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HAL Id: tel-00880759https://tel.archives-ouvertes.fr/tel-00880759
Submitted on 6 Nov 2013
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Characterization of anisotropy in a karstified carbonateplatform using seismic and electrical resistivity
methods : a joint approachJan Beres
To cite this version:Jan Beres. Characterization of anisotropy in a karstified carbonate platform using seismic and elec-trical resistivity methods : a joint approach. Earth Sciences. Université Paris Sud - Paris XI, 2013.English. NNT : 2013PA112214. tel-00880759
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Seismic anisotropy analysis at the Low-Noise Underground Laboratory(LSBB) of Rustrel (France)
Ján Bereš a, Hermann Zeyen a,⁎, Guy Sénéchal b, Dominique Rousset b, Stéphane Gaffet c
a UMR 8148 IDES, CNRS-Université Paris-Sud XI, Bât. 504, cedex F-91405 Orsay, Franceb FR 2952, IPRA, Université de Pau et des Pays de l'Adour, Cedex BP 1155F-64013 Pau Francec UMR GEOAZUR 6526, UNS/CNRS/OCA, 250, rue Albert Einstein—Bât. 4, Sophia-Antipolis—F-06560 Valbonne, France
a b s t r a c ta r t i c l e i n f o
Article history:
Received 24 November 2012
Accepted 16 April 2013
Available online 29 April 2013
Keywords:
Horizontal transverse isotropy
Seismic anisotropy
Cross-hole tomography
Hydro-geophysics
Karst
Time lapse
Seismic anisotropy of a fractured karstic limestonemassif in sub-parallel underground galleries is studied. As the
fractures are mostly vertically oriented, the seismic properties of the massif are approximated by horizontal
transverse isotropy (HTI). Several data inversion methods were applied to a seismic dataset of arrival-times of
P and S-waves.
The applied methods include: isotropic tomography, simple cosine function fit, homogeneous Monte-Carlo
anisotropic inversion for the parameters of horizontal transverse isotropy and anisotropic tomography for
tilted transversely isotropic bodies. All methods lead to the conclusion that there is indeed an anisotropy
present in the rock massif and confirm the direction of maximum velocity parallel to the direction of fracturing.
Strong anisotropy of about 15% is found in the studied area. Repeated measurements show variations of the
P-wave parameters, but not of the S-wave parameters, which is reflecting a change in water saturation.
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
In May 2005 and June 2011 seismic data were acquired between twonearly parallel sub-horizontal underground galleries approximately100 mapart. These galleries formpart of the LSBB (Laboratoire Souterrainà Bas Bruit; Low Noise Underground Laboratory), a system of under-ground tunnels in southern France built for the command of French nu-clear forces that was converted into a research laboratory in 1998. Thedata served in the first place for a tomographic study of the site. However,soon it became clear that we have to deal with important anisotropy ofseismic velocities. In this publication, we present an analysis of the ac-quired data in termsof quasi-P-wave (qP) and quasi-S-waves (qS) veloc-ities and anisotropy distribution. In the following, we will omit theletter q for brevity. If the anisotropy is due to sub-parallel rock fractur-ing, the mechanical properties of the rock should depend on the watercontent in those fractures. Acquisition of seismic data in two differentyears with different water content should then show different anisot-ropy magnitudes. Therefore, we will present also a time lapse analysisof the data from both years.
The laboratory is located in a karstic limestone massif containingfractures and faults with a predominant N30°E direction, (Thiébaud,2003) (simplified sketch in Fig. 1). The properties of the investigatedpart of the massif are influenced mostly by minor fractures, majorfaults are not present. However, the rock is intensely deformed by
subvertical and subparallel cracks. Different types of limestone arepresent and observable at the surface. Sub-horizontal alternations ofmassive banks and friable layers (dipping with 25° in N120–130°direction) are interrupted by sub-vertical reef structures striking inE–W to WNW–ESE direction (Thiébaud, 2003).
