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
Ž
. Stevens 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 .
Fig. 1. Example of the shape of a pillar Pillar 1 , and position of the radar investigations.
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 .
profile. d Profile after Hilbert transform.
two successive profiles has yielded a theoretical indication of the angle by means of the following
equation:
a s arcsin Rrd ,
1
Ž .
Ž .
Ž 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, allowing 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 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 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 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 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
Ž .
Grandjean 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
