Q tomogrphy towrs true mplitue imge n improve su-krst imge Yng He n Jun Ci, TGS Summry A frequeny omin tomogrphi inversion ws evelope to estimte frequeny epenent energy ttenution y using prestk epth migrtion ommon imge gthers (CIGs). The frequeny epenent ttenution is estimte from the entroi frequeny ifferene for refletions in CIGs. Migrtion streth n ghost effets re tken into ount to get orret mesurements of frequeny. This metho mkes orretion for these ftors to otin orret frequeny ifferene, utilizes the tul ry pths n vois using mplitue informtion. It is reltively insensitive to some of mplitue loss ftors, suh s geometri spreing, refletion n trnsmission loss, soure n reeiver rition ptterns. Q tomogrphy ws use to erive the Q moel for krst mei. The ompenstion of mplitue loss improves the su-krst mplitue fielity. Introution The propgtion of seismi wve through the erth is ffete y ttenution ue to inelsti nture. Assuming ttenution is linerly epenent on frequeny n Q is inepenent on frequeny, mplitue spetr hnge fter ttenution. The high frequenies of the seismi signl re ttenute more thn the low frequenies. The hnges in seismi mplitue spetr serve s oserve t for ttenution estimtion. Attenution of the reeive signls is etermine y its propgtion pth through the Q moel. Tking tul ry pth informtion into ount, Q moel is estimte y tomogrphi inversion. Q tomogrphy lgorithms re lssifie into two min tegories se on how t info is use. One tegory utilizes mplitue-spetr-rtio metho for estimting Q. The nturl log spetr rtio etween refletions with n without ttenution gives estimtion of Q moel (Dsgupt n Clrk 1998). But mny ftors ffet mplitues, inluing sttering, geometri spreing, soure n reeiver iretivity, rition ptterns n trnsmission /refletion effets. These ftors re ssume to e frequeny inepenent, whih re iffiult to exlue. The other tegory mesures the reltive shift of the entroi or ominnt frequeny of the signl spetrum. It might otin relile ttenution estimtes from the reltive mesurements. Qun n Hrris (1997) evelope metho for estimting seismi ttenution se on frequeny shift t. They erive the reltionship etween Q moel n entroi frequeny shift for Gussin, oxr n tringulr spetr. Zhng n Ulryh (2002) erive n nlytil reltionship etween Q-ftor n seismi t pek frequeny vrition for Riker wvelet. Hu et l. (2011) esigne souremplitue spetrum fitting funtion to hnle symmetri soure mplitue spetr. The shpe n the nwith of the funtion re etermine y two prmeters seprtely, whih mkes it onvenient to fit vrious symmetri soure mplitue spetr. The mesurement se on frequeny shifts oul e more relile when solute mplitue is not use. These frequeny Q estimtion methos re one in t omin, otining intervl ttenution iretly from prestk gthers y mesuring frequeny of seismi signls. Piking prestk events on omplex t is onsiere unfesile, euse of low signl-to-noise level or omplex rrivls relte to heterogeneous veloity moels. Differing from previous pprohes, we operte on epth migrte CIG gthers in imging omin. The key of our pproh is to otin entroi frequeny ifferene from 3D prestk epth migrte CIG gthers. After otining the frequeny ifferene, they n e use s oserve t to reonstrut the ttenution istriution tomogrphilly. Metho To otin orret entroi frequeny from epth migrte gthers, we nee to mke orretions for migrtion streth first. Migrtion streth is rete when mpping n input time soure wvelet to its equivlent vertil epth. It uses loss of frequeny nwith n wvelet istortion. There re numer of ftors ffeting the streth of events in epth, suh s refletion ngle, struture ip n lol veloity. With some geometry nlysis, migrtion streth is relte to inient ngle, whih suggests tht working in ommon ngle omin is vntgeous. So we mppe the ommon offset gthers into ommon ngle gthers n extrte frequeny from ngle-epenent refletions. Figure 1 isplys CIG gther rete y Kirhhoff prestk epth migrtion with grient veloity. The offset rnge is out twie tht of the epth. Note tht streth t fr offsets is more evient thn ner offsets t shllow epth where inient re lrge. Also the streth vries with epth t given offset. Besies, the refletion in the eep is wier euse the veloity is higher. The migrtion streth is esrie s the following eqution, z 1 v z os( ) os( ) v r 2012 SEG DOI http://x.oi.org/10.1190/segm2012-1220.1 SEG Ls Vegs 2012 Annul Meeting Pge 1