2. Data acquisition
In 2005, 120 sledge hammer blasts carried out against the verticalwall of one of the sub-horizontal galleries (“anti-blast gallery”, Fig. 1)were recorded by 12,250 Hz geophones fixed in horizontal positionon the wall of the opposite sub-horizontal but not parallel gallery(“main gallery”), recording horizontal movements with the aim ofdoing a cross-hole tomography. Shot as well as station separationwas 1 m (i.e. shot profile of 120 m and geophone profile of 122 mlength). In the South, along the transversal gallery (Fig. 2), the twogalleries are 100 m apart from each other, at the northern end ofthe measurements the distance increases to 108 m. In this way, wecovered an azimuthal range of about 100°, from−50° to +50°, defin-ing the zero azimuth as the direction perpendicular to the anti-blastgallery. This setup is similar to horizontal cross borehole measure-ments, with one difference that the boreholes start within the massifand not at the surface. Fig. 2a shows the position of shots and re-ceivers as well as the rays of three example shots. The data qualityallowed us to pick some 22,500 P-wave first arrival times (Fig. 3)and additional 2700 Sparal-wave arrivals (S-waves polarised parallel
Journal of Applied Geophysics 94 (2013) 59–71
⁎ Corresponding author. Tel.: +33 169154909.
0926-9851/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.jappgeo.2013.04.008
Contents lists available at SciVerse ScienceDirect
Journal of Applied Geophysics
j ourna l homepage: www.e lsev ie r .com/ locate / jappgeo
to the fractures) for the measurements of the year 2005. The arrivalsof the Sprp-waves (polarised normal to the fractures—after Rüger,1997) were not possible to pick as the y cannot be distinguished be-hind the Sparal-waves. These data were acquired during a periodwith significant water content in the massif.
In 2011, a second campaign was conducted, where shots wereexecuted not only in the anti-blast gallery but also in the transversalgallery (Fig. 2b), extending in this way the angle coverage from 100°to almost 140°. Other parameters remained unchanged. More than26,000 P-wave first arrival times and 6500 Sparal-wave arrivals werepicked. This dataset was acquired during a dry period.
3. Data Analysis
3.1. Isotropic Cross Hole Tomography
Fig. 3 shows all measured P-wave and Sparal-wave arrival times fromMay 2005 as function of offset. For an isotropic and homogeneousvelocity distribution, one should expect all points lying on a straightline. The scatter of the arrival times shows that the rocksmust be inhomo-geneous in the area. As a first step, we did standard isotropic cross-holetomography using the code pstomo_eq (Tryggvason and Linde, 2006).Since the galleries are not parallel and do not have the same slope, wehad to use a 3D programme that takes the real geometry into consider-ation. The resulting model (Fig. 4) explains the data well with a standarddeviation of 0.29 ms, however, it shows clear artefacts (red ellipse areas),especially in the NE and SW corners, where velocities that are unrealisti-cally high for limestones (e.g. Fournier et al., 2011; Jeanne et al., 2012).This result can be explained by the fact that rays travelling in SW–NE di-rection have smaller travel-times than those travelling in NW–SE direc-tion. The tomographic inversion algorithm gives realistic velocities inthe centre, where the ray density is highest (Fig. 5). However, it tries tocompensate the travel time differences in the areas that are less wellconstrained due to smaller ray density. This result indicates presence ofanisotropy. It is well known that P-wave travel-times corresponding toan anisotropic medium may be explained also by a more complicated
isotropic velocity distribution, but, the resulting velocities are then usu-ally not geologically meaningful (e.g. Grechka, 2009). Also the two welldistinguished branches in Fig. 3 indicating two different velocities canbe explained by anisotropy.
3.2. Cosine Function Fit
Therefore, as a first test of anisotropy, we fitted the observed travel-times to a simple cosine function assuming seismically homogeneousmaterial (i.e. straight rays):
t d;φð Þ ¼d
v0 þ dv⋅ cos 2 φ−φ0ð Þ½ ð1Þ
where t is the measured travel time [ms], d the offset [m] taking intoaccount the 3D coordinates of shot and receiver points, ф the angleof ray departure (ф = 0° is perpendicular to the wall of the anti-blastgallery), v0 the average velocity [km/s], dv the amplitude of anisotropy[km/s] andф0 the direction of the high velocity directionwith respect tothe direction perpendicular to the anti-blast gallery.
