ARTICLE

P-P wave and P-S converted wave separation and de-noising combining with SVD and f-k filtering

HONGYAN SHEN1,2 LI PAN2 QINGCHUN LI3 YUEYING YAN1 BAOWEI ZHANG4
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2 Mewbourne College of Earth and Energy, University of Oklahoma, Norman, OK 73019, U.S.A.,
4 Langfang Geophysical and Geochemical Exploration Institute, Langfang, Hebei 065000, P.R. China.,
JSE 2016, 25(2), 147–162;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

Shen, 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.

Keywords
Singular Value Decomposition (SVD)
f-k filtering
P-P waves
P-S converted waves
seismic wave field separation
de-noising
References
  1. Adizua, O.F., Ebeniro, J.O. and Ehirim, C.N., 2015. Application of the Frequency- Wave Number
  2. (F-K) and the Radial Trace Transform (RTT) in the Attenuation of Coherent Noise in
  3. Onshore Seismic Data. Asian J. Earth Sci., 8: 15-23. doi: 10.3923/ajes.2015.15.23.
  4. Artola, F.A.V., Leiderman, R., Fontoura, $.A.B. and Silva, M.B.C., 2004. P-S converted wave:
  5. conversion point and zero-offset energy in anisotropic media. J. Appl. Geophys., 56:
  6. 155-163. doi: 10.1016/j.jappgeo.2004.04. 007.
  7. Askari, R. and Siahkoohi, H.R., 2008. Ground roll attenuation using the S and x-f-k transforms.
  8. Geophys. Prosp., 56: 105-114. doi: 10.1111/j.1365- 2478.2007.00659.x
  9. Bekara, M. and Baan, M.V., 2007. Local singular value decomposition for signal enhancement of
  10. seismic data. Geophysics, 72(2): V59-65. doi: 10.1190/1. 2435967.
  11. Chiu, S.K. and Howell, J.E., 2008. Attenuation of coherent noise using localized-adaptive
  12. eigenimage filter. Expanded Abstr., 78th Ann. Internat. SEG Mtg., Las Vegas: 2541-2545.
  13. doi: 10.1190/1.3063871.
  14. Cooley, J.W. and Tukey, J.W., 1965. An algorithm for the machine calculation of complex Fourier
  15. series. Mathemat. Computat., 19: 296-301. http://www.jstor.org/stable/2003354.
  16. DeAngelo, M.V., Remington, R., Murray, P.E., Hardage, B.A., Graebner, R. and Fouad, K.,
  17. Multicomponent seismic technology for imaging deep gas prospects. The Leading
  18. Edge, 23: 1270-1281. doi:10.1190/leedff.23.1270_1.
  19. P-P WAVE & P-S CONVERTED WAVE SEPARATION 161
  20. Duncan, G. and Beresford, G., 1994. Slowness adaptive f-k filtering of prestack seismic data.
  21. Geophysics, 50: 140-147. doi: 10.1190/1.1443525.
  22. Embree, P., Burg, J.P. and Backus, M.M., 1963. Wide-band velocity filtering: The pie-slice
  23. process. Geophysics, 28, 948-974. doi: 10.1190/1.1439310.
  24. Fail, J.P. and Grau, G., 1963. Les filters en eventail. Geophys. Prosp., 11: 131-163.
  25. doi: 10.1111/j.1365-2478.1963.tb02031.x.
  26. Franco, R. and Musacchio, G., 2001. Polarization filter with singular value decomposition.
  27. Geophysics, 66: 932-938. doi: 10.1190/1.1444983.
  28. Freire, S.L.M. and Ulrych, T.J., 1988. Application of singular value decomposition to vertical
  29. seismic profiling. Geophysics, 53: 778-785. doi: 10.1190/1. 1442513.
  30. Gao, L., Chen, W., Wang, B. and Gao, J., 2013. Zero-offset VSP wavefield separation using
  31. two-step SVD approach (in Chinese). Chin. J. Geophys., 56: 1667-1675.
  32. doi: 10.6038/cjg20130524.
  33. Grechka, V., and Tsvankin, I., 2002. PP+PS=SS. Geophysics, 67: 1961-1971. doi:
  34. 1190/1.1527096.
  35. Hemon, C.H. and Mace, D., 1978. The use of the Karhunen-Loeve transformation in seismic data
  36. processing. Geophys. Prosp., 26: 600-626. doi: 10.1111 /j.1365-2478.1978.tb01620.x.
  37. Jackson, G.M., Mason, I.M. and Greenhalgh, S.A., 1991. Principal component transforms of
  38. triaxial recordings by singular value decomposition. Geophysics, 56: 528-533.
  39. doi: 10.1190/1.1443068.
