1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 65, Issue 3
  5. Article
Volume 65, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Linear prediction filters are an effective tool for reducing random noise from seismic records. Unfortunately, the ability of prediction filters to enhance seismic records deteriorates when the data are contaminated by erratic noise. Erratic noise in this article designates non‐Gaussian noise that consists of large isolated events with known or unknown distribution. We propose a robust ‐ projection filtering scheme for simultaneous erratic noise and Gaussian random noise attenuation. Instead of adopting the ℓ‐norm, as commonly used in the conventional design of ‐ filters, we utilize the hybrid ‐norm to penalize the energy of the additive noise. The estimation of the prediction error filter and the additive noise sequence are performed in an alternating fashion. First, the additive noise sequence is fixed, and the prediction error filter is estimated via the least‐squares solution of a system of linear equations. Then, the prediction error filter is fixed, and the additive noise sequence is estimated through a cost function containing a hybrid ‐norm that prevents erratic noise to influence the final solution. In other words, we proposed and designed a robust M‐estimate of a special autoregressive moving‐average model in the ‐ domain. Synthetic and field data examples are used to evaluate the performance of the proposed algorithm.

© 2017 European Association of Geoscientists & Engineers © 2016 European Association of Geoscientists & Engineers
Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12429
2016-08-25
2024-04-18

