access icon free Denoising of pre-stack seismic data using subspace estimation methods

Denoising is one of the core steps in seismic data processing flow. The seismic gather consists of multiple traces captured at different receivers. A set of receivers observe waves which are reflected from the same reflection point. Those traces need to be grouped together as they contain the same information about the earth subsurface layers. This is done by finding a common mid-point (CMP) between the source and geophones. The time delay between CMP gathered traces are corrected by the normal move out correction method but the individual traces are corrupted by noise. In this paper we, propose a method for denoising individual traces. The set of traces can be modelled as belonging to a low-dimensional subspace of an ambient signal space. This allows for construction of sparse representations of each trace in terms of other traces in the CMP gather. The resulting sparse representations are subsequently utilised to construct approximations of individual traces and thus, noise is suppressed. We constructed, the approximations using orthogonal matching pursuit. We applied proposed method to synthetic and field seismic data, the proposed technique performs better on established benchmarks while capturing the true locations of weak reflections and effectively attenuating the random noise.

Inspec keywords: iterative methods; signal representation; seismology; signal denoising; geophysical signal processing

Other keywords: receivers; sparse representations; time delay; pre-stack seismic data denoising; subspace estimation methods; low-dimensional subspace; geophones; ambient signal space; earth subsurface layers; seismic data processing flow; random noise; common mid-point; CMP; orthogonal matching pursuit; field seismic data

Subjects: Numerical approximation and analysis; Data and information; acquisition, processing, storage and dissemination in geophysics; Geophysical techniques and equipment; Interpolation and function approximation (numerical analysis); Digital signal processing; Interpolation and function approximation (numerical analysis); Signal processing and detection; Geophysics computing; Seismology; Instrumentation and techniques for geophysical, hydrospheric and lower atmosphere research

References

    1. 1)
      • 19. Liu, G., Chen, X.: ‘Noncausal f–x–y regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data’, J. Appl. Geophys., 2013, 93, pp. 6066.
    2. 2)
      • 2. Karimpouli, S., Hassani, H., Nabi-Bidhendi, M., et al: ‘Application of probabilistic facies prediction and estimation of rock physics parameters in a carbonate reservoir from Iran’, J. Geophys. Eng., 2013, 10, (1), p. 015008.
    3. 3)
      • 66. Anvari, R., Siahsar, M.A.N., Gholtashi, S., et al: ‘Seismic random noise attenuation using synchrosqueezed wavelet transform and low-rank signal matrix approximation’, IEEE Trans. Geosci. Remote Sens., 2017, 55, (11), pp. 65746581.
    4. 4)
      • 18. Wang, Y.: ‘Random noise attenuation using forward-backward linear prediction’, J. Seism. Explor., 1999, 8, pp. 133142.
    5. 5)
      • 22. Chen, Y., Ma, J.: ‘Random noise attenuation by f–x empirical-mode decomposition predictive filtering’, Geophysics, 2014, 79, (3), pp. V81V91.
    6. 6)
      • 6. Upadhyay, S.K.: ‘Seismic reflection processing: with special reference to anisotropy’ (Springer Science and Business Media, Berlin, 2013).
    7. 7)
      • 17. Abma, R., Claerbout, J.: ‘Lateral prediction for noise attenuation by t–x and f–x techniques’, Geophysics, 1995, 60, pp. 18871896.
    8. 8)
      • 23. Zhang, R., Ulrych, T.: ‘Physical wavelet frame denoising’, Geophysics, 2003, 68, pp. 225231.
    9. 9)
      • 60. Tropp, J.A.: ‘Greed is good: algorithmic results for sparse approximation’, IEEE Trans. Inf. Theory, 2004, 50, (10), pp. 22312242.
    10. 10)
      • 15. Galbraith, M., Yao, Z.: ‘FX plus deconvolution for seismic data noise reduction’, Soc. Explor. Geophys., SEG technical program expanded abstracts, 2012, pp. 14.
    11. 11)
      • 54. Beck, A., Teboulle, M.: ‘A fast iterative shrinkage-thresholding algorithm for linear inverse problems’, SIAM J. Imaging Sci., 2009, 2, (1), pp. 183202.
    12. 12)
      • 7. Eaton, D.W., Milkereit, B., Salisbury, M.H., et al: ‘Hardrock seismic exploration’ (Society of Exploration Geophysicists, Tulsa, Okla, 2003).
    13. 13)
      • 50. Dorst, L., Fontijne, D., Mann, S., et al: ‘Geometric algebra for computer science: an object-oriented approach to geometry’ (Morgan Kaufmann Publishers Inc., San Francisco, 2009).
    14. 14)
      • 5. Siahsar, M.A.N., Gholtashi, S., Abolghasemi, V., et al: ‘Simultaneous denoising and interpolation of 2D seismic data using data-driven non-negative dictionary learning’, Signal Process., 2017, 141, pp. 309321.
    15. 15)
      • 14. Yaru, X., Xiaohong, C.: ‘Random noise attenuation based on orthogonal polynomials transform’, Soc. Explor. Geophys., SEG technical program expanded abstracts, 2009, pp. 33773380.
    16. 16)
      • 29. Liu, W., Cao, S., Chen, Y., et al: ‘An effective approach to attenuate random noise based on compressive sensing and curvelet transform’, J. Geophys. Eng., 2016, 13, pp. 135145.
    17. 17)
      • 51. Oreifej, O., Shah, M.: ‘Robust subspace estimation using low-rank optimization’ (Springer, London, 2014), pp. 5567.
    18. 18)
      • 62. Liu, W., Cao, S., Wang, Z.: ‘Application of variational mode decomposition to seismic random noise reduction’, J. Geophys. Eng., 2017, 14, (4), p. 888.
    19. 19)
      • 9. Berkhout, A.J., Verschuur, D.J.: ‘Estimation of multiple scattering by iterative inversion, part 1 theoretical consideration’, Geophysics, 1997, 62, pp. 15861595.
    20. 20)
      • 52. Yang, J., Luo, L., Qian, J., et al: ‘Nuclear norm based matrix regression with applications to face recognition with occlusion and illumination changes’, IEEE Trans. Pattern Anal. Mach. Intell., 2017, 39, (1), pp. 156171.
    21. 21)
      • 25. Liu, W., Cao, S., Chen, Y..: ‘Seismic time-frequency analysis via empirical wavelet transform’, IEEE Geosci. Remote Sens. Lett., 2015a, 13, pp. 2832.
    22. 22)
      • 45. Beckouche, S., Ma, J.: ‘Simultaneous dictionary learning and denoising for seismic data’, Geophysics, 2014, 79, pp. A27A31.
    23. 23)
      • 31. Wu, X., Uden, R., Chapman, M..: ