Synthetic modelling study of the effect of attenuation anisotropy in fractured media

Size: px

Start display at page:

Download "Synthetic modelling study of the effect of attenuation anisotropy in fractured media"

Octavia Eleanore Burke
5 years ago
Views:

1 Synthetic mdelling study f the effect f attenuatin anistrpy in fractured media Ekanem, A. M. 1, 2, Li, X-Y. 1, 2, Chapman, M. 1,2 and Main, I.G. 1 1 Schl f Gesciences, University f Edinburgh, West Mains Rad, Edinburgh, EH9 3JW, UK 2 British Gelgical Survey, Murchisn Huse, West Mains Rad, Edinburgh, EH9 3LA, UK Summary We present the results f a synthetic mdelling study f the effect f attenuatin anistrpy in fractured media. Our theretical mdel is made up f ne anistrpic and three istrpic hrizntal layers. The anistrpic layer cnsists f a prus fluid-saturated material with aligned vertical fractures, and squirt flw between the pres in the matrix is taken int cnsideratin. We used the spectral rati methd t cmpute the seismic quality factr, Q, frm the synthetic data in fur azimuthal directins relative t the fracture strike. The results f ur measurement indicate that attenuatin increases with incidence angle and azimuth away frm the fracture strike. Azimuthal variatins in the induced attenuatin are elliptical and the fracture rientatins btained frm the axes f the ellipse are cnsistent with the theretical mdel. We cnclude that these effects, if bserved in field data, culd be used t determine fracture rientatins in the subsurface t supplement the use f ther seismic attributes.

2 Intrductin A suite f aligned fractures are knwn t cause seismic attenuatin, in which gescientists have taken an increasing interest ver recent years. Attenuatin anistrpy has been bserved in bth field and labratry data (e.g. Rathre et al. 1995; Lu et al. 2006; Maultzsch et al. 2007; etc) and has been linked t fracture prperties. As attenuatin anistrpy cntinues t gain ppularity as a useful explratin tl, a cncerted effrt is needed t get mre insight f its characteristics, using theretical mdels t aid ur understanding f the underlying physics. In this paper, we have carried ut a synthetic mdeling study f P-wave attenuatin anistrpy in fractured media. Our theretical mdel cnsists f ne anistrpic and three istrpic hrizntal layers. The elastic parameters f the material f the anistrpic layer were cmputed using the dynamic equivalent-medium thery f Chapman (2003) and we used the classical spectral rati methd t cmpute the induced attenuatin fr selected ffsets at fur azimuths relative t the fracture strike directin. Our results indicate that the azimuthal variatins f attenuatin are apprximately elliptical and the inferred fracture rientatins are cnsistent with the theretical mdel. Theretical mdel and experimental set-up The theretical mdel is made up f ne anistrpic and three istrpic hrizntal layers. The anistrpic layer cnsists f a prus fluid-saturated material with aligned vertical fractures, and squirt flw between the pres in the matrix is taken int cnsideratin. The elastic prperties f the material are cmputed using the prelastic mdel f Chapman (2003) which cnsiders the pre space f the rck t cnsist f spherical pres and circular cracks f small aspect rati. The pressure difference generated when a seismic wave prpagates thrugh the medium causes fluid exchange between the fractures and the surrunding pre space, resulting in attenuatin and dispersin. Chapman s (2003) prelastic mdel predicts anistrpic velcity dispersin and attenuatin in the seismic frequency range, with attenuatin increasing with plar angle and azimuth away frm the fracture strike. Details f the theretical mdel parameters are given in Table 1. The third layer cnstitutes the anistrpic layer. Table 1: Theretical mdel parameters Layer parameters Layer v p (m/s) v s (m/s) ρ (Kg/m 3 ) Thickness (m) Half space Fracture mdel parameters Prsity 0.08 Crack density 0 Fracture density 0.1 Fracture radius 10cm Fluid bulk 2.0Gpa mdulus Frequency Relaxatin time tau0 50Hz 2e-5s The synthetic data were cmputed frm the theretical mdel using the Aniseis sftware (Taylr 2001) which makes use f the reflectivity methd, at fur azimuths 0, 45, 60 and 90 relative t the fracture strike directin which crrespnds t 0 azimuth. A Ricker wavelet with a centre frequency f 25Hz and a start time f 100ms was used as the surce wavelet. The surce is an explsive surce and was placed n the surface f the mdel. 21 gephnes were als placed n the surface f the mdel, at a regular spacing f 200m, and a surce - receiver spacing f 200m was maintained. Data were recrded with a sampling interval f 1ms and a ttal time f 3s. Sample synthetic data are given in Figure 1.