The resulting best fitting parameters for P-waves and Sparal-wavesare given in Table 1. The overall data misfit (fourth column in Table 1for each year) corresponds to 60% travel time variance reduction withrespect to the best fitting isotropic model and >99% with respect tothe measured data. σ represents the standard deviation calculated as:
σ ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
N−1
X
N
i¼1
tcalculated−tmeasuredð Þ2
v
u
u
t ð2Þ
We also calculated the average velocity for all rays departingwithin bins of 5° and plotted these data for both years for P- andS-waves of both years as function of departure angle (Fig. 6) togetherwith the best fitting cosine approximations. Bigger uncertainty barsfor the year 2011 are due to a different experimental mounting of the
Fig. 1. Location of the study area and fracture/faults setting. Fractures visible at the surface are shown with long red lines (thick lines: major faults, thin lines minor ones). Short red
lines indicate faults visible in the galleries. The red oval represents the investigation zone.
60 J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
geophones on the walls which produced some additional noise due togeophone vibrations after the first arrival.
3.3. Monte Carlo Inversion of Anisotropic Stiffness Coefficients
In order to determine more precisely the anisotropic seismic proper-ties of the rock massif, we developed a Monte Carlo programme based
on theMarkov chain algorithm. In themost general case, 21 independentstiffness coefficients are needed to describe anisotropic seismic velocitydistribution (e.g. Grechka, 2009). Grechka and Kachanov (2006), exam-ined the media with penny shaped cracks and came to conclusion thatwhen the cracks are not co-planar, resulting anisotropy is orthorhombic.The number of independent stiffness coefficients for such a mediumdecreases to nine.
Fig. 2. a) Example of rays from 3 shot points (May 2005). b) Example of rays from 5 shot points (June 2011). Missing rays are due to noise at the corresponding receiver.
61J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
However, in the plane, perpendicular to the plane of fractures, inthis case, the symmetry is equivalent to transverse isotropy wherethe number of independent stiffness coefficients decreases further-more to five The third dimension does not influence the velocities inthe two studied dimensions, and the third orthorhombic plane andits respective coefficients have no effect on studied dimensions. Ifthe fractures would not be oriented vertically, but with an importantangle, using this simplification of transversely isotropic medium,would lead to an error of the maximum velocity. The real velocitywould be higher if the velocity in direction of the unused orthorhombicaxiswas higher, and smaller in the other case. As Grechka andKachanov(2006) state, there is virtually no effect on the stiffness matrix if thecrack faces are corrugated or not.
Therefore, the massif is considered as a medium with an isotropyplane parallel to the principal fracture planes (Tsvankin et al., 2010)containing the maximum velocity. The minimum velocity is parallel tothe symmetry axis perpendicular to the fractures. In the studied area,sub-vertical cracks lead to a horizontal transversely isotropic mediumapproximation (HTI).
This simplification leads to a reduction of the number of coeffi-cients to five stiffness coefficients and the angle of direction of thesymmetry axis. The coefficients stem from the matrix of stiffnesscoefficients expressed in Voigt notation (Winterstein, 1990), andderived from the stress–strain relationship:
τi ¼ Cij·ε; ð3Þ
CHTIð Þ
¼
c11 c12 c12 0 0 0c12 c22 c23 0 0 0c12 c23 c22 0 0 00 0 0 c44 0 00 0 0 0 c66 00 0 0 0 0 c66
2
6
6
6
6
6
6
4
3
7
7
7
7
7
7
5
ð4Þ
For HTI, the stiffness coefficients are connected to velocities in thefollowing way (modified from Grechka's VTI coefficients, 2009):
V2p ¼
1
2ρFþ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
c11−c66ð Þ cos2 ϕð Þ− c22−c66ð Þ sin2 ϕð Þ 2
þ 4 c12 þ c66ð Þ2 cos2 ϕð Þ sin2 ϕð Þ
q
ð5Þ
V2Sprp ¼
1
2ρF−
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
c11−c66ð Þ cos2 ϕð Þ− c22−c66ð Þ sin2 ϕð Þ 2
þ 4 c12 þ c66ð Þ2 cos2 ϕð Þ sin2 ϕð Þ
q
ð6Þ
V2Sparal ¼
1
ρc66 cos
2ϕð Þ þ c44 sin
2ϕð Þ
n o
ð7Þ
where
• Vsprp stands for Swave velocity, forwhich particlemovementwith respect to fractures depends on propagation direction,polarised normal to fractures, (Rüger, 1997);
Fig. 3. a) Travel times vs. offset of all measured P-wave arrival time in 2005. b) Travel times vs. offset of all measured S-wave arrival times in 2005.
