Robust surface-consistent residual statics and phase correction part 2

Transcription

1 Robust surfac-consistnt rsidual statics and phas corrction part 2 Ptr Cary*, Nirupama Nagarajappa Arcis Sismic Solutions, A TGS Company, Calgary, Albrta, Canada. Summary In land AVO procssing, nar-surfac htrognity issus ar rsolvd by surfac-consistnt procssing. It is prsumd that th amplitud and phas corrctions ar takn car of by surfacconsistnt dconvolution and statics solution is applid indpndntly of th phas. Du to nois, th surfac consistnt rsidual wavlt phas stimation is unrliabl. Givn th rlation btwn statics and phas, solving for statics alon whn phas rrors xist will rsult in ovr or undrstimation of statics. W thrfor propos a surfac-consistnt mthod to rsolv rsidual statics & phas simultanously by maximizing th stack powr. rrors stimatd by th mthod corrlat with faturs of surfac topography and with diffrnt sourc typs dmonstrating that th mthod is robust. Introduction Variabl sourc and rcivr typs, coupling variations, and variabl nar-surfac conditions ar th main rasons why surfac-consistnt procssing tchniqus (dconvolution, statics, scaling) ar standardly applid to land sismic data. Howvr, bcaus surfac-consistnt mthods ar statistical, factors such as nois prvnt surfac-consistnt procsss from vr working prfctly, spcially if th nois is surfac-consistnt as wll as th signal. For xampl, w xpct that surfac-consistnt nois will gnrat surfac-consistnt rrors in wavlt phas aftr surfac-consistnt dconvolution. Howvr wavlt phas can b difficult to stimat rliably in th prsnc of nois, so mthods that try to stimat phas typically suffr from a lack of robustnss. W hav dvlopd a robust mthod of stimating surfac-consistnt rsidual wavlt phas that is basd on th simultanous maximization of stack-powr as a function of both statics and phas. Ral data xampls show that stack-powr and imag quality ar improvd in a robust fashion with th simultanous stimation of statics and phas corrctions. W typically apply th procss aftr rsidual statics ar applid, and w obsrv that th algorithm coms up with statics and phas corrctions that ar strongly anti-corrlatd. W xplain th obsrvd anti-corrlation by th fact that prvious rsidual statics stps in th procssing flow wr improprly trying to corrct rsidual phas rrors with statics corrctions. Maps of phas rrors oftn show good corrlation with faturs of th surfac topography. In addition, phas diffrncs btwn diffrnt sourc typs ar rliably stimatd with th nw algorithm whn compard with a standard mthod of phas stimation at ovrlapping CDP stack locations. Ths obsrvations lad us to bliv that th phas rrors that ar stimatd with this mthod ar ral and ar bing robustly stimatd. Mthod A considrabl amount of prvious work on surfac-consistnt phas stimation has bn don by Tanr t al. (1974, 1980, 1981), Sword (1983), Downi (1988), Ronn and Clarbout (1985), Cambois and Stoffa (1993), Guo and Zhou (2001). Dspit all of this prvious work, surfac-consistnt phas stimation is gnrally nvr includd in standard procssing flows. This is prsumably du to doubts about th rliability of th phas stimats. GoConvntion 2014: FOCUS 1

2 W hav chosn to us th following tchniqus and assumptions in ordr to obtain a robust mthod of surfac-consistnt phas stimation: A constant (frquncy-indpndnt) phas rotation is assumd for ach sourc and rcivr. Rlativ (not absolut) surfac-consistnt phas variations ar stimatd. and statics corrctions ar simultanously stimatd. Th mthod of stack-powr maximization (Ronn and Clarbout, 1985) is xtndd bcaus of its robustnss in th prsnc of nois. Figur 1 shows a simpl synthtic xampl that illustrats what w bliv could b happning to th sismic wavlt during a typical land procssing flow: aftr surfac-consistnt dconvolution, both rsidual statics and phas rrors may xist as in Figur 1(a). Surfac-consistnt rsidual statics is dsignd to improv th cohrnc of vnts, so it dos this by aligning paks with paks and troughs with troughs as bst it can, dspit th phas variations, as shown in Figur 1(b). On ral data, it would b difficult to know that phas rrors rmain in th data bcaus th cohrnc of th vnts appars good. Our mthod simultanously stimats both statics and phas corrctions, and thrfor finds th optimum solution in Figur 1(c). Th diffrnc btwn th cohrnc of th wavlts in Figur 1(b) and 1(c) may not appar to b larg, but this amount of diffrnc could asily b significant whn analysing th data for subtl stratigraphic faturs, AVO variations or rsrvoir attributs. Figur 1: A simpl synthtic xampl showing (a) a gathr with surfac-consistnt statics and phas variations, (b) th sam gathr aftr surfac-consistnt rsidual statics corrction, and (c) th sam gathr aftr simultanous surfac-consistnt statics and phas corrction. Ral Data Exampl W us a 3D datast from Ohio (Firston 3D) to illustrat th statics & phas stimation mthod. This datast was acquird with thr diffrnt sourc typs as shown in Figur 2(a). Vibrosis with a nonlinar swp was usd on th roads in th north part of th survy, Vibrosis with a linar swp was usd on th roads lswhr in th survy, and dynamit was usd btwn th roads. Figur 2(b) shows th sourc phas solution from our simultanous phas and statics stimation mthod. Thr is an obvious corrlation of phas with sourc typ. Th man and standard dviation of th phas as a function of sourc typ was found to b: dynamit: -25±18 ; nonlinar Vibrosis - 104±16 ; linar Vibrosis: 17±18. Ths avrag phas stimats wr confirmd by a sparat analysis of phas diffrncs btwn stackd tracs formd with ach diffrnt sourc typ. Figur 3(a) shows th spatial variations in rcivr phas that wr dtrmind by th simultanous statics and phas stimation. Ths rcivr phas variations show an obvious corrlation with faturs in th surfac topography shown in Figur 3(b). Figur 4 shows an xampl of an inlin from th northrn part of th survy with and without th phas and statics corrctions applid. Th input to th simultanous statics and phas stimation was th prstack data that wnt into th stack in Figur 4(a), which has two prvious passs of rsidual statics applid. Whn comparing th stacks with and without surfac-consistnt phas corrctions, w not GoConvntion 2014: FOCUS 2 (b

