Geophysical Journal International

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1 Geophysical Journal International Geophys. J. Int. (2013) Geophysical Journal International Avance Access publishe February 5, 2013 oi: /gji/ggs130 Shear wave anisotropy from aligne inclusions: ultrasonic frequency epenence of velocity an attenuation J. J. S. e Figueireo, 1,2, J. Schleicher, 2,3 R. R. Stewart, 4 N. Dayur, 4 B. Omoboya, 4 R. Wiley 4 an A. William 4 1 Faculty of Geophysics, Feeral University of Pará(UFPA),Belém, PA, Brazil, jasomjose@gmail.com 2 National Institute of Petroleum Geophysics (INCT-GP), Salvaor, BA, Brazil, Department of Applie Mathematics, IMECC/University of Campinas (UNICAMP), Campinas, SP, Brazil, Allie Geophysical Laboratories, University of Houston, Houston, Texas, USA, TX Accepte 2012 December 30. Receive 2012 December 24; in original form 2011 December 13 SUMMARY To unerstan their influence on elastic wave propagation, anisotropic cracke meia have been wiely investigate in many theoretical an experimental stuies. In this work, we report on laboratory ultrasoun measurements carrie out to investigate the effect of source frequency on the elastic parameters (wave velocities an the Thomsen parameter γ ) an shear wave attenuation) of fracture anisotropic meia. Uner controlle conitions, we prepare anisotropic moel samples containing penny-shape rubber inclusions in a soli epoxy resin matrix with crack ensities ranging from 0 to 6.2 per cent. Two of the three cracke samples have 10 layers an one has 17 layers. The number of uniform rubber inclusions per layer ranges from 0 to 100. S-wave splitting measurements have shown that scattering effects are more prominent in samples where the seismic wavelength to crack aperture ratio ranges from 1.6 to 1.64 than in others where the ratio varie from 2.72 to The sample with the largest cracks showe a magnitue of scattering attenuation three times higher compare with another sample that ha small inclusions. Our S-wave ultrasoun results emonstrate that elastic scattering, scattering an anelastic attenuation, velocity ispersion an crack size interfere irectly in shear wave splitting in a source-frequency epenent manner, resulting in an increase of scattering attenuation an a reuction of shear wave anisotropy with increasing frequency. Key wors: Boy waves; Coa waves; Seismic anisotropy; Seismic attenuation; Wave scattering an iffraction; Wave propagation. GJI Seismology 1 INTRODUCTION Cracks an fractures in subsurface rocks are strong inicators of lithologic stress. Moreover, many hyrocarbon reservoirs are situate in anisotropically cracke an fracture meia. Thus, unerstaning wave propagation in such meia is of utmost importance to be able to extract a maximum of information from seismic ata, which has motivate many stuies in earthquake seismology an seismic exploration of hyrocarbon reservoirs (Crampin 1981; Thomsen 1986, 1995; Crampin et al. 1999; Crampin & Peacock 2005; Crampin & Gao 2010). Because of the geological complexities often attene by natural fracture structures, reliable conclusions about elastic properties are usually ifficult to achieve with sufficient accuracy from fiel ata. Thus, numerical an physi- Formerly at: CEP/UNICAMP, Department of Petroleum Engineering, Campinas (SP), Brazil. cal simulations of elastic wave propagation in anisotropic meia base on some previous knowlege are generally use as a tool to enhance the unerstaning of this complexity structures. However, numerical simulation of wave propagation in cracke meia can be computationally an mathematically expensive an intense (Huson 1981; Crampin 1981; Huson et al. 2001). When scattering effects are taken into account, these costs become even more significant (Willis 1964; Mal 1970; Yang & Turner 2003, 2005). Moreover, such a computational approach can only stuy phenomena that are sufficiently well escribe by the unerlying equations. Unfortunately, in many situations some of the assumptions mae in numerical moelling may be oversimplifie, constraining, or even questionable. Some ifficulties with the unerstaning an interpretation of ata from both fiel acquisition an anisotropic moelling can be overcome using experimentally scale physical moelling. Laboratory measurements have been shown to be a useful tool for moelling conitions present in the fiel, helping to reuce uncertainties C The Authors Publishe by Oxfor University Press on behalf of The Royal Astronomical Society. 1

2 2 J. J. S. e Figueireo et al. about elastic parameters in numerical methos. Assa et al. (1992, 1996), Wei (2004) an Wei et al. (2007) establishe an experimental relationship between crack ensity an shear velocity base on theoretical preictions by Huson (1981). Melia & Carison (1984) investigate the effect of layere meia on compressional wave propagation in a series of experiments in anisotropic samples. They note that P-wave ispersion in anisotropic layere meia is a function of the concentration of ifferent layere materials as well as the thickness of the layers. In a similar approach, Marion et al. (1994) an Rio et al. (1996) stuie ispersion an multiple scattering of short an long wavelengths in stratifie meia. The main proposal of these latter works was to establish a escription of wave propagation in the transition zone between ray theory an equivalent meium theory. Other sets of experimental work performe by Rathore et al. (1995) an Peacock et al. (1994) emonstrate the feasibility of ultrasonic measurements to stuy wave propagation in artificially cracke porous meia. Using experimental ata obtaine by Rathore et al. (1995), the theoretical preictions of Thomsen (1995) for aligne cracks in porous rock receive strong support. More recently, experiments by Tillotson et al. (2011) have suggeste the possible use of shear wave ata to iscriminate fluis on the basis of viscosity variations. In anisotropic cracke