P555 Local Stretch Zeroing NMO Correction N. Kazemi* (University of Tehran) & H.R. SiahKoohi (University of Tehran) SUMMARY We present a meod of normal moveout (NMO) correction called local stretch zeroing (LSZ) meod at avoids NMO stretch. This is done by eliminating ose eoretical curves at generate interpolated data samples responsible for NMO stretch. The original sampling interval is preserved by zero padding and reassigning of true data samples. The LSZ meod eliminates all interfering reflection events at far offsets by optimally selection of mute zone. The results are generally higher frequency an a normal stack and contain less noise. The meod loses its efficiency when CMP data is over- or under-nmo corrected. Performance of e meod is compared to conventional NMO correction Taner et al. (969) using bo synetic and real data. 7 nd EAGE Conference & Exhibition incorporating SPE EUROPEC Barcelona, Spain, 4-7 June
Introduction In conventional seismic survey (CMP meod) reflection events are appeared in coherence and hyperbolic forms. The NMO correction is applied to seismic reflection data to transform traces recorded at nonzero offset into traces at appear to have been recorded at zero offset. Semblance based meods are often used for calculating NMO velocities Dix (955). As shown firstly by Buchholtz (97), conventional application of NMO correction to a CMP reflection generates a stretch which increases wi offset and decreases wi zero-offset time. Avoiding wavelet stretching due to NMO correction prevents e degrading action of wavelet stretching. Due to monotonically increment of velocity wi dep, tails of e eoretical curves at different zero offset times are converged and a number of eoretical curves may pass rough adjacent time samples. Therefore, after NMO correction new data samples are generated by interpolation and stretching is anticipated. This is e major short come of e conventional meod. In is study, we present a stretch free NMO correction meod. The meod improves e conventional procedure by eliminating of sample interpolation and optimally selection of mute zone. The Assume a CMP gaer wi n seismic reflection events ( h( ti, vi ), i,,..., n) and corresponding velocity model determined by linear interpolation of picked NMO velocities (Figure ). Based on e picked velocities, CMP gaer is divided into (n-) time gates (Figure -b). To eliminate e NMO stretch from i reflection event in e i time gate of CMP gaer e proposed meod performs as follow: Figure a) A synetic seismic CMP gaer wi n reflection events ( h( ti, vi ), i,,..., n), b) velocity model corresponding to seismic reflection events in (a) determined by linear interpolation of picked NMO velocities. ) Based on e velocity model, in conventional NMO a number of eoretical curves fitted to e data samples of CMP gaer. The number of curves equals to e number of zero-offset time data samples wiin e gate. The LSZ meod selects e first eoretical curve wiin e gate as a base, to measure time differences between base and e rest of e curves at a given offset (i.e. x ). ) At, ose eoretical curves at have time difference smaller an e half of e x sampling interval t are removed. This avoids generation of new data samples due to e interpolation during NMO correction, which is usual in conventional meod. 3) The comparison of time difference is continued until we reach a eoretical curve wi time difference greater an e half sampling interval. This curve is considered a new base eoretical curve and comparison is continued. 4) Steps and 3 are continued until we reach to e end of e time gate. 5) The conventional NMO correction is applied on e seismic data wiin e i time gate of CMP gaer using e preserved eoretical curves. The corrected data samples will be 7 nd EAGE Conference & Exhibition incorporating SPE EUROPEC Barcelona, Spain, 4-7 June
irregular and eir time intervals may be greater an or equal to e original sampling interval. The LSZ meod by reassigning of data samples, regularize em to e precorrection sampling interval. In some offsets it is possible to pad zeroes until reach e end of e time gate. The number of padded zeroes will be equal to e number of deleted eoretical curves. In fact e proposed meod loses no information during NMO correction, but removes stretching by preventing e generation of new data samples during interpolation. This is valid until we reach an offset which we call X. According to (figure ), at X e wavelet of reflection event is limited to starting and terminating eoretical curves of e time gate (green colored wavelet). LSZ meod will construct is wavelet wiout stretching because e preserved eoretical curves (during steps to 4) contain all data samples of e wavelet (pink colored wavelet, Figure ). Figure The imum offset at which a wavelet is completely preserved after NMO correction by e LSZ meod wi no stretch (wavelet before NMO (green) after NMO (pink) colored). X The is in fact e limit for e LSZ meod for complete and wiout stretching correction of a reflection event. Beyond X alough e wavelet is corrected wi no stretching, but LSZ meod loses some of e data samples of wavelet. The lost data samples of e wavelet are recovered at e beginning of e next time gate. To prevent interference between e leftovers of e wavelet from previous time gate wi wavelets in new time gate, e meod considers it as a noise. For is reason e mute zone of LSZ meod for each reflection event starts from its X. The selected X as onset of mute zone for each time gate is in fact e optimally selected offset for muting, because at offsets larger an wavelets begins to interfere wi wavelets of e next reflection event. X Real and synetic seismic data examples To evaluate e performance of e LSZ in comparison to e conventional NMO correction meod, we applied meods on bo synetic and real CMP gaers. Synetic CMP gaer consists of 8 traces indicating five reflection events wi dominant frequency of 35 Hz (furer details are given in Table ). (Figure 3a to 3f) indicate e synetic CMP gaer before and after NMO correction using conventional meod wi 5% stretch limit and e LSZ meod. As seen from e (figure 3), e LSZ meod preserved e shallowest reflection event wiout stretching up to meter offset. This offset is increased for deeper events (Figure 3e-f). However, e conventional meod preserved e shallowest reflection event up to approximately e same offset wi 5% stretch limit (Figure 3c-d). Table () Velocity analysis parameters of synetic CMP gaer. Vnmo (m/sec) 3 5 7 3 9 Zero-offset Time (sec).4.7.9..4 7 nd EAGE Conference & Exhibition incorporating SPE EUROPEC Barcelona, Spain, 4-7 June
CMP gaer Syntetic CMP gaer.5.5-3a.5 3 4 3b 3 3c 3e NMO Correction wi 5% Stretching.5.5 3 4.5.5 3 4 3d 3f NMO Correction wi 5% Stretching.5.5 3.5.5 3 Figure 3a) Wiggle/variable area and b) variable density representation of synetic CMP gaer, c- d)nmo corrected gaer in (a) by conventional meod wi 5% stretch mute limit, e-f) NMO corrected gaer in (a) by LSZ meod. (Figure 4) indicates a real CMP gaer after NMO correction using conventional meod wi 5% stretch limit and e LSZ meod. Shallow reflection events well preserved by e LSZ meod. (Figure 5) compares e performances of two meods in preserving e characteristics of e input seismic data (i.e. shape and frequency content of wavelet) after stacking. (Figure 5-left) indicates zero-offset synetic trace (trace a) to be compared to e stacked traces (traces b to e) obtained from 7 nd EAGE Conference & Exhibition incorporating SPE EUROPEC Barcelona, Spain, 4-7 June
NMO Correction wi 5% Stretching.5.5 5 5 5 5 Figure 4 a) NMO corrected real CMP gaer using conventional meod. B) NMO corrected real CMP gaer using e LSZ meod. NMO corrected gaers in (Figure 3). In addition, e amplitude spectra of e traces are shown in (Figure 5-right). As seen in e Figure, e events are well preserved by LSZ meod compare to e 5% and5% stretch limit of e conventional meod. - -4 Zero-offset Trace NMO Wi 5% Stretch Limit NMO Wi 5% Stretch Limit Log(Amplitude) -6-8 - - -4 4 6 8 Frequency(Hz) Figure 5 left).a)a zero-offset trace of synetic CMP gaer, b) stacked trace of NMO corrected gaer (shown in Figure 4c), c) stacked trace of NMO corrected gaer (shown in Figure 4e) and d) stacked trace of NMO corrected gaer (shown in Figure 4g). Right) Normalized Amplitude spectra of traces (a-d). Conclusions The meod introduced in is paper performed stretch free NMO correction and retained all true data samples. In is meod linear data interpolation step of conventional meod is replaced by eliminating some eoretical curves, zero padding, and reassigning of true data samples. Optimal determination of mute zone by e LSZ meod eliminates all interfering reflection events at far offsets and decreases e mute zone especially at shallower reflection events. The results of LSZ meod contained less noise as well as higher frequency content an normal stack. Reference Dix C.X. 955. Seismic velocities from surface measurements. Geophysics, 68-86. Taner M.T. and Koehler F. 969. Velocity spectra-digital computer derivation and application of velocity functions. Geophysics 34, 859-88. Buchholtz, H., 97, A note on signal distortion due to dynamic (NMO) corrections: Geophys. Prosp.,, 395-4. 7 nd EAGE Conference & Exhibition incorporating SPE EUROPEC Barcelona, Spain, 4-7 June