ARTICLE

Cascaded deconvolution filters

LAURENCE R. LINES1 SVEN TREITEL2
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1 Department of Geoscience, University of Calgary, Calgary, Alberta, Canada T2N 1N4.,
2 TriDekon Inc., Tulsa, OK 74114, U.S.A.,
JSE 2018, 27(6), 543–554;
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

Lines, L.R. and Treitel, S., 2018. Cascaded deconvolution filters. Journal of Seismic Exploration, 27: 543-556. There are few seismic wavelets that have an exact inverse filter for deconvolution, but one of these is an exponentially damped sinusoid. As shown by Lines and Treitel, this wavelet has an exact 3-term inverse. Unlike most seismic wavelets, a Wiener deconvolution filter can be designed that shapes this wavelet to an output that is a nearly perfect spike. For the majority of seismic wavelets where a perfect spike is not achievable, one can shape the actual wavelet to an exponentially damped sinusoid prior to the application of a Wiener filter that will spike the exponentially damped wavelet. This appears to hold some promise, as shown by a computational example.

Keywords
seismic deconvolution
seismic wavelets
Wiener filtering
References
  1. Dey, A., 1999. An analysis of seismic wavelet estimation, M.Sc. thesis, University of
  2. Calgary.
  3. Lines, L. and Treitel, S., 1983. Digital filtering with the second moment norm.
  4. Geophysics, 48: 508-513.
  5. Papoulis, A., 1962. The Fourier Integral and its Applications. McGraw-Hill Book Co.
  6. Inc., New York.
  7. Robinson, E.A., 1954. Predictive Decomposition of Time Series with Application to
  8. Seismic Exploration. Ph.D. thesis, Massachusetts Institute of Technology,
  9. Cambridge.
  10. Robinson, E.A., 1967. Statistical Communication and Detection. Hafner Publishing Co.,
  11. New York.
  12. Robinson, E.A. and Treitel, S., 2008. Digital Imaging and Deconvolution. The ABCs of
  13. Seismic Exploration and Processing. SEG, Tulsa, OK.
  14. Treitel, S. and Lines, L.R., 1982. Linear inverse theory and deconvolution. Geophysics,
  15. 47: 1153-1159.
  16. Robinson, E.A., 1967. Statistical Communication and Detection. Hafner Publishing Co.,
  17. New York.
  18. Robinson, E.A. and Treitel, S., 2008. Digital Imaging and Deconvolution. The ABCs of
  19. Seismic Exploration and Processing. SEG, Tulsa, OK.
  20. Treitel, S. and Lines, L.R., 1982. Linear inverse theory and deconvolution. Geophysics,
  21. 47: 1153-1159.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing