GPR and seismic imaging in a gypsum quarry

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1 Ž. Journal of Applied Geophysics GPR and seismic imaging in a gypsum quarry Xavier Derobert ), Odile Abraham LCPC Centre de Nantes, Section Reconnaissance et Geophysique, Route de Bouaye, BP Bouguenais Cedex, France Received 16 June 1999; accepted 30 June 2000 Abstract A combination of ground penetrating radar Ž GPR. and seismic imaging has been performed in a gypsum quarry in western Europe. The objective was to localize main cracks and damaged areas inside some of the pillars, which presented indications of having reached stress limits. The GPR imaging was designed from classical profiles with GPR processes and a customized, PC-based image-processing software. The detection of energy reflection seems to be an efficient process for localizing damaged areas. Seismic tomographic images have been obtained from travel time measurements, which were inverted using a simultaneous iterative reconstruction technique Ž SIRT. technique in order to provide a map of seismic velocities. 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 the pillar s internal stress, while radar data serve to localize the main cracks. Moreover, these imaging processes present similarities 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 revealed stability problems which require local reinforcement. The galleries concerned have a section of approximately 6 m in width and 7 m in height; the pillars have a square section, with a minimum side length of 7 m. During mining operations at the quarry, no special precautions had been implemented. The result 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.: q ; fax: q address: xavier.derobert@lcpc.fr Ž X. Derobert.. cluding mineralogical, mechanical and ultra-sonic tests, have shown no significant seismic anisotropy. In some areas, the high density of fracturing and the potential for cross-cracking, combined with the damaged zones, has imposed the need to determine the distribution or continuity of the fractures. For this purpose, a non-destructive testing Ž NDT. campaign has been carried out to select certain pillars that present damage characteristics. The objective herein was to localize the disaggregated areas inside these pillars, which correspond to high levels of stress, along with the main cracks. Two complementary techniques were employed: seismic tomography and radar investigation. Ground penetrating radar Ž GPR. is a very useful technique for carrying out geological NDT, which detects dielectric contrasts at the boundary planes by r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. Ž. PII: S

2 158 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) the reflection of electromagnetic Ž EM. pulses. The degree of crack detection depends on various parameters, such as the equivalent target section and the filling of cracks by clay, water or air. In general, the rock s dielectric attenuation is very low, thereby suggesting several meters of radar investigation Ž Stevens et al., 1995; Toshioka et al., The literature does provide some results concerning the coefficient of reflection as a function of the dielectric contrast and the incident angle of the target section, which can be modeled in order to predict the potential expected resolution Ž Olhoeft, Although this technique is quick and easy to use, its major limitation lies in its inability to yield information on the state of stress in the structure. For this reason, a secondary campaign of seismic tomography is to produce a map of objects internal mechanical properties in a non-invasive fashion. By measuring the travel times of the compression wave between source and receiver points around the object, it is possible to calculate a map of the compression wave velocity. In the case of an a priori homogeneous material, the appearance of a zone of lower velocity indicates that the material has weathered locally. Seismic transmission tomography using travel times is more sensitive to zones of micro-cracking than to isolated cracks, especially if the micro-cracks are not closed and if the material is damaged. In the case of a homogeneous medium, the difference in travel times, both with and without an isolated crack, might very well be of the same order of magnitude as the level of accuracy in the times chosen. Spathis et al. Ž showed that the rising time is often more sensitive to cracking than the travel time. Consequently, radar and seismic tomography are fully complementary, by virtue of their ability to provide different information in the geological diagnostic process Ž MacCann et al., Radar investigation 2.1. Experimental set-up Our GPR system is an SIR-10A, manufactured by GSSI, and is associated with two 500 MHz shielded antennae in one box. The range has been selected in order to ensure reaching the backs of the pillars, i.e. 170 ns for an average thickness of 7 m. The choice of the frequency has resulted from a compromise between the maximum depth investigation and the resolution. Since tens of pillars were targeted by this GPR investigation, including some with inaccessible sides, we had to choose the highest frequency able to reach the other side of the pillars. A time-varying gain has been applied providing amplitude compensation for the attenuation of the medium and the spreading loss of the travelling signals. The result gives similar amplitude to the reflected pulses from the surface and from the bottom of the pillar. The comparison between the two non-destructive techniques only concerned four of the pillars. We took measurements at a height corresponding to the minimum section of the pillar, around m, Ž. Fig. 1. Example of the shape of a pillar Pillar 1, and position of the radar investigations.