meia, the influence of frequency on properties of wave propagation is etermine by the size of the heterogeneities (Assa et al. 1992, 1996; Wei 2004; Wei et al. 2007). However, quantification of this influence is still esirable. To better unerstan the influence of cracks an fractures on the frequency response in such meia, we conucte a series of experiments aime at extening the work of the cite authors. We use a shear wave source with ifferent frequencies: low frequency (LF = 90 khz), intermeiate frequency (IF = 431 khz) an high frequency (HF = 840 khz) to carry out experiments on a reference sample without inclusions an three other samples with ifferent inclusion sizes, thereby simulating ifferent crack ensities. In this arrangement, shear wave splitting was observe with ifferent magnitues as a function of frequency. In the same set of experiments, we also quantifie attenuation using the frequency shift metho (Quan & Harris 1997). Our results show that S-wave attenuation, both intrinsic an ue to scattering (Toksoz & Johnston 1981; Görich & Müller 1987; Tselentis 1998), correlates irectly with shear wave splitting, which in turn is relate to crack ensity. Furthermore, we observe that the anisotropy parameter γ (Thomsen 1986) varies with frequency an crack size. 2 EXPERIMENTAL PROCEDURE The construction of the cracke samples as well as the ultrasonic measurements were carrie out at the Allie Geophysical Laboratories (AGL) at the University of Houston, Texas. Uner controlle conitions, we constructe three cracke samples (M2, M3 an M4) with ifferent crack ensities an one uncracke sample (M1) for reference. Pictures of all samples are shown in Fig. 1. Figure 1. (a) From right to left: Photograph of the reference sample M1 (uncracke) an cracke samples M2, M3; (b) sample M4. Also shown are the orientations of the coorinate systems. All ultrasonic measurements were mae in the Y irection. The sample size in the Y irection is quantifie in Table 1.

3 Shear wave anisotropy from aligne inclusions 3 Table 1. Physical parameters of samples M1, M2, M3 an M4. Precision of length measurements is about 0.02 cm. Sample Dimensions of fracture zone Measure Number Crack Crack Cracks Aspect Crack X Y Z Volume length of iameter aperture per ratio ensity (cm) (cm) (cm) (cm 3 ) (cm) layers (cm) (cm) layer (per cent) M M M M M M Figure 2. (a) Device evelope for S-wave polarization rotation an velocity measurements. (b) Sketch of experiment use for seismogram recors. 2.1 Sample preparation The isotropic sample M1 consists of a single cast of epoxy resin. Samples M2 an M3 contain cracks aligne along the Y an X irections, respectively. Sample M4 has three ifferently cracke regions, but five ifferent positions use for measurements, labelle 1 5 in Fig. 1. Positions 2 an 4 are at the bounaries between the three ifferent regions. The cracke samples were constitute one layer at a time, alternating with the introuction of rubber cracks. To reuce possible bounary effects to a minimum, the time interval between the creation of separate layers was kept as short as possible. Constant layer thickness (0.5 cm for M2 an M4 an 0.25 cm for M3) was ensure by using the same volume of epoxy resin poure for each layer. After each layer with inclusions was ae to the sample, air was extracte using a vacuum pump to avoi inhomogeneities in the epoxy resin (material of the matrix). The soli rubber material use to simulate the cracks in samples M2 an M4 was neoprene rubber, while in sample M3 we use silicone rubber. The compressional wave-velocity ratio was aroun 1.5 between soli epoxy an neoprene an about 2.25 between soli epoxy an silicone rubber. Note that these values are only rough estimates, because the S-wave velocity in rubber was ifficult to etermine ue to the low shear moulus of this material. The physical parameters of the inclue rubber cracks in each sample are isplaye in Table 1. The crack ensity ɛ in the cracke samples was etermine by ɛ = Nπr 2 h, (1) V where N is total number of inclusions, r is their raius, h is the inclusion s thickness (crack aperture) an, finally, V is the volume of the cracke region for each sample (see Fig. 1). Eq. (1) is a moification of the relation of Huson (1981) for crack ensity estimation. 2.2 Ultrasonic measurements We carrie out ultrasonic measurements using the Ultrasonic Research System at AGL with the pulse transmission technique. The sampling rate per channel for all experiments was 0.1 µs. Fig. 2(a) shows the evice evelope for recoring S-wave seismograms with rotating polarization. The source an receiver transucers were arrange on opposing sies of the samples, separate by the measuring length (see Table 1). To ensure the wave propagation to take place insie the esire region of the samples, the transucers on either sie were place at the centre of each region. The initial shear wave polarization was parallel to the cracks. Changes in polarization were achieve by rotating both transucers by 10 egrees at a time until polarization was again parallel (i.e )tothexz-plane (see Fig. 2b). In total, 19 traces were recore in each seismic section with 20-fol stack to eliminate ambient noise. The polarizations of 0 an 180 correspon to the fast S wave (S1) an 90 correspons to the slow S wave (S2). The reproucibility of the ultrasonic recorings for all samples was ensure by preserving the same physical conition of the complete electronic apparatus. Furthermore, the same coupling between transucers an samples was guarantee by a holer with a spring attache (see Fig. 2). In orer to establish goo contact between transucer an sample, a very slim layer of natural honey was place at the surface of the samples. The source wavelet functions generate by the employe transucers as well as their physical specifications are shown in Table 2. More information about these transucers can be foun at the website of the manufacturer. 1 The fiel conition for these transucer 1

