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Ž .Journal of Applied Geophysics 45 2000 157–169www.elsevier.nlrlocaterjappgeo

GPR and seismic imaging in a gypsum quarry

Xavier Derobert), Odile Abraham´LCPC — Centre de Nantes, Section Reconnaissance et Geophysique, Route de Bouaye, BP 4129-44341 Bouguenais Cedex, France

Received 16 June 1999; accepted 30 June 2000

Abstract

Ž .A combination of ground penetrating radar GPR and seismic imaging has been performed in a gypsum quarry inwestern Europe. The objective was to localize main cracks and damaged areas inside some of the pillars, which presentedindications of having reached stress limits. The GPR imaging was designed from classical profiles with GPR processes and acustomized, PC-based image-processing software. The detection of energy reflection seems to be an efficient process forlocalizing damaged areas. Seismic tomographic images have been obtained from travel time measurements, which were

Ž .inverted using a simultaneous iterative reconstruction technique SIRT technique in order to provide a map of seismicvelocities. The imaging and techniques employed are compared herein.

The two techniques are complementary; seismic tomography produces a map of velocities related to the state of thepillar’s internal stress, while radar data serve to localize the main cracks. Moreover, these imaging processes presentsimilarities with respect to the damaged zone detection. q 2000 Elsevier Science B.V. All rights reserved.

Keywords: Ground penetrating radar; Seismic; Data processing; Imaging; Fractures; Damaged zones

1. Introduction

A gypsum quarry in western Europe has revealedstability problems which require local reinforcement.The galleries concerned have a section of approxi-mately 6 m in width and 7 m in height; the pillarshave a square section, with a minimum side length of7 m. During mining operations at the quarry, nospecial precautions had been implemented. The re-sult is manifested in the irregularity of the pillars’shape and the many visible cracks on their sides.Laboratory experiments on numerous samples, in-

) Corresponding author. Tel.: q33-2-40-84-59-11; fax: q33-2-40-84-59-97.

Ž .E-mail address: [email protected] X. Derobert .´

cluding mineralogical, mechanical and ultra-sonictests, have shown no significant seismic anisotropy.

In some areas, the high density of fracturing andthe potential for cross-cracking, combined with thedamaged zones, has imposed the need to determinethe distribution or continuity of the fractures. For this

Ž .purpose, a non-destructive testing NDT campaignhas been carried out to select certain pillars thatpresent damage characteristics. The objective hereinwas to localize the disaggregated areas inside thesepillars, which correspond to high levels of stress,along with the main cracks. Two complementarytechniques were employed: seismic tomography andradar investigation.

Ž .Ground penetrating radar GPR is a very usefultechnique for carrying out geological NDT, whichdetects dielectric contrasts at the boundary planes by

0926-9851r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0926-9851 00 00025-2

( )X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 2000 157–169´158

Ž .the reflection of electromagnetic EM pulses. Thedegree of crack detection depends on various param-eters, such as the equivalent target section and thefilling of cracks by clay, water or air. In general, therock’s dielectric attenuation is very low, therebysuggesting several meters of radar investigationŽ .Stevens et al., 1995; Toshioka et al., 1995 . Theliterature does provide some results concerning thecoefficient of reflection as a function of the dielectriccontrast and the incident angle of the target section,which can be modeled in order to predict the poten-

Ž .tial expected resolution Olhoeft, 1998 . Althoughthis technique is quick and easy to use, its majorlimitation lies in its inability to yield information onthe state of stress in the structure.

For this reason, a secondary campaign of seismictomography is to produce a map of objects’ internalmechanical properties in a non-invasive fashion. Bymeasuring the travel times of the compression wavebetween source and receiver points around the ob-ject, it is possible to calculate a map of the compres-sion wave velocity. In the case of an a priori homo-geneous material, the appearance of a zone of lowervelocity indicates that the material has weatheredlocally.