3 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) 159 at which point the horizontal seismic tomography was conducted Ž see Fig. 1.. The advantage of using the minimum section is that every radar echo detected before the back of the pillar corresponded to an internal heterogeneity inside the pillar. Moreover, this section also corresponds to the maximum stresses being sought by geologists. To obtain an indication of the inclination of the fractures, parallel profiles have been generated. The time lag recorded, on the same presumed crack, for Fig. 2. Processing applied to GPR data Ž Pillar 1.. Ž a. Untreated data. Ž b. Profile after filtering and surface normalization. Ž c. Migrated profile. Ž. d Profile after Hilbert transform.

4 160 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) two successive profiles has yielded a theoretical indication of the angle by means of the following equation: a s arcsinž Rrd., Ž 1. where R represents the distance lag Žafter 2D migration., in meters, and d the distance between the two profiles, considering the case of the investigated vertical side. 3D radar processing has already been studied ŽGrandjean and Gourry, 1996; Grasmueck, 1996., and our equation is merely a simplification in order to obtain information on the level of inclination of the cracks. As observed in Fig. 1, the shape of the pillars does not justify the processing of a large number of radar profiles using this hypothesis. Depending on the shape of the investigated pillars, two or three radar profiles have been developed, at a spacing of 40 cm. Moreover, a thin carriage, including a survey wheel, has been built, allowing us to record accurate scans, at a constant height, from the untreated surface of the pillars. Measurements were carried out in 1 day by three operators Žtwo would have sufficed Classical GPR data processing Successive processing steps have been employed with a commercial software Ž WinRad from GSSI. in order to localize cracks and damaged zones from the different sides Ž see Fig. 2a.. After a vertical high-pass filter Ž over 250 MHz. on the profiles, the first step consisted of normalizing the surface in distance by adding an EM velocity. For this, we compared the thickness of different pillars and the corresponding double travel times. Results from the velocity measurement fluctuated from 11.6 to 11.9 cm ns y1 ; these measurements take into account the possibility of errors due to the 3D shape of the pillar. We then assumed a constant velocity for each pillar. Surface normalization enables comparing the perpendicular, or opposite, radar profiles from the same pillar section and localizing the cracks detected from the different sides. To accomplish this step, we used the geometrical data from a surveyor; data which were also necessary for the seismic tomographies. Afterwards, frequency bandpass filters were applied in order to remove all noise. This step is focused primarily on the major reflectors Žsee Fig. 2b.. The next step involved the use of a time migration to focus the EM energy and establish a relation between time and distance. A Kirchhoff method was used with a specific hyperbolic width of 2 m, due to the number of scans per meter. Since the migration attenuates the amplitude of the signals, a constant gain value of 3 was applied on the profiles Ž Fig. 2c.. The main limitation of this process concerns the fact that the migration itself does not take into account the topography, and distort the shape of the surface. By compensating this distortion with a new surface normalization, we can displace reflectors slightly from their correct position. This problem is focused mainly in the edges of the pillars, or when the topography presents an important gradient. Lehmann and Green Ž have adapted a topographic migration for GPR data based on an algorithm proposed by Wiggins Ž for seismic data collected in mountainous areas, and have shown that topographic migration should be recommended when surface gradient exceed f 10%. For our particular application, some mere calculations can show that the positioning error remains under 0.5 m, even if some areas present surface gradient over 10%, and which can be considered as an acceptable approximation. Finally, we concluded this processing with a Hilbert transform in order to present the reflected energy Ž see Fig. 2d.. The result is a map showing dark plots that correspond to fracture zones Ž Grandjean and Gourry, All of these steps can be considered as classical processing in the localization of fractures or damaged areas, and they provide the basis for the radar imaging. 3. Seismic tomographic investigation 3.1. Experimental set-up Even though the geometry of a pillar is essentially 3D, we carried out our measurements in 2D. In the present case, the experimental and processing times for 3D seismic analysis are indeed prohibitive since many pillars are being studied.