4 4 J. J. S. e Figueireo et al. Table 2. Physical parameters of transucers use to recor S wave seismograms in the samples epicte in Fig. 1. Transucer Catalogue Transucer Ricker Near fiel frequency number iameter wavelet istance 90 khz V mm ( t 3 + 3t)e t cm 431 khz V151-RB 25 mm (t 2 t 1)e t cm 840 khz V153-RB 13 mm (t 2 t 1)e t cm was verifie base on the relationship of Thompson & Chimenti (1995), N = D2 λ 2, (2) 4λ where D is the transucer s iameter an λ is the ominant wavelength in the sample. The values of the ratio between the measuring length of the samples (see Table 1) an the near-fiel istance shown in Table 2 is greater than 1 for all transucers. Therefore, the far-fiel conition is satisfie for all recorings. 2.3 Attenuation estimation proceure We start by analysing the S-wave source signatures an Fourier amplitue spectra of the three source transucers use to obtain the ata later on (see Figs 3a an b). The small seconary peak in the spectrum of the signature of the 90-kHz transucer (blue line in Fig. 3b) can be attribute to some artefact in the piezoelectric crystal use for this transucer. Since the amplitue of this seconary peak is rather small, we can neglect its presence in the further analysis. To simplify the interpretation of the spectra, we performe a Gaussian non-linear fit to each amplitue spectrum (see Fig. 3c). The time winows use to evaluate the Fourier spectra of the signature traces were 10 µs for the IF an HF sources an 28 µs for the LF transucer. We use this Gaussian fit to etermine the centroi frequency as well as the variance of frequency content. This information is require later on for the attenuation estimation using the frequency shift metho (Quan & Harris 1997). The frequency-shift metho etermines the quality factor Q of a seismic event from a comparison of the centroi frequency before an after a transmission experiment. We applie this metho using a source-signature trace an the S-wave arrival after transmission through our samples. The experimental setup is epicte schematically in Fig. 4. Accoring to Matsushima et al. (2011), the frequency shift between the two events etermines the Q factor as Q = σ s 2π t, (3) f where t is the traveltime ifference between two ifferent recorings, f = (f i f o ) is the ifference in centroi frequency between the source (f i ) an the sample-trace pulse f o after Gaussian non-linear fit an σs 2 is the corresponing variance of the source frequency (as epicte in Fig. 4c). It shoul be note that the frequencyshift metho measures total attenuation without istinction of the physical effects that might be causing it. Note that, even though the frequency shift metho is a stable metho to estimate attenuation, the associate etermination of the variance is very sensitive to the noise (Nunes et al. 2011). Thus, to avoi overestimation of the attenuation, the noise in the transmission seismograms of our experiments was significantly reuce by 20-fol stack for each recore trace. We see in Fig. 3(a) that all transucers have an intrinsic time elay. For all S-wave transucers use in this work, we estimate a elay time of 2.7 µs. For the velocity calculations, the elay time was subtracte from the observe arrival time. The accuracy of time picking was ±0.1 µs, which allows to etermine the wave velocities with an accuracy of ±0.3 per cent. 3 EXPERIMENTAL RESULTS In this section, we present our experimental results for S-wave splitting in three cracke samples an one uncracke sample. It also inclues a frequency-omain attenuation analysis in the three ifferent frequency ranges (LF, IF an HF). Figure 3. The time omain, S-wave source signatures of the three transucers: LF = 90 khz, IF = 431 khz an HF = 840 khz. (b) Fourier transform of each signature trace. (c) Fourier transform after Gaussian nonlinear fit. Here the ominant frequencies have become 89, 386 an 805 khz. 3.1 Shear wave seismograms We start with the analysis of the transmission seismograms for the low, intermeiate an high-frequency sources in samples M2 an M3. They are epicte in Fig. 5, which also inclues the corresponing seismograms for the isotropic sample M1 for reference. All seismograms in Fig. 5 are scale to the maximum of the respective section. We observe shear wave splitting for all frequencies in both samples M2 an M3. The magnitue of this birefringence epens on the source frequency. As expecte, the isotropic sample M1 shows uniform S-wave arrivals for all polarizations an all recoring frequencies, not separating fast (S1, 0 an 180 )an slow (S2, 90 ) S waves. In sample M2, the time elay observe between the arrivals associate with S1 an S2, that is, the fast an slow shear waves, was 6.9 µs for LF ata (Fig. 5a) an 1.7 µs for IF ata (Fig. 5b). Despite the slightly larger measuring length in sample M3 (with smaller cracks), the time elays were smaller here. We foun 3.9 an 1.5 µs

5 Shear wave anisotropy from aligne inclusions 5 Figure 4. (a) Schematic representation of two recoring with ifferent source receiver spacing. (b) Signature source trace (top) an pulse-transmission trace (bottom). (c) The corresponing Fourier spectra with central frequency at fi (input source signature) an fo (output pulse-transmission signature). Figure 5. S-wave seismograms as a function of change in polarization from 0 to 180 for samples M1 (isotropic), M2 an M3 in the (a) low, (b) intermeiate an (c) high frequency range. for LF an IF ata, respectively (see Figs 5a an b). In the case of the high frequency measurement, sample M2 (see Fig. 5c) shows fast an slow shear wave arrivals that are har to interpret, which probably can be attribute to the pulse wavelength being of the same orer as the size of the cracks. We will elaborate on this in the next section. Similarly, ue to the small ratio between wavelength an crack size (see next section), the sample M3 for HF source presents a time elay of 0.8 µs.