Seismic transmission tomography using traveltimes is more sensitive to zones of micro-crackingthan to isolated cracks, especially if the micro-cracksare not closed and if the material is damaged. In thecase of a homogeneous medium, the difference intravel times, both with and without an isolated crack,might very well be of the same order of magnitudeas the level of accuracy in the times chosen. Spathis

Ž .et al. 1983 showed that the rising time is oftenmore sensitive to cracking than the travel time.

Consequently, radar and seismic tomography arefully complementary, by virtue of their ability toprovide different information in the geological diag-

Ž .nostic process MacCann et al., 1988 .

2. Radar investigation

2.1. Experimental set-up

Our GPR system is an SIR-10A, manufactured byGSSI, and is associated with two 500 MHz shieldedantennae in one box. The range has been selected inorder to ensure reaching the backs of the pillars, i.e.170 ns for an average thickness of 7 m. The choiceof the frequency has resulted from a compromisebetween the maximum depth investigation and theresolution. Since tens of pillars were targeted by thisGPR investigation, including some with inaccessiblesides, we had to choose the highest frequency able toreach the other side of the pillars. A time-varyinggain has been applied providing amplitude compen-sation for the attenuation of the medium and thespreading loss of the travelling signals. The resultgives similar amplitude to the reflected pulses fromthe surface and from the bottom of the pillar.

The comparison between the two non-destructivetechniques only concerned four of the pillars. Wetook measurements at a height corresponding to theminimum section of the pillar, around 1.30–1.40 m,

Ž .Fig. 1. Example of the shape of a pillar Pillar 1 , and position of the radar investigations.

( )X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 2000 157–169´ 159

at which point the horizontal seismic tomographyŽ .was conducted see Fig. 1 . The advantage of using

the minimum section is that every radar echo de-tected before the back of the pillar corresponded toan internal heterogeneity inside the pillar. Moreover,

this section also corresponds to the maximum stressesbeing sought by geologists.

To obtain an indication of the inclination of thefractures, parallel profiles have been generated. Thetime lag recorded, on the same presumed crack, for

Ž . Ž . Ž . Ž .Fig. 2. Processing applied to GPR data Pillar 1 . a Untreated data. b Profile after filtering and surface normalization. c MigratedŽ .profile. d Profile after Hilbert transform.


two successive profiles has yielded a theoreticalindication of the angle by means of the followingequation:

asarcsin Rrd , 1Ž . Ž .Žwhere R represents the distance lag after 2D migra-

.tion , in meters, and d the distance between the twoprofiles, considering the case of the investigatedvertical side. 3D radar processing has already been

Žstudied Grandjean and Gourry, 1996; Grasmueck,.1996 , and our equation is merely a simplification in

order to obtain information on the level of inclina-tion of the cracks. As observed in Fig. 1, the shapeof the pillars does not justify the processing of alarge number of radar profiles using this hypothesis.Depending on the shape of the investigated pillars,two or three radar profiles have been developed, at aspacing of 40 cm. Moreover, a thin carriage, includ-ing a survey wheel, has been built, allowing us torecord accurate scans, at a constant height, from theuntreated surface of the pillars. Measurements were

Žcarried out in 1 day by three operators two would.have sufficed .

2.2. Classical GPR data processing

Successive processing steps have been employedŽ .with a commercial software WinRad from GSSI in

order to localize cracks and damaged zones from theŽ .different sides see Fig. 2a . After a vertical high-pass

Ž .filter over 250 MHz on the profiles, the first stepconsisted of normalizing the surface in distance byadding an EM velocity. For this, we compared thethickness of different pillars and the correspondingdouble travel times. Results from the velocity mea-surement fluctuated from 11.6 to 11.9 cm nsy1 ;these measurements take into account the possibilityof errors due to the 3D shape of the pillar. We thenassumed a constant velocity for each pillar.

Surface normalization enables comparing the per-pendicular, or opposite, radar profiles from the samepillar section and localizing the cracks detected fromthe different sides. To accomplish this step, we usedthe geometrical data from a surveyor; data whichwere also necessary for the seismic tomographies.