3 that th phas charactr of th horizons appars to b bcom mor consistnt with th corrctions applid (.g. th rd horizon btwn 800 and 850ms). (a) Figur 2(a): Shot map of th Firston 3D: Grn: Vibrosis with nonlinar swp, Rd: Vibrosis with linar swp, Blu: dynamit. Figur 2(b): Sourc phas variations as dtrmind by simultanous static and phas stimation. An obvious corrlation of phas with sourc typ can b obsrvd. (b) (a) (b) Figur 3(a): Rcivr phas variations as dtrmind by simultanous statics and phas stimation. Th colour scal is blu: -30, grn: 0, rd: 30. Figur 3(b) CDP lvations: 950ft (blu) to 1350ft (rd). Thr is a clar corrlation of rcivr phas and drainag faturs in th surfac topography. Figur 5 shows cross-plots of th surfac-consistnt statics and phas for all sourcs (lft) and rcivrs (right) in th 3D survy. W s that th algorithm has stimatd statics and phas rrors that ar strongly anti-corrlatd. W bliv that this anti-corrlation of statics and phas is du to th fact that prvious applications of rsidual statics in th procssing flow hav trid to produc cohrnt vnts by using statics to corrct for phas rrors. For xampl, if th contours in Figur 6 rprsnt th stack-powr of a shot or rcivr as a function of statics and phas, and th grn dot in Figur 6(a) rprsnts th phas and statics rror aftr dconvolution, thn rsidual statics will mov th grn dot along a lin of constant phas to th location in Figur 6(b) in ordr to maximiz th stack powr. Th subsqunt simultanous statics and phas corrction will mov th grn dot along th rd lin to th tru stackpowr maximum. Rgardlss of th original location of th grn dot, th statics and phas will li somwhr along th rd lin, as obsrvd in Figur 5. GoConvntion 2014: FOCUS 3

4 Figur 4(a)(top): Exampl of an inlin bfor statics and phas corrction, and. Figur 4(b)(bottom): with phas and statics corrctions applid. Figur 5: Cross-plots of statics vrsus phas for all sourcs (lft) and rcivrs (right) in th Firston 3D survy. (a) (b) (c) Figur 6: Exampl of a shot or rcivr with a statics and phas rror rprsntd by th grn dot on a map of contourd stack-powr (a) aftr dconvolution, (b) aftr rsidual statics, and (c) aftr simultanous statics and phas corrction. GoConvntion 2014: FOCUS 4

5 Conclusions W hav prsntd th basic mthodology of a mthod for simultanously stimating surfacconsistnt phas and statics rrors. Not only is th mthod robust, but th phas rrors that it stimats appar to b rliabl bcaus th stack-powr is improvd, th phas maps mak physical sns in rlation to surfac faturs, corrlation with sourc typ, and th obsrvd anti-corrlation of statics and phas stimats. W xpct this mthod to b capabl of rsolving short to mdium wavlngth phas rrors, but as with all surfac-consistnt mthods, long wavlngth variations in phas will b virtually impossibl to rsolv. Acknowldgmnts W thank TGS for prmission to publish this papr. Th data xampl is th Firston 3D (Ohio) from th TGS multi-clint data library. Rfrncs Cambois. G. and Stoffa, P. [1993], Surfac-consistnt phas dcomposition in th log/fourir domain, Gophysics, 58, Downi, A. L. [1988], Nar-surfac corrctions, 58 th SEG Annual Intrnational Mting, Extndd Abstracts, Guo, J. and Zhou, X. [2001], Surfac-consistnt phas corrctions, 71 st SEG Annual Intrnational Mting, Extndd Abstracts. Ronn, J. and Clarbout, J.F. [1985], Surfac-consistnt rsidual statics stimation by stack-powr optimization, Gophysics, 50, Sword, C. [1983], Th gnralizd frquncy-dpndnt surfac-consistnt statics problm: Stanford Expl. Proj. Rp. 35, Tanr, M.T. and Coburn, K.W. [1980], Surfac-consistnt stimation of sourc-and-rcivr rspons functions, 50 th SEG Annual Intrnational Mting, Extndd Abstracts. Tanr, M.T. and Kohlr, F., [1981], Surfac-consistnt corrctions, Gophysics, 46, Tanr, M.T. Kohlr, F. and Alhilali, K.A. [1974], Estimation and corrctions of nar-surfac tim anomalis, Gophysics, 39, GoConvntion 2014: FOCUS 5