AccScience Publishing / JSE / Article
Submit to JSE
Cite this article
36
Views
Journal Browser
Volume | Year
Issue
Search
Forthcoming Issue
Current Issue
View All
News and Announcements
View All
ARTICLE

3D seismic interpolation with a low redundancy, fast curvelet transform

JINGJIE CAO1 ,  JINGTAO ZHAO2
Show Less
1 Shijiazhuang University of Economics, Shijiazhuang, Hebei 050031, P.R.China.,
2 Research Institute of Petroleum Exploration & Development, PetroChina, Beijing 100083, P.R.China.,
JSE 2015, 24(2), 121–134;
Submitted: 25 October 2014 | Accepted: 12 December 2014 | Published: 1 May 2015
© 2015 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/ )
Download PDF
Cite
XML
Abstract

Cao, J. and Zhao, J., 2015. 3D seismic interpolation with a low redundancy, fast curvelet transform. Journal of Seismic Exploration, 24: 121-134. Seismic data interpolation is one of the main challenges encountered during pre-processing. It can provide reliable data for processes that require regular and dense sampling, like migration and multiple elimination. At present, a transform method which is based on the sparseness of signals in a transformed domain, is a commonly used strategy to get promising results. Among different transforms, the curvelet transform has optimal sparse expression for wave-fronts, thus it can be seen as a good candidate for seismic interpolation. However, the high redundancy of the 3D curvelet transform makes it computationally expensive, especially for massive data processing. Woiselle et al. (2011) proposed a new implementation of the curvelet transform, which reduces the redundancy to 10 for a 3D transform. In this paper, this new implementation is introduced to improve the computational efficiency of curvelet-based interpolation. The merits of the new implementation are discussed and the low redundancy is proven through numerical tests. Numerical results on 3D interpolation based on the new transform show that the CPU time it costs is about 1/4 of the original curvelet transform. Thus, the Woiselle’s curvelet transform is a good balance between redundancy, rapidity and performance.

Keywords
curvelet transform
seismic interpolation
sparse optimization
one-norm
References
  1. Abma, R. and Kabir, N., 2006. 3D interpolation of irregular data with a POCS algorithm. Geophysics, 71:E91-E97.
  2. Beckouche, S. and Ma, J., 2014. Simultaneous dictionary leanring and denoising for seismic data.Geophysics, 79: A27-A31.
  3. Blumensath, T. and Davies, M., 2008. Iterative thresholding for sparse approximations. J. Fourier Analys.Appl., 14: 629-654.
  4. Candés, E., Demanet, L., Donoho, D. and Ying, L., 2006. Fast discrete curvelet transforms. Multiscale.Model. Sim., 5: 861-899.134 CAO & ZHAO
  5. Candés, E. and Donoho, D., 2000. Curvelets - A surprisingly effective nonadaptive representation for objectswith edges. Vanderbilt Univ. Press: 105-120.
  6. Candés, E. and Donoho, D., 2004. New tight frames of curvelets and optimal representation of objects withpiecewise C2 singularities. Communic. Pure Appl. Mathemat., 57: 219-266.
  7. Cao, J., Wang, Y., Zhao, J. and Yang, C., 2011. A review on restoration of seismic wavefields based onregularization and compressive sensing. Inverse Prob. Sci. Engin., 19: 679-704.
  8. Chauris, H. and Nguyen, T., 2008. Seismic demigration/migration in the curvelet domain. Geophysics, 73:S35-S46.
  9. Chen，S.，Donoho，D. and Saunders, M., 1998. Atomic decomposition by basis pursuit. SIAM J. Sci.Comput., 20: 33-61.
  10. Daubechies, I., Defrise, M. and Mol, C.D., 2004. An iterative thresholding algorithm for linear inverseproblems with a sparsity constraint. Communic. Pure Appl. Mathemat., 57: 1413-1457.
  11. Fomel, S. and Liu, Y., 2010. Seislet transform and seislet frame. Geophysics, 75(3): V25-V38.
  12. Hennenfent, G. and Herrmann, F., 2006. Seismic denoising with non-uniformly sampled curvelets. Comput.Sci. Engin., 8: 16-25.
  13. Herrmann, F. and Hennenfent, G., 2008. Non-parametric seismic data recovery with curvelet frames.Geophys. J. Internat., 173: 233-248.
  14. Herrmann, F., Moghaddam, P. and Stolk, C., 2008a. Sparsity- and continuity-promoting seismic imagerecovery with curvelet frames. Appl. Comput. Harmon. Anal., 24: 50-173.
  15. Herrmann, F., Wang, D., Hennenfent, G. and Moghaddam, P., 2008b. Curvelet-based seismic dataprocessing: a multiscale and nonlinear approach. Geophysics, 73(1): Al-A5.
  16. Kumar, V. and Herrmann, F., 2008. Deconvolution with curvelet-domain sparsity. Expanded Abstr., 78thAnn. Internat. SEG Mtg., Las Vegas: 1996-2000.
  17. Kumar, V., Oueity, J., Clowes, R.M. and Herrmann, F., 2011. Enhancing crustal reflection data throughcurvelet denoising. Tectonophysics, 508: 106-116.
  18. Lin, T. and Herrmann, F., 2013. Robust estimation of primaries by sparse inversion via one-normminimization. Geophysics, 78(3): R133-R150.
  19. Liu, B. and Sacchi, M., 2004. Minimum weighted norm interpolation of seismic records. Geophysics, 69:1560-1568.
  20. Naghizadeh, M., 2009. Parametric reconstruction of multidimensional seismic records. Ph.D. thesis Universityof Alberta, Edmonton.
  21. Neelamani, R., Baumstein, A., Gillard, D., Hadidi, M. and Soroka, W., 2008. Coherent and random noiseattenuation using the curvelet transform. The Leading Edge, 27: 240-248.
  22. Sacchi, M. and Liu. B., 2005. Minimum weighted norm wavefield reconstruction for AVA imaging.Geophys. Prosp., 53: 787-801.
  23. Sacchi, M. and Ulrych, T., 1996. Estimation of the discrete Fourier transform, a linear inversion approach.Geophysics, 61: 1128-1136.
  24. Sacchi. M. and Verschuur, D. and Zwartjes, P., 2004. Data reconstruction by generalized deconvolution.
  25. Expanded Abstr., 74th Ann. Internat. SEG Mtg., Denver: 1989-1992.
  26. Sacchi, M., Ulrych, T. and Walker, C., 1998. Interpolation and extrapolation using a high resolution discrete
  27. Fourier transform. IEEE T. Signal Process., 46: 31-38.
  28. Soubaras, R., 2004. Spatial interpolation of aliased seismic data. Expanded Abstr., 74th Ann. Internat. SEGMtg., Denver: 1167-70.
  29. Starck, J., Candés, E. and Donoho, D., 2002. The curvelet transform for image denoising. IEEE Trans.Image Process., 11: 670-684.
  30. Trad, D., Ulrych, T. and Sacchi, M., 2002. Accurate interpolation with high-resolution time-variant Radontransforms. Geophysics, 67: 644-656.
  31. Tang, G., Ma, J. and Yang, H., 2012. Seismic data denoising based on learning-type overcompletedictionaries. Appl. Geophys., 9: 27-32.
  32. Woiselle, A., Starck, J. and Fadili, J., 2011. 3D Data denoising and inpainting with the low-redundancy fastcurvelet transform. J. Math. Imaging. Vis., 39: 121-139.
  33. Yang, P., Gao, J. and Chen, W., 2012. Curvelet-based POCS interpolation of nonuniformly sampled seismicrecords. J. Appl. Geophys., 79: 90-99.
  34. Yarham, C. and Herrmann, F., 2008. Bayesian ground-roll separation by curvelet-domain sparsity promotion.
  35. Expanded Abstr., 78th Ann. Internat. SEG Mtg., Las Vegas: 3662-3666.
  36. Zwartjes, P. and Gisolf, A., 2006. Fourier reconstruction of marine-streamer data in four spatial coordinates.Geophysics, 71(6): V171-V186.
  37. Zwartjes, P. and Gisolf, A., 2007. Fourier reconstruction with sparse inversion. Geophys. Prosp., 55:199-221.
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here
Accept