  40. Jones, I.F. and Levy, S., 1987. Signal-to-noise ratio enhancement in multichannel seismic data via
  41. the Karhunen-Loeve transform. Geophys. Prosp., 35(1): 12-32.
  42. doi: 10.1111/j.1365-2478.1987.tb00800.x.
  43. Li, X., Dai, H., Mueller, M.C. and Barkved, O.I., 2001. Compensating for the effects of gas
  44. clouds on C-wave imaging: A case study from Valhall. The Leading Edge, 20: 1022-1028.
  45. doi: 10.1190/1.1487307.
  46. Li, X. and Yuan, J., 2003. Converted-wave moveout and conversion-point equations in layered VTI
  47. media: theory and applications. J. Applic. Geophys., 54: 297-318.
  48. doi: 10.1016/j.jappgeo.2003.02.001.
  49. Lu, R.S., Willen, D.E. and Watson, I.A., 2003. Identifying, removing, and imaging P-S
  50. conversions at salt-sediment interfaces. Geophysics, 68: 1052-1059. doi: 10.1190/1.1581076.
  51. Meier, M.A. and Lee, P.J., 2009. Converted-wave resolution. Geophysics, 74(2): Q1-Q16.
  52. doi: 10.1190/1.3074303.
  53. Porsani, M.J., Silva, M.G. and Melo, P.E.M, 2009: Ground-roll attenuation based on SVD
  54. filtering. Expanded Abstr., 79th Ann. Internat. SEG Mtg., Houston: 3381-3385.
  55. doi: 10.1190/1.3255563.
  56. Sengbush, R.L. and Foster, M.R., 1968. Optimum multichannel velocity filters. Geophysics, 33:
  57. 11-35. doi: 10.1190/1.1439913.
  58. Shen, H. and Li, Q., 2008. Seismic wave fields separation and noise attenuation in frequency
  59. domain via singular value decomposition. Proc. 3rd Internat. Conf. Environ. Engineer.
  60. Geophys., Near-Surf. Geophys. Human Activ., Wuhan: 178-181.
  61. Shen, H. and Li, Q., 2009. Seismic wave field separation and noise attenuation in linear domain via
  62. SVD. Expanded Abstr., 79th Ann. Internat. SEG Mtg., Houston: 3386-3389.
  63. doi: 10.1190/1.3255564.
  64. Shen, H. and Li, Q., 2010. SVD (Singular Value Decomposition) seismic wave field noise
  65. elimination (in Chinese). Oil Geophys. Prosp., 45: 185-189.
  66. Shen, H. and Li, Q., 2012a. Seismic wave field separation and de-noising in linear domain via
  67. singular value decomposition (SVD) (in Chinese). J. China Coal Soc., 37: 627-633.
  68. Shen, H. and Li, Q., 2012b. Seismic wavefield separation and de-noising for P-P wave and P-S
  69. wave by singular value decomposition (SVD) (in Chinese). Oil Geophys. Prosp., 47:
  70. 690-697.
  71. Stewart, R.R., Gaiser, J.E., Brown, R.J. and Lawton, D.C., 2003. Converted-wave seismic
  72. exploration. Applicat. Geophys., 68: 40-57. doi: 10.1190/1. 1543193.
  73. 162 SHEN, PAN, LI, YAN & ZHANG
  74. Treitel, S., Shanks, J.L. and Frasier, C.W., 1967. Some aspects of fan filtering. Geophysics, 32:
  75. 789-800. doi: 10.1190/1.1439889.
  76. Vrabie, V.D., Le-Bihan, N. and Mars, J.L., 2006. Multicomponent wave separation using
  77. HOSVD/unimodal ICA subspace method. Geophysics, 71(5): V133-V143.
  78. doi: 10.1190/1.2435967.
  79. Wiggins, R.A., 1966. w-k filter design. Geophys. Prosp., 14: 427-440.
  80. doi: 10.1111/j.1365-2478.1966.tb02246.x.
  81. Yan, Y., Xu, Z., Yi, M. and Wei, X., 2012. Application of 3D vertical seismic profile
  82. multi-component data to tight gas sands. Geophys. Prosp., 60: 138-152.
  83. doi: 10.1111/j.1365-2478.2011.00978.x.
  84. Yilmaz, O., 2001. Seismic Data Analysis. SEG, Tulsa, OK.
  85. Zhao, B., Wang, D., Shi, S., Shen, L., Miao, X. and Wang, P., 2011. Three-component
  86. converted-wave data inversion and application: A case study of Sulige gas field, China.
  87. Expanded Abstr., 81st Ann. Internat. SEG Mtg., San Antonio: 1759-1763.
  88. doi: 10.1190/1.3627546.
  89. Zhou, B. and Greenhalgh, S.A., 1994. Wave-equation extrapolation-based multiple attenuation: 2-D
  90. filtering in the f-k domain. Geophysics, 59: 1377-1391. doi: 10.1190/1.1443696.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing