Abstract
We provide a new theoretical contribution to the geophysical signal processing on how the ghost operator can be approximately analytically modeled. We derive a time-space-domain receiver ghost modeling operator for a wavefront traveling under a flat sea surface. The operator can be used to model the ghost wavefront on the native acquisition geometry without going into the temporal or spatial Fourier domain. We demonstrate the ghost operator with a multivariate generalization of the Gaussian function in conjunction with a hyperbolic traveltime function and compared it with modeled Green’s functions. This multivariate special function was specifically conceived for seismic data decomposition and promotes the signal cone of the data. Its composition with the hyperbolic traveltime function also ensures signal cone preservation and stable ghost operator computation. The ghost model derived is valid independent of streamer depth, i.e., for shallow as well as deep towed-streamer geometry, and it can also be extended to the source ghost. The proposed method, when combined with an appropriate data decomposition approach, provides a step toward developing deghosting algorithms in the native acquisition geometry with minimal user-defined parameters.
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References
Amundsen, L.: Wavenumber-based filtering of marine point-source data. Geophysics 58, 1335–1348 (1993)
Caprioli, P., Roth, J., Rickett, J., Vassallo, M.: Joint adaptive deghosting and designature. In: 81st EAGE Conference and Exhibition 2019, European Association of Geoscientists & Engineers, pp. 1–5 (2019)
Engquist, B., Zhao, H.: Approximate separability of the Green’s function of the Helmholtz equation in the high frequency limit. Commun. Pure Appl. Math. 71, 2220–2274 (2018)
Gelfand, I., Shilov, G.: Generalized Functions: Properties and operations, by IM Gel’fand and GE Shilov, translated by E. Saletan. Academic Press, Cambridge (1964)
Olver, F.W., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions Hardback and CD-ROM. Cambridge university press, Cambridge (2010)
Özdemir, A.K., Caprioli, P., Özbek, A., Kragh, E., Robertsson, J.O.: Optimized deghosting of over/under towed-streamer data in the presence of noise. Lead. Edge 27, 190–199 (2008)
Posthumus, B.J.: Deghosting using a twin streamer configuration. Geophys. Prospect. 41, 267–286 (1993)
Rickett, J.: Successes and challenges in 3d interpolation and deghosting of single-component marine-streamer data. In: SEG Technical Program Expanded Abstracts 2014: Society of Exploration Geophysicists, pp. 3599–3604 (2014)
Rickett, J., van Manen, D., Loganathan, P., Seymour, N.: Slanted-streamer data-adaptive deghosting with local plane waves: Presented at the 76th EAGE Conference and Exhibition 2014 (2014)
Sønneland, L., Berg, L.E., Eidsvig, P., Haugen, A., Fotland, B., Vestby, J.: 2-d deghosting using vertical receiver arrays. In: SEG Technical Program Expanded Abstracts 1986. Society of Exploration Geophysicists, pp. 516–519 (1986)
Yarman, C.E., Kumar, R., Rickett, J.: A model-based data-driven dictionary learning for seismic data representation. Geophys. Prospect. 66, 98–123 (2017)
Yarman, E., Ramírez, A.C.: Directional wavefield decomposition. Geophysics 78, WA71–WA76 (2013)
Acknowledgements
We thank James Rickett and Kemal Øzdemir for fruitful discussions. We thank Schlumberger for permitting to publish this work.
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Yarman, C.E. Time-space modeling of receiver ghost in the native acquisition coordinates: a step toward a non-Fourier-based deghosting. SIViP 17, 1661–1667 (2023). https://doi.org/10.1007/s11760-022-02376-z
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DOI: https://doi.org/10.1007/s11760-022-02376-z