Estimation of Thomsen s anisotropy parameter, delta, using CSP gathers.

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1 Estmaton of delta Estmaton of Thomsen s ansotropy parameter, delta, usng CSP gathers. Pavan Elapavulur and John C. Bancroft ABSTRACT In order to extend the sesmc processng technques to ansotropc meda, a measure of the dfferent parameters of ansotropy s requred. The purpose of ths study s to estmate the Thomsen s parameter, (delta), for transversely sotropc (TI) meda. Thomsen s ansotropc normal moveout equaton (NMO) s used to determne (delta). It s also shown that estmated usng common Scatter Pont (CSP) gathers s more accurate than those estmated from common md pont (CMP) gathers. INTRODUCTION Earth s fundamentally ansotropc but most of the processng algorthms assume the deal condton of sotropy, ths faulty assumpton leads to erroneous magng and thus faulty nterpretatons. Backus (1962) stated that f the layered earth s probed wth an elastc wave of wavelength much longer than the typcal layer thckness the wave propagates through ths medum as t were n a homogenous and ansotropc medum. Alkalfah and Tsvankn (1994) used an nverson scheme over the nonhyperbolc equaton to estmate Thomsen s ansotropc parameters. Haase(1998) showed that the non hyperbolc moveout observed wth the flat reflectors n the plans data s due to the transverse sotropy(even though the ndvdual layers are sotorpc). He also estmated Thomsen s ansotropy parameters n the plans data. In ths study we estmate Thomsen s parameter usng the Thomsen s ansotropc NMO equaton, wth the assumpton of weak ansotropy. The man dea s to use veloctes estmated from the common scatter pont (CSP) gather and the veloctes from the sonc log run n a well, nearest to the sesmc lne to estmate the value of. THEORY The most common measure of P wave ansotropy s the rato between the horzontal and vertcal P wave veloctes, typcally between 1.05 to 1.1 and s often as large as 1.2 (Sherff 1991). Thomsen (1986) ntroduced a more effectve and a scentfc measure of ansotropy. He ntroduced the constants ε, γ, and as effectve parameters of measure of ansotropy. Accordng to Thomsen, s the most crtcal measure of ansotropy and t doesn t nvolve the horzontal velocty at all n ts defnton. Therefore measurng s very mportant for processes lke depth magng. Accordng to Told et.al (1999) The depth effects are carred by the parameter whch must therefore be measured wth help of well control. CREWES Research Report Volume 13 (2001) 479

2 Elapavulur and Bancroft Usng week ansotropy approxmaton and Thomsen s parameters, the phase velocty, V can be wrtten as equaton 1. It s a functon of phase angle θ. (Thomsen, 1986). ( θ ) ( 1 sn 2 θ cos 2 θ ε sn 4 θ ) V = V + + (1) 0 Under the short spread assumpton (the half offset s smaller than the depth of the reflector, typcally the moveout s hyperbolc n hyperbolc even n ansotropc meda at shorter offsets), the NMO velocty s controlled by only the Thomsen s parameter. (Thomsen, 1986). Ths s shown n equaton 2 (Thomsen, 1986) ( ) V p = V p + (2) ( ) Common Shot Pont (CSP) gathers A common scatter pont gather s a pre-stack mgraton gather that collects all the nput traces that contan energy from a vertcal array of scatter ponts. The dstance from the surface locaton of the scatter pont to the source and recever defnes the offsets n a CSP gather, but not the source recever offset. The CSP gather s smlar n appearance to a common md pont (CMP) gather. They both defne a subsurface locaton, and are sorted by offsets. Hence all the traces n the prestack mgraton aperture, regardless of the source or recever poston, may be used to form a CSP gather. The offsets n a CSP gather are defned as gven by equaton 3 (Bancroft, et.al, 1998) 4xh e = + (3) 2 2 tvrms h x h Where x s dstance between CMP and the CSP gathers locaton and h s half the source recever offset, Vrms s the RMS velocty. Advantages of CSP gather A CSP gather s characterzed by ts very hgh fold, ncreasng the SNR, whch makes velocty pckng more accurate. Generally CSP gathers have larger offsets when compared to CMP gathers. The semblance plot of the CSP gather shows tghter clusterng of energy, whch enables (and requres) more accurate pckng of veloctes. It has been shown by Bancroft (1996) that NMO veloctes estmated usng a CSP gather are more accurate than veloctes estmated over a CMP gather. 480 CREWES Research Report Volume 13 (2001)