6 6 J. J. S. e Figueireo et al. Table 3. Source centroi frequencies f s an respective variances σ s, as well as sample-trace centroi frequencies f m of samples M1, M2 an M3 for polarizations S1 an S2. Source frequency (khz) Centroi frequency f s (khz) Variance σ s (khz) Sample-trace Sample S1 S2 S1 S2 S1 1 S2 1 S1 2 S2 2 centroi M frequency f m M (khz) M Frequency analysis The next step consists of analysing the Fourier spectra of the above seismograms an their respective Gaussian non-linear fit spectra. The purpose is to analyse the shear wave scattering an attenuation in the samples. The results are explaine below an summarize in Table Sample M1 We start with the ata for sample M1 (left column of Fig. 5). The re box in the seismograms mark the time winow use to perform the FFT operation over the traces corresponing to the 0 (S1) an 90 (S2) polarizations. We observe from the resulting normalize amplitue spectra (Fig. 6) that in this isotropic epoxy resin sample M1, the peak for the HF waves is the most strongly shifte one. The ominant frequency is shifte from 840 khz (source frequency) to 552 khz (frequency response), while the shift for IF is from 431 khz to 317 khz an the one for LF is 90 khz to 87.5 khz. This very small shift, which means that the LF waves are almost unattenuate, can be attribute to the fact that in this frequency range, the wavelength is of about the orer of the sample size (eviating by only a factor 1.5) Sample M2 The corresponing spectra for sample M2 are epicte in Fig. 7. In this sample, the ratio of wavelength to crack size ranges from 0.37 (HF) to 3.57 (LF) (see Table 4) an hence effects associate with scattering or iffraction as well as effective meia are expecte to be seen at the same time (Marion et al. 1994; Gibson et al. 2000; Matsushima et al. 2011). In the HF spectra (see Fig. 7c) obtaine from the seismograms in the centre of Fig. 5c, we observe two inepenent peaks for both the S1 an S2 waves. The reason becomes evient from Table 4, which presents the ratio between crack size an seismic wavelength for S1 an S2 waves in samples M2 an M3 in the LF, IF an HF range. The effective crack iameter in Table 4 is that of an equivalent sphere with the same volume V c as the cracks, that is, = 3 3Vc 4π. The contributions of the wavefiel at the highest frequencies travel practically unaffecte in the nearly homogeneous meium between the cracks, giving rise to an unperturbe S-wave arrival of the observe wavefiel at almost the same traveltime as in the isotropic sample M1 (see left seismograms in Fig. 5c). Contributions at the lowermost frequencies propagate as if in an effective meium, almost unperturbe from the iniviual cracks, because the crack size is much smaller than the wavelength. On the other Figure 6. Fourier spectra for sample M1 using S-wave sources in the (a) LW, (b) IF an (c) HF range.