5 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) 161 Since the major zone of interest is that around the pillar s smallest section, it was decided to perform a horizontal tomography at this level. In most cases, the four sides of the pillar were all accessible, thereby allowing for good ray coverage. Similarly, we performed a vertical tomography with source and receiver points located on two opposite faces. The objective was twofold: to control the state of the pillar vertically, and to ascertain whether the horizontal tomography plane was located in the area of the pillar where the velocities were highest. This approach prevented against the misinterpretation of artifacts that may arise from a 3D velocity distribution where the horizontal tomography plane may be surrounded by higher horizontal velocity zones. In such a case, the ray paths would not be in the tomography plane, as presumed in the inversion process, and the calculations performed would be erroneous due to an incorrect ray geometry assumption. During an initial series of experiments, we determined an optimum spacing for the source and receiver points such that the information contained on the tomography maps was sufficient to perform the same diagnostic evaluation as with a larger, AsuperabundantB number of rays Žtypically 2000 rays in the horizontal tomography.. In the horizontal tomography, we located nine equidistant sourcerreceiver points on each side Ž see Fig. 3a.. Sources and receivers never belong to the same face; hence, the total number of source receiver combinations was reduced to a maximum of 477. In the vertical tomography, we located 18 equidistant source points on one side and 18 equidistant receiver points on the opposite side; hence, the total number of source receiver combinations was reduced to a maximum of 324. Afterwards, a surveyor provided us with all of the NGF ŽFrench geographic standards. coordinate points. A Krenz data-acquisition system of transitory signals Ž the TRC 4000 and TRC 4011 model., with sampling frequencies of up to 1 MHz on 10 channels Ž 10 bits., was used to collect and store the seismic signals on a microcomputer. Since the shortest source receiver travel times are around 0.1 ms, the sampling frequency used was 1 MHz, in order to ensure acquiring a sufficient number of points for the selection of arrival times. The source consisted of a hammer coupled with a pre-amplified Bruel and Kjaer accelerometer Žno , with the trigger being the hammer stroke. The receivers were nine other pre-amplified Bruel and Kjaer accelerometers. Both the receiver and source signals were recorded on the microcomputer for all of the possible source receiver combinations. The time picking was carried out subsequently in the laboratory. These arrival times and the coordinates were then fed into the RAI-2D algorithm for inversion. The tomography algorithm used in this paper, RAI-2D, was developed by the LCPC laboratory Ž Cote ˆ et al., It has already led to numerous applications in both soil surveying ŽAbraham et al., and the NDT of structures ŽCote ˆ and Abraham, 1995; Abraham et al., RAI-2D has been inspired by the simultaneous iterative reconstruction technique Ž SIRT. method Ž Gilbert, The domain of investigation is discretized into a mesh of points, on which the slowness is defined Žsee Fig. 3b.. One of the key RAI-2D features pertains to its zone of influence which, as opposed to a block-discretization grid, is used when searching for rays to calculate the slowness at a given grid point. RAI-2D is also characterized by its use of circular analytical rays. The level of accuracy for civil engineering purposes of this simple and rapid inversion technique, which has been tested using both synthetic and field data, is similar to that provided by more standard methods based on complex ray paths Detailed results on Pillar 1 It is recommended to include certain complementary information with the final velocity map in order to guarantee the quality of the survey and facilitate its interpretation. First of all, the algorithm s convergence should be tracked from a statistical point of view Ž mean residual, standard deviation.. Furthermore, the residual statistics of each source and receiver should be checked so as to eliminate those sources andror receivers displaying out-of-scale statistical values. Secondly, since both the precision and resolution of the velocity map are linked to the ray coverage, the plot of the ray should at least be given.

6 162 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) 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 the velocity is less precise than in zones with well-distributed and large numbers of rays. Fig. 4 shows the horizontal and vertical seismic tomographic results for Pillar 1. In both cases, the grid size is 0.4 m=0.4 m, and the results listed are those obtained after 10 iterations. Both inversions did converge Ž see Fig. 4c.. The number of rays is maximized Ž 324. in the vertical tomography. In the horizontal tomography, several sources and receivers were eliminated due to poor statistical values. The out-of-scale values of several source and receiver statistics can be explained by the heavily damaged surface of the pillar at certain locations. Consequently, the final number of rays is reduced to 350 in the horizontal tomography. The vertical tomography Ž see Fig. 4a. shows that the highest velocities are located near the smallest pillar horizontal section, as would be expected. The information on the top and bottom of the tomography plane is less precise than in the middle due to ray bending Ž see Fig. 4b.. Indeed, those two areas are crossed by a very small numbers of rays and the velocity information is here only indicative.

7 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) 163 Ž. Ž.Ž. Ž. Fig. 4. a Vertical and horizontal seismic tomographies Pillar 1. b Ray curve density. c Convergence parameters.