62 J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
Fig. 4. P-wave velocity distribution obtained from 3D isotropic cross-hole tomography using the real field geometry. The very high velocities in the upper right and lower left
corners and the low velocities in the opposite corners are artefacts due to neglecting anisotropy. The black dots correspond to the positions of shots (left) and receivers (right).
Big red arrow: direction of high velocity, small red arrow: direction of low velocity obtained from cosine fit described later.
Fig. 5. Ray coverage for isotropic tomography. N ray represents density of rays per m2.
63J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
• Vsparal stands for S wave velocity, with particle movementalways parallel to fractures;
• F = (c11 + c66) cos2(ϕ) + (c22 + c66) sin
2(ϕ);• ρ is the rock density taken here as 2500 kg.m−3;• ϕ represents the angle between propagation direction and
isotropy axis
In the coordinate system of anisotropy, we define the direction ofthe isotropy axis and therefore also of low velocity as XHTI. The isotropyplane of high velocity is then parallel to YHTI and ZHTI. This coordinatesystem is rotatedwith respect to the one of the underground laboratory,where the X-axis is defined perpendicular to the anti-blast gallery, by anangleф0 in the X–Yplane. The Z axis of the laboratory and the anisotropy
coordinate systems are the same due to the essentially 2D configurationof the data acquisition. This angle of rotation is one of the unknowns inthe inversion.
Although it is common to express anisotropy in reflection seismicsin terms of Thomsen's parameters (Thomsen, 1986) or Thomsen'stype parameters derived for HTI media (Rüger, 1997; Tsvankin,1997), we are inverting for the stiffness coefficients as they providethe direct physical information about the medium. If only P-waveinformation were available, Thomsen's parameters ε and δ could beuniquely resolved, whereas the stiffness coefficients c12 and c66 wouldbe linearly dependent. However, the joint inversion of P and S-wavearrivals allows a unique resolution of all five stiffness parameters neces-sary for HTI anisotropy and the rotation angle. Thomsen's parameters
Table 1
Summary of best fitting parameters for simple cosine fit.
Wave type 2005 2011
v0 [km/s] dv [km/s] ф0[°] σ [ms] v0 [km/s] dv [km/s] ф0 [°] σ [ms]
P 4.69 ± 0.03 0.45 ± 0.02 43 ± 3 0.98 4.63 ± 0.03 0.61 ± 0.04 40 ± 2 1.14
Sparal 2.61 ± 0.01 0.17 ± 0.01 43 ± 3 1.37 2.61 ± 0.02 0.13 ± 0.03 35 ± 6 3.45
Fig. 6. Average velocities for all rays departing from the shot points within a range of angles of ± 2.5°, with optimum velocity adjustments from cosine fit function. 0° departure
corresponds to the direction perpendicular to the anti-blast gallery. Error bars correspond to standard deviation of average velocities. Left column 2005, right column 2011. First
row velocities P-waves, second row velocities S-waves.
64 J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
can then easily be calculated from the stiffness parameters, as well asthe velocities in the direction of the symmetry axis, VP0 and VS0.
Apart from the angle of rotation ϕ0, the independent coefficientsneeded to be calculated for this model are in Voigt notation: c11, c22,c12, c66 and c44 (Grechka, 2009). Coefficients c11 and c22 are the coeffi-cients that relate to the velocities of P-waves parallel to the anisotropyaxes, where c11 is related to the minimum velocity and c22 to the
maximum velocity. The coefficients c44 and c66 are mainly controlledby the S velocities, although c66 enters also the equation for P velocitieswhere, it is related to c12, leading to a strong linear dependency be-tween these two parameters in the absence of S-wave travel times.
During the inversion, beginning with an arbitrary starting model, theprogramme modifies randomly all parameters at the same time withina predefined model space and with a Gaussian probability-density func-tion around each actual model parameter. The fit of the newmodel mea-sured in a least squares sense with respect to measured and calculatedtravel-times is compared with the one of the former model. If the newmodel fits the data better than the formermodel, it is introduced in an as-semblage of acceptedmodels and the followingmodel is searched aroundthe new model (i.e., the centre of the probability-density function isshifted from the former to the new model); if not, the new model isrejected and the former model is repeated in the mentioned assemblage.The area was supposed to be homogeneous, i.e. no ray bending was con-sidered andwe inverted only for the average stiffness parameters. As out-put, the programme gives a list of all coefficient combinations with theirrespective misfits (root mean square—RMS of the differences betweenmeasured and calculated travel-times). The best fitting model after500,000 iterations is displayed in Table 2 and Fig. 7.
The inversions for both years correspond quite well to their cosineapproximations for both wave types. Fig. 8 displays the histogram ofinverted parameters for all models yielding a fit within 10% of thebest solution.
Table 2
Summary of best fitting parameters for Monte Carlo inversion (units of coefficients:
[(km/s)2 · (g/cm3)]).
Parameters 2005 2011
All shots Without transverse gallery
c11 44.9 36.9 37.1
c22 65.9 67.6 69.2
c12 25.4 23.3 23.8
c44 19.3 18.3 19.7
c66 14.8 15.3 15.4
ϕ0[°] −43.9 −53.1 −52.7
Vp min [km/s] 4.23 3.84 3.85
Vp max [km/s] 5.13 5.2 5.26
Vs min [km/s] 2.43 2.47 2.48
Vs max [km/s] 2.78 2.71 2.81
RMS [ms] 0.47 0.91 0.82
Fig. 7. Travel-times measured (black) andmodelled (red) (Monte Carlo approach). Upper row shows results for 2005, lower row those for 2011; left column: P waves, right column:
S waves.
65J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
3.4. Anisotropic Tomography
The previous results show that the approximation of the rock by anHTI medium explains most of the data, however the spread of themea-sured travel-times around the synthetic ones shows that the area is nothomogeneous. Therefore, we used the 3D seismic anisotropy tomogra-phy programme “3Dray_gTI0” (Zhou and Greenhalgh, 2008), designedfor tilted transversely isotropicmedia (TTI) in order to invert for the dis-tribution of stiffness parameters. Tilting in 3D is done using 2 rotationalangles in spherical coordinates. Since we are dealing with an HTI medi-um, the first rotation angle of the symmetry axis is set to 90° with re-spect to a VTI model being the reference model of 3Dray_gTI0. Thesecond anglewasfixed as previously obtained from theMonte-Carlo in-version. As the massif is rather homogeneous and the direction of thefractures does not show important changes in the studied area, we didnot invert for the angles because the sensitivity of velocity with respectto the angle is very small around the optimum angle and small changes
in angles would not affect the result but make the inversion ratherunstable (Golikov and Stovas, 2012).
We modified the programme to our needs, implementing a dataco-variance matrix that allows for taking account of variable datauncertainties for the model construction (Menke, 1984). These datauncertainties were measured during picking of arrival times anddepend on visually determined data quality. P-wave picks have inaverage smaller uncertainties than S-wave picks.
