JSEJournal of Seismic Exploration0963-0651AccScience PublishingArticleP-P wave and P-S converted wave separation and de-noising combining with SVD and f-k filteringhttps://geophysical-press.com/journal/JSE/articles/249SHENHONGYAN,PANLI,LIQINGCHUN,YANYUEYING,ZHANGBAOWEI20162522016-04-01Shen, H., Pan, L., Li, Q., Yan, Y. and Zhang, B., 2016. P-P wave and P-S converted wave separation and de-noising combining with SVD and f-k filtering. Journal of Seismic Exploration, 25: 147-162. Wave model separation and de-noising of P-P waves and P-S converted waves is a vital task in seismic data processing. In a multi-mode seismic wave field, P-P waves have the dissimilar characteristics in comparison with other seismic signals: the energy is relatively strong, and the propagation law and coherence are more obvious to be observed (with a hyperbolic law). As for P-S converted events, they have large differences in velocity and frequency characteristics compared to other seismic wave modes. This article puts forward a P-P wave, P-S converted wave separation and de-noising workflow by combining Singular Value Decomposition (SVD) and f-k filtering. First, align P-P waves by NMO correction to make they achieve the best coherence in the transverse direction. Then, by extracting the singular values of the P-P waves through SVD, the P-P waves can be separated. Finally, by using an f-k filtering method, P-S converted waves and other noises can be separated. In this way, the complementary advantages of the SVD and the f-k filtering techniques are combined in wave field separation and de-noising, and can avoid the ineffectiveness in separation the P-P waves and P-S converted waves by only SVD or only an f-k filtering technique. Model and actual seismic data have been processed with this method, and good results have been achieved.Singular Value Decomposition (SVD), f-k filtering, P-P waves, P-S converted waves, seismic wave field separation, de-noising

Adizua, O.F., Ebeniro, J.O. and Ehirim, C.N., 2015. Application of the Frequency- Wave Number(F-K) and the Radial Trace Transform (RTT) in the Attenuation of Coherent Noise inOnshore Seismic Data. Asian J. Earth Sci., 8: 15-23. doi: 10.3923/ajes.2015.15.23.Artola, F.A.V., Leiderman, R., Fontoura, $.A.B. and Silva, M.B.C., 2004. P-S converted wave:conversion point and zero-offset energy in anisotropic media. J. Appl. Geophys., 56:155-163. doi: 10.1016/j.jappgeo.2004.04. 007.Askari, R. and Siahkoohi, H.R., 2008. Ground roll attenuation using the S and x-f-k transforms.Geophys. Prosp., 56: 105-114. doi: 10.1111/j.1365- 2478.2007.00659.xBekara, M. and Baan, M.V., 2007. Local singular value decomposition for signal enhancement ofseismic data. Geophysics, 72(2): V59-65. doi: 10.1190/1. 2435967.Chiu, S.K. and Howell, J.E., 2008. Attenuation of coherent noise using localized-adaptiveeigenimage filter. Expanded Abstr., 78th Ann. Internat. SEG Mtg., Las Vegas: 2541-2545.doi: 10.1190/1.3063871.Cooley, J.W. and Tukey, J.W., 1965. An algorithm for the machine calculation of complex Fourierseries. Mathemat. Computat., 19: 296-301. http://www.jstor.org/stable/2003354.DeAngelo, M.V., Remington, R., Murray, P.E., Hardage, B.A., Graebner, R. and Fouad, K.,Multicomponent seismic technology for imaging deep gas prospects. The LeadingEdge, 23: 1270-1281. doi:10.1190/leedff.23.1270_1.P-P WAVE & P-S CONVERTED WAVE SEPARATION 161Duncan, G. and Beresford, G., 1994. Slowness adaptive f-k filtering of prestack seismic data.Geophysics, 50: 140-147. doi: 10.1190/1.1443525.Embree, P., Burg, J.P. and Backus, M.M., 1963. Wide-band velocity filtering: The pie-sliceprocess. Geophysics, 28, 948-974. doi: 10.1190/1.1439310.Fail, J.P. and Grau, G., 1963. Les filters en eventail. Geophys. Prosp., 11: 131-163.doi: 10.1111/j.1365-2478.1963.tb02031.x.Franco, R. and Musacchio, G., 2001. Polarization filter with singular value decomposition.Geophysics, 66: 932-938. doi: 10.1190/1.1444983.Freire, S.L.M. and Ulrych, T.J., 1988. Application of singular value decomposition to verticalseismic profiling. Geophysics, 53: 778-785. doi: 10.1190/1. 