Q tomogrphy where θ is inient ngle etween imging ry pth n struture refletion plne, α is ipping ngle of struture plne, n v is lol veloity t refletion point, v r is referene veloity t referene lotion. z is the smple intervl t referene lotion. The rtio of z' n z represents migrtion streth. z' is use to resmple the gthers to un-streth the refletion events in epth. Figure 1 isplys the un-strethe gthers. Note tht fter unstrething, ll refletions from ifferent offsets n epth hve the sme thikness in epth. Struture ip is pike from stking imges n use for orretion for ipping refletions. Besies migrtion streth, soure n reeiver hve frequeny-epenent iretivity ue to surfe ghosts (Hustet n Clrk, 1999). Figure 2 isplys omprison of shot gthers for two ounry onitions. The moele spetr re lerly ffete y iretivity. The fr offset ppers to e of higher frequeny thn the ner offset. The surfe of the oen ts s n ousti mirror, using ghost effets in reore seismi t. The time ely etween the primry wvefiel n the ghost wvefiel vries with tke-off ngle from soure n inient ngle t reeiver, thus les to frequeny-epenent iretivity. Figure 3 isplys omprison of CIG gthers migrte for syntheti t with soring n free-surfe ounry onitions. The ominnt frequeny shift in the gther with free-surfe ounry onition is less evient thn the one with soring ounry euse ghost effets pper to suppress the streth. The presene of ghost omplites the Q estimtion. To mke orretion for the ghost effet, frequeny hnge with iretions is ounte to otin the orret entroi frequeny. Figure 1: ) Gther from Kirhhoff Depth Migrtion. ) Gther fter un-strething. Figure 2: ) A shot gther for horizontl refletion with soring ounry. ) with free surfe ounry. Figure 3: ) Common offset gther with soring ounry. ) with free surfe ounry. Note the spetr omprison for ner n fr offsets. First, len soure wvelet nees to e estimte. Diret rrivl is hrterize y soure wvelet plus its ghost refletion from the ir-wter interfe. The time ely etween them is smll when the epth of soure n reeiver is smll. The soure wvelet n the ghost re of opposite sign in mplitue n their mplitues re lmost 2012 SEG DOI http://x.oi.org/10.1190/segm2012-1220.1 SEG Ls Vegs 2012 Annul Meeting Pge 2
Q tomogrphy of the sme mgnitue ue to lmost perfet mirror refletion from ir-wter interfe. Thus the iret rrivl is erivtive of the len soure wvelet (Niu, personl ommunition). By integrtion of iret rrivl, the soure wvelet n e estimte. For eh refletion pike in CIGs, tke-off ngle from soure n inient ngle t reeiver were ompute n the surfe ghost spetrl responses ue to soure n reeiver were evlute n orrete from the mesure frequeny. ttenution effet n e quntittively estimte y Q tomogrphy. Exmples First we verify the vliity of our frequeny pproh with syntheti test. Figure 4 shows two imensionl erth moel of three horizontl lyers n gs poket in whih Q properties re lele. For onventionl migrtion, Figure 4 shows oth mplitue n frequeny loss for the refletion eneth the ttenution zone. Figure 4 shows the un-strethe gthers fter migrtion streth is remove. For etil, Figure 5 is zoom-in isply for 3 lotions of Figure 4. The refletion in the mile (Figure 5) eneth e e f f Figure 4: ) Moel with 1/Q n veloity lele. ) Gther from onventionl Kirhhoff Prestk Depth Migrtion. ) Gther fter un-strething. ) Pike frequeny isplye on gther. e) Reonstrute 1/Q moel isplye with sme sle s. f) Gther fter Q migrtion. Resiul frequeny shift fter un-strething n ghostorretion of pike refletions long the moveout urves serves s the input t to estimte the intervl Q. The ownshift in entroi frequeny is proportionl to pth integrl through the ttenution istriution. Seismi Figure 5: Zoom-in isply of the gther efore (,,) n fter un-strething (,e,f) for figure 4 n 4. the ttenution zone is roene in omprison to the refletion on the right (Figure 5). The refletions fter ttenution (Figure 5, ) hve phse hnge in omprison to non-ttenute refletion (Figure 5). Figure 4 shows the entroi frequeny pike on the un-strethe gthers. Note tht the frequeny pttern through the moel gives inition of the high ttenution zone. On the ege of the gs poket, strong migrtion swing is oserve. The rossorreltion vlue of the gther n the stk is use with 2012 SEG DOI http://x.oi.org/10.1190/segm2012-1220.1 SEG Ls Vegs 2012 Annul Meeting Pge 3