The inversion is non-linear and it is therefore done by a series ofiterations. The parameters of the starting model were set to the out-put values of the homogeneous Monte-Carlo anisotropic inversionon a 10 × 10 m grid. After 20 iterations, the model stabilized. Theresulting parameters are shown in Figs. 9 and 10. Fig. 11 shows thecorresponding travel times of P-waves and for the S-waves. In aver-age, the result is similar to the Monte-Carlo results. Joint RMS misfitsof the P and S travel times are 0.46 ms and 1.30 ms for 2005 and2011, respectively.
Fig. 8. Histogram of all inverted parameters for models within 10% of the best solution for Monte-Carlo anisotropic inversion.
66 J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
The degree of resulting anisotropy is best displayed through the dis-tribution of Thomsen's parameter ε, δ and γ (modified from Thomsen,1986).
ε ¼c22−c112c11
ð8aÞ
γ ¼c44−c662c66
ð8bÞ
δ ¼c12 þ c66ð Þ2− c11−c66ð Þ2
2c11 c11−c66ð Þð8cÞ
The parameter ε is a measure of the difference of coefficients c11and c22, and therefore of the difference between P-velocities in thedirections of the principal anisotropy axes. It controls the near-verticalanisotropy. The parameter γ is a measure of the difference of coeffi-cients c44 and c66, and therefore of the difference between S velocitiesin the directions of the principal anisotropy axes. Both are intuitive tounderstand and vanish in anisotropic media (modified for HTI fromGrechka, 2009). The combination of stiffness coefficients in δ is chosenin such way that it includes coefficient c12 without the coefficient c22and becomes useful for near horizontal propagation of elastic waves(modified for HTI from Thomsen, 1986).
Fig. 10. Results June 2011: Parameters variations were allowed within fixed boundaries (limits of the colour bars) considered to be physically possible.
Fig. 9. Results May 2005: Parameter variations were allowed within fixed boundaries (limits of the colour bars) considered to be physically possible.
67J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
In addition to Thomsen's parameters, we calculated the velocitiesaveraged over all angles at each grid node in order to see the impor-tance of lateral velocity variations. Figs. 12 and 13, show the distributionof these averaged velocities and the coefficients ε, δ and γ. It is interest-ing that the structures observed on these maps generally do not showthe same directions as the fractures. It seems that they aremore relatedto variable rigidity in the limestones than to fracturing. The direction ofreef structures observed at the surface striking between N90° andN110°, corresponds well with the directions of average velocities.
4. Discussion and Conclusions
Seismic P-wave and S-wave travel-times in sub-parallel under-ground galleries were measured. Standard 2D seismic tomographyresulted in velocities that are unrealistic for the present limestones,mainly in areas with bad ray-coverage. This was interpreted as asign of anisotropy of the rock massif. Data was therefore treatedby several anisotropic approaches. The seismic velocities weremodelledby simple cosine fit and two independent anisotropic inversion schemes.They all give similar results in terms of high and low velocities and thedirection of maximum velocity corresponds well with the direction ofthe main fracture systems observed between the two galleries, as hasto be expected.
An independent confirmation of the anisotropywould be obtained, ifwe could quantify the S-wave splitting. However, using the coefficientsobtained, it is easy to calculate (Eq. (7)) that for our offsets of 100–150 m arrivals of both S-waves are so close to each other that they arenear resolution limit (1 to 1.5 periods of arrival time differences).
