1887
Volume 69, Issue 1
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Erratic noise often has high amplitudes and a non‐Gaussian distribution. Least‐squares–based approaches therefore are not optimal. This can be handled better with non–least‐squares approaches, for example based on Huber norm which is computationally expensive. An alternative method has been published which involves transforming the data with erratic noise to pseudodata that have Gaussian distributed noise. It can then be attenuated using traditional least‐squares approaches. This alternative method has previously been used in combination with a curvelet transform in an iterative scheme. In this paper, we introduce a median‐filtering step in this iterative scheme. The median filter is applied following the slope direction of the seismic data to maximally preserve the energy of useful signals. The new method can suppress stronger erratic noise compared with the previous iterative method, and can better deal with random noise compared with the single‐step implementation of the median filter. We apply the proposed robust denoising algorithm to a synthetic dataset and two field data examples and demonstrate its advantages over three different noise attenuation algorithms.

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/content/journals/10.1111/1365-2478.13032
2020-12-12
2021-01-18
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References

  1. Abma, R. and Claerbout, J. (1995) Lateral prediction for noise attenuation by t−x and f−x techniques. Geophysics, 60, 1887–1896.
    [Google Scholar]
  2. Anderson, R.G. and McMechan, G.A. (1989) Automatic editing of noisy seismic data 1. Geophysical Prospecting, 37(8), 875–892.
    [Google Scholar]
  3. Beaton, A.E. and Tukey, J.W. (1974) The fitting of power series, meaning polynomials, illustrated on band‐spectroscopic data. Technometrics, 16(2), 147–185.
    [Google Scholar]
  4. Beylkin, G. (1987) Discrete radon transform. IEEE Transactions on Acoustics, Speech, and Signal Processing, 35(2), 162–172.
    [Google Scholar]
  5. Canales, L. (1984) Random noise reduction. 54th Annual International Meeting. Tulsa, OK: Society of Exploration Geophysicists. Expanded Abstracts, pp. 525–527.
  6. Candes, E., Demanet, L., Donoho, D. and Ying, L. (2006) Fast discrete curvelet transforms. Multiscale Modeling & Simulation, 5(3), 861–899.
    [Google Scholar]
  7. Candès, E.J., Li, X., Ma, Y. and Wright, J. (2011) Robust principal component analysis?Journal of the ACM (JACM), 58(3), 11.
    [Google Scholar]
  8. Cao, J. and Zhao, J. (2015) 3D seismic interpolation with a low redundancy, fast curvelet transform. Journal of Seismic Exploration, 24(2), 121–134.
    [Google Scholar]
  9. Chen, K. and Sacchi, M.D. (2014) Robust reduced‐rank filtering for erratic seismic noise attenuation. Geophysics, 80(1), V1–V11.
    [Google Scholar]
  10. Chen, K. and Sacchi, M.D. (2017) Robust f‐x projection filtering for simultaneous random and erratic seismic noise attenuation. Geophysical Prospecting, 65(3), 650–668.
    [Google Scholar]
  11. Chen, Y. (2015) Deblending using a space‐varying median filter. Exploration Geophysics, 46, 332–341.
    [Google Scholar]
  12. Chen, Y. (2020) Fast dictionary learning for noise attenuation of multidimensional seismic data. Geophysical Journal International, 222, 1717–1727.
    [Google Scholar]
  13. Chen, Y. and Fomel, S. (2015) Random noise attenuation using local signal‐and‐noise orthogonalization. Geophysics, 80, WD1–WD9.
    [Google Scholar]
  14. Chen, Y., Fomel, S. and Hu, J. (2014) Iterative deblending of simultaneous‐source seismic data using seislet‐domain shaping regularization. Geophysics, 79, V179–V189.
    [Google Scholar]
  15. Chen, Y., Zu, S., Wang, Y. and Chen, X. (2020) Deblending of simultaneous‐source data using a structure‐oriented space‐varying median filter. Geophysical Journal International, 222(1), 1805–1823.
    [Google Scholar]
  16. Dondurur, D. and Karslı, H. (2012) Swell noise suppression by Wiener prediction filter. Journal of Applied Geophysics, 80, 91–100.
