C-wave event automated registration using a nonlinear global search method

Transcription

1 C-wave event automated regstraton usng a nonlnear global search method Shuangquan Chen*,1, Xang-Yang L 1,2 and Xaomng L 1 1 CNPC Keylab of Geophyscal Prospectng, Chna Unversty of Petroleum, Bejng, , CHINA 2 Brtsh Geologcal Survey, Murchson House, West Mans Road, Ednburgh EH9 3LA, UK Summary For multcomponent sesmc data jont processng and nterpretaton, event regstraton of C-waves n the P-wave tme doman s a crtcal step, whch s one of the bottlenecks that lmts further applcaton of the multcomponent data. In order to solve ths problem, we use the Needleman- Wunsch (NW) algorthm, a nonlnear global optmzaton method developed for amno acd sequence algnment n protens, to algn C-wave events. The objectve functon s to maxmze the waveform smlarty to compensate for the dfferent reflectvtes of P-wave and C-wave. Both numercal modelng and feld data examples are used to llustrate the methodology and ts effcency and robustness for event regstraton.

2 Introducton The jont processng and nterpretaton of multcomponent sesmc data can provde valuable addtonal nformaton that can reveal subtle detals of hydrocarbon reservors. In partcular, the velocty rato (γ 0 ) of P- and S-waves can be used to dstngush hydrocarbons (L and Zhang, 2011). The successful applcaton of C-waves (converted PS-waves) depends on the ablty for correct C- wave event regstraton n the P-wave tme doman (Gaser 1996). Gaser (1996) frst gave a detaled correlaton method for obtanng the vertcal velocty rato γ 0, and showed that both the average and nterval γ 0 can be obtaned by maxmzng the correlaton functon of waveform smlarty of P- and C-wave sesmc traces. Followng Gaser (1996), smlar methods have been proposed for P- and C-wave event regstraton, such as constant γ 0 scannng and pckng (Van Dok and Krstansen 2003), nstantaneous-phase tme slces method (Nahm and Duhon, 2003), and automatc matchng method usng least squares fttng (Sergey 2003, 2005). More recently, Yuan et al. (2008) used constraned smulated annealng to maxmze the smlarty objectve functon wth tme-varyng spectral whtenng and phase correcton, and Gaser (2011) proposed a frequency correcton to compensate for the waveform dstorton after tme matchng of P- and C-waves. Chen and L (2012) proposed the use of matchng workflow based on nverted attrbutes from the prestack P-wave gathers, whch mproved waveform smlarty. Theoretcally speakng, P- and C-wave event regstraton usng an automated method s often dffcult to acheve. The man reasons are the hghly nonlnear soluton of the process and the dfferent waveform characterstcs between P- and C-waves. In ths paper, we propose a C-wave automatc event algnment method wth the Needleman-Wunsch (NW) algorthm by searchng for a global best correlaton of P- and C-wave data. Synthetc and feld data are used to llustrate ths approach. Methodology For C-wave automatc event regstraton, there are three man assumptons. Frst, we consder that the P- and C-wave mages contan the prmary reflectons only, and the free surface or nter-bed multples have been attenuated. Secondly, t assumes that the sesmc reflectons from both P-wave and C-wave data are correctly postoned laterally by the mgraton processng. We only regster the vertcal traveltmes of P- and C-waves. Fnally, the waveform smlarty of the two types of data has been mproved usng an nverson method (Chen and L 2012). The man cost functon s the normalzed cross-correlaton or smlarty of P- and C-wave sesmc trace as Et () = 2 2 [ ] P() tc wt (), (1) P () t C wt () [ ] where w(t) s the warpng functon to transform P-S travel tme nto the P-P tme doman. The velocty rato of P- and S-waves can be obtaned from the warpng functon as dw() t γ () t = 2 1. (2) dt By usng cross-correlaton, the dfference n P- and C-wave events can be nsgnfcant n a gven tme wndow. Gaser (1996) proposed a smlar approach for manual pckng of the velocty rato. Here we mplement the smlarty spectrum n a dfferent fashon to obtan a global maxmum value for the event matchng. The nverson process fnds the warpng functon w(t) to maxmze the cost functon n Equaton (1), n searchng for the best regstraton for C-wave and P- wave data. The procedure s hghly non-lnear, wth many local maxma. Unless a good ntal warpng functon s avalable, any

