News and Announcements
ARTICLE
3D post-stack one-way migration using curvelets
BINGBING SUN1,2 ,
HERVÉ CHAURIS2,3 ,
JIANWEI MA1
Show Less
1
Institute of Seismic Exploration, School of Aerospace, Tsinghua University, Beijing 100084, P.R. China.,
2
Centre de Géosciences, Mines Paristech, 35 rue Saint-Honoré, 77300 Fontainebleau, France.,
3
UMR-Sisyphe 7619, France.,
JSE 2011, 20(3), 257–271;
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
Sun, B., Chauris, H. and Ma, J., 2011. 3D post-stack one-way migration using curvelets. Journal of Seismic Exploration, 20: 257-271. The classical one-way approximation extrapolates the wavefield from the surface. At each depth level, time shifts are applied in the spatial and wavenumber domains. These shifts are function of the local velocity model. In this paper, following the same strategy as the beamlet migration, we formulate the split-step Fourier method in the curvelet domain. Curvelets are fairly local in the spatial and wavenumber domains, justifying the use of local velocity values in the one-way strategy. In practice, the wavefield is decomposed into 2D curvelets at each extrapolation depth and for fixed frequencies. The derivation is validated through an application on 3D zero-offset migration in a heterogeneous model. This work should be understood as an important step towards a better understanding of the wave propagation in a multi-scale and multi-directional perspective.
Keywords
migration
curvelets
3D
post-stack
References
- Aminzadeh, F., Brac, J. and Kunz, T., 1997. 3-D Salt and Overthrust Models. SEG, Tulsa.
- Candés, E. and Demanet, L., 2005. The curvelet representation of wave propagators is optimally
- sparse. Communic. Pure Appl. Mathemat., 58: 1472-1528.
- Candés, E., Demanet, L., Donoho, D. and Ying, L., 2006. Fast discrete curvelet transform. SIAM
- Multiscale Model. Simulat., 5: 861-899.
- Candés, E. and Donoho, D., 2004. New tight frames of curvelets and optimal representations of
- objects with C? singularities. Communic. Pure Appl. Mathemat., 57: 219-266.
- Cao, J. and Wu, R., 2009. Fast acquisition aperture correction in prestack depth migration using
- beamlet decomposition. Geophysics, 74: S67-S74.
- Cerveny, V. (Ed.), 2001. Seismic Ray Tracing. Cambridge University Press, Cambridge.
- Chauris, H. and Nguyen, T., 2008. Seismic demigration/migration in the curvelet domain.
- Geophysics, 73: S35-S46.
- Chen, L., Wu, R. and Chen, Y., 2006. Target-oriented beamlet migration based on
- Gabor-Daubechies frame decomposition. Geophysics, 71: $37-S52.
- Douma, H. and de Hoop, M.V., 2007. Leading-order seismic imaging using curvelets. Geophysics,
- 72: §231-S248.
- Ferguson, R., 2005. A quantitative comparison of one-way extrapolation operators. J. Seismic
- Explor., 14: 75-104.
- Gazdag, J., 1981. Modeling of the acoustic wave equation with transform methods. Geophysics, 46:
- 854-859.
- Gazdag, J. and Sguazzero, P., 1984. Migration of seismic data by phase shift plus interpolation.
- Geophysics, 49: 124-131.
- Herrmann, F.J., Wang, D. and Verschuur, D.J., 2008. Adaptive curvelet-domain primary-multiple
- separation. Geophysics, 73: A17-A21.
- Le Rousseau, J. and de Hoop, M., 2001. Modeling and imaging with the scalar generalized-screen
- algorithms in isotropic media. Geophysics, 66: 1551-1568.
- Liu, L. and Zhang, J., 2006. 3D wavefield extrapolation with optimum split-step Fourier method.
- Geophysics, 71: 95-108.
- Lowenthal, D., Lu, L., Robertson, R. and Sherwood, J., 1976. The wave equation applied to
- migration. Geophys. Prosp., 24: 380-399.
- Ma, J. and Plonka, G., 2010. The curvelet transform: a review of recent applications. IEEE Signal
- Proc. Magaz., 27: 118-133.
- Margrave, G. and Ferguson, R., 1999. Wavefield extrapolation by nonstationary phase shift.
- Geophysics, 64: 1067-1078.
- 3D POST-STACK MIGRATION 271
- Noble, M., 1992. Inversion non linéaire de Données de Prospection Petroliere. Ph.D. thesis,
- Université Paris 7, Paris.
- Steinberg, B., 1993. Evolution of local spectra in smoothly varying nonhomogeneous environments -
- local canonization and marching algorithms. J. Acoust. Soc. Am., 93: 2566-2580.
- Steinberg, B. and Birman, R., 1995., Phase-space marching algorithm in the presence of a planar
- wave velocity discontinuity - a qualitative study. J. Acoust. Soc. Am., 98: 484-494.
- Stoffa, P.L., Fokkema, J.T., de Luna Freire, R. and Kessinger, W., 1990. Split-step Fourier
- migration. Geophysics, 55: 410-421.
- Sun, B., Ma, J., Chauris, H. and Yang, H., 2009. Solving wave equations in the curvelet domain:
- a multi-scale and multi-directional approach. J. Seismic Explor., 18: 385-399.
- Wu, R. and Chen, L., 2001. Beamlet migration using Gabor-Daubechies frame propagator.
- Extended Abstr., 63rd EAGE Conf., Amsterdam: 74.
- Wu, R., Wang, Y. and Luo, M., 2008. Beamlet migration using local cosine basis. Geophysics, 73:
- $207-S217.
- Wu, R.S. and Jin, S., 1997. Windowed GSP (generalized screen propagators) migration applied to
- SEG-EAGE salt model data. Expanded Abstr., 67th Ann. Internat. SEG Mtg., Dallas: 937-