3 Estmaton of delta METHOD Calculaton of V V s the nterval NMO velocty estmated from the semblance analyss usng the procedure descrbed below. The short spread normal moveout(nmo) of an N layered transverse sotropc (TI) medum as gven by Alkhalfah and Tsvankn n 1995 can be wrtten as equaton (4) 2 [ ] t N 2 1 V ( ) p V ( p) 0 = 1 = τ (4) whereτ s the 2-way zero-offset traveltme to the bottom of the N th layer, t o s the 2 way zero offset traveltme for an ndvdual layer and V ( p) s the root-meansquare velocty of the NMO velocty n each layer taken at the ray parameter p (Alkhalfah and Tsvankn, 1995). In the case of a flat layered earth the equaton (4) reduces to the Dx equaton. In order to obtan the NMO velocty n any layer (ncludng the one mmedately above the reflector), we need to apply the Dx formula (Dx, 1955) to the NMO veloctes from the top V ( 1) and the bottom V () of the layer (Alkhalfah and Tsvankn, 1995). 2 2 t0 () V () t0 ( 1) V ( 1) [ V ] = (5) t0 () t0 ( 1) t o s the 2 way zero offset traveltme for an ndvdual layer. V () s estmated from the velocty analyss over the CSP/CDP gathers formed at the CDP pont, whch s closest to the well locaton. Calculaton of V 0 V 0 s the nterval vertcal velocty. Ths can be estmated from well logs or VSP measurements. In ths study Veloctes were estmated from the sonc log recorded at the well located nearest to the sesmc lne. Calculaton of Usng both of the veloctes V and V 0 the value of can be estmated at each tme step usng equaton (2), whch can be wrtten as equaton (6). CREWES Research Report Volume 13 (2001) 481

4 Elapavulur and Bancroft 2 ( V ) ( ) 2 V0 1 = 1 (6) 2 where V s the nterval velocty and V s the vertcal velocty. 0 CASE STUDY Ths technque wll now be tested over a synthetc ansotropc data generated usng NORSAR2D software. Norsar 2D s ray tracng program based on the ray theory by (Cerveny, 1985). A layered geologc model (fgure 1) was bult wth 9 flat layers n t. The model s bult n the depth doman and s 6kms deep. The thnnest layer s of thckness 0.5 km and ts velocty s 1000m/s. A 40hz zero-phase Rcker wavelet was used for the generaton of sesmograms wthout volatng the raytracng assumptons. There are 101 shots n total and 300 recevers per shot. The shot spacng was 40m and recever spacng was 20m. Fgure 1 shows the layered model wth table (1) showng the values of the materal propertes vz. P-wave velocty S-wave velocty Densty ε and Interface P-velocty S velocty Densty ε Table 1. Materal propertes of the model used. 482 CREWES Research Report Volume 13 (2001)

5 Estmaton of delta FIG. 1. The Geologcal model. Ths model data was used to test the above method. The algorthm can be descrbed as follows: Perform semblance analyss on the gathers to yeld V. Use equaton (5) to estmate the nterval NMO veloctes Determne the value of V 0, the vertcal velocty, from the VSP data/sonc logs. Use equaton (6) to calculate. Semblance analyss was performed on both common md pont (CMP) and common scatter pont (CSP) gathers (Fgures 2 &3). The values of were calculated usng the NMO veloctes from both the CMP and CSP gathers. Tables (2 and 3) show the values of calculated usng CMP and CSP gathers respectvely. CREWES Research Report Volume 13 (2001) 483

6 Elapavulur and Bancroft FIG. 2. The semblance plot over a CDP gather. FIG. 3. The semblance plot over a CSP gather. 484 CREWES Research Report Volume 13 (2001)

7 Estmaton of delta V (CMP) V 0, (model) (estmated) Table 2. s calculated usng CMP gathers. V (CSP) V 0, (model) (estmated) Table 3. s calculated usng CSP gathers. It s evdent from the tables (2 and 3) that the values of estmated usng CSP gathers are much more accurate than those calculated usng CMP gathers. CREWES Research Report Volume 13 (2001) 485

8 Elapavulur and Bancroft Error analyss The values of estmated are heavly dependent on the veloctes estmated from the semblance analyss. We dd a smple error analyss by ntroducng an error nto the NMO veloctes estmated from the CSP gather. The results are shown n the Fgure 4. For a 0-10% error n veloctes we encountered around % error n the values of estmated. As the veloctes estmated from a CSP gather are more accurate, s can be estmated wth better confdence usng the CSP veloctes. % error Error plot of deltas estmated ntervals where delta s estmated 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% FIG. 4. The error plot. Feld data Ths method was appled over the sesmc data collected over the Blackfoot feld. Blackfoot feld s near Strathmore, Alberta and s operated by PanCanadan petroleum. A 3C 3D data was acqured by CREWES n The Blackfoot Feld s located n Townshp 23, Range 23, West of 4 th merdan, n south central Alberta. Geology The geology of Blackfoot feld has been dscussed n detal by Mller et. al (1995). Ths s a very bref revew of the lthology of the formatons of nterest to ths work. The reservor rocks n ths feld are Glaucontc ncsed valleys n Lower Manvlle group of lower Cretaceous. Coals, Vkng formaton and Base of fsh scales shales overle these reservor rocks. A lne numbered 20M vertcal that has a well (#09-08) located very near to t was chosen to test ths method. The fgure 5 shows the poston of the well on the CDP plot. Fgure 6 shows the poston of the well on the stacked secton. CMP and CSP gathers are the formed at CDP 149, whch s nearest to the well locaton. Semblance analyss was performed on both CSP and CDP gathers formed at ths locaton. The veloctes estmated were used n the algorthm dscussed above to estmate the values of. 486 CREWES Research Report Volume 13 (2001)

