, PVC filled with water, and PVC filled with air.


v migration to correctly position the objects, themigration velocities being calculated from thediffraction 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 withŽ . Ž . Ž .300 Fig. 4b , 500 Fig. 4c , and 900 MHz Fig. 4d

antennas. These sections show reflected anddiffracted signals in response to the different objectslocated in compartment 3: the lateral limit of the pitŽ . Ž . Ž .P , a void D and different kinds of pipes E1–E9 .In particular, these sections illustrate the variations inthe maximum depth of penetration and resolutionwith frequency. The radar wave penetrates down tothe bottom of the pit with the 300 and 500 MHzantennas, as its reflection can be observed at about85 ns, whereas with the 900 MHz antenna, the waveis entirely attenuated at about 50 ns. Taking thevelocities calculated from the transmission measure-ments, the corresponding penetration depths can beestimated at around 4.5 and 2 m for the 300–500 and900 MHz antennas, respectively. Similarly, the sig-nal resolution, which we define here as a quarter ofthe ratio between the velocity and nominal frequencyof the returned signal, can be estimated from these

Ž .sections. For example, on profile 6 Fig. 4 , theresolution increases from 0.03 to 0.14 m when con-sidering 900 and 500 MHz antennas. Other GPRsections 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 the900 MHz antenna in compartment 4 so as to obtain a3D data cube measuring 22=5.2 m. To reduce thevolume of data without degrading the quality, datawere resampled with inter-scans of 2 and 10 cmalong the y- and x-axes, respectively, meaning thatthe final 3D data set was composed of 1101=53scans. This experiment was performed in order tohighlight the out-of-plane signals produced by side

Ž .echoes, already described by Olhoeft 1994 . Thestudy area is known to present longitudinal hetero-geneities — such as pipes — along the y-axis. Ifthese 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 theŽ .data cube with no migration Fig. 5a , 2D migration

Ž . Ž .in the x,t plane Fig. 4b , and 3D migration in theŽ . Ž .x, y,t volume Fig. 5c . Fig. 5d indicates the loca-tion of the two sections and that of the buriedobjects. Analysis of these sections, particularly forthe two signals enhanced by white arrows, reveals aremarkable difference depending on whether 2D or3D migration was performed, with 3D migrationoffering a better focused signal than 2D migration.

Fig. 5. Schematic block-diagram of compartment 4 showing theburied objects and the vertical sections used to analyse the 3D

Ž .data cube d . Vertical sections through the 3D data cube withoutŽ . 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 arrowsŽ . Ž .highlight the signatures of a single pipe O and a set of pipes E .


This confirms the existence of out-of-plane signals, aphenomenon 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 intervalŽ . Ž .velocity curve c . Interval velocity curves calculated for all the CMPs were superposed onto the interpolated velocity field d . Migrated

Ž .section of the compartment 2 along the x-axis and borehole information for comparison e . Note the high velocity layer at a depth of 1.5 mcorresponding to the gneiss at B 14r20 mm.


2.4. CMP measurements

CMPs were recorded in compartment 2, which iscomposed of seven horizontal layers of the differentmaterials. The bistatic acquisition device consisted oftwo antennas that were moved symmetrically apartfrom a central point. The resulting data set — CMPgathers — is composed of a series of scans with thesame CMP, and recorded with increasing transmit-ter–receiver offsets. This measurement configurationis used to estimate velocity variations with depth by

Ž .applying the appropriate Normal Move Out NMOŽcorrections 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 antennasevery 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 theexpression of the time correction D t as a function ofvelocity V and offset x:

1r22xD ts t 1y . 6Ž .2 2ž /V t

The appropriate velocity law was then estimatedŽfrom the semblance diagram, calculated with Neidel

.and Taner, 1971 :2ny1

A t , jŽ .Ýž /js0

S t s . 7Ž . Ž .ny12n A t , jŽ .Ý

js0

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 equationŽ .Dix, 1955 . Depending on the CMP gather, thenumber of constant velocity layers varies from fiveto seven, and depending on the layer considered, theinterval velocity ranges from 0.07 to 0.17 mrns.Lateral velocity variations are observed within lay-ers. Two principal causes can be proposed, the firstinvolving the processing sequence and essentiallydue 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 velocityfield was computed from previous velocity analysesŽ .Fig. 6d . A correlation between borehole informa-

Ž .tion and the migrated section Fig. 6e indicated thatmost of the reflections are related to dielectric con-trasts due to lithology.

Because the materials in compartment 2 are thesame as those used to fill the other compartments,the CMP averaged velocities and those calculatedfrom 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 datarecorded at the LCPC test site using the differentGPR acquisition techniques and the results obtainedfrom 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 GPRapplied to civil-engineering auscultation.