  • From This Site

    /content/journals/10.1111/1365-2478.12429
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. AbmaR. and ClaerboutJ.1995. Lateral prediction for noise attenuation by t‐x and f‐x techniques. Geophysics60, 1887–1896.
     [Google Scholar]
  2. AravkinA., van LeeuwenT. and HerrmannF.2011. Robust full‐waveform inversion using the student's t distribution. 81st SEG annual international meeting, Expanded Abstracts, 2669–2673.
  3. BekaraM. and van der BaanM.2010. High‐amplitude noise detection by the expectation‐maximization algorithm with application to swell‐noise attenuation. Geophysics75, V39–V49.
     [Google Scholar]
  4. BluT., DragottiP.‐L., VetterliM., MarzilianoP. and CoulotL.2008. Sparse sampling of signal innovations. IEEE Signal Processing Magazine25, 31–40.
     [Google Scholar]
  5. BrossierR., OpertoS. and VirieuxJ.2010. Which data residual norm for robust elastic frequency‐domain full waveform inversion? Geophysics75, R37–R46.
     [Google Scholar]
  6. BubeK. and LanganR.1997. Hybrid minimization with applications to tomography. Geophysics62, 1183–1195.
     [Google Scholar]
  7. CamboisG. and FreletJ.1995. Can we surgically remove swell noise? 65th SEG annual international meeting, Expanded Abstracts, 1381–1384.
  8. CanalesL.L.1984. Random noise reduction. 54th SEG annual international meeting, Expanded Abstracts, 525–527.
  9. ChaseM.K.1992. Random noise reduction by FXY prediction filtering. Exploration Geophysics23, 51–56.
     [Google Scholar]
  10. ChenK.2013. Robust matrix rank reduction methods for seismic data processing. MSc thesis, University of Alberta, Canada.
     [Google Scholar]
  11. ChenK. and SacchiM.D.2013. Robust reduced‐rank seismic denoising. 83rd SEG annual international meeting, Expanded Abstracts, 4272–4277.
  12. ChenK. and SacchiM.D.2014. Making f‐x projection filters robust to erratic noise. 84th SEG annual international meeting, Expanded Abstracts, 4371–4375.
  13. ChenK. and SacchiM.D.2015. Robust reduced‐rank filtering for erratic seismic noise attenuation. Geophysics80, V1–V11.
     [Google Scholar]
  14. ClaerboutJ.F. and MuirF.1973. Robust modelling with erratic data. Geophysics38, 826–844.
     [Google Scholar]
  15. CraseE., PicaA., NobleM., McDonaldJ. and TarantolaA.1990. Robust elastic nonlinear waveform inversion: Application to real data. Geophysics55, 527–538.
     [Google Scholar]
  16. ElbothT., PresterudI. and HermansenD.2010. Time‐frequency seismic data de‐noising. Geophysical Prospecting58, 441–453.
     [Google Scholar]
  17. ElbothT., ReifB.A. and AndreassenO.2009. Flow and swell noise in marine seismic data. Geophysics74, Q17–Q25.
     [Google Scholar]
  18. FoxA.J.1972. Outliers in time series. Journal of the Royal Statistical Society (B)34, 350–363.
     [Google Scholar]
  19. GholamiA. and SacchiM.D.2012. A fast and automatic sparse deconvolution in the presence of outliers. IEEE Transactions on Geoscience and Remote Sensing, 1–12.
     [Google Scholar]
  20. GolubG.H. and PereyraV.1973. The differentiation of pseudo‐inverses and nonlinear least squares problems whose variables separate. SIAM Journal on Numerical Analysis10, 413–432.
     [Google Scholar]
  21. GuittonA. and SymesW.2003. Robust inversion of seismic data using the Huber norm. Geophysics68, 1310–1319.
     [Google Scholar]
  22. GulunayN.1986. FXDECON and complex wiener prediction filter. 56th SEG annual international meeting, Expanded Abstracts, 279–281.
  23. HaT., ChungW. and ShinC.2009. Waveform inversion using a back‐propagation algorithm and a Huber function norm. Geophysics74, R15–R24.
     [Google Scholar]
  24. HampelF.R.1985. The breakdown points of the mean combined with some rejection rules. Technometrics27, 95–107.
     [Google Scholar]
  25. HarrisP. and WhiteR.1997. Improving the performance of f‐x prediction filtering at low signal‐to‐noise ratios. Geophysical Prospecting45, 269–302.
     [Google Scholar]
  26. HuberP.1981. Robust Statistics. John Wiley & Sons, Inc.
     [Google Scholar]
  27. IbrahimA. and SacchiM.D.2014. Simultaneous source separation using a robust radon transform. Geophysics79, V1–V11.
     [Google Scholar]
  28. KaufmanL.1975. A variable projection method for solving separable nonlinear least squares problems. BIT Numerical Mathematics15, 49–57.
     [Google Scholar]
  29. KayS.1978. Improvement of autoregressive spectral estimates in the presence of noise. IEEE International Conference on Acoustics, Speech, and Signal Processing3, 357–360.
     [Google Scholar]
  30. KayS. and MarpleS.1981. Spectrum analysis ‐ A modern perspective. Proceedings of the IEEE69, 1380–1419.
     [Google Scholar]
  31. LiY., ZhangY. and ClaerboutJ.2012. Hyperbolic estimation of sparse models from erratic data. Geophysics77, V1–V9.
     [Google Scholar]
  32. LiuY., LiuN. and LiuC.2015. Adaptive prediction filtering in t‐x‐y domain for random noise attenuation using regularized nonstationary autoregression. Geophysics80, V13–V21.
     [Google Scholar]
  33. MaronnaR., MartinR. and YohaiV.2006. Robust statistics: Theory and methods. John Wiley & Sons, Inc.
  34. NaghizadehM. and SacchiM.D.2010. Seismic data reconstruction using multidimensional prediction filters. Geophysical Prospecting58, 157–173.
     [Google Scholar]
  35. OropezaV. and SacchiM.D.2011. Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics76, V25–V32.
     [Google Scholar]
  36. OzdemirA.K., OzbekA., FerberR. and ZeroukK.1999. f‐xy projection filtering using helical transformation. 69th SEG annual international meeting, Expanded Abstracts, 1231–1234.
  37. SacchiM.D.2008. SeismicLab: http://seismic‐lab.physics.ualberta.ca.
  38. SacchiM.D.2009. FX Singular Spectrum Analysis. CSPG CSEG CWLS Convention.
  39. SacchiM.D. and KuehlH.2001. ARMA formulation of FX prediction error filters and projection filters. Journal of Seismic Exploration3, 185–197.
     [Google Scholar]
  40. ScalesJ. and GersztenkornA.1988. Robust methods in inverse theory. Inverse Problems4, 1071.
     [Google Scholar]
  41. SchonewilleM., VignerA. and RyderA.2008. Swell‐noise attenuation using an iterative FX prediction filtering approach. 78th SEG annual international meeting, Expanded Abstracts, 2647–2651.
  42. SoubarasR.1994. Signal‐preserving random noise attenuation by the f‐x projection. 64th SEG annual international meeting, Expanded Abstracts, 1576–1579.
  43. SoubarasR.1995. Prestack random and impulsive noise attenuation by f‐x projection filtering. 65th SEG annual international meeting, Expanded Abstracts, 711–714.
  44. SoubarasR.2000. 3D projection filtering for noise attenuation and interpolation. 70th SEG annual international meeting, Expanded Abstracts, 2096–2099.
  45. StoicaP. and MosesR.2005. Spectral Analysis of Signals. Prentice Hall, Inc.
     [Google Scholar]
  46. TaylorH., BanksS. and McCoyL.1979. Deconvolution with the ℓ1 norm. Geophysics44, 39–52.
     [Google Scholar]
  47. TrickettS.2008. F‐xy Cadzow noise suppression. 78th SEG annual international meeting, Expanded Abstracts, 2586–2590.
  48. TuftsD. and KumaresanR.1982. Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood. Proceedings of the IEEE70, 975–989.
     [Google Scholar]
  49. UlrychT. and SacchiD.2005. Information‐based inversion and processing with applications. In: Handbook of Geophysical Exploration: Seismic Exploration. Elsevier Science.
     [Google Scholar]
  50. UlrychT.J. and ClaytonR.W.1976. Time series modelling and maximum entropy. Physics of the Earth and Planetary Interiors12, 188–200.
     [Google Scholar]
  51. YuleG.U.1927. On a method of investigating periodicities in disturbed series, with special reference to Wolfer's sunspot numbers. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character226, 267–298.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12429
Loading
Robust f‐x projection filtering for simultaneous random and erratic seismic noise attenuation
Geophysical Prospecting 65, 650 (2017); https://doi.org/10.1111/1365-2478.12429
/content/journals/10.1111/1365-2478.12429
/content/journals/10.1111/1365-2478.12429
Loading

Data & Media loading...

  • Article Type: Research Article
Keyword(s): Inverse problem; Noise; Signal processing

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error