7 Shear wave anisotropy from aligne inclusions 7 Figure 7. Fourier spectra for sample M2 using S-wave sources in the (a) LW, (b) IF an (c) HF range. Table 4. Seismic wavelength λ to effective crack iameter ratio for polarizations S1 an S2. Note that for sample M2 at HF, there are two peaks in the spectrum of S1 an S2, resulting in two values in the respective lines of this table. Source frequency (khz) Centroi wavelength (M2) λ (cm) Centroi wavelength (M3) λ (cm) Sample Crack volume V c (mm 3 ) Eff. Diameter (cm) M M λ S1 λ S2 λ S1 λ S2 λ S11 han, intermeiate frequency contributions with wavelengths of the orer of the effective size of the scatterers suffer from the strongest attenuation from scattering at the cracks. Thus, these contributions are almost completely missing in the receiver wavefiel, resulting in two peaks at either sie of the resulting amplitue spectrum. Note that Figs 7(a) an (b) o not exhibit a secon peak, inicating that the high frequencies that suffer very little attenuation are not present in these wavefiels. This is corroborate by the seismograms in Figs 5(a) an (b), in which the S-waves arrivals are recore at a significantly later time than in the isotropic sample M1. Note that in the HF range (see Fig. 7c), the spectra of the S1 an S2 polarization exhibit two visible ifferences. (1) The shift of ominant frequency is stronger for the S1 polarization (from 840 khz to 172 khz) than for S2 (from 840 khz to khz). (2) The secon peak at higher frequencies is much more pronounce relative to the first one for the S2 polarization than for S1. In the LF an IF ranges, the S1 an S2-wave polarizations exhibit a nearly ientical behaviour. While for LF, almost no frequency shift is observe (see Fig. 7a), the IF range exhibits a pronounce frequency shift (see Fig. 7b). The rather strong frequency shift for both polarizations for IF an HF may be explaine by the fact that in the strongly attenuate frequency ranges, the wavelengths are of the size of the inclusions lengths, which increases the scattering-relate attenuation (see Table 4). The ifference in the frequency shift between the polarizations an the fact that the secon peak is much stronger for the S1 than for the S2 polarization inicates that scattering attenuation is ominant when the polarization is parallel to the crack, but that intrinsic attenuation becomes more important when the polarization is perpenicular to the cracks. For a better unerstaning of the two separate peaks, we applie a ban-pass filter of khz (perfect pass between 50 an 350 khz, with linear cut-off ramps in the ranges khz an khz) to the HF ata of sample M2 (centre panel of Fig. 5c, replotte in Fig. 8a). The Cut-off frequency of 400 khz approximately coincies with the en of the first peak in Fig. 7(c). The result is epicte in Fig. 8(b). The HF part, obtaine as the ifference between the original an filtere seismograms, is shown in Fig. 8(c). Note that after filtering, shear wave splitting with a magnitue of 1.4 µs becomes visible (Fig. 8b), which coul not be observe before. This corroborates our interpretation that the low-frequency part of the wavefiel behaves as if travelling in an effective anisotropic meium. On the other han, the seismic section in Fig. 8(c) correspons to the combine frequency content of the two high-frequency peaks at 750 khz (S2) an 820 khz (S1) of Fig. 7(c). No shear wave splitting is visible in Fig. 8(c), inicating λ S21 λ S12 λ S22

8 8 J. J. S. e Figueireo et al. Figure 8. (a) S-wave seismogram for sample M2 (b) The same ata after application of ban-pass filter khz (S-wave time elay is 1.4 µs). (c) High-frequency section after subtraction of (b) from (a). Figure 9. Fourier transform spectra for sample M3 using S-wave sources in the (a) LW, (b) IF an (c) HF range. that the high-frequency part of the wavefiel behaves as if travelling in an isotropic meium with the velocity of uncracke epoxy resin Sample M3 In sample M3, none of the frequency ranges prouces a secon peak (see Fig. 9), because the cracks are too small an too sparsely istribute to allow for perceptible scattering attenuation. All wave propagation is in the effective-meium regime. However, like in sample M2, also in this sample the shift in frequency associate with the perpenicular polarization (S2) is more prominent than the one for S1. As mentione before (see Table 4), the pulse-wavelengthto-crack-size ratio for M3 ranges from 1.39 to 6.21, that is, the wavelengths are not much smaller than the crack size. This explains why there is less unscattere wave propagation an less unperturbe energy as compare to sample M Velocity results Samples M2 an M3 We etermine the S-wave velocities from the picke traveltimes of the first breaks. Fig. 10 epicts the resulting velocities of the fast (V S1 )anslow(v S2 ) shear waves as functions of sample wavepropagation frequency accoring to Table 3. Fig. 10(a) shows that the isotropic meium suffers of very little ispersion. The ispersion effect because of the cracks is more prominent for sample M2 (Fig. 10b) than for sample M3 (Fig. 10b). We also note that in all cracke samples, the S2 wave is more ispersive. From these velocity values, we calculate Thomsen s anisotropy parameter γ using the relationship γ = 1 2 ( V 2 S1 V 2 S2 ) 1. (4)

