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1 Title: Estimating v v s ratio from converted waves: a 4C case examle Xiang-Yang Li 1, Jianxin Yuan 1;2,Anton Ziolkowski 2 and Floris Strijbos 3 1 British Geological Survey, Scotland, UK 2 University of Edinburgh 3 Shell UK Exloration and Production Ltd.

2 Summary The traditional method to obtain v v s ratio is to correlate P -wave with S-wave data, if both are recorded, or to erform AVO modelling, if only P -wave is recorded. Here, we resent a 4C case examle from the North Sea (courtesy of Shell Exloration) and demonstrate how the v v s ratio can be estimated from such data robustly and consistently, without the need of correlation. Our aroach is based on the exact traveltime euation for P -SV converted waves (P S-waves, in short) in a single-layer medium. For multi-layered media, the PS traveltime can be aroximately modelled using an euivalent single-layer medium with Dix-tye root-mean-suared (rms) roerties. The aroach leads to the develoment of velocity ratio sectra instead of the more traditional velocity sectra. Alication of this method to the North Sea data yields a better stacked PS-section, and uality measurements of the v v s ratio across the whole section. Introduction Poisson's ratio is comletely determined by the v v s ratio, and both are imortant uantities for lithology rediction and uid substitution for reservoir modelling and simulation (e.g. Tatham 1982; Robertson 1987; Iverson et al. 1989, and among others). For marine seismic data, AVO modelling has been the only ractical method to obtain S-wave information until the emergence of the marine 4C technology, which oens new oortunities to obtain S-wave information from P -SV converted waves (P S-waves) recorded at the seabed. Most existing analysis techniues for PS-waves are based on the Taylor series exansion of PS travel-time euation (e.g. Tessmer and Behle 1988; Thomsen 1998). This aroach yields eective PS velocities, and reuires P- and PS-correlation for estimating the v v s ratio. Unfortunately P- and PS-correlation is known to be a major issue of joint P- and PS-rocessing and interretation (Gaiser 1996). Here, we utilize the euivalent medium concet of Zhang (1996) and the concet of velocity ratio sectrum of Behle and Dohr (1985), and resent an imroved aroach for convertedwave velocity analysis. Theory and method Travel-time euation for a single-layer model. The PS-wave travel time t s (P down and S u) from a reector at deth z can be written as t s 1 v x 2 + z 2 + v (x, x ) 2 + z 2 ; (1) where v and v s are, resectively, the P - and S-wave velocities of the medium, v v s is velocity ratio, and x is the conversion oint oset. x can be calculated iteratively by (Zhang 1996) x (new) (x (old) z) 2 ( 2, 1) 2 +(x (old) z) 2 ( 2, 1) : (2) An euivalent medium to a multi-layer model. Consider a stack of n layers with a constant v v s, and each layer has arameters(v k, v sk,t k and t sk ), where v k and v sk are the interval

3 P - and S-velocities, and t k and t sk are the interval P - and S-traveltimes, resectively, in the k-th layer. A euivalent medium can be dened as nx nx vkt 2 k vskt 2 sk ev 2 ; ev nx 2 s ; nx ev ; z ev ev s 1+ t s0; (3) t k t sk where t s0, ev and ev s are the eective PS-wave zero-oset time, P - and S-wave velocities of the euivalent single-layer medium, resectively. The PS-wave travel time from the bottom of the n-layer can then be aroximated as t s 1 s sx ev 2 ev 2 + s0 1+ t + (x, x ) ev 2 ev t s0 : (4) Synthetic tests Euation (4) is a non-hyerbolic euation. If known ev,say, obtained from rocessing of the vertical comonent data, euation (4) can be used to erform non-hyerbolic moveout correction, scanning over and t s0 to build u a sectrum to estimate the v v s ratio, without the need to exand the euation in Taylor series, nor the need for correlation. Although the euivalent-medium aroach is develoed for models with a constant velocity ratio, synthetic tests show that for models with a varying v v s ratio, the aroach can still be alied with sucient accuracy for arameter estimation and data rocessing. Table 1 shows a ve-layer model with v v s varying from 2.5 to 1.82, and Figure 1 shows the corresonding synthetic PS-data and v v s sectra. The v v s ratio can be uniuely determined, and errors are usually small, less than 2% (Table 2). k z k v k v sk Table 1: Model arameters. k t s0k(ms) error(%) Table 2: Comarison of estimated with the model arameters Time(sec) (a) (b) (c) (d) Figure 1: v v s ratio analysis: a synthetic data examle for the model in Table 1. Figure 2: A common receiver gather from the 4C North Sea dataset: (a) hydrohone, (b) inline, (c) crossline and (d) vertical comonents, resectively. (Courtesy of Shell Exloration, UK).