3.1. On penetration and resolution

The GPR profiles in Fig. 4 show reflections fromŽ .the boundaries of the test site P , and some diffrac-

Ž . Ž .tions from a void D or pipes E1–E9 buried incompartment 3. The frequency effect of the source isclearly illustrated in terms of penetration and resolu-tion.

In order to estimate the penetration and resolutionof radar waves according to the physical character-istics of the different compartments, we tried tomatch observed GPR profiles with those calculatedby forward modeling. The advantage of this methodis the full integration of the wave propagation phe-nomena. The modeling principle, taken from Bitri

Ž .and Grandjean 1998 and fully presented in theAppendix, is based on upward extrapolation of thewavefield in the frequency–wavenumber domain byusing a phase-shift technique. The medium parame-


ters are explicitly introduced in the numerical grid asthe relative permittivity:

´0Ks ,

´void

and the quality factor:

1 v´X

vŽ .Qs s ,Ytand sqv´ vŽ .

Ž .taken as the reverse of the loss tangent Bano, 1996 .It was demonstrated in these studies that the mediumparameters are respectively associated to propagationparameters, namely velocity, attenuation and wavedispersion. As suggested by Turner and SigginsŽ .1994 , the approximation of a constant Q attenua-tion model leads to consider the Q values as validonly 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 observedsections was performed to estimate these quantities

characterizing the materials composing the site. Theposition and nature of the buried objects was knownand imposed in these models.

The section presented in Fig. 4c was modeledaccording to the dielectric models presented in Fig.7a and b; the corresponding synthetic section ispresented in Fig. 7c. The dielectric models wereadjusted so that the curvature of the hyperbolas andthe limit of GPR signal penetration respected Fig. 4c,indicating a good estimation of the wave velocityand attenuation. This procedure was repeated for allthe GPR profiles. The values of the K and Qparameters attributed to the different media of thecompartments, and the related parameters for theextreme 300 and 900 MHz frequencies are presentedin Table 1.

The response to the heterogeneities also meritsanalysis 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 reflectedsignal 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 3Ž . Ž .compare with Fig. 3c , and the computed synthetic section c . The method for estimating velocity from hyperbola curvature and the limit

Žof penetration are indicated. Pspit limit reflection; Dsvoid diffraction; E1–E9sdiffraction of three sets of pipes E1–E4–E7,.E2–E5–E8, and E3–E6–E9 made respectively of iron, PVC filled with water, and PVC filled with air.


shape. On the contrary, when objects are too smallcompared to wavelength, they are difficult to identifybecause 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 smallpipes, except for the pipe containing water. In this

Ž .case Fig. 4c , pipe diameter is 4 cm, with pipe E1made of metal iron and pipes E2 and E3 made ofPVC containing water and air, respectively. TheGPR responses to pipes E1 and E2 show one andtwo hyperbolas, respectively. For E1, the observedsignal represents diffraction of the wave on themetallic pipe, whereas for E2, echoes from the topand bottom of the pipe are observed, which occurs

Ž .when the medium inside the pipe water in this casehas a sufficiently low velocity to separate the twoechoes of the returned signal. In comparison, thesignal of pipe E3 containing air shows a differentpattern because the velocity through air is higher,thus rendering the two echoes mixed and indis-cernible.

3.2. On Õelocity and attenuation

The velocity values obtained from surface–bore-hole tomography, 2D profiling and CMP analysis aresummarized in Table 1. For each compartment of thesite, the deviation between the velocity values esti-mated from the three considered techniques is only afew centimeters per nanosecond, which indicatescoherent results and a good reliability for eachmethod. However, local heterogeneities in themedium can produce a dispersion of the attenuationand velocity values, leading to some difficulties inrecovering the main structures. For example, Fig. 6dand e shows the complexity involved in correlatingthe information derived from interval velocity curveswith 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 beexplained 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 lawŽ .Olhoeft, 1980 :

KsK x1 K x 2 . . . K x i 8Ž .1 2 i

where K ) is the effective permittivity, and K andi

x the permittivity and volume fraction of the ithi

medium, respectively. Assuming that bulk gneissŽpermittivity is that of compartment 5 6.9 — gneiss

.at B 0r20 mm and thus low porosity , that air) Žpermittivity is 1, and that K s3 i.e. the permittiv-

. Ž .ity measured in compartment 4 , Eq. 8 gives aporosity for compartment 4 of about 0.3, which is ingood agreement with the sample measurements.

On the contrary, the values of attenuation factorestimated from the attenuation tomography and 2Dprofiling show a higher disparity, insofar as theformer are systematically lower than that latter. Be-cause the surface–borehole and 2D surface surveys

Ž .were carried out respectively with low 100 MHzŽ .and high 300, 500 and 900 MHz antennas, this

disparity could result to the approximation intro-Žduced 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, forexample 100 to 900 MHz. The increasing value of Qwith frequency observed here has already been de-

Ž .scribed by Powers and Olhoeft 1994 and HollenderŽ .and Tillard 1998 . This shows the limitations of the

constant Q model and prevents representation of amaterial attenuation by a single parameter because italso depends on the frequency used.

In the case of the LCPC test site, the maximumdepth of penetration and resolution vary respectivelyfrom 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 studyhas demonstrated the potentiality of three differentGPR techniques when applied to civil-engineeringinvestigations, provided that the appropriate recom-mendations are respected.

v When boreholes are available, velocity and at-tenuation tomography is suitable for estimating thedielectric properties of a medium. Heterogeneitiescan also be imaged provided that they are larger thanthe wavelength. The ray coverage and angular reso-lution used in the reconstruction algorithm must alsobe adapted.

v 2D surface profiling is best suited to quicklyimaging small diffracted objects such as pipes, voids,etc. During migration of the GPR sections from time


to depth domain, out-of-plane signals generate arti-facts when the structures are not perfectly cylindri-cal. For advanced studies, modeling algorithms canbe used to estimate dielectric properties of themedium and heterogeneities.

v For sub-horizontally layered media, CMP pro-cessing by NMO analysis and semblance diagramscan be used to recover velocity variations with depth.This technique offers a resolution in relation to thefrequency used. In our case, the 100 MHz signal hastoo 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 outon the LCPC test site led us to consider the differentcapabilities of these techniques for civil-engineeringsounding applications in urban environments. Al-though velocity and attenuation distributions can beefficiently recovered by surface–borehole tomogra-phy, boreholes are generally not available. In thiscase, velocity distribution with depth can be success-fully estimated from CMP measurements, providedthat the medium is sub-horizontally layered. Monos-tatic 2D surface profiling is well adapted to quicklylocating underground heterogeneities with a rela-tively high reliability and, provided that control bymodeling is carried out, velocity and attenuation datacan be approximately estimated.

4. Conclusion

In the framework of a study dedicated to estimat-ing the performance of GPR for civil-engineeringapplications, three sounding techniques were testedon the LCPC test site at Nantes, France: surface–borehole tomography, 2D surface profiling and CMPanalysis.

After processing according to three techniques,the results are coherent in terms of velocity andattenuation values. Monostatic 2D surface profilingis the fastest and most reliable way of imagingsub-surface structures. Forward modeling can also beused to analyse this response in order to obtain morequantitative interpretations. In reality, the choiceof the sounding technique depends on the kind ofproblem to be resolved and the field conditions. Ifboreholes are available, velocity and attenuation

tomography is suitable for estimating the dielectricproperties of a medium. Heterogeneities can also beimaged depending on limitations due to aperture-re-lated resolution and Fresnel zone dimension. CMPanalysis can be used to recover the velocity field ifthe substratum is sub-horizontally layered. This in-formation is then used to correctly image the monos-tatic sections. The performance of each technique ismainly conditioned by the material properties. In ourcase, depending on the kind of material soundedŽ .silt, limestone sand, gneiss with different grain sizeand the source frequency used, resolution and attenu-ation vary from a few centimeters to 0.25 m andfrom 2.5 to 45 dBrm, respectively. The penetrationdepth varies from approximately 1 to 5 m, makingGPR a convenient tool for civil-engineering sound-ing applications.

Acknowledgements

This work was carried out with the support ofBRGM and the National Project on Trenchless works.We would like to thank LCPC for letting us use thetest site, and for the technical support during theacquisition campaign. We also thank Rowena Steadfor careful editing of the final manuscript.

Appendix A. GPR modeling method

The starting point is a solution of Maxwell’sŽequation in the frequency–wavenumber domain v,

.k . This expression gives the electric field E gener-ated by a source located at depth z, propagatingupward through a homogeneous medium prior to

Žbeing recorded at the surface Bitri and Grandjean,.1998 :

E k ,k , zs0,v sE k ,k , z ,v eyi k z z A1Ž .Ž . Ž .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 angularfrequency, and i is the imaginary unit in the complex

Ž .space. Eq. A1 is associated to the dispersion equa-tion relating k to k , k and k, defined as thez x y

wavenumber in the propagation direction:

2 2 2k s k yk yk A2Ž .(z x y


k is generally a complex quantity ksbq ia , wherethe real and imaginary parts refer respectively to thephase and attenuation factors, and depend on thedielectric properties of the medium according to the

Ž .classical relation Ward and Hohmann, 1987 :

2(ks v ´my ivms A3Ž .

where ´ , m and s are respectively the complexdielectric permittivity, the magnetic permeability andthe electric conductivity. To take into account thedispersion process in which dielectric parameters aredependent on frequency, a Q constant relaxationmodel can be used, as mentioned by Turner and

Ž .Siggins 1994 . The dielectric permittivity becomesŽ .Bano, 1996 :

ny1v ny1

´ v s´ yi A4Ž . Ž . Ž .0 ž /v0

in which ´ and v are two constants taken respec-0 0

tively as the reference permittivity and frequency.The index n is related to the quality or dissipationfactor Q:

2 v´X

vŽ .y1ns tan Q where Qs A5Ž . Ž .Y

p sqv´ vŽ .

Ž . Ž .By combining Eqs. A3 and A4 k, which isnow dependent on frequency:

Ž .ny1 r2v

k v sv m´Ž . ( 0 ž /v0

=p p

cos 1yn q isin 1yn A6Ž . Ž . Ž .4 4

Assuming that we define a reference velocity V0

as:

1r2v´ vŽ .0

V s ,0 w xRe k

we find

Ž .ny1 r2v v p

k v s 1q tan 1ynŽ . Ž .ž /ž /V v 40 0

A7Ž .

and the expressions of a and b becomes:

v p vas tan 1yn and bs A8Ž . Ž .

V 4 Vp p

vŽ1yn.r2Ž .for V sV defined as the phase veloc-p 0

v0ity.

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 itsdowngoing Ey and upgoing Eq components, andstate that:

E k ,k , zs0,v sEq k ,k , z ,v eyi k z z A9aŽ .Ž . Ž .x y x y

provided that the phase velocity is divided by two.This assumption refers to the exploding source modelŽ .Claerbout, 1985 . In the case of a ID medium,where variations of dielectric parameters are onlyobserved along the z direction, we can express theabove equation as:

E k ,k , zs zyD z ,vŽ .x y

sR k ,k , z Eq k ,k , z ,v eyi k z D z A9bŽ .Ž . Ž .x y x y

where D z is the discretization step along z, andŽ .R k ,k , z is the space Fourier transform of thex y

medium impedance contrasts. Using a phase-shiftŽ .method Gazdag, 1978 , the upgoing wave is con-

volved to the R function from zsz prior tomax

being extrapolated upward to z–D z until zs0.Because the extrapolation in the Fourier domain

Ž .demands a homogeneous medium in x, y,D z lay-ers, two computational steps are needed. In a firstinstance, the medium properties are averaged in lay-

Ž .ers x, y,D z , so that the medium becomes horizon-Ž . Ž .tally stratified and Eqs. A9a and A9b can be

applied. For that, the wavenumber k is calculatedz m

from the averaged medium properties ´ , s andm m

m . In a second instance, a correction term is appliedmŽ .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 2i k yk yk y k yk yk D z' 'z m x y x y z x yŽ .e A10Ž .where k is the exact wavenumber calculated withx y z

non-averaged dielectric parameters. In view of theŽ .difficulties in calculating the square roots, Eq. A10


is approximated with a zero order Taylor expansion,giving the approximated correction term:

e iŽk m zyk x y z .D z . A11Ž .Finally, the antenna spectral signature and its

radiation pattern have to be taken into account. Theantenna spectral content is integrated by multiplyingthe extrapolated field by the tapering function:

2vyvcG v sexp y withŽ . ž /ž /s

v y1 PBŽ .N vss A12Ž .

vc

where v and v are respectively the centre andc N

Nyquist angular frequencies, and B is the band-v

width. The term related to the 3D antenna pattern isŽ .then applied to E k ,k , zs0,v according to ana-x y

lytical solutions of a single element steady stateŽ .dipole Arcone, 1995 :

cosu sinwE sKIi 1r22 21yn sin w yncosuŽ .

cosu sinwE syiKIe 1r22 2n sin wy1 q incosuŽ .

E sKcoswHi

=

1r22 21yn sin w qncosuŽ .2sin ucosu 1r22 2n 1yn sin w ycosuŽ .

2cos uy 1r22 21yn sin w yncosuŽ .

E sKcoswHe

=

1r22 2n sin wy1 y incosuŽ .2sin ucosu 1r22 2n n sin wy1 q icosuŽ .

2cos uqi A13Ž .1r22 2n sin wy1 q incosuŽ .

where K is a constant related to the antenna, n is the5refraction 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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