9 Shear wave anisotropy from aligne inclusions 9 Figure 10. Velocity plots for samples M1 (a), M2 (b) an M3 (c) as a function of effective ominant frequency. The ispersion curves show that in the investigate frequency range, the polarization S2 is more influence by frequency than S1 for both cracke samples M2 an M3. Figure 11. Anisotropy parameter γ calculate from the S-wave velocities of Fig. 10 using eq. (4). The graphs of the anisotropy parameter γ for samples M2 an M3 (Fig. 11) show that γ ecreases with increasing ominant frequency in the samples. For both samples containing cracks, splitting is more pronounce at the lowest frequency (90 khz) than at intermeiate an high frequencies (431 an 840 khz). As expecte from the anisotropic theories for cracke meia (Huson 1981; Crampin 1984), at LF the value of γ = 12.2 per cent in sample M2 is higher than γ = 7.2 per cent in sample M3, which has a lower crack ensity than sample M2. However, at the highest frequency, the value of γ = 2.0 per cent in sample M2 is equal to the one for M3. While these values of the velocities an anisotropy parameter γ seem to be in conflict with stanar anisotropic theories, a better unerstaning can be obtaine when plotting them as a function of the ratio between centroi wavelength an effective crack size (see Fig. 12). From Fig. 12, we can infer a relationship between anisotropy an seismic frequency (or wavelength) relative to crack size. When plotte as a function of λ/, the velocities in both samples exhibit an approximately linear behaviour. The ifferent polarizations with respect to the crack orientations give rise to ifferent slopes (see Figs 12a an b). Further investigations will be necessary to etermine wether the variation of the slope as a function of S-wave polarization coul be use for an estimation of crack orientation. From these velocity values, we extracte the anisotropy parameter γ as a function of λ/ by means of eq. (4), where at each frequency, we have use a measure velocity value for one polarization an the linearly interpolate one for the other polarization. The resulting γ values are even better approximate by a straight line (Fig. 12c). At long wavelengths (LF), where effective-meia theory is more realistic (see Table 4) the effective anisotropy parameter γ is higher than at

10 10 J. J. S. e Figueireo et al. Figure 12. Linear fit of velocity as function of ratio between wavelength an effective crack size for polarization S1 an S2. (a) sample M2 an (b) sample M3. (c) Anisotropy parameter γ calculate from eq. (4). short wavelengths (HF). These velocity results allow to conjecture that the magnitue of shear wave splitting epens on ominant source frequency, crack size an ensity. Further experiments will be necessary to establish how the slope of γ over λ/ epens on the physical crack parameters Sample M4 Sample M4 was evise to stuy the effect of ifferent crack ensity at constant crack aperture. In this sample, all cracks have the same aperture (0.091 cm), but three ifferent iameters (0.7, 0.44 an 0.32 cm) an thus ifferent aspect ratios (0.13, 0.20 an 0.28). Together with ifferent numbers of cracks per layer, this le to ifferent ensities (8.4, 9.3 an 6.8 per cent) in the three regions of sample M4. The physical information of this sample is containe also in Table 1. To separately interpret the S1 an S2 waves in the HF seismograms, we applie again the khz banpass filter. The S-wave velocities of the fast an slow shear waves at the five measurement points in sample M4 are summarize in Table 5 an graphically represente in Fig Size effect investigation The above observations regaring the epenence of the anisotropy on the size parameters of the cracks are confirme from the results in sample M4. Table 5 shows the velocity values of S1 an S2 waves in samples M1, M2, M3 an M4 together with the relevant physical crack parameters iameter, aperture an ensity. We see that a simultaneous ecrease in iameter, aperture, an ensity, from sample M2 to M3, le to ecreasing S1 an HF S2 velocities, while only LF an IF S2 velocities increase as expecte. On the other han, from the measuring points M4-1, M4-3 an M4-5, we see that the velocities are practically insensitive to the crack iameter. Slight velocity variations seem to be correlate with ecreasing crack ensity. Comparing the values for M2 with those for M4-1, where the crack size is the same, we see no sensitivity of LF an IF S1 velocities to crack ensity, while S2 an HF S1 velocities consistently ecrease with increasing ensity. Generalizing these observations to the assumption that a crack ensity increase shoul never result in increase velocities, we can stuy the influence of the crack aperture by comparing the values for M3 with those for M4-3, where the crack size is very similar. We see that an increase in crack aperture causes a measurable increase in the S1 velocities for all frequencies an in the HF S2 velocities. The strong reuction in the LF an IF velocities between samples M3 an M4-3 can probably be attribute to the ifference in crack ensity. From the observe epenencies of the shear wave velocities on the physical crack parameters, we infer that crack aperture is the most important parameter for shear wave splitting. The crack ensity is somewhat less important, an the crack iameter seems to have the least influence. While the effective crack size etermines scattering attenuation, it oes not seem to be a etermining parameter for the S-wave velocity. Further experiments varying only one crack parameter at a time will be neee for a more conclusive stuy. As shown in Fig.13,S-wave splitting oes not show a strong epenency on the physical crack parameters that were varie in sample M4. In Figs 13(a) an (b), where long wavelengths are