8 164 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) The horizontal tomography reveals a large damaged zone inside the section extending downwards Ž see Fig. 4a.. The rays tend to travel around this damaged area. Apart from a small zone in the upper right-hand part, the pillar is quite damaged. Its mean Ž y1 velocity 3811 m s. is well below the average velocity of mechanically sound pillars at this level Ž y1 around 4500 m s.. 4. Comparison and interpretation As previously discussed, these two geophysical techniques provide complementary information. The first classical means of combination therefore is to superimpose the cracks detected by GPR onto the seismic tomography displaying the velocities. We would expect to be able to correlate the localization of the main cracked areas by GPR with the damaged zones corresponding to low seismic velocities. The major problem herein concerns the human factor, which influences the selection of certain cracks over others, thereby implying that an absence of cracks signifies a homogeneous area. The choice of which cracks to retain depends on the relative amplitude of each of their echoes. This logical comparison reveals its drawbacks either when numerous pillars or when different processing users are involved Radar tomography In order to take into account all of the diffracted signals, radar processing is conducted automatically. By virtue of the possibility to survey from all sides of the pillars, coupled with the fact that the depth investigated is greater than the thickness, each profile presents information on every area of the pillars. An accurate localization of the diffracting areas enables mapping the pillar by adding this information by a classical imaging process. This information, generated from the echoes, depends on the depth of the cracks, their target section and their filling. However, since the pillars display a high number of cracks Ž many of which are visible., small discontinuities, voids or diffracting points, the amplitude and the number of echoes are proportional to the level of damage in a given area. So, the principle of this radar tomography is to design a square imaging section from each GPR profile, perfectly localized in a common coordinate system. For that purpose, processed GPR profiles need to be extended. Indeed, they are 10 m deep, and need some more scans on both sides in order to reach 10 m large. This process is available in the software WinRad by copying and adding the first and the last scan until the GPR central section is correctly positioned on the pillar location. Since these profiles were already migrated and surface normalized, the four maps can be superimposed in order to represent the pillar by a radar image. The dark plots are then added, thus increasing the darkness, with the assumption that the result is correlated with a high damage level. This last step is accomplished by means of an image processing software for PCs called APIC- TUREB, which has been designed and developed at the LCPC laboratory by J.M. Molliard. Analysis and processing on gray-level pictures is possible through the use of its own library of filters, morphologies, averages, operations and false colors. Moreover, macro-orders allow automating the radar imaging process Ž 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 beyond the pillars, and to allow paying special attention to those areas located very close to the borders. We consider that the dark plots have been roughly correctly added, due firstly to the fact that the surface normalization gets corrected by the half-wavelength of the radar pulse, which allows positioning the maximum reflected energy from each profile at the same place for each fracture. The second reason is that the visual investigation showed only vertical, or sub-vertical, external cracks on the pillars, i.e. no 3D migration corrections are necessary on the profiles Comparison Fig. 6 presents both tomographies simultaneously for Pillar 1. The shape of the dark plots is completely

9 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) 165 Ž. Fig. 5. Radar tomography by image processing Pillar 1. different due to the large number of data Žseveral hundred seismic data points vs. several thousand radar data points., yet we are still tempted to correlate both of these tomographic images. GPR processing was carried out to focus the presentation not only on the cracks but also on the diffracting 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 energy resulting from the main cracks, which can locally increase the apparent EM damage level. For this reason, it is useful to include the information from the presentation of the cracks into the radar imaging.

10 166 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) Fig. 6. Radar and seismic imaging on Pillar 1. Similarly, the damage zones are localized by low seismic velocities Ž plotted in dark.. Pillar 1 therefore appears to be a good example of a non-homogeneous pillar, in which most of the damaged zones are detected either by GPR or by seismic imaging. Both the left and center parts of the pillar display lower seismic velocities and higher densities of EM reflected energy at the same locations. This kind of correlation is confirmed in Pillar 2 by the sub-vertical narrow damaged area in the center of the pillar, which has been detected by either one of the two NDT approaches Ž see Fig. 7.. Fig. 7. Radar and seismic imaging on Pillar 2.

11 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) 167 Fig. 8. Radar and seismic imaging on Pillar 3. The overlap of the main cracks on the radar tomography is significant, as shown in the center part where the dark plots are not caused only by the presence of a single major crack. For all of the tomographies studied, a comment on the border effects is necessary. Due to the low density of rays near the corners, the values of seismic velocities are not accurate, and in most instances should be used with caution. Hence, both the seismic tomography and the ray curve density map must be presented. For GPR imaging, the localization of the bottom of the pillar is inaccurate for each profile, and especially for unevenly-shaped pillar. Moreover, the Fig. 9. Radar and seismic imaging on Pillar 4.

