Abstract
Surface-related multiples prediction by inverse scattering series (ISS) is a completely data-driven method, which does not require a priori subsurface velocity information, and has the advantage of being suitable for complex structures compared with model-driven methods based on wave equations. But its computation and memory requirement are substantial. We propose a high-efficiency algorithm for the prediction of surface-related multiples by ISS in the curvelet domain. Firstly, we perform curvelet transform (CT) on shot gathers; secondly, we select few curvelet coefficient matrices for surface-related multiple prediction by ISS; thirdly, we perform inverse CT to the predicted multiples in the curvelet domain; lastly, we use matched filtering and subtraction to obtain primaries. Numerical experiments show that the proposed method not only improves computational efficiency and saves memory, but also achieves the same results compared with conventional ISS.
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Araujo, F.V., Weglein A. B., Carvalho, P.M., and Stolt, R.H., Inverse scattering series for multiple attenuation: An example with surface and internal multiples, SEG Technical Program Expanded Abstracts, 1994, 1039–1041. https://doi.org/10.1190/geo2017-0173.1
Berkhout A J. Seismic migration: Imaging of acoustic energy by wavefield extrapolation. Elsevier Science Publ. Co., Inc., 1982. https://doi.org/10.1016/0040-1951(85)90080-0
Berkhout, A. J., & Verschuur, D. J. (1997a). Estimation of multiple scattering by iterative inversion Part i: Theoretical Considerations. Geophysics, 62(5), 1586–1595. https://doi.org/10.1190/1.1444261
Berkhout, A. J., & Verschuur, D. J. (1997b). Estimation of multiple scattering by iterative inversion, Part II: Practical aspects and examples. Geophysics, 62(5), 1596–1611. https://doi.org/10.1190/1.1444262
Berryhill, J. R., & Kim, Y. C. (1986). Deep-water peglegs and multiples: emulation and suppression. Geophysics, 51, 2177–2184. https://doi.org/10.1190/1.1442070
Candes, E., & Donoho, D. (2004). New tight frames of and optimal representations of objects with piecewise C2 singularities. Communications on Pure and Applied Mathematics, 57(2), 219–266. https://doi.org/10.1002/cpa.10116
Claerbout, J. F. (1968). Synthesis of a layered medium from its acoustic transmission response. Geophysics, 33(2), 264–269. https://doi.org/10.1190/1.1439927
Dragoset B. A practical approach to surface multiple attenuation. The Leading Edge, 1999, 104–108. https://doi.org/10.1190/1.1820117
Duncan, G., & Beresford, G. (1994). Slowness adaptive F-K filtering of prestack seismic data. Geophysics, 59(1), 140–147. https://doi.org/10.1190/1.1443525
Embree, P., Burg, J. B., & Backus, M. M. (1963). Wide-band velocity filtering—the pie-slice process. Geophysics, 16(1), 63–80. https://doi.org/10.1190/1.1439310
Herrmann, Felix J.; Gilles Hennenfent, Non-parametric seismic data recovery with curvelet frames. Geophysical Journal International , 2008, 173(4): 233–248. https://doi.org/10.1111/j.1365-246X.2007.03698.x
Herrmann, Felix J., Wang, Deli, Verschuur, Dirk J. Adaptive curvelet-domain primary-multiple separation. Geophysics, 2008, 73(3):A17–A21. http://dx.doi.org/https://doi.org/10.1190/1.2904986
Kelamis, P. G. (2000). Surface-related multiple elimination on land seismic data-strategies via case studies. Geophysics, 65, 719–734. https://doi.org/10.1190/1.1444771
Li, X., & Hu, T. Y. (2009). Surface-related multiple removal with inverse scattering series method Chinese J. Geophysics, 52(6), 1633–1640. https://doi.org/10.3969/j.issn.0001-5733.2009.06.026
March, D. W., & Bailey, A. D. (1983). A review of the two-dimensional transform and its use in seismic processing. First Break, 1, 9–21. https://doi.org/10.3997/1365-2397.1983001
R T, Formal solutions of inverse scattering problems I, Journal of Mathematical Physics,1968,1819–1822. https://doi.org/10.1063/1.1664766
Ryu, J. V. (1982). Decomposition (DECOM) approach applied to wave field analysis with seismic reflection records. Geophysics, 47(6), 869–883. https://doi.org/10.1190/1.1441354
Tim T.Y. Lin ∗ and Felix J. Herrmann. Compressed wavefield extrapolation,Geophysics, 2007,72(5):1997. https://doi.org/10.1190/1.2792882
Verschuur D. J, Berkhout A J., and C.P.A. Wapenaar, Adaptive surface-related multiple elimination. Geophysics, 1992, 57: 1166–1177. http://dx.doi.org/https://doi.org/10.1190/1.1443330
Wapenaar, Thorbecke. Marchenko imaging,Geophysics, 2014, Vol, 79(3): WA39–WA57. https://doi.org/10.1190/geo2013-0302.1
Weglein A. B., Fernanda V Araujo. An inverse-scattering series method for attenuating multiples in seismic reflection data. Geophysics, 1997. 62:1975–1989. https://doi.org/10.1190/1.1444298
Weglein A. B., Robert H Stolt., Topical review: Inverse scattering series and seismic exploration, Inverse Problems, 2003, 19, 27–83. https://doi.org/10.1088/0266-5611/19/6/R01
Weglein, A. B. (1999). Multiple attenuation: an overview of recent advances and the road ahead. The Leading Eage, 18(1), 40–44. https://doi.org/10.1190/1.1438150
Wiggins J, W., Attenuation of complex water-bottom multiples by wave-equation-based predication and subtraction. Geophysics, 1988, 53: 1527–1539. https://doi.org/10.1190/1.1442434
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This research is funded by the National Natural Science Foundation of China (grant no. 41630964). We appreciate the editors and reviewers for the critical and constructive comments, which significantly improved the quality of this paper.
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Zhang, B., Geng, J. High-Efficiency Prediction of Surface-Related Multiples by Inverse Scattering Series in the Curvelet Domain. Pure Appl. Geophys. 179, 2201–2214 (2022). https://doi.org/10.1007/s00024-022-03033-9
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DOI: https://doi.org/10.1007/s00024-022-03033-9