Multi-azimuth Prestack Time Migration for General Anisotropic, Weakly Heterogeneous Media - Field Data Examples

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1 Multi-azimuth Pestack Time Migation fo Geneal Anisotopic, Weakly Heteogeneous Media - Field Data Examples S. Beaumont* (EOST/PGS) & W. Söllne (PGS) SUMMARY Multi-azimuth data acquisition has shown benefits in noise eduction and stuctue illumination, which leads geneally to impoved seismic images. Howeve the cuent time pocessing, which is based on independent pocessing of the data fom the diffeent pedominant azimuths, may lead to destuctive intefeences and deteioation of the final stacked image when the eath model is anisotopic o lateally heteogeneous. In ode to solve this poblem a pestack time migation fo anisotopic, weakly heteogeneous media has been ecently intoduced and tested on synthetic data. In this wok, we an a fist field data application on a multi-azimuth data set. Fom data in thee diffeent acquisition azimuths we pefomed migation velocity analysis to build azimuth-dependent migation opeatos. We pocessed the data in paallel also with conventional naow azimuth pestack time migation in ode to assess the pefomance of the new appoach.

2 Intoduction Acquisition of data ove the same aea with diffeent azimuths (multi-azimuth data acquisition) allows building stacked volumes with bette signal to noise atio and geneally impoved taget illumination (e.g., Manning et al., 007). Howeve, the cuent time pocessing is not sufficiently adapted to this data acquisition appoach. Indeed, data fom diffeent pedominant azimuthal diections ae pocessed independently, with azimuthally independent time velocity functions, and ae combined (stacked togethe) only at the vey last imaging step. As a consequence, one and the same image point in geneal heteogeneous and anisotopic media may be placed at diffeent time positions fo diffeent azimuths, which may lead to destuctive intefeences and a deteioation of the image. In ode to extend pestack time migation to anisotopic and weakly heteogeneous media, a new method fo multi-azimuth pestack time migation (MAPSTM) has been developed (e.g., Söllne et al., 010). This method allows computing the azimuthal diffaction time functions necessay to build the diffaction stack using the most geneal fom of Hamilton s pincipal equation. Stating fom conventional naow-azimuth pestack time migations and velocity analysis on data fo at least thee independent azimuths, time migation velocity ellipses can be build, and subsequently the azimuthal diffaction time functions calculated. This method, peviously tested on synthetic data, is in this wok fo the fist time tested and successfully applied on a multi-azimuth data example acquied in the Nile Delta in 003. Theoy Multi-azimuth pestack time migation: The migation used in this method is a Kichhoff-type migation, which consists of summing (in the input data space) the amplitudes along the diffaction time function fo the endpoint of a given image ay, and placing this sum (in the output data space) onto the two-way time and the suface position of that image ay. Thus, to pefom this migation, the diffaction time function is equied fo all the suface gid points of the output data space at all elevant two-way times. We assume the subsuface is well modeled by a pile of anisotopic weakly heteogeneous layes sepaated by abitaily dipping, smoothly cuved intefaces. We assume futhe that taveltimes of tansmitted ays ae with sufficient accuacy expessed by second ode appoximations aound one selected image ay (consideed as cental ay), and build the taveltime of tansmitted ays using Hamilton s point chaacteistic (Buchdahl, 1970; Botfeld, 1989; Mose and Čevený, 007; Söllne et al., 010): 1 t ( x 0) t x B A x (1) x, The one-way taveltimes t (x,x =0) fo any tansmitted ay stating at the eceive position x (at the suface) and ending at x =0 (the endpoint of the cental ay) ae calculated in equation 1 fom the exact taveltime along the cental ay, t 0, and the x suface-to-suface paaxial matices A 0 and B 0. The elements of the suface-to-suface paaxial matices (Botfeld, 1989) ae commonly obtained fom dynamic ay tacing fo given model paametes (Hubal et al., 199; Čevený, 001). A bette appoximation of the tansmitted times ae achieved by squaing on both sides of equation 1 and dopping the tems of powe highe than two: t ( x x, 0) x B0 A0x. () The taveltime expession in equation is a hypebolic appoximation of t (Usin, 198). Moeove, as the matix combination B -1 0 A 0 is a symmetic x matix, it can be eplaced in equation by its thee (unknown) components denoted as U 11, U 1, U. The eceive position vecto can also be expessed by its azimuth (angle between eceive position vecto and x-axis) and the distance, d, between the eceive and the image ay. Hence, the taveltime t can now be witten as d t, (3) ( ) V TM