Q tomogrphy threshol to ontrol the qulity of the piking. Figure 4e shows the estimte Q moel, in whih Q nomlies re well reovere though there is some smoothing lekge long ounry. Figure 4f shows the gther fter Q migrtion. The mplitue n frequeny ontent of the refletions eneth the ttenution zone is well ompenste. Also note tht the phse is orret. Next step is to test it with fiel t. For Hernno survey in the estern Gulf of Mexio, ronte krst zones re often foun over the Flori Esrpment shown in Figure 6. The krst zones hve signifintly slower veloities thn the surrouning seiments. The size of these krsts is usully few meters to few hunre meters. Attenution in krst zones n e high ue to frtures n unonsolite rok, using the mplitue imming eneth it. Spetrl mesurements of the refletions re omplite y interferene effets resulting from losely spe events. To uil Q moel in krst zone, two isolte horizons re pike in the eep to voi jent refletions. Frequeny mesurement is omplete for the refletions long the horizons fter migrtion streth n ghost effets re remove. Then the frequeny shift is use for inversion of Q moel. Figure 6 shows the reonstrute 1/Q nomlies. The estimte Q moel then is use in Q migrtion to ompenste the mplitue n frequeny loss in imging. Figure 6 shows the stking imge fter Q migrtion. Conlusions We hve evelope frequeny omin tomogrphi inversion to estimte qulity ftor Q. The t use to estimte ttenution is extrte from the entroi frequeny ifferene of refletions in prestk epth migrte CIGs. Migrtion streth n ghost effets re orrete to otin the entroi frequeny ifferene etween migrtion gthers from ifferent epth, lotions n offsets. This metho utilizes the tul ry pths n vois using mplitue informtion. The syntheti n rel t exmples vlite this ttenution tomogrphy n show its effet in mplitue n frequeny ompenstion. Aknowlegments Authors woul like to thnk Sng Suh n Shuqin Dong for generting the syntheti t. Thnk Ho Xun, Zhiqing Guo, Xinsong Zeng n Bin Wng for helpful vie uring this projet, n Chuk Mson for proof reing. We thnk the mngement of TGS for permission to pulish this pper. The Hernno survey is oopertive effort etween TGS n PGS. Figure 6: ) Stk imge isplye with horizons overli. ) Stk imge fter Q migrtion. ) Veloity moel of Krst zone with low veloity. ) 1/Q moel estimte from Q tomogrphy. 2012 SEG DOI http://x.oi.org/10.1190/segm2012-1220.1 SEG Ls Vegs 2012 Annul Meeting Pge 4
http://x.oi.org/10.1190/segm2012-1220.1 EDITED REFERENCES Note: This referene list is opy-eite version of the referene list sumitte y the uthor. Referene lists for the 2012 SEG Tehnil Progrm Expne Astrts hve een opy eite so tht referenes provie with the online mett for eh pper will hieve high egree of linking to ite soures tht pper on the We. REFERENCES Dsgupt, R., n R. A. Clrk, 1998, Estimtion of Q from surfe seismi refletion t: Geophysis, 63, 2120-2128. Hu, W., J. Liu, L. Ber, n C. Mrinkovih, 2011, A roust n urte seismi ttenution tomogrphy lgorithm: SEG, Expne Astrts, 30, 2727-2731. Hustet, B., n R. A. Clrk, 1999, Soure/reeiver rry iretivity effets on mrine seismi ttenution mesurements: Geophysil Prospeting, 47, 1105-1119. Qun, Y., n J. M. Hrris, 1997, Seismi ttenution tomogrphy using the frequeny shift metho: Geophysis, 62, 895-905. Zhng, C. n T. J. Ulryh, 2002, Estimtion of qulity ftors from CMP reors: Geophysis, 67, 1542-1547. 2012 SEG DOI http://x.oi.org/10.1190/segm2012-1220.1 SEG Ls Vegs 2012 Annul Meeting Pge 5