Advertisement

Post-stack high-resolution deconvolution using Cauchy norm regularization with FX filter weighting

  • Hakan Karslı
  • Recep Güney
  • Mustafa Senkaya
Original Paper
  • 123 Downloads

Abstract

High-resolution deconvolution can mathematically be viewed as a regularized inverse problem. Besides, the result of the high-resolution deconvolution is generally accepted as reflectivity series of the layered media. On the other hand, lateral continuity is frequently poorer than vertical resolution on post-stack seismic section after application of any high-resolution deconvolution. However, because of the ill-posed inherent of the deconvolution problem, the Cauchy norm regularization term, a non-quadratic prior-information is widely used to provide the stability and uniqueness of the problem. But, it does not provide adequate quality of deconvolution if the noise in the data is strong. In this study, a stable and high-resolution deconvolution of post-stack seismic data was accomplished by an iterative inversion algorithm incorporating the Cauchy norm regularization with FX filter weighting. Cauchy norm regularization was utilized to force the solution to a spikiness structure, while the effective random noise reduction was performed by using the FX filter. Applications to synthetic and real post-stack data showed that the resolution in the vertical direction and continuity in the lateral direction are better improved. Thus, we think that this process makes seismic sections obtained especially from thin layered sedimentary basins more interpretable.

Keywords

Cauchy regularization High-resolution deconvolution Reflectivity estimation FX filtering Post-stack seismic data 

References

  1. Burg JP (1975) Maximum entropy spectral analysis. PhD thesis, Stanford UniversityGoogle Scholar
  2. Canales L (1994) Random noise reduction. 54th Annual International Meeting, SEG, Expanded Abstracts, 1994, pp 525–527Google Scholar
  3. Claerbout JF (1976) Fundamentals of geophysics data processing. McGraw-Hill Inc., New YorkGoogle Scholar
  4. Claerbout J, Muir F (1973) Robust modelling with erratic data. Geophysics 38(5):826–844.  https://doi.org/10.1190/1.1440378 CrossRefGoogle Scholar
  5. Cooke DA, Schneider WA (1983) Generalized linear inversion of reflection seismic data. Geophysics 48(6):665–676.  https://doi.org/10.1190/1.1441497 CrossRefGoogle Scholar
  6. Debeye HWJ, van Riel P (1990) LP-norm deconvolution. Geophys Propect 38(4):381–404.  https://doi.org/10.1111/j.1365-2478.1990.tb01852.x CrossRefGoogle Scholar
  7. Dobroka M, Szegedi H (2014) On the generalization of seismic tomography algorithms. Am J Comput Math 4(01):37–46.  https://doi.org/10.4236/ajcm.2014.41004 CrossRefGoogle Scholar
  8. Fleming JS, Goddard BA (1974) A technique for the deconvolution of the renogram. Phys Med Biol 19(4):546–549.  https://doi.org/10.1088/0031-9155/19/4/014 CrossRefGoogle Scholar
  9. Gulunay N (1986) FXDECON and complex Wiener prediction filter. Expanded Abstracts, 56th Annual International Meeting. SEG, Houston, 1986, pp 279–281Google Scholar
  10. Heimer A, Cohen I (2008) Multichannel blind seismic deconvolution using dynamic programming. Signal Process 88(7):1839–1851.  https://doi.org/10.1016/j.sigpro.2008.01.022 CrossRefGoogle Scholar
  11. Hestenes M, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 49(6):409–436.  https://doi.org/10.6028/jres.049.044 CrossRefGoogle Scholar
  12. Leinbach J (1995) Wiener spiking deconvolution and minimum-phase wavelets: a tutorial. Lead Edge 14(3):189–192.  https://doi.org/10.1190/1.1437110 CrossRefGoogle Scholar
  13. O’Brien M, Sinclair A, Kramer S (1994) Recovery of sparse spike time series by L1 norm decovolution. IEEE Trans Signal Process 42(12):3353–3356.  https://doi.org/10.1109/78.340772 CrossRefGoogle Scholar
  14. Oldenburg DW, Scheuer TL (1983) Recovery of the acoustic impedance from reflection seismograms. Geophysics 48(10):1318–1337.  https://doi.org/10.1190/1.1441413 CrossRefGoogle Scholar
  15. Robinson EA, Treitel S (1980) Geophysical signal analysis. Prentice-Hall, Englewood CliffsGoogle Scholar
  16. Sacchi MD (1997) Reweighting strategies in seismic deconvolution. Geophys J Int 129(3):651–656.  https://doi.org/10.1111/j.1365-246X.1997.tb04500.x CrossRefGoogle Scholar
  17. Sacchi MD, Ulrych TJ (1995) High-resolution velocity gathers and offset space reconstruction. Geophysics 60(4):1169–1177.  https://doi.org/10.1190/1.1443845 CrossRefGoogle Scholar
  18. Sacchi MD, Wang J, Kuehl H (2006) Regularized migration/inversion: new generation of imaging algorithms. CSEG Recorder, Special Edition 31:54–59Google Scholar
  19. Seislab (2015) http://seismic-lab.physics.ualberta.ca. Accessed 20 May 2015
  20. Soubaras R (1994) Signal-preserving random noise attenuation by the f-x projection. 64th Annual International Meeting, SEG, Expanded Abstracts, 1994, pp 1576–1579Google Scholar
  21. Titterigton DM (1985) General structure of regularization procedures in image reconstruction. Astron Astrophys 144:381–387Google Scholar
  22. Treitel S (1974) The complex wiener filter. Geophysics 39(2):169–173.  https://doi.org/10.1190/1.1440419 CrossRefGoogle Scholar
  23. Velis DR (2008) Stochastic sparse-spike deconvolution. Geophysics 73(1):R1–R9.  https://doi.org/10.1190/1.2790584 CrossRefGoogle Scholar
  24. Walden AT, Hosken JWJ (1986) The nature of the non-gaussianity of primary reflection coefficients and its significance for deconvolution. Geophys Prospect 34(7):1038–1066.  https://doi.org/10.1111/j.1365-2478.1986.tb00512.x CrossRefGoogle Scholar
  25. Walker C, Ulrych TJ (1983) Autoregressive modeling of the acoustic impedance. Geophysics 48(10):1338–1350.  https://doi.org/10.1190/1.1441414 CrossRefGoogle Scholar
  26. Wang J, Sacchi MD (2008) Structure-and-amplitude preserving multi-channel deconvolution. CSPG CSEG CWLS Convention, Canada, 2008, pp 729–732Google Scholar
  27. Wang J, Wang X, Perz M (2006) Structure preserving regularization for sparse deconvolution. 76th Annual International Meeting, SEG, Expanded Abstracts, 2006, p 2072–2076Google Scholar
  28. Yilmaz Ö (2001) Seismic data analysis: processing, inversion, and interpretation of seismic data. SEG, Tulsa.  https://doi.org/10.1190/1.9781560801580 CrossRefGoogle Scholar
  29. Zala CA (1992) High-resolution inversion of ultrasonic traces. IEEE Trans Ultrason 39:438–463CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2017

Authors and Affiliations

  1. 1.Department of Geophysics, Engineering FacultyKaradeniz Technical UniversityTrabzonTurkey
  2. 2.General Directorate of Mineral Research and ExplorationAnkaraTurkey

Personalised recommendations