4 A real data examle We resent a 4C-data examle from the North Sea. Yuan et al. (1998) discussed the data characteristics in more detail. The dataset was recorded by the Geco-Prakla dro-drag cable (Figure 2). The following acuisition arameters were used: cable length: 3km; water deth: m; max. oset: 4.4km; source interval: 25m; number of channels (receiver interval in bracket): hydrohone- 60 (25m), vertical geohone - 60 (25m), inline geohone (12.5m), and crossline geohone - 60 (25m); samling rate (2ms); recording: 10 seconds. The rocessing stes are: 1) rocessing the vertical comonent data to obtain P-wave stacking velocities; 2) binning CCPs (common conversion oints) using constant velocity ratio; 3) velocity ratio analysis; 4) nal stack and correlation. As shown in Figure 3, high-uality ratio sectra are obtained which allow uniue determination of the velocity ratio. Such analysis may be erformed for a series of CCPs across the survey line, and a contour ratio section can then be built u (Figure 4). The obtained ratio is a function of t s0, and, combined with the P -wave stacking velocities, a function of t 0, can hel in the correlation of P - and PS-stacked sections (Figures 5 and 6). Note that these stacking velocity ratios reveal the long-wave length v v s relationshi which can be used as an initial inut for short-wave length inversion based on amlitude information. Conclusions The double suare-root euation for calculating P-SV travel time in a single-layer medium can be extended into multi-layered media by the euivalent medium aroach. Avelocity-ratio sectrum can then be obtained from the converted-wave data if the P -wave velocities are known. This allows the uniue determination of the v v s ratio from multicomonent data. Although the aroach assumes a constant velocity ratio, it can be alied, with sucient accuracy, to to cases with dethvarying v v s ratio, as demonstrated by both the synthetic and real data examles. This aroach can also be extended into anisotroic media (Yuan and Li 1998). Acknowledgements We thank Shell Exro for roviding these data. This work has been artly funded by the University of Edinburgh industry-sonsored roject \Processing of Three-comonent Sea Floor Seismic Data,", and by the British Geological Survey (BGS). The work is ublished with the aroval of the Director of BGS. References Behle, A. and Dohr, G., Converted waves in exloration seismics. in Dohr, G., Ed., Seismic shear-waves, Part B: Alications. Geohysical Press 15B, Gaiser, J.E., Multicomonent v v s correlation analysis. Geohysics 61, Iverson, W.P., Fahmy, B.A. and Smithson, S.B., v v s from mode-converted P -SV reections. Geohysics 54, Robertson, J.D., Carbonate orosity from S/P traveltime ratios. Geohysics 52, Tatham, R.H., v v s and lithology. Geohysics 47, Tessmer, G., and Behle, A., 1988, Common reection oint data-stacking for converted waves: Geohys. Pros. 36, Thomsen, L.A., 1998, Converted-wave reection seismology over anisotroic, inhomogeneous media: 68th Internat. Mtg., Soc. Exlor. Geohys., Exanded Abstracts, Yuan, J., and Li, X.-Y., 1998, A new aroach for converted-wave moveout in transversely isotroic media: 68th Internat. Mtg., Soc. Exlor. Geohys., Exanded Abstracts, Yuan, J., X.-Y. Li, Ziolkowski, A. and Strijbos, F. 1998a, Processing 4C sea-oor seismic data: A case examle from the North Sea: 68th Ann. Internat. SEG Mtg., Exanded Abstracts, Zhang, Y., 1996, Nonhyerbolic converted wave velocity analysis and normal moveout: 66th Ann. Internat. SEG Mtg., Exanded Abstracts,

5 Velocity Ratio Figure 3. v v s sectra of selected CCPs for the data shown in Figure 2. The solid line resents the icked velocity ratio curve. Figure 4. The contour v v s ratio section for the North Sea data in Figure 2, obtained from ratio sectra as shown in Figure 3. Figure 5. The nal stacked section of the vertical comonent. Figure 6: The nal stacked section of the horizontal inline comonent.