Field measurements and processing

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 heterogeneities 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 ´ 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, 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, 2D r3D 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 . buried object pipe, void, block, stone, etc. , the GPR signals acquired will vary because they are affected by lithology, granulometry and the presence of diffractors. In addition, the nature and dimension of host materials and buried objects make this site representative of true civil-engineering contexts. Fur- thermore, as LCPC positioned with high precision all the objects and the limits of each compartment dur- ing the construction of the site, geophysical anoma- lies can be correlated to them without doubt. 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 . 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 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. t s p l d l 1 Ž . Ž . H l 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. P s D y1 T 2 Ž . Ž . 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 A Ž . as described in Olsson et al. 1992 . The measured amplitudes A of the transmitted signal are then inverted assuming the following relation: e ya l A s A D u ,f D u ,f 3 Ž . Ž . Ž . T T R R l Ž . Where D u ,f is the radiation pattern correction for a ray with azimuth f and elevation u from the Ž . Ž . vertical, with f , u and f , u being azimuths T T R R 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 A q 20 log D u ,f D u ,f 20 log l q 20 log A Ž . Ž . Ž . T T E E s a l. 4 Ž . 20 log e Ž . As Eq. 4 is linear with regard to a and r, the left-hand term can be estimated for each transmis- sion measurement so that: y20 log A q 20 log D u ,f D u ,f y 20 log l q 20 log A Ž . Ž . Ž . T T E E s a l d l. 5 Ž . Ž . H 20 log e l Ž . 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 . velocity tomogram using curved rays c , and attenuation tomogram d . The black circles indicate the antenna positions. See Fig. 1 for legend. 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 m rns. Similarly, the averaged attenua- tion values are estimated respectively at 9.5, 4.3, 2.6 Ž . and 6.9 dB rm Table 1 . Compartments 3 and 5 are Ž . characterized by mean velocity 0.12 m rns and Ž . attenuation 4.3–6.9 dB rm values compared to compartments 1 and 4 that are filled with highly Ž . contrasted materials: high attenuation 9.5 dB rm Ž . and low velocity 0.09 m rns for compartment 1, Ž . and low attenuation 2.6 dB rm and high velocity Ž . 0.17 m rns 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 Ž . D, B1, B2, M , this is not the case for other signals Ž . e.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 Ž . Ž . 1991 , Williamson and Worthington 1993 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 lrR s 58.8 tan DF Ž . where l is the wavelength, R is the raypath length and DF 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 14 r20 5: Gneiss 0 r20 A Surface borehole tomography Ž . V m rns 0.09 0.12 0.17 0.12 Ž . a dBrm 9.5 4.3 2.6 6.9 B 2D profiling K 13 6 3 5.5 Q 7 20 30 7 Ž . V m rns 0.07 0.12 0.17 0.13 Ž . a dB rm 15–45 6–20 1.5–4.5 9–27 300 – 900 MHz Ž . P m 1.5–1 4.5–2 4.5–4.5 2.5–1.5 300 – 900 MHz Ž . r m 0.15–0.03 0.14–0.03 0.23–0.06 0.16–0.04 300 – 900 MHz C CMP analysis Ž . V m rns – 0.10 0.15 0.10 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 . MHz b , 500 MHz c , and 900 MHz d . P s pit limit; D s void; E1–E9 s 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, 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 . Ž . Ž . P , a void D and different kinds of pipes E1–E9 . 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 Ž . Ž . x, y,t volume Fig. 5c . Fig. 5d indicates the loca- 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 . highlight the signatures of a single pipe O and a set of pipes E . 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 . 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 m corresponding to the gneiss at B 14 r20 mm. 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 correction D t as a function of velocity V and offset x: 1 r2 2 x D t s t 1 y . 6 Ž . 2 2 ž V t The appropriate velocity law was then estimated Ž from the semblance diagram, calculated with Neidel . and Taner, 1971 : 2 n y1 A t , j Ž . Ý ž j s0 S t s . 7 Ž . Ž . n y1 2 n A t , j Ž . Ý j s0 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 Ž . Dix, 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 m rns. 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 Ž . Fig. 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