12 168 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) shape of the pillar can disturb some parts of the tomography near the borders. Pillar 3, in which the left and lower sides are not perpendicular, provides a good example. The last GPR scan, at the border of both profile s sides, has been copied and then repeated in order to lengthen the profiles to the right dimension for image processing Žprinciple presented Fig. 5, on Side A.. The information related to this last part of the GPR profiles can interfere with the imaging. Thus, both the upper left-hand and lower right-hand parts of Pillar 3 do present some inaccurate results. With respect to the seismic tomographies, Pillars 3 and 4 are more homogeneous and display high velocities Ž see Figs. 8 and 9.. The ray coverage and inversion 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 to be heterogeneous. The dark plot density is low and roughly constant in the maps, which suggests that the radar and seismic imaging are in accordance. We must nonetheless be careful to avoid linking the EM power reflection directly to low seismic velocities. Even though we cannot distinguish seriously damaged zones on the radar tomographies, we are still not in a position to assume that these pillars are mechanically sound. Confirmation can only come from seismic investigation, which correlates high velocities with mechanical soundness. 5. Conclusion This work has been conducted in order to compare two kinds of tomographies, using EM and seismic waves, as well as to propose to geologists a radar imaging technique for quarry pillars. Seismic tomography presents the tremendous advantage of providing direct information on the soundness of surveyed structures or pillars. Low velocities are characteristic of damaged zones, while for these specific gypsum pillars, sound zones are correlated with levels of around 4400 m s y1. The main limitations herein stem from the impossibility of detecting major cracks in a homogeneous material, and the overall cost implied. GPR has been proposed as a complementary technique. This useful device is applied to localize fractures in rocks or pillars. Its main drawback lies in the associated human factor when interpreting the GPR profiles. The level of distinction of major fractures can vary with respect to time or with respect to the geophysicist. Moreover, this factor exhibits the same variability in defining diffracting areas. This paper has thus presented a potentially useful automatic processing technique which enables constructing a damage-related radar image that can support the superimposed drawing of main cracks. GPR profiles are filtered, surface normalized, migrated, Hilbert transformed and, at last, added in order to present an image of the reflected energy. This technique s primary advantage is its readability, along with its geophysical comments, for geologists. The second advantage is its comparability with other imaging techniques Žsuch as seismic tomography. 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 energy reflection and low seismic velocities. This observation will have to be confirmed under other test conditions and on other materials in order to accurately determine the limitations of this analogy. Acknowledgements The authors wish to thank J.M. Molliard, from the LCPC- Image Processing Section, for his kind help and high-performance imaging software APIC- TUREB, which facilitated the last radar processing sequence. References Abraham, O., Derobert, X., Alexandre, J., Seismic and electromagnetic tomography applied to historical buildings: a case history. 2nd Meeting EEGS, Nantes Abraham, O., Ben Slimane, K., Cote, ˆ Ph., Seismic tomography: factoring anisotropy into iterative geometric reconstruction algorithms. Int. J. Rock Mech. Mining Sci. 35 Ž. 1,

13 X. Derobert, O. AbrahamrJournal of Applied Geophysics 45 ( 2000) 169 Cote, ˆ Ph., Lagabrielle, R., Gautier, V., D and 3D Reconstructions Using Pseudo-rays. EAEG, Paris, Cote, ˆ Ph., Abraham, O., Seismic Tomography in Civil Engineering. NDT-CE, Berlin, pp Gilbert, P., Iterative methods for the three dimensional reconstruction of an object from projections. J. Theor. Biol., Grandjean, G., Gourry, C., GPR data processing for 3D fracture mapping in a marble quarry Ž Thassos, Greece.. J. Appl. Geophys. 36 Ž. 1, Grasmueck, M., D ground-penetrating radar applied to fracture imaging in gneiss. Geophysics 61 Ž. 4, Lehmann, F., Green, A.G., Topographic migration of georadar data. Proc. 8th Int. Conf. on GPR, Gold Coast, Australia, May MacCann, D.M., Jackson, P.D., Fenning, P.J., Comparison of the seismic and ground probing radar methods in geological surveying. IEE Proc. Ž. 4, , part F. Olhoeft, G.R., Electrical, magnetic, and geometric properties that determine ground penetrating radar performance. Proc. 7th Int. Conf. on GPR, Lawrence, KS, USA, May. Spathis, A.T., Blair, D.P., Grant, J.R., Seismic pulse assessment of the changing rock mass condition induced by mining. Int. J. Rock Mech. Mining Sci. 22 Ž. 5, Stevens, K.M., Lodha, G.S., Hollowaay, A.L., Soonawala, N.M., The application of ground penetrating radar for mapping fractures in plutonic rocks within the Whiteshell Research Area, Pinawa, Manitoba, Canada. J. Appl. Geophys. 33 Ž 1 3., Toshioka, T., Tsuchida, T., Sasahara, K., Application of GPR to detecting and mapping cracks in rock slopes. J. Appl. Geophys. 33 Ž 1 3., Wiggins, J.W., Kirchhoff integral extrapolation and migration of nonplanar data. Geophysics 49 Ž. 8,