www.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 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
Ž .
inverted using a simultaneous iterative reconstruction technique 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.q2000 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 approxi-mately 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 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:q 33-2-40-84-59-97.
Ž .
E-mail address: [email protected] 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
Ž .
purpose, a non-destructive testing 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.
Ž .
Ground penetrating radar GPR is a very useful technique for carrying out geological NDT, which detects dielectric contrasts at the boundary planes by
0926-9851r00r$ - see front matterq2000 Elsevier Science B.V. All rights reserved.
Ž .
Ž .
the reflection of electromagnetic EM pulses. The degree of crack detection depends on various param-eters, 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
ŽStevens et al., 1995; Toshioka et al., 1995 . 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
poten-Ž .
tial expected resolution Olhoeft, 1998 . 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 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 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
Ž .
et al. 1983 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
diag-Ž .
nostic process MacCann et al., 1988 .
2. 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 compen-sation 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 1.30–1.40 m,
Ž .
at which point the horizontal seismic tomography
Ž .
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 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
Ž . Ž . Ž . Ž .
Fig. 2. Processing applied to GPR data Pillar 1 . a Untreated data. b Profile after filtering and surface normalization. c Migrated Ž .
two successive profiles has yielded a theoretical indication of the angle by means of the following equation:
asarcsin R
Ž
rd ,.
Ž .
1Ž
where R represents the distance lag after 2D
migra-.
tion , in meters, and d the distance between the two profiles, considering the case of the investigated vertical side. 3D radar processing has already been
Ž
studied 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 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, includ-ing a survey wheel, has been built, allowinclud-ing us to record accurate scans, at a constant height, from the untreated surface of the pillars. Measurements were
Ž
carried out in 1 day by three operators two would
.
have sufficed .
2.2. Classical GPR data processing
Successive processing steps have been employed
Ž .
with a commercial software WinRad from GSSI in order to localize cracks and damaged zones from the
Ž .
different sides see Fig. 2a . After a vertical high-pass
Ž .
filter 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 mea-surement fluctuated from 11.6 to 11.9 cm nsy1; 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 per-pendicular, 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 ap-plied in order to remove all noise. This step is
Ž
focused 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 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
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 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.
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 data collected in mountainous areas, and have shown that topographic migration should be recommended when surface gradient exceed f10%. 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 approxi-mation.
Finally, we concluded this processing with a Hilbert transform in order to present the reflected
Ž .
energy see Fig. 2d . The result is a map showing dark plots that correspond to fracture zones
ŽGrandjean and Gourry, 1996 ..
All of these steps can be considered as classical processing in the localization of fractures or dam-aged areas, and they provide the basis for the radar imaging.
3. Seismic tomographic investigation
3.1. Experimental set-up
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 per-formed a vertical tomography with source and re-ceiver points located on two opposite faces. The objective was twofold: to control the state of the pillar vertically, and to ascertain whether the hori-zontal 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 distribu-tion 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 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 on the tomography maps was sufficient to perform the same diagnostic evaluation as with a larger,
Asuper-Ž
abundantBnumber of rays typically 2000 rays in the
.
horizontal tomography . In the horizontal tomogra-phy, we located nine equidistant sourcerreceiver
Ž .
points on each side 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
Ž
us 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 channels
Ž10 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
Ž
pre-amplified Bruel and Kjaer accelerometer no.
.
4381 , 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 inver-sion.
The tomography algorithm used in this paper, RAI-2D, was developed by the LCPC laboratory
ŽCote et al., 1992 . It has already led to numerous
ˆ
. Žapplications in both soil surveying Abraham et al.,
. Ž
1998 and the NDT of structures Cote and Abra-
ˆ
.
ham, 1995; Abraham et al., 1996 . RAI-2D has been inspired by the simultaneous iterative reconstruction
Ž . Ž .
technique SIRT method Gilbert, 1972 . The do-main of investigation is discretized into a mesh of
Ž
points, 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 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 tech-nique, which has been tested using both synthetic and field data, is similar to that provided by more standard 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 order to guarantee the quality of the survey and facilitate its interpretation. First of all, the algorithm’s conver-gence should be tracked from a statistical point of
Ž .
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-dis-tributed 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
Ž .
did converge see Fig. 4c . The number of rays is
Ž .
maximized 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. Conse-quently, the final number of rays is reduced to 350 in the horizontal tomography.
Ž .
The vertical tomography 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 tomogra-phy plane is less precise than in the middle due to
Ž .
Ž . Ž . Ž . Ž .
The horizontal tomography reveals a large dam-aged zone inside the section extending downwards
Žsee 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
Žaround 4500 m sy1..
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 com-parison reveals its drawbacks either when numerous pillars or when different processing users are in-volved.
4.1. 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 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 information by a classical imaging process.
This information, generated from the echoes, de-pends on the depth of the cracks, their target section and 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 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 superim-posed 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
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 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 sur-face normalization gets corrected by the half-wave-length 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 pro-files.
4.2. Comparison
Ž . Fig. 5. Radar tomography by image processing Pillar 1 .
Ž
different due to the large number of data several hundred 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 the presentation not only on the cracks but also on the diffracting areas. These areas can be considered as
Fig. 6. Radar and seismic imaging on Pillar 1.
Similarly, the damage zones are localized by low
Ž .
seismic velocities 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 re-flected 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
Ž .
either one of the two NDT approaches see Fig. 7 .
Fig. 8. Radar and seismic imaging on Pillar 3.
The overlap of the main cracks on the radar tomog-raphy 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
seis-mic 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 espe-cially for unevenly-shaped pillar. Moreover, the
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 re-peated in order to lengthen the profiles to the right
Ž
dimension for image processing principle 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 inaccu-rate results.
With respect to the seismic tomographies, Pillars 3 and 4 are more homogeneous and display high
Ž .
velocities 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 seri-ously 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 com-pare 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 ad-vantage 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 sy1. The main limitations herein stem from the impossibility of 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 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 con-structing a damage-related radar image that can sup-port 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 readabil-ity, along with its geophysical comments, for geolo-gists. The second advantage is its comparability with
Ž
other 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 test conditions 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 the LCPC- Image Processing Section, for his kind help and high-performance imaging software APIC-TUREB, which facilitated the last radar processing sequence.
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