3 lnear search method wll probably fall nto a local mnmum or maxmum (Fomel 2003). To avod any manual pckng, we adopt a global search method, the Needleman-Wunsch algorthm, as our search engne. It performs a global algnment on two sequences and s commonly used n bonformatcs to algn proten or nucleotde sequences (Needleman and Wunsch 1970). The NW algorthm s an teratve method n whch all possble pars of amno acds (one from each strng) are set up n a 2D matrx; algnments are represented as pathways through ths array. The optmum algnment s the path connectng maxmum scorng values. Ths approach s an example of dynamc programmng, whch n petroleum sesmology has been appled to sesmc modelng (Darby and Nedell, 1966), an earler approach to trace algnment (Kruse, 1988). In our sesmc case we do not expect or need exact pont-wse ampltude matchng; our nterest s smlarty of the waveform or one wndowed sze of wavelet. Therefore, a more approprate measure of smlarty n the sesmc case s a wndow sze correlaton. So, we use the dea n a smlarty functon as σ (, j) = n τ = n x y + τ j+ τ n 2 n 2 x n y τ= + τ τ= n j+ τ, (3) + ε where x and y represent the P- and C-wave traces, n s the correlaton wndow length, and ε s the stablzaton denomnator. Here, we use the wndowed cross-correlaton for nonlnear trace algnment whch nvolves an NW-type algorthm. Fgure 1 shows a sketch of the NW-type matchng algorthm. Fgure 1. Sketch for C-wave regstraton usng the NW-type approach. The wndowed crosscorrelaton values; the search result usng a NW engne, and the black blocks ndcate the maxmum cost path for C-wave regstraton relatve to the P-wave. For the whole sesmc dataset regstraton, as each trace par s algned alone, we usng multple traces correlaton coeffcent to mprove the regstraton results to ensure lateral consstence. In ths way, an ntermedate trace receves many partal algnments and a fnal algnment from ts nearest neghbor, whch tself may be modfed several tmes. Synthetc and feld data examples A smple synthetc test s shown n fgure 2. Convolvng the reflectvtes calculated from a wellloggng curve wth sesmc wavelet generates the P- and C-wave traces. We use a Rcker wavelet wth a prmary frequency of 30 Hz for P- and C-waves. Throughout the automatc matchng usng our approach n the prevous context, a good estmaton of Vp/Vs s obtaned (the sold red lne n Fgure 2a), and C-wave reflectons are correctly regstered wth P-wave reflectons (Fgure 2b). In fgure2b, we compared the P-wave trace, C-wave trace n P-S travel tme, PPS nverson trace usng the method

4 proposed by Chen and L (2012) and C-wave warped trace usng the automatc NW matchng method. Comparng wth the regstraton result usng the NW method, the nverted PPS trace and C-wave warped trace are almost dentcal. For real data applcaton, the proposed regstraton algorthm has been successfully tested on a feld dataset from Southwest Chna (Fgure 3). Compared wth P-wave data, the frequency content of C- wave data s often lower. Usng the proposed NW searchng algorthm, we can mprove the estmaton of the Vp/Vs rato and the frequency content of C-wave data after warpng. The results are shown n Fgure 3. The warped C-wave secton matches the P-wave secton (Fgure 3a) very well, as seen n the cross-secton comparson. The estmated Vp/Vs model s shown n Fgure 3b, and a sharp varaton of Vp/Vs rato can be observed n the shallow part of the secton γ nt Tme (ms) Fgure 2. Model nterval velocty rato Vp/Vs (black lne) and the nterval Vp/Vs obtaned from the automatc regstraton approach (red lne); P-wave trace and C-wave trace n P-S travel tme; PPS trace nverted by the prestack P-wave gathers (Chen and L 2012); C-wave warped trace by NW automatc searchng method. Conclusons We have used the Needleman-Wunsch (NW) algorthm to perform a nonlnear global optmzaton durng the P- and C-wave event regstraton. The effcent mplementaton of ths algorthms makes t possble to carry out the regstraton automatcally, Both synthetc and feld data are used to llustrate the algorthm, whch verfes the proposed method and confrms that P and C-wave event regstraton can be effectvely performed usng the proposed algorthm.

5 Fgure 3. Comparson of C-wave (left) and P-wave (rght) automatc regstraton sectons; the estmated Vp/Vs velocty rato γ 0. Acknowledgements We thank SINOPEC for permsson to show the data. Ths work s partally supported by the Natonal Natural Scence Foundaton of Chna, No , and the Ednburgh Ansotropy Project (EAP) at the Brtsh Geologcal Survey (BGS). The work s publshed wth the permsson of the EAP sponsors and the BGS Executve Drector (NERC). References Chen S. and L X.-Y., 2012, The use of attrbutes matchng for PP- and PS-wave event regstraton, 74 th Ann. Int. Mtg: Eur. Assn. Geosc. Eng., P132 Fomel S. and Backus M., 2003, Multcomponent sesmc data regstraton by least squares: 73 rd Annual Internatonal Meetng, SEG, Expanded Abstracts, Fomel S., Backus M., Fouad K. and Wnters G., 2005, A multstep approach to multcomponent sesmc mage regstraton wth applcaton to a West Texas carbonate reservor study: 75th Annual Internatonal Meetng, SEG, Expanded Abstracts, Gaser J. E., 1996, Multcomponent Vp/Vs correlaton analyss: Geophyscs, 61, Gaser J. E. and Verm R., 2011, Velocty-based wavelet correctons for doman transformaton: 73rd EAGE Conference & Exhbton, Extended Abstract B004. L X.-Y. and Zhang Y. G., 2011, Sesmc reservor characterzaton: how can multcomponent data help? J. Geophys. Eng. 8: Nahm J. W. and Duhon M. P., 2003, Interpretaton and practcal applcatons of 4C-3D sesmc data, East Cameron gas felds, Gulf of Mexco: The Leadng Edge, Needleman S. B. and Wunsch C. D., 1970, A general method applcable to the search for smlartes n the amno acd sequence of two protens, Journal of Molecular Bology, 48 (3): States D., Agarwal J. P., Gaasterland T., Hunter L. and Smth R. Eds., 1984, Proceedngs of the Fourth Internatonal Conference on Artfcal Intellgence (AAAI-84): Unversty of Texas Press. Van Dok R. and Krstansen P., 2003, Event regstraton and Vp/Vs correlaton analyss n 4C processng: 73rd Annual Internatonal Meetng, SEG Expanded Abstracts, Yuan J., Nathan, G., Calvert A. and Bloor R., 2008, Automated C-wave regstraton by smulated annealng: 78th Annual Internatonal Meetng, SEG Expanded Abstracts,