Afterwards, frequency bandpass filters were ap-plied in order to remove all noise. This step is

Žfocused primarily on the major reflectors see Fig..2b .The next step involved the use of a time migration

to focus the EM energy and establish a relationbetween time and distance. A Kirchhoff method wasused with a specific hyperbolic width of 2 m, due tothe number of scans per meter. Since the migrationattenuates the amplitude of the signals, a constant

Ž .gain value of 3 was applied on the profiles Fig. 2c .The main limitation of this process concerns the

fact that the migration itself does not take intoaccount the topography, and distort the shape of thesurface. By compensating this distortion with a newsurface normalization, we can displace reflectorsslightly from their correct position. This problem isfocused mainly in the edges of the pillars, or whenthe topography presents an important gradient.

Ž .Lehmann and Green 2000 have adapted a topo-graphic migration for GPR data based on an algo-

Ž .rithm proposed by Wiggins 1984 for seismic datacollected in mountainous areas, and have shown thattopographic migration should be recommended whensurface gradient exceed f10%. For our particularapplication, some mere calculations can show thatthe positioning error remains under 0.5 m, even ifsome areas present surface gradient over 10%, andwhich can be considered as an acceptable approxi-mation.

Finally, we concluded this processing with aHilbert transform in order to present the reflected

Ž .energy see Fig. 2d . The result is a map showingdark plots that correspond to fracture zonesŽ .Grandjean and Gourry, 1996 .

All of these steps can be considered as classicalprocessing in the localization of fractures or dam-aged areas, and they provide the basis for the radarimaging.

3. Seismic tomographic investigation

3.1. Experimental set-up

Even though the geometry of a pillar is essentially3D, we carried out our measurements in 2D. In thepresent case, the experimental and processing timesfor 3D seismic analysis are indeed prohibitive sincemany pillars are being studied.


Since the major zone of interest is that around thepillar’s smallest section, it was decided to perform ahorizontal tomography at this level. In most cases,the four sides of the pillar were all accessible, therebyallowing for good ray coverage. Similarly, we per-formed a vertical tomography with source and re-ceiver points located on two opposite faces. Theobjective was twofold: to control the state of thepillar vertically, and to ascertain whether the hori-zontal tomography plane was located in the area ofthe pillar where the velocities were highest. Thisapproach prevented against the misinterpretation ofartifacts that may arise from a 3D velocity distribu-tion where the horizontal tomography plane may besurrounded by higher horizontal velocity zones. Insuch a case, the ray paths would not be in thetomography plane, as presumed in the inversionprocess, and the calculations performed would beerroneous due to an incorrect ray geometry assump-tion.

During an initial series of experiments, we deter-mined an optimum spacing for the source and re-ceiver points such that the information contained onthe tomography maps was sufficient to perform thesame diagnostic evaluation as with a larger, Asuper-

ŽabundantB number of rays typically 2000 rays in the.horizontal tomography . In the horizontal tomogra-

phy, we located nine equidistant sourcerreceiverŽ .points on each side see Fig. 3a . Sources and

receivers never belong to the same face; hence,the total number of source™ receiver combinationswas reduced to a maximum of 477. In the verticaltomography, we located 18 equidistant sourcepoints on one side and 18 equidistant receiver pointson the opposite side; hence, the total number ofsource™ receiver combinations was reduced to amaximum of 324. Afterwards, a surveyor provided

Žus with all of the NGF French geographic stan-.dards coordinate points.

A Krenz data-acquisition system of transitory sig-Ž .nals the TRC 4000 and TRC 4011 model , with

sampling frequencies of up to 1 MHz on 10 channelsŽ .10 bits , was used to collect and store the seismicsignals on a microcomputer. Since the shortestsource–receiver travel times are around 0.1 ms, thesampling frequency used was 1 MHz, in order toensure acquiring a sufficient number of points for theselection of arrival times.