9 Estmaton of delta The poston of the well FIG. 5 Poston of the well on the CDP plot. The poston of the well FIG. 6 Poston of the well on the stacked secton. The followng fgures (7 and 8) show the semblances plots of CDP and CSP gathers at CDP 149 respectvely. CREWES Research Report Volume 13 (2001) 487

10 Elapavulur and Bancroft FIG. 7 Semblance plot over a CDP gather. FIG. 8 Semblance plot over a CSP gather. The veloctes estmated from the semblance analyss over CMP and CSP gathers were used to estmate the values of for the formatons of nterest. Table 4 shows the formaton namng conventon used here. Tables 5 and 6 show the values of estmated from CMP and CSP gathers respectvely. 488 CREWES Research Report Volume 13 (2001)

11 Estmaton of delta Abbrevaton Unt Name BFS Base of Fsh Scales Zone MANN Blarmore- Upper Mannvlle COAL Coal Layer GLCTOP Glaucontc Channel porous Sandstone unt MISS Shunda Mssssppan Table 4. Formaton namng conventons. Formaton V (CMP) V 0, (estmated) BFS MANN COAL GLCTOP MISS Table 5. s calculated usng CMP gathers. Formaton V (CSP) V 0, (estmated) BFS MANN COAL GLCTOP MISS Table 6. s calculated usng CSP gathers. CREWES Research Report Volume 13 (2001) 489

12 Elapavulur and Bancroft DISCUSSION AND CONCLUSIONS Estmaton of ansotropy parameters s an mportant aspect n sesmc analyss. Thomsen s ansotropc parameter has an effect on the depth calculatons. The estmaton s hghly dependent on the estmaton NMO velocty. The error analyss of s estmated proves how mportant s estmaton of accurate NMO veloctes s. It has also been showed that estmated usng CSP gathers are more accurate than that of those estmated from CMP gathers. Extendng ths analyss to the real feld data, we found that the shales and coals show very sgnfcant ansotropy. The vertcal veloctes estmated from a sonc log were used n ths study. The veloctes from sonc log are greater than the sesmc veloctes. Vertcal nterval veloctes estmated from VSP data would gve more accurate estmates n ths area. ACKNOWLEDGEMENTS We acknowledge the CREWES sponsors for ther contnued support. We thank Ian Watson for helpng wth the nterpretaton of Blackfoot data. REFERENCES Alkhalfah, T. and Tsvankn, I., 1995, Velocty analyss for transversely sotropc meda: Geophyscs, Soc. Of Expl. Geophys., 60, Backus, G. E., 1962, Long-wave elastc ansotropy produced by horzontal layerng: J.Geophys Res., 70, Bancroft, J.C., 1996, Velocty senstvty for equvalent offset prestack mgraton, Ann. Mtg: Can. Soc. Of Expl Geophys. Bancroft, J.C., Geger, H.D. and Margrave, G.F., 1998, The equvalent offset method of prestack tme mgraton: Geophyscs, Soc. Of Expl. Geophys., 63, Cerveny, V., The applcaton of numercal modellng of sesmc wavefelds n complex structure. Sesmc shear waves, Part A: Theory (ed. G Dhor). Pp Geophyscal press, London. Dx, C.H., 1955, Sesmc veloctes from surface measurements: Geophyscs, Soc. Of Expl. Geophys., 20, Haase, Armn. B., 1998, Non hyperbolc moveout n plans data and the ansotropy queston: Recorder, Can. Soc. of Expl Geophys. Nov, 1998, Mller, S.L.M., Aydemr, E.O. and Margrave, G.F., 1995, Prelmnary nterpretaton of P-P and P-S sesmc data from Blackfoot broad-band survey: Crewes Research Report 1995, Ch 42. Sherff, R. E., 1991, Encyclopedc Dctonary of Exploraton Geophyscs, Encyclopedc dctonary of exploraton geophyscs: Soc. of Expl. Geophys., 384. Thomsen, L., 1986, Weak elastc ansotropy: Geophyscs, Soc. Of Expl. Geophys., 51, Told, J., Alkhalfah, T., Berthet, P., Arnaud, J., Wllamson, P. and Conche, B., 1999, Case study of estmaton of ansotropy: The Leadng Edge, 18, no. 5, CREWES Research Report Volume 13 (2001)