11 Shear wave anisotropy from aligne inclusions 11 Table 5. Velocity values for samples M1, M2, M3 an M4 for LF, IF an Hf ranges together with crack iameters an crack apertures. The velocity of the higher-frequency event in M2 is the same as for S1 of the lower-frequency event for both polarizations, that is, V(S1 2 ) = V(S2 2 ) = 1267 m s 1. Source frequency (khz) Sample Crack parameters Shear wave velocities Diameter Aperture Eff. Size Density V(S1) V(S2) V(S1) V(S2) V(S1) V(S2) (cm) (cm) (cm) (per cent) (m s 1 ) (ms 1 ) (ms 1 ) (ms 1 ) (ms 1 ) (ms 1 ) M M M M M M Figure 13. Velocities for five ifferent points in sample M4 an the respective anisotropic parameter γ associate with these velocities for S-wave source transucers: (a) LF, (b) IF an (c) HF ranges. ominant, the anisotropy parameter γ slightly ecreases with reuce crack ensity an iniviual crack length. On the other han, for high frequency (see Fig. 13c), a ecrease in crack ensity or crack size leas to a slight increase in magnitue of γ.however, the variations are very small. 3.5 Shear wave attenuation measurement To estimate the shear wave attenuation, we applie the frequencyshift metho of Quan & Harris (1997) using a source-signature trace an the S-wave arrivals from the pulse-transmission experiment. The etails of the proceure are escribe in Section 2.3. The centroi frequencies an respective variances of sources in the ifferent frequency ranges, as well as the centroi frequencies of samples M1, M2 an M3 for polarizations S1 an S2 after Gaussian non-linear fit are presente in Table 3. Using the values from Table 3 an the first-break arrival traveltimes of the S1 an S2 waves in the seismic profiles shown in Fig. 5, we calculate the quality factor from eq. (3). Note again that the re- Table 6. Quality factor estimates for samples M1, M2 an M3. Source frequency 90 khz 431 khz 840 khz Sample Q (S 1 ) Q (S 2 ) Q (S 1 ) Q (S 2 ) Q (S 1 ) Q(S 2 ) M M M sulting values for Q, presente in Table 6, refer to total attenuation, incluing intrinsic an scattering attenuation. Fig. 14 shows a graphical representation of the corresponing attenuation values (Q 1 ), together with error bars estimate from the neighboring traces. We see that in all samples the attenuation increases with increasing frequency, an the increase in the cracke samples M2 an M3 is stronger than in the isotropic sample M1. In sample M2, the behaviour of the two polarizations is not significantly ifferent, but iffers istinctly from that in sample M1. In sample M3, the S2 wave is significantly stronger attenuate than the S1 wave.

12 12 J. J. S. e Figueireo et al. Figure 14. Total attenuation Q 1 total as a function of effective ominant frequency. (a) Comparison of sample M2 to M1. (b) Comparison of sample M3 to M1. Figure 15. Scattering attenuation Q 1 scattering for the shear wave polarizations S1 an S2 in samples (a) M2 an (b) M3. Since the epoxy resin that constitutes the backgroun meium of samples M2 an M3 is very similar to sample M1, we can assume that the intrinsic attenuation in the resin of samples M2 an M3 is approximately equal to the total attenuation in sample M1, that is, Q 1 resin Q 1 total (M1). Thus, we can calculate the attenuation effects ue to the presence of the rubber inclusions using the approach of Brown & Seifert (1997) an Tselentis (1998). For this purpose, we linearly interpolate the value of the intrinsic resin attenuation Q 1 resin in moel M1 (moel without inclusions) as a function of frequency, an subtract the result from the total attenuation Q 1 total M2 an M3 at the same frequencies, that is, for samples Q 1 inclusions = Q 1 total Q 1 resin. (5) Since the rubber inclusions are much smaller than the involve wavelengths, we assume that the intrinsic attenuation insie the rubber cracks is much smaller than the attenuation effect of scattering. Thus, from now on we will briefly refer to Q 1 inclusions Q 1 scattering as scattering attenuation. Fig. 15 shows that the so-obtaine scattering attenuation Q 1 scattering for both (fast an slow) polarizations increases with increasing source frequency from LF to HF in both samples M2 an M3. Note that at LF, we observe little scattering attenuation with Q 1 s 0.01 in both samples. In sample M2, both S1 an S2 polarizations exhibit a very similar behaviour of the scattering behaviour, while in sample M3, the S2 wave is clearly more attenuate than the S1 wave. Another ifference between the samples regars the increase of scattering attenuation with frequency. While in sample M3 the scattering attenuation increases linearly from LF to HF for S2, its slope rises between IF an HF for S1. On the other han, the slope ecreases significantly for both S1 an S2 in sample M2. This latter behaviour is consistent with our previous interpretation that for higher frequencies, there are more an more waves that can propagate in the space between the cracks in the isotropic backgroun meium in sample M2. 4 DISCUSSION All our above observations inicate that the S2 wave is more strongly influence by cracks in the meium when the propagation is closer to the effective-meium conition, that is, for low an intermeiate frequencies. However, the main ifference between the behaviours of Q 1 s in the samples is note in the intermeiate an high-frequency regimes. At these frequencies, the S1 attenuation is increase with respect to S2. We see in Fig. 15 for equivalent high frequency the scattering attenuation of the S1 wave in sample M2 is per cent stronger than that of S1 in sample M3 while for the S2 polarization this ifference is only per cent. Note that the ifferent material of the inclusions (neoprene in sample M2, silicone in sample M3) i not seem to have a strong influence on the attenuation in our experiments. Intuitively, one shoul expect that the significantly lower value of the shear wave moulus for silicone (μ sil 1.0 MPa) than for neoprene (μ neo 3.6 MPa) woul lea to much stronger attenuation. However, we observe stronger attenuation in sample M2, where the cracks are mae of neoprene rubber. This inicates that the influence of crack size an aperture is much more prominent than that of the crack filling. Moreover, it is consistent with our assumption that the attenuation ue to the presence of cracks in the samples is etermine