The source consisted of a hammer coupled with aŽpre-amplified Bruel and Kjaer accelerometer no.

.4381 , with the trigger being the hammer stroke. Thereceivers were nine other pre-amplified Bruel andKjaer accelerometers. Both the receiver and sourcesignals were recorded on the microcomputer for allof the possible source™ receiver combinations. Thetime picking was carried out subsequently in thelaboratory. These arrival times and the coordinateswere then fed into the RAI-2D algorithm for inver-sion.

The tomography algorithm used in this paper,RAI-2D, was developed by the LCPC laboratoryŽ .Cote et al., 1992 . It has already led to numerousˆ

Žapplications in both soil surveying Abraham et al.,. Ž1998 and the NDT of structures Cote and Abra-ˆ

.ham, 1995; Abraham et al., 1996 . RAI-2D has beeninspired by the simultaneous iterative reconstruction

Ž . Ž .technique SIRT method Gilbert, 1972 . The do-main of investigation is discretized into a mesh of

Žpoints, on which the slowness is defined see Fig..3b . One of the key RAI-2D features pertains to its

zone of influence which, as opposed to a block-dis-cretization grid, is used when searching for rays tocalculate the slowness at a given grid point. RAI-2Dis also characterized by its use of circular analyticalrays. The level of accuracy for civil engineeringpurposes of this simple and rapid inversion tech-nique, which has been tested using both syntheticand field data, is similar to that provided by morestandard methods based on complex ray paths.

3.2. Detailed results on Pillar 1

It is recommended to include certain complemen-tary information with the final velocity map in orderto guarantee the quality of the survey and facilitateits interpretation. First of all, the algorithm’s conver-gence should be tracked from a statistical point of

Ž .view mean residual, standard deviation . Further-more, the residual statistics of each source and re-ceiver should be checked so as to eliminate thosesources andror receivers displaying out-of-scale sta-tistical values. Secondly, since both the precision andresolution of the velocity map are linked to the raycoverage, the plot of the ray should at least be given.


Ž . Ž .Fig. 3. a Location of the sources and receivers on the pillar. b Discretization grid with the circular zone of influence.

For instance, in zones with few rays, the value of thevelocity is less precise than in zones with well-dis-tributed and large numbers of rays.

Fig. 4 shows the horizontal and vertical seismictomographic results for Pillar 1. In both cases, thegrid size is 0.4 m=0.4 m, and the results listed arethose obtained after 10 iterations. Both inversions

Ž .did converge see Fig. 4c . The number of rays isŽ .maximized 324 in the vertical tomography. In the

horizontal tomography, several sources and receiverswere eliminated due to poor statistical values. Theout-of-scale values of several source and receiver

statistics can be explained by the heavily damagedsurface of the pillar at certain locations. Conse-quently, the final number of rays is reduced to 350 inthe horizontal tomography.

Ž .The vertical tomography see Fig. 4a shows thatthe highest velocities are located near the smallestpillar horizontal section, as would be expected. Theinformation on the top and bottom of the tomogra-phy plane is less precise than in the middle due to

Ž .ray bending see Fig. 4b . Indeed, those two areasare crossed by a very small numbers of rays and thevelocity information is here only indicative.


Ž . Ž . Ž . Ž .Fig. 4. a Vertical and horizontal seismic tomographies Pillar 1 . b Ray curve density. c Convergence parameters.


The horizontal tomography reveals a large dam-aged zone inside the section extending downwardsŽ .see Fig. 4a . The rays tend to travel around thisdamaged area. Apart from a small zone in the upperright-hand part, the pillar is quite damaged. Its mean

Ž y1 .velocity 3811 m s is well below the averagevelocity of mechanically sound pillars at this levelŽ y1 .around 4500 m s .