3 with V ( ) TM { U11 cos ( ) U 1 cos( )sin( ) U sin ( )}. (4) V TM (α ) epesents the time migation velocity ellipse. Although equations 3 and 4 have fomal similaity with the NMO velocity deived by Gechka and Tsvankin (1999), the azimuth angle has diffeent meaning hee (it is not elated to the acquisition azimuth) and V NMO and V TM ae equal solely in the tivial case when the image ays and the nomal ays ae identical. Afte epeating above deivation fo the tansmitted ay fom any souce at the suface to the end point of the cental ay and summing the two taveltimes, we obtain the complete diffaction time function of a diffaction point at the endpoint of the image ay: t TM d d. (5) V s t 0 TM ( ) VTM ( s) Pestack time-migation using the diffaction time function t TM fom equation 5 geneates flat offset panels in all azimuthal diections only if the V TM ellipse is coect. As a consequence one can eplace the dynamic ay tacing by tial multi-azimuth pestack time migations to detemine the diffaction time function. Azimuthal velocity analysis: As the depth model needed fo ay tacing is geneally not known at time pocessing stage, eplacing ay tacing by tial time migations followed by velocity analysis has an obvious advantage. Looking fo a pactical appoach fo velocity analysis, we deive the diffaction time function afte expessing in equation 1 the eceive position vecto, =m+h, by midpoint m and half offset h vectos. Following Hubal and Key (1980), we obtain t D ( m, h) m B 0 A 0m h B 0 A 0h. (6) The hypebolic appoximation with inseted V TM fom equation 4, with d m = m, and d h = h, becomes td( m, h) 4t0 4dm / VTM ( m) 4dh / VTM ( h). (7) The diffaction time function t D (m,h) in equation 7 is because of its sepaation in midpoint and offset dependent moveout tems a suitable expession fo V TM updating in a velocity analysis scheme. A fist tial migation of common offset panels (using equation 5), on one pedominant azimuth, with non-azimuthal velocities will most pobably esult into non-flat image gathes. As d m goes to zeo fo a migated image point, the emaining offset dependent moveout tem in equation 7 is added using the same tial velocity. Subsequently, velocity analysis is applied to flatten the image gathe, again using only the offset dependent tem in equation 7. This pocedue gives an updated velocity field fo the azimuth α h, and fom at least thee independent pedominant azimuth diections the updated V TM ellipse is econstucted. Field data example The data was acquied duing a multi-azimuth suvey in the Nile Delta, in deep wate (Keggin et al., 007; van de Bug et al., 010). This aea is chaacteized by a complex wate bottom and shallow channel systems made of gas hydates, above the Messinian. The complex laye, which appeas as a stong eflecto aound thee seconds in the seismic data, is composed of maine sediments and anhydite deposits. Six azimuths wee acquied, evey thity degees. But fo this study only thee diffeent pedominant azimuths wee available: the azimuths 60, 10 and 150. The data fo each azimuth wee pepocessed to emove multiples, and then (afte azimuthal velocity analysis) migated with both a multi-azimuth pestack time migation (MAPSTM) and a naow-azimuth pestack time migation (NAPSTM), in ode to assess the pefomance of the new method. We will now compae the esults fom the naow-azimuth and multi-azimuth pestack time migations, fo the case whee the thee available azimuths have been combined. Figue 1-a shows a zoom on the stacked volumes, in the cases of the MAPSTM (on the left) and the NAPSTM (on the

4 ight). We can see that the quality of the image is good in both cases, but an impovement with the MAPSTM is clealy visible on the places shown by ed maks. On the top of the image, we can see the continuity of eflectos which was almost not visible in the case of the NAPSTM. On the bottom of the image, we can obseve moe details in the shape of the eflecto in the case of the MAPSTM. a) b) c) Figue 1 a) Compaison of the MAPSTM (on the left) and the NAPSTM (on the ight) fo the thee azimuths combined. b) Compaison between the combined azimuths and the azimuth 60 fo the MAPSTM (on the left) and the NAPSTM (on the ight). c) Compaison between the combined azimuths and the azimuth 10 fo the MAPSTM (on the left) and the NAPSTM (on the ight). d) Compaison between the combined azimuths and the azimuth 150 fo the MAPSTM (on the left) and the NAPSTM (on the ight). In figues b), c) and d), the combined azimuths ae on the left hand-side of the ed line on the stacked section, and the single azimuths ae on the ight. When compaing the same stacked sections fo the thee azimuths combined with the ones fo a single azimuth, it appeas that thee is a shift fo the eflectos in the case of the NAPSTM. This type of mismatch is discussed in moe detail based on a synthetic example in Söllne et al. (010). Figues 1- b,c,d show the compaison between the combined azimuths and the single ones (espectively 60, 10, and 150 ) fo the MAPSTM (on the left) and the NAPSTM (on the ight). Following the same eflecto in the case of the multi-azimuth pestack time migation, we can see that thee is a vey good match in the time position between the stacked sections fo one azimuth and fo the combined azimuth stack. In the case of the naow-azimuth pestack time migation, we obseve a shift in time d)