13 by scattering an that intrinsic attenuation within the cracks can be neglecte. There are many ifficulties that are encountere in the laboratory an fiel to accurately measure an attenuation value (intrinsic, scattering or apparent). Effects relate to the near-fiel, spherical ivergence, bounaries, reflectors, coupling an scattering are factors that change the amplitue of a seismic trace. To avoi these effects, we use a metho that basically epens on the frequency shift observe in the irect-arrival measurements at two ifferent spacings. This metho, which oes not require any amplitue ratio approach (like, e.g. the spectral ratio), was establishe by Quan & Harris (1997). As shown above, the application of this metho requires two wave traces recore at two ifferent positions. Due to the characteristics of the experimental setup in this work, we strongly believe that the application of the frequency shift-metho i not lea to overestimation of attenuation. The results obtaine from our three cracke samples have shown evience of the frequency-epenent behaviour of wave propagation in anisotropic elastic meia. The rubber inclusions use in this work simulate ieal cylinrical cracks consisting of soli material showing a low shear moulus as compare to the surrouning matrix. Our experiments use an iealize fracture system exhibiting aligne crack istributions with ifferent fracture parameters. The size of the iniviual cracks was much below the seismic wavelengths. Our results inicate that the attenuation in such a system epens stronger on the geometric properties of the cracks than on the filling material. Regaring the geometric parameters, crack aperture an crack ensity were more important than crack iameter. Waves in ifferent frequency ranges react slightly ifferent to these parameters. 5 CONCLUSIONS This experimental stuy aime to investigate the influence of source frequency on elastic wave propagation in anisotropic meia containing aligne penny-shape cracks. The results show that the magnitue of S-wave birefringence in cracke meia irectly epens on the source frequency as well as crack size an ensity. In the low-frequency range, splitting was more conspicuous in all cracke samples than for intermeiate an higher frequencies. For increasing frequencies, the magnitue of S-wave splitting (measure by means of the S-wave Thomson anisotropy parameter) ecreases rastically. Low-pass filtering of high-frequency ata turne out to be helpful to make a small shear wave splitting visible. This splitting was higher for larger cracks with smaller ensity. We observe the ispersive effect of cracke meia to be higher for the (slow) S2 than for the (fast) S1 polarization. Furthermore this ispersion is preominant when the crack length is smaller or of the same orer as the wavelengths use in the investigation. Moreover, the lower the source frequency was, the more pronounce were the observe ispersive effects. Contrary to the typical behaviour of shear wave splitting, the S1 wave seems to be more influence by scattering than S2 when the crack size is larger than the wavelength. If this statement can be confirme by future experiments, the crack aperture may be less relevant than the iniviual crack size in the HF range. An aitional experiment in the high-frequency range with the same crack aperture but varying crack size an ensity showe an almost constant but slightly increasing anisotropy parameter with ecreasing crack size. From our experiments, we can establish an orer of importance for the influence of ifferent physical crack parameters on shear Shear wave anisotropy from aligne inclusions 13 wave birefringence in anisotropic cracke meia. Our results show that the crack aperture is the most relevant parameter, followe by crack ensity. Of the geometric crack parameters, their iameter seems to have the least influence on shear wave velocities. Particularly in the low-frequency case, where the S-wave propagation behaves like in an effective meium, the anisotropic parameter γ oes not strongly epen on the crack size, but much more on the crack ensity. Because of our strict aherence to scalability of the experiments (except, of course, regaring the physical imensions of the sources an receivers), we expect the results of our laboratory measurements to apply corresponingly in the seismic frequency range. As iscusse by Shaw (2005), the knowlege about fracture parameters such as ensity, size, spacing an aperture can help to reuce uncertainties in seismic hyrocarbon exploration in fracture meia. We believe that the main contribution of this work is to provie more ata to better unerstan the epenence of seismic wave propagation on the properties of fracture reservoirs, with special regar to source frequency an fracture parameters. Moreover, the ata set supplie by these laboratory measurements can be use for theoretical moel valiation. However, further moel experiments uner variation of a single parameter will be necessary to further corroborate our finings. ACKNOWLEDGMENTS This work was mae possible by the financial an facility support at Allie Geophysics Laboratories, University of Houston. The authors are grateful to Dr. Leon Thomsen an Dr. Evgeny Chesnokov (AGL) for their expertise an avice, an to two anonymous referees whose remarks greatly helpe to improve the manuscript. The first author wishes to thank CAPES an CNPq from Brazil for his scholarship (contract # /2009-9). 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