The amount of anisotropy depends on the fracture density in therocks (e.g. Best et al., 2007; Prasad and Nur, 2003), on the wave typeand on the filling of the fractures: For P-waves, anisotropy should beweaker for water-saturated rocks than for dry rocks due to strong vari-ation of compressibility. This change in anisotropy should be principallydue to a change in minimum velocity, which is strongly affected by thefractures, whereas the maximum velocity is mainly controlled by therock matrix. In contrast, S-waves should hardly react on the amountof saturation, since the rigidity is near zero as well for air as for water.We observed much stronger anisotropy for P-waves in June 2011(dryer period) than in May 2005 (wetter period), whereas no signifi-cant variation of S-wave anisotropy was observed between the twomeasurements. In order to be sure that this difference is not related tointegrating additional shot points in 2011, we inverted the 2011 dataalso without the travel times from the shots in the transverse gallery.The results were the samewithin a few percent (Table 2). The observedvariations fit thus well to a difference in rock saturation between spring2005 and summer 2011. Similar results were obtained in the studyconducted by Schubnel et al. (2006). Depending on fracture density,velocities of saturated samples are larger than the velocities of drysamples. The higher the fracture density, the bigger is the difference be-tween the dry and the saturated samples. Although their study wasconducted on a different rock type (granite), their normalized resultscould be used for comparison with our data. Velocity in slow directioncould be as small as 40% of the maximum velocity for a crack densityequal to 1, where crack density q is defined as q ¼ 1
V ∑N
r3i , r being thecrack radius, N total number of cracks embedded in a representativevolume V. For crack density equal to 0.1 the slow velocity reaches 80%of the maximum velocity. In 2011, being the dryer period, the slow
Fig. 11. Results anisotropic tomography offset vs. travel-time. Top row May 2005; bottom row June 2011. Left column: graphs for P-waves; right column graphs for S-waves.
68 J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
velocity in our case reaches 73% of the maximum velocity, therefore ifanisotropy is only due the cracks in our massif, their density could beslightly above 0.1. According to Bakulin's equation 18 based on S-wavevelocities (Bakulin et al., 2000), the crack density has a value q = 0.10in 2005 and q = 0.08 in 2011. The crack density should be equal forboth campaigns and this slight variation can result from different geome-tries during acquisition in both years and/or uncertainties during pickingof travel times. Bakulin's equation 17 based on P-wave velocities givesclearly different values for 2005 (0.06, i.e. 40% less than for S-waves),whereas values are similar to those of S-waves in 2011 (0.07). This con-firms the interpretation of nearly dry fractures in 2011 and partly saturat-ed ones in 2005, since for S-waves, the corresponding coefficient ΔT isindependent of saturation, whereas for p-waves, ΔΝ becomes zero forwater saturated fractures and gives an apparent fracture density of zero.
Porosity of lower cretaceous carbonates at the LSBB site can have dif-ferent values. Our studied area is situated in the Urgonian facies fromUpper Barremian to Aptian. They are characterised by an average poros-ity of 10%. (Mauffroy, 2010). Fournier et al. (2011) conducted laboratorymeasurements on samples collected from nearby locations and fromour site. According to their results, velocities of unfractured limestonereach up to 6.2 km/s and decrease with increasing porosity. As thestudy was conducted on small samples, where anisotropy was not
considered, we are comparing their results with our average velocityobtained from Monte Carlo inversion (4.8 km/s). This velocity corre-sponds to a porosity of about 15% in good agreement with the valuepublished by Mauffroy (2010). Above the main gallery, Mauffroy(2010) obtained an isotropic seismic tomography image on a verticalplane oriented 40° with respect to the fast direction between the sur-face and the gallery. She obtained a velocity of 4.8–4.9 km/s which isalso in good agreement with our results in this direction. According tothe results of their tomography, a porosity of 13% was calculated.
If velocity variations are only due to anisotropy, Thomsen's coefficientε should be inversely proportional to the averaged velocities. Increase ofanisotropy should be due to an increase of fracture density and thereforeto a reduction mainly of the minimum velocity. Comparing the distribu-tions in Figs. 12 and 13, one can see in general an anti-correlation be-tween ε and average velocities. Deviations from this show again thatpart of the velocity variations must be related also to material changes.
Acknowledgements
The authors acknowledge partial financing by project GUTEC of thePIR-PACEN du CNRS. The field work in the galleries would not have
Fig. 12. Results 2005: a) Average velocity, b) Thomsen's parameter ε, c) Thomsen's parameter δ and d) Thomsen's parameter γ.
69J. Bereš et al. / Journal of Applied Geophysics 94 (2013) 59–71
Fig. 13. Results 2011: a) Average velocity, b) Thomsen's parameter ε, c) Thomsen's parameter δ and d) Thomsen's parameter γ.
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been possible without the support of the technical staff. We thank ananonymous reviewer for his thoughtful suggestions.
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