1442513.Gao, L., Chen, W., Wang, B. and Gao, J., 2013. Zero-offset VSP wavefield separation usingtwo-step SVD approach (in Chinese). Chin. J. Geophys., 56: 1667-1675.doi: 10.6038/cjg20130524.Grechka, V., and Tsvankin, I., 2002. PP+PS=SS. Geophysics, 67: 1961-1971. doi:1190/1.1527096.Hemon, C.H. and Mace, D., 1978. The use of the Karhunen-Loeve transformation in seismic dataprocessing. Geophys. Prosp., 26: 600-626. doi: 10.1111 /j.1365-2478.1978.tb01620.x.Jackson, G.M., Mason, I.M. and Greenhalgh, S.A., 1991. Principal component transforms oftriaxial recordings by singular value decomposition. Geophysics, 56: 528-533.doi: 10.1190/1.1443068.Jones, I.F. and Levy, S., 1987. Signal-to-noise ratio enhancement in multichannel seismic data viathe Karhunen-Loeve transform. Geophys. Prosp., 35(1): 12-32.doi: 10.1111/j.1365-2478.1987.tb00800.x.Li, X., Dai, H., Mueller, M.C. and Barkved, O.I., 2001. Compensating for the effects of gasclouds on C-wave imaging: A case study from Valhall. The Leading Edge, 20: 1022-1028.doi: 10.1190/1.1487307.Li, X. and Yuan, J., 2003. Converted-wave moveout and conversion-point equations in layered VTImedia: theory and applications. J. Applic. Geophys., 54: 297-318.doi: 10.1016/j.jappgeo.2003.02.001.Lu, R.S., Willen, D.E. and Watson, I.A., 2003. Identifying, removing, and imaging P-Sconversions at salt-sediment interfaces. Geophysics, 68: 1052-1059. doi: 10.1190/1.1581076.Meier, M.A. and Lee, P.J., 2009. Converted-wave resolution. Geophysics, 74(2): Q1-Q16.doi: 10.1190/1.3074303.Porsani, M.J., Silva, M.G. and Melo, P.E.M, 2009: Ground-roll attenuation based on SVDfiltering. Expanded Abstr., 79th Ann. Internat. SEG Mtg., Houston: 3381-3385.doi: 10.1190/1.3255563.Sengbush, R.L. and Foster, M.R., 1968. Optimum multichannel velocity filters. Geophysics, 33:11-35. doi: 10.1190/1.1439913.Shen, H. and Li, Q., 2008. Seismic wave fields separation and noise attenuation in frequencydomain via singular value decomposition. Proc. 3rd Internat. Conf. Environ. Engineer.Geophys., Near-Surf. Geophys. Human Activ., Wuhan: 178-181.Shen, H. and Li, Q., 2009. Seismic wave field separation and noise attenuation in linear domain viaSVD. Expanded Abstr., 79th Ann. Internat. SEG Mtg., Houston: 3386-3389.doi: 10.1190/1.3255564.Shen, H. and Li, Q., 2010. SVD (Singular Value Decomposition) seismic wave field noiseelimination (in Chinese). Oil Geophys. Prosp., 45: 185-189.Shen, H. and Li, Q., 2012a. Seismic wave field separation and de-noising in linear domain viasingular value decomposition (SVD) (in Chinese). J. China Coal Soc., 37: 627-633.Shen, H. and Li, Q., 2012b. Seismic wavefield separation and de-noising for P-P wave and P-Swave by singular value decomposition (SVD) (in Chinese). Oil Geophys. Prosp., 47:690-697.Stewart, R.R., Gaiser, J.E., Brown, R.J. and Lawton, D.C., 2003. Converted-wave seismicexploration. Applicat. Geophys., 68: 40-57. doi: 10.1190/1. 1543193.162 SHEN, PAN, LI, YAN & ZHANGTreitel, S., Shanks, J.L. and Frasier, C.W., 1967. Some aspects of fan filtering. Geophysics, 32:789-800. doi: 10.1190/1.1439889.Vrabie, V.D., Le-Bihan, N. and Mars, J.L., 2006. Multicomponent wave separation usingHOSVD/unimodal ICA subspace method. Geophysics, 71(5): V133-V143.doi: 10.1190/1.2435967.Wiggins, R.A., 1966. w-k filter design. Geophys. Prosp., 14: 427-440.doi: 10.1111/j.1365-2478.1966.tb02246.x.Yan, Y., Xu, Z., Yi, M. and Wei, X., 2012. Application of 3D vertical seismic profilemulti-component data to tight gas sands. Geophys. Prosp., 60: 138-152.doi: 10.1111/j.1365-2478.2011.00978.x.Yilmaz, O., 2001. Seismic Data Analysis. SEG, Tulsa, OK.Zhao, B., Wang, D., Shi, S., Shen, L., Miao, X. and Wang, P., 2011. Three-componentconverted-wave data inversion and application: A case study of Sulige gas field, China.Expanded Abstr., 81st Ann. Internat. SEG Mtg., San Antonio: 1759-1763.doi: 10.1190/1.3627546.Zhou, B. and Greenhalgh, S.A., 1994. Wave-equation extrapolation-based multiple attenuation: 2-Dfiltering in the f-k domain. Geophysics, 59: 1377-1391. doi: 10.1190/1.1443696.