4. Comparison and interpretation

As previously discussed, these two geophysicaltechniques provide complementary information. Thefirst classical means of combination therefore is tosuperimpose the cracks detected by GPR onto theseismic tomography displaying the velocities. Wewould expect to be able to correlate the localizationof the main cracked areas by GPR with the damagedzones corresponding to low seismic velocities.

The major problem herein concerns the humanfactor, which influences the selection of certaincracks over others, thereby implying that an absenceof cracks signifies a homogeneous area. The choiceof which cracks to retain depends on the relativeamplitude of each of their echoes. This logical com-parison reveals its drawbacks either when numerouspillars or when different processing users are in-volved.

4.1. Radar tomography

In order to take into account all of the diffractedsignals, radar processing is conducted automatically.By virtue of the possibility to survey from all sidesof the pillars, coupled with the fact that the depthinvestigated is greater than the thickness, each pro-file presents information on every area of the pillars.An accurate localization of the diffracting areas en-ables mapping the pillar by adding this informationby a classical imaging process.

This information, generated from the echoes, de-pends on the depth of the cracks, their target sectionand their filling. However, since the pillars display a

Ž .high number of cracks many of which are visible ,small discontinuities, voids or diffracting points, the

amplitude and the number of echoes are proportionalto the level of damage in a given area.

So, the principle of this radar tomography is todesign a square imaging section from each GPRprofile, perfectly localized in a common coordinatesystem. For that purpose, processed GPR profilesneed to be extended. Indeed, they are 10 m deep, andneed some more scans on both sides in order toreach 10 m large. This process is available in thesoftware WinRad by copying and adding the firstand the last scan until the GPR central section iscorrectly positioned on the pillar location.

Since these profiles were already migrated andsurface normalized, the four maps can be superim-posed in order to represent the pillar by a radarimage. The dark plots are then added, thus increasingthe darkness, with the assumption that the result iscorrelated with a high damage level.

This last step is accomplished by means of animage processing software for PCs called APIC-TUREB, which has been designed and developed atthe LCPC laboratory by J.M. Molliard. Analysis andprocessing on gray-level pictures is possible throughthe use of its own library of filters, morphologies,averages, operations and false colors. Moreover,macro-orders allow automating the radar imaging

Ž .process see Fig. 5 .The borders of the pillars are drawn over the radar

tomographies in order to localize the damaged areas,to avoid taking into account the gray values beyondthe pillars, and to allow paying special attention tothose areas located very close to the borders.

We consider that the dark plots have been roughlycorrectly added, due firstly to the fact that the sur-face normalization gets corrected by the half-wave-length of the radar pulse, which allows positioningthe maximum reflected energy from each profile atthe same place for each fracture. The second reasonis that the visual investigation showed only vertical,or sub-vertical, external cracks on the pillars, i.e. no3D migration corrections are necessary on the pro-files.

4.2. Comparison

Fig. 6 presents both tomographies simultaneouslyfor Pillar 1. The shape of the dark plots is completely


Ž .Fig. 5. Radar tomography by image processing Pillar 1 .

Ždifferent due to the large number of data severalhundred seismic data points vs. several thousand

.radar data points , yet we are still tempted to corre-late both of these tomographic images.

GPR processing was carried out to focus thepresentation not only on the cracks but also on thediffracting areas. These areas can be considered as

small discontinuities, voids or diffracting points,which are correlated with a specific level of damage.However, we must take into account the EM energyresulting from the main cracks, which can locallyincrease the apparent EM damage level. For thisreason, it is useful to include the information fromthe presentation of the cracks into the radar imaging.


Fig. 6. Radar and seismic imaging on Pillar 1.

Similarly, the damage zones are localized by lowŽ .seismic velocities plotted in dark . Pillar 1 therefore

appears to be a good example of a non-homogeneouspillar, in which most of the damaged zones aredetected either by GPR or by seismic imaging. Boththe left and center parts of the pillar display lower

seismic velocities and higher densities of EM re-flected energy at the same locations.

