ACQUISITION APERTURE CORRECTION IN ANGLE-DOMAIN TOWARDS THE TRUE- REFLECTION RTM

Transcription

1 ACQUISITION APERTURE CORRECTION IN ANGLE-DOMAIN TOWARDS THE TRUE- REFLECTION RTM Rui Yan *, Huimin Guan, Xiao-Bi Xie, Ru-Shan Wu, IGPP, Eath an Planetay Sciences Depatment, Univesity of Califonia, Santa Cuz, TOTAL E&P Summay Due to the limitation of acquisition apetue, RTM, though as a tue-amplitue popagato, cannot povie a tueeflection image. To elate the image amplitue with the taget eflectivity, we popose an amplitue coection in the ip angle omain fo RTM. The stacke migation image is ecompose into ip-angle epenent patial images, which ae compensate iniviually by the coesponing acquisition ip esponse (ADR). Then, coecte images ae summe up to fom a new image consistent with the taget impeance contast. ADR is fomulate as the enegy contibute fom all possible combinations of incient an scattee plane waves to the image with specific ip angle. D SEG/EAGE moel is use to emonstate the impovement in the image amplitue obtaine by applying the ip-angle omain amplitue coection. Intouction In aition to povie coect geometical locations of subsuface stuctues, the tue-eflection imaging stives to give coect image amplitue, which eveals the eflection/scatteing stength of the subsuface stuctues. Howeve, even with accuate wave popagatos, the limite acquisition apetue an the complex ovebuen stuctue usually pevent us fom obtaining coect image amplitue. The combine effects fom these two factos can cause iegula illuminations to subsuface stuctues, leaing to biase image amplitue. To tackle this poblem, Taantola (987) teate the image pocess as an invese poblem an solve it in an iteative way. Howeve, the esulte appoach usually is too expensive to pactice. In aition, the instability an non-uniqueness ae othe unattactive featues of the geneal invese appoach. Anothe appoach lies between the conventional migation an geneal invesion. It opeates on (filte) image fiel an makes the amplitue popotional to the tue-eflectivity thee. In oe to istinguish the imaging povie coect eflectivity fom the imaging using tue-amplitue popagatos, we name the fome as tue-eflection imaging (Wu et al., 004) o tue-eflectivity migation. Along this iection, Gelius et al. (00) fomulate the wavenumbe-omain esolution function an use it to coect the migation image. This appoach has been applie to the ay-base migation (Gelius et al., 00; Lecomte et al., 003, 008) an one-way wave migation (Xie et al., 005; Wu et al., 006). Wu et al. (004) popose to compensate the image amplitue in local image matix (LIM), which is in eflection an ipping angle omain, an geneate by one-way beamlet popagato. Wu an Luo (005) teste iffeent appoaches fo coection an emonstate that the coection in ip angle omain has the geatest impovement to eliminate the acquisition effect. Late, base on the LEF (local exponential fame) ecomposition, seveal authos (Jin et al., 006; Cao an Wu, 009; Mao an Wu, 00) woke to spee up this technique. In this pape, we evelop an amplitue coection algoithm implemente in the ip angle omain to emove the acquisition configuation effect an popagation path effects though complex ovebuens. We will stat fom the theoy of amplitue coection in ip angle omain. The metho use to calculate the ip-angle omain patial image will be povie in the secon pat. Thi, we fomulate apetue ip esponse (ADR), which seves as the amplitue coection facto. Both the ADR an ip-angle omain patial images ae obtaine in RTM scheme. Finally, we use D synthetic examples to emonstate the impact of ADR coection on the image amplitue. Theoy Consie a suvey system compose of a shot locate at s an a geophone locate at g to image the subsuface taget egion V suouning. The wave eflecte fom V eaches to the eceive can be expesse as D,, k G ;, m G ;,,() g s 0 s g V whee is fequency, m c c is the velocity petubation; c0 is the backgoun wavenumbe; c 0 is the local backgoun velocity. G; s, is the Geen s function fom souce location s to the taget location ; G ;, is the Geen s function fom geophone location g g to taget location. The ecipocity ; g, G g;, G is use hee. Fo a system compose of multiple shots an geophones, the image can be fome by * I, G; s, D g; s, G; g,.() s g n