    [Google Scholar]
  17. Elad, M. and Aharon, M. (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing, 15(12), 3736–3745.
    [Google Scholar]
  18. Fomel, S. (2007) Local seismic attributes. Geophysics, 72(3), A29–A33.
    [Google Scholar]
  19. Fomel, S. and Liu, Y. (2010) Seislet transform and seislet frame. Geophysics, 75, V25–V38.
    [Google Scholar]
  20. Gan, S., Wang, S., Chen, Y., Chen, X. and Xiang, K. (2016) Separation of simultaneous sources using a structural‐oriented median filter in the flattened dimension. Computers & Geosciences, 86, 46–54.
    [Google Scholar]
  21. Gulunay, N. (1986) Fx decon and complex wiener prediction filter. 56th Annual International Meeting. Tulsa, OK: Society of Exploration Geophysicists. Expanded Abstracts, pp. 279–281.
  22. Halliday, D.F., Curtis, A., Robertsson, J.O.A. and van Manen, D.‐J. (2007) Interferometric surface‐wave isolation and removal. Geophysics, 72, A69–A73.
    [Google Scholar]
  23. Holland, P.W. and Welsch, R.E. (1977) Robust regression using iteratively reweighted least‐squares. Communications in Statistics‐Theory and Methods, 6(9), 813–827.
    [Google Scholar]
  24. Huang, W., Wang, R., Chen, Y., Li, H. and Gan, S. (2016) Damped multichannel singular spectrum analysis for 3D random noise attenuation. Geophysics, 81(4), V261–V270.
    [Google Scholar]
  25. Huber, P.J. et al. (1964) Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.
    [Google Scholar]
  26. Karsli, H. and Bayrak, Y. (2004) Using the Wiener–Levinson algorithm to suppress ground‐roll. Journal of Applied Geophysics, 55(3‐4), 187–197.
    [Google Scholar]
  27. Karslı, H. and Dondurur, D. (2018) A mean‐based filter to remove power line harmonic noise from seismic reflection data. Journal of Applied Geophysics, 153, 90–99.
    [Google Scholar]
  28. Karsli, H., Dondurur, D. and Çifçi, G. (2006) Application of complex‐trace analysis to seismic data for random‐noise suppression and temporal resolution improvement. Geophysics, 71(3), V79–V86.
    [Google Scholar]
  29. Li, C., Liu, G., Hao, Z., Zu, S., Mi, F. and Chen, X. (2018a) Multidimensional seismic data reconstruction using frequency‐domain adaptive prediction‐error filter. IEEE Transactions on Geoscience and Remote Sensing, 56(4), 2328–2336.
    [Google Scholar]
  30. Li, Y., Zhang, Y., Huang, X., Zhu, H. and Ma, J. (2018b) Large‐scale remote sensing image retrieval by deep hashing neural networks. IEEE Transactions on Geoscience and Remote Sensing, 56(2), 950–965.
    [Google Scholar]
  31. Liu, C., Wang, D., Hu, B. and Wang, T. (2016) Seismic deconvolution with shearlet sparsity constrained inversion. Journal of Seismic Exploration, 25(5), 433–445.
    [Google Scholar]
  32. Liu, G. and Chen, X. (2013) Noncausal f‐x‐y regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data. Journal of Applied Geophysics, 93, 60–66.
    [Google Scholar]
  33. Liu, G., Chen, X., Du, J. and Wu, K. (2012) Random noise attenuation using f‐x regularized nonstationary autoregression. Geophysics, 77(2), V61–V69.
    [Google Scholar]
  34. Liu, G., Liu, Y., Li, C. and Chen, X. (2018) Weighted multisteps adaptive autoregression for seismic image denoising. IEEE Geoscience and Remote Sensing Letters, 15(9), 1342–1346.
    [Google Scholar]
  35. Liu, Y., Fomel, S., Liu, C., Wang, D., Liu, G. and Feng, X. (2009a) High‐order seislet transform and its application of random noise attenuation. Chinese Journal of Geophysics, 52, 2142–2151.
    [Google Scholar]
  36. Liu, Y., Fomel, S. and Liu, G. (2010) Nonlinear structure‐enhancing filtering using plane‐wave prediction. Geophysical Prospecting, 58, 415–427.
    [Google Scholar]
  37. Liu, Y., Liu, C. and Wang, D. (2009b) A 1D time‐varying median filter for seismic random, spike‐like noise elimination. Geophysics, 74, V17–V24.
    [Google Scholar]
  38. Lu, Y. and Lu, W. (2009) Edge‐preserving polynomial fitting method to suppress random seismic noise. Geophysics, 74, V69–V73.
    [Google Scholar]
  39. Mousavi, S.M. and Langston, C.A. (2016a) Adaptive noise estimation and suppression for improving microseismic event detection. Journal of Applied Geophysics, 132, 116–124.
    [Google Scholar]
  40. Mousavi, S.M. and Langston, C.A. (2016b) Hybrid seismic denoising using higher‐order statistics and improved wavelet block thresholding. Bulletin of the Seismological Society of America, 106(4), 1380–1393.
    [Google Scholar]
  41. Mousavi, S.M., Langston, C.A. and Horton, S.P. (2016) Automatic microseismic denoising and onset detection using the synchrosqueezed continuous wavelet transform. Geophysics, 81(4), V341–V355.
    [Google Scholar]
  42. Naghizadeh, M. and Sacchi, M.D. (2010) Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data. Geophysics, 75, WB189–WB202.
    [Google Scholar]
  43. Oh, H.‐S., Nychka, D.W. and Lee, T. (2007) The role of pseudo data for robust smoothing with application to wavelet regression. Biometrika, 94(4), 893–904.
    [Google Scholar]
  44. Oropeza, V. and Sacchi, M. (2011) Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics, 76, V25–V32.
    [Google Scholar]
  45. Sacchi, M.D. (1997) Reweighting strategies in seismic deconvolution. Geophysical Journal International, 129(3), 651–656.
    [Google Scholar]
  46. Schonewille, M., Vigner, A. and Ryder, A. (2008) Swell‐noise attenuation using an iterative fx prediction filtering approach. SEG Technical Program Expanded Abstracts 2008. Tulsa, OK: Society of Exploration Geophysicists. pp. 2647–2651.
  47. Siahsar, M.A.N., Abolghasemi, V. and Chen, Y. (2017a) Simultaneous denoising and interpolation of 2D seismic data using data‐driven non‐negative dictionary learning. Signal Processing, 141, 309–321.
    [Google Scholar]
  48. Siahsar, M.A.N., Gholtashi, S., Kahoo, A.R., Chen, W. and Chen, Y. (2017b) Data‐driven multi‐task sparse dictionary learning for noise attenuation of 3D seismic data. Geophysics, 82(6), V385–V396.
    [Google Scholar]
  49. Sweldens, W. (1995) Lifting scheme: a new philosophy in biorthogonal wavelet constructions: wavelet applications in signal and image processing III. Proceedings of SPIE 2569, San Diego, CA. Bellingham, WA: SPIE. pp. 68–79.
  50. Trickett, S., Burroughs, L. and Milton, A. (2012) Robust rank‐reduction filtering for erratic noise. SEG Technical Program Expanded Abstracts 2012. Tulsa, OK: Society of Exploration Geophysicists. pp. 1–5.
  51. Verschuur, D.J. (1991) Surface‐related multiple elimination: an inversion approach. PhD Thesis, Delft University of Technology.
  52. Verschuur, D.J., Berkhout, A.J. and Wapenaar, C.P.A. (1992) Adaptive surface‐related multiple elimination. Geophysics, 57, 1166–1177.
    [Google Scholar]
  53. Wang, C., Zhu, Z., Gu, H., Wu, X. and Liu, S. (2018) Hankel low‐rank approximation for seismic noise attenuation. IEEE Transactions on Geoscience and Remote Sensing, 57, 1–13.
    [Google Scholar]
  54. Wong, R.K. and Lee, T.C. (2017) Matrix completion with noisy entries and outliers. The Journal of Machine Learning Research, 18(1), 5404–5428.
    [Google Scholar]
  55. Ying, L., Demanet, L. and Candes, E. (2005) 3D discrete curvelet transform. In Wavelets XI, Vol. 5914. Bellingham, WA: International Society for Optics and Photonics. p. 591413.
    [Google Scholar]
  56. Zhang, D., Verschuur, E., Qu, S. and Chen, Y. (2020) Surface‐related multiple leakage extraction using local primary‐and‐multiple orthogonalization. Geophysics, 85(1), V81–V97.
    [Google Scholar]
  57. Zhao, Q., Du, Q., Gong, X. and Chen, Y. (2018) Signal‐preserving erratic noise attenuation via iterative robust sparsity‐promoting filter. IEEE Transactions on Geoscience and Remote Sensing, 56(6), 1558–0644.
    [Google Scholar]
  58. Zhu, W., Mousavi, S.M. and Beroza, G.C. (2019) Seismic signal denoising and decomposition using deep neural networks. IEEE Transactions on Geoscience and Remote Sensing, 57(11), 9476–9488.
    [Google Scholar]
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