5 fo some eflectos between the stacked sections fo one azimuth and fo the combined azimuths. This is paticulaly visible fo the azimuths 10 and 150 (Figues 1-c and 1-d), along the stong eflecto aound 3.5s. These diffeences in the image time position of one and the same eflecto fo diffeent azimuths, in the case of the NAPSTM, explain why the quality of the image afte stacking all azimuths is at some places degaded. Conclusions In ode to solve the mismatch poblem which geneally occus when the data coming fom diffeent azimuths ae stacked, a new method of multi azimuth pestack time migation has ecently been developed (Söllne et al., 010). Stating fom the most geneal fom of Hamilton s pincipal equation, an azimuthal time migation velocity function and a diffaction time function ae built, valid fo anisotopic and weakly heteogeneous media, fo small and intemediate offsets. In azimuthal velocity analysis, we split the diffaction time function in midpoint and offset dependent moveout tems and use fo velocity updates only the offset dependent tem, in migated image gathes. Fom the updated velocities in thee pedominant azimuthal diections we built the velocity ellipse fo the fist un of MAPSTM. The esulting migated gathes wee stacked, o altenatively used in a second iteation of velocity analysis. The pesented migation esults fom the Nile Delta multi-azimuth suvey ae based on one single velocity iteation. The same data wee also pocessed with a naow-azimuth pestack time migation, in ode to assess the pefomance of MAPSTM. It appeaed that the quality of the esults was good in both cases. Howeve, the esolution and stuctue delineation was geneally bette in MAPSTM, because the mismatch poblem occued in NAPSTM was solved and less destuctive intefeences wee obseved. Acknowledgements We highly acknowledge BP and RWE Dea fo poviding the data and fo pemission to publish this wok. We thank ou colleagues Konstantin Koch, and Seongbok Lee fo help with data pocessing and softwae suppot. Refeences Botfeld, R. [1989] Geometical ay theoy: Rays and taveltimes in seismic systems (second-ode appoximations of the taveltimes). Geophysics 54, Buchdahl, H.A. [1970] An intoduction to Hamiltonian Optics. Dove Publications, New Yok. Čevený, V. [001] Seismic ay theoy. Cambidge Univesity Pess, Cambidge. Gechka, V., Tsvankin, I. and Cohen, J.K. [1999] Genealized Dix equation and analytic teatment of nomal-moveout velocity fo anisotopic media. Geophysical Pospecting, 47, Hubal, P. and Key, T. [1980] Inteval Velocities fom Seismic Reflection Time Measuements. Society of Exploation Geophysicists, Tulsa, Oklahoma. Hubal, P., Schleiche, J. and Tygel, M. [199] Thee-dimensional paaxial ay popeties Pat I. Basic elations. Jounal of Seismic Exploation, 1, Keggin, J., Benson, M., Rietveld, W., Manning, T., Cook, P. and Page, C. [007] Multi-azimuth 3D povides obust impovements in Nile Delta seismic imaging. Fist Beak, 5(3), Manning, T., Shane, N., Page, C., Baley, B., Rietveld, W. and Keggin, J. [007] Quantifying and inceasing the value of multi-azimuth seismic. The Leading Edge, 6, Mose, T.J. and Čevený, V. [007] Paaxial ay methods fo anisotopic inhomogeneous media. Geophysical Pospecting, 55, Söllne, W., Tsvankin, I. and Silva, E.F.F. [010] Multi-azimuth pestack time migation fo anisotopic weakly heteogeneous media. Jounal of Seismic Exploation, 19, Usin, B. [198] Quadatic wavefont and taveltime appoximations in inhomogeneous layeed media with cuved intefaces. Geophysics, 47, van de Bug, D.W., Lin, S., Zhou, C. and Jiao, J. [010]. Multi-azimuth high esolution tomogaphy Application to offshoe Nile Delta. 7 nd EAGE Confeence & Exhibition, Expanded Abstact B04.

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