3 Q estimatin We used the spectral rati methd (e.g. Tnn, 1991) t estimate the seismic quality factr, Q frm the synthetic data fr selected ffsets. In each gather, the first trace frm the tp mdel reflectin was used as the reference trace fr cmparisn f the spectral ratis. We perfrmed a simple least square regressin f the Lg f the Pwer Spectral Ratis (LPSR) against frequency accrding t the equatin: P ( f ) 2 ln ( ) f ( t t ) Q P ( f ) = 2ln RG 2π ref / (1) 1 where P 2 (f) is the spectral pwer f the target reflectin (tp r bttm fractured layer) and P 1 (f) is the spectral pwer f the reference trace, f is the frequency, R is the reflectivity term, G is the gemetrical spreading term, t is the travel-time f the target reflectin, t ref is travel-time f the reference event and Q is the quality factr dwn t the reflectr. Figure 1: Sample synthetic gathers. 0 azimuth 90 azimuth. Red and green arrws indicate tp and bttm fractured layer reflectins respectively; the pink circle highlights the cnverted wave. We used a cnstant FFT time windw f 140ms t cmpute the pwer spectra, and a bandwidth f 20-90Hz where the spectral rati plts were stable (Figure 2) fr the regressin. Fr a given ffset, we cmputed Q dwn t the reflectr frm the slpe, p f the least square regressin given by: With the tw pair f Q values cmputed fr the tp and bttm fractured layer, we used the layerstripping methd f Dasgupta and Clark (1998) t cmpute the interval Q value in the fractured layer using the equatin: [ tn tn 1] Qi = (3) t / Q t / Q where Q n and Q n-1 are the quality factrs fr the reflectrs at the tw-way traveltimes f t n and t n-1 crrespnding t the tp and bttm f the fractured layer respectively. Results ( t t ) Q p = 2π r ef / n n n 1 n 1 The results f ur study shw that attenuatin varies bth with incidence angle and azimuth relative the fracture strike directin. Attenuatin increases with incidence angle and als away frm the fracture strike directin with maximum attenuatin nrmal t the fractures (Figure 3a). Azimuthal (2)

4 variatins in the attenuatin are elliptical t a gd apprximatin (Figure 3b). Hwever, the results shw that a minimum f 400m ffset (8.4 incidence angle) is required t reveal the azimuthal variatins. The majr axis f the Q - ellipse crrespnds t the fracture strike where attenuatin is a minimum, while the minr axis crrespnds t the fracture nrmal where attenuatin is a maximum. Figure 2: Lg Pwer Spectral Rati (LPSR) against frequency. Tp fracture layer reflectin bttm fractured layer reflectin. Bxes indicate the respective ffsets. Plts are stable within the frequency bandwidth f 20 t 90 Hz. The attenuatin anistrpy als beys a csine fit f the frm (Maultzsch et al. 2007): ΔQ 1 = C1+ C2cs[ 2( ϕ ϕ )] (4) where C1 is an arbitrary cnstant, C2 is the magnitude f azimuthal variatin, φ is the azimuthal angle and φ is the fracture nrmal directin at which attenuatin is maximum. Figure 4 shws the csine fits t the Q results fr selected ffsets. The azimuth f maximum attenuatin frm the fits is 90 which crrespnds t the fracture nrmal. The magnitude f the attenuatin anistrpy increases with incidence angle (ffset). Figure 3: Attenuatin results. Q prfile with incidence angles. Attenuatin increases with incident angles. There is n significant change f attenuatin with incidence angle at the fracture strike azimuth. Q anistrpy ellipse. Azimuthal variatins in Q are elliptical and the fracture rientatins are derived frm the axes f the ellipses. Cnclusin The results f ur synthetic mdelling study shw that attenuatin increases with incidence (plar) angle and als increases away frm the fracture strike directin, which is cnsistent with the predictins f Chapman s mdel (2003) and the results f similar studies f Maultzsch et al (2007) in

5 a walkaway VSP setting. Azimuthal variatins in the induced attenuatin are elliptical and the fracture rientatins are quite easily btained frm the axes f the ellipse. We cnclude that if attenuatin anistrpy is bserved in field data, it culd be a ptential tl t determine fracture rientatins in the subsurface t supplement the use f amplitudes, travel time, velcity and AVO gradient attributes. Figure 4: Csine fits f estimated 1/Q values against azimuth fr given ffsets. Degree f anistrpy increases with ffset (incidence angle). N azimuthal variatins are bserved at 200m ffset (4.2 incidence angle). Acknwledgement We are grateful t the spnsrs f the Edinburgh Anistrpy Prject (EAP) fr supprting the prject and the permissin t shw the results. Special thanks t the Akwa Ibm State University f Technlgy (AKUTECH) - Nigeria fr prviding spnsrship t Ekanem s studies at the University f Edinburgh. References Chapman M Frequency-dependent anistrpy due t mes-scale fractures in the presence f equant prsity. Gephysical Prspecting, 51, Dasgupta, R. and Clark, R., Estimatin f Q frm surface seismic reflectin data. Gephysics, 63(6): Lu, M., Arihara, N., Wang, S., Di, B., and Wei, J., Abnrmal transmissin attenuatin and its impact n seismic-fracture predictin A physical mdelling study. Gephysics, 71, D15 D22 Maultzsch, S., Chapman, M. Liu, E. and X. Y. Li, Mdelling and analysis f attenuatin anistrpy in multi-azimuth VSP data frm Clair field. Gephysical Prspecting, 55, Rathre, J.S., Fjaer, E. and Renlie, L P- and S-wave anistrpy f a synthetic sandstne with cntrlled crack gemetry. Gephysical Prspecting, 43, Tnn, R., The determinatin f the seismic quality Q frm VSP data: A cmparisn f different cmputatinal methds. Gephysical Prspecting, 39, 1-27 Taylr, D., ANISEIS v5.2 Manual. Applied Gephysical Sftware Inc., Hustn.

GBT X-band (9 GHz): Pointing Stability

GBT X-band (9 GHz): Pointing Stability GBT X-band (9 GHz): Pinting Stability Dana S. Balser, Rnald J. Maddalena, Frank Ghig, & Glen I. Langstn 10 March 2002 Abstract The pinting stability f the GBT is evaluated by tracking the half-pwer pint