This kind of correlation is confirmed in Pillar 2by the sub-vertical narrow damaged area in thecenter of the pillar, which has been detected by

Ž .either one of the two NDT approaches see Fig. 7 .




The overlap of the main cracks on the radar tomog-raphy is significant, as shown in the center partwhere the dark plots are not caused only by thepresence of a single major crack.

For all of the tomographies studied, a commenton the border effects is necessary. Due to the lowdensity of rays near the corners, the values of seis-

mic velocities are not accurate, and in most instancesshould be used with caution. Hence, both the seismictomography and the ray curve density map must bepresented.

For GPR imaging, the localization of the bottomof the pillar is inaccurate for each profile, and espe-cially for unevenly-shaped pillar. Moreover, the



shape of the pillar can disturb some parts of thetomography near the borders. Pillar 3, in which theleft and lower sides are not perpendicular, provides agood example. The last GPR scan, at the border ofboth profile’s sides, has been copied and then re-peated in order to lengthen the profiles to the right

Ždimension for image processing principle presented.Fig. 5, on Side A . The information related to this

last part of the GPR profiles can interfere with theimaging. Thus, both the upper left-hand and lowerright-hand parts of Pillar 3 do present some inaccu-rate results.

With respect to the seismic tomographies, Pillars3 and 4 are more homogeneous and display high

Ž .velocities see Figs. 8 and 9 . The ray coverage andinversion convergence are similar to that of Pillar 1:they are not shown here for purposes of conciseness.These seismic results demonstrate that the pillars are

Ž y1 .mechanically sound velocities around 4400 m s .In this context, the radar imaging does not seem tobe heterogeneous. The dark plot density is low androughly constant in the maps, which suggests that theradar and seismic imaging are in accordance.

We must nonetheless be careful to avoid linkingthe EM power reflection directly to low seismicvelocities. Even though we cannot distinguish seri-ously damaged zones on the radar tomographies, weare still not in a position to assume that these pillarsare mechanically sound. Confirmation can only comefrom seismic investigation, which correlates highvelocities with mechanical soundness.

5. Conclusion

This work has been conducted in order to com-pare two kinds of tomographies, using EM andseismic waves, as well as to propose to geologists aradar imaging technique for quarry pillars.

Seismic tomography presents the tremendous ad-vantage of providing direct information on thesoundness of surveyed structures or pillars. Lowvelocities are characteristic of damaged zones, whilefor these specific gypsum pillars, sound zones arecorrelated with levels of around 4400 m sy1. Themain limitations herein stem from the impossibilityof detecting major cracks in a homogeneous mate-rial, and the overall cost implied.

GPR has been proposed as a complementary tech-nique. This useful device is applied to localize frac-tures in rocks or pillars. Its main drawback lies in theassociated human factor when interpreting the GPRprofiles. The level of distinction of major fracturescan vary with respect to time or with respect to thegeophysicist. Moreover, this factor exhibits the samevariability in defining diffracting areas.

This paper has thus presented a potentially usefulautomatic processing technique which enables con-structing a damage-related radar image that can sup-port the superimposed drawing of main cracks. GPRprofiles are filtered, surface normalized, migrated,Hilbert transformed and, at last, added in order topresent an image of the reflected energy.

This technique’s primary advantage is its readabil-ity, along with its geophysical comments, for geolo-gists. The second advantage is its comparability with

Žother imaging techniques such as seismic tomogra-.phy or probing techniques, for developing a proper

diagnostic evaluation of the state of the structure.Comparative experiments have been performed on

four pillars; results suggest some strong analogies.Damaged zones seem to correspond with radar en-ergy reflection and low seismic velocities. This ob-servation will have to be confirmed under other testconditions and on other materials in order to accu-rately determine the limitations of this analogy.

Acknowledgements

The authors wish to thank J.M. Molliard, from theLCPC- Image Processing Section, for his kind helpand high-performance imaging software APIC-TUREB, which facilitated the last radar processingsequence.

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