2 TRUE-REFLECTION RTM By summing up all the ip-angle components, we will get the space-omain moel paamete. I, m, (0) R, Next, we escibe how to calculate I an, R., Figue. The cooinate system use in angle-omain analysis. Substituting Dg; s, with equation will esult in I, mr,,, (3) V whee * R,, k G ;, G ;, 0 s s s g, (4) * G ; g, G; g, n is the esolving kenel. In equation 4, two Geen s functions come fom the ata an two ae fom the migation pocess. The image can be consiee as the convolution of the esolving kenel an the moel paamete. In anothe wo, the esolving kenel maps a scatteing point in moel space into the image space. It inclues the effects of both the acquisition (moeling) an imaging (invesion) (Wu et al., 006). The convolution in space omain coespons to the multiplication in wavenumbe omain, so equation 3 can be expesse as (Xie et al., 005; Xie et al., 006) Ik,, mk, Rk,,, (5) whee I k,, Rk,, an mk, ae wavenumbe-omain epesentations of the image, esolving kenel an moel. Equation 5 can be tansfome fom the wavenumbe omain to ip angle omain I,, m, R,,, (6) followe by integate ove to obtain I, m, R,, (7) whee I, I,,, (8) R, R,,, (9) whee is the ip angle; I, an R, ae D ip-angle omain patial image an acquisition ip esponse (ADR), espectively. Dip-angle omain patial image The ip-angle omain patial image I can be obtaine by ecomposing the migation image with local slant stacks: ik - Ik,, W -Ie, () followe by patial econstuction I, Ik,, kk, () W - is the spatial sampling winow centee at whee I is the final stacke migation image; k an ae ; the length an the pola angle of wavenumbe vecto k. Figue. (a) The D SEG/EAGE salt moel. (b) The conventional RTM image. Figue 3. (a) Illumination which only consies souce enegy an (b) image compensate by the souce illumination.

3 Figue 4. Patial images fo iffeent ip angles, with (a) -5º, (b) 5º, (c) -45º an () 45º. Figue 5. ADRs fo selecte ip angles, with (a) -5º, (b) 5º, (c) -45º an () 45º. Figue 6. Patial images compensate by ADRs fo selecte ip angles, with (a) -5º, (b) 5º, (c) -45º an () 45º.

4 TRUE-REFLECTION RTM Acquisition ip esponse (ADR) We tansfom equation 4 to incient angle s an scatteing angle g (Figue ): s, g,, s g 0 s, ; s, R J J k G s g, (3) * * G s, ; s, G g, ; g, Gg, ; g, n The above equation gives the taget illumination contibute fom a local incient wave popagating along an a local scatte wave popagating along g ; s coefficients J s an J g ae esulte fom souce- an eceive-sie Jacobians when we change the integation fom slowness omain to angle omain. It is k 0 fo D case. G,, is the plane wave component of Geen s function, an can be obtaine by local slant stacks (Xie an Wu, 00; Xie an Yang, 008; Yan an Xie, 0). The epesentation of Rs, g,, R,,, s g s g though cooinate tansfom can be tansfome to, (4), (5) whee is the eflection angle. Summing up all the eflection angles fo a local eflecto with ip angle will esult in the taget illumination, calle acquisition ip esponse (ADR) R,, R,,,. (6) Fo commonly use seismic souce functions such as the Ricke wavelet, the majo enegy is caie by waves nea the ominant fequency. Theefoe, the acquisition ip esponse at the ominant fequency is a goo appoximation of amplitue coection facto. R, R,, 0, (7) whee 0 is the ominant fequency of the souce. Numeical example As an example, we conuct the amplitue coection on D SEG/EAGE salt moel (Figue a). The obsevation system fo the moel is compose of 35 shots with an inteval of 60 feet. Each shot is matche with 76 left-sie eceives sepaate by 80 feet. Figue b shows the aw RTM image. Figue 3 shows the illumination which only consies souce enegy an the image coecte by the souce illumination. Though the amplitues of the image ae moe balance than the conventional image, it ignoes the popagation effects fom the taget to the geophones as well as the apetue effects. We ecompose the stacke migation image into ip-angle omain an show fou sample patial images in Figue 4. Figue 5 isplays the coesponing ADR. By compaing the patial image an ADR, we notice that the amplitues of the images ae consistent with the ADR stength. We coect iniviual patial images with the ADRs an the esults ae shown in Figue 6. Then all the coecte images ae summe up to fom the final image which is shown in Figue 7. Afte the coection, the image amplitues of eflectos with iffeent ipping angles become moe balance an the stuctues appea moe continuous. The subsalt stuctues ae geatly enhance, paticulaly fo steep stuctues. Ovelappe on the image ae the wiggle isplay of the image amplitue an the tue eflectivity. They match with each othe vey well. Conclusions Une the RTM famewok, we fomulate a ip-angle omain amplitue coection metho fo tue eflection imaging. We ecompose the migation image an Geen s function to the ip angle omain. The ecompose Geen s function is use to constuct the ADR. In the ip-angle omain, the patial images ae coecte with the ADR an coecte images ae stacke to obtain the final image. Compae to the coection only consie the souce enegy, coection with the ADR shows significant impovement in image amplitue. Acknowlegements This eseach is suppote by TOTAL E&P an WTOPI consotium at the Univesity of Califonia, Santa Cuz. The authos thank the TOTAL management fo the pemission to publish the pape. The authos also appeciate Jian Mao, Jun Cao an Mingqiu Luo s helpful iscussions. Figue 7: The migation image compensate by ADR. Ovelappe wiggles ae eflectivity (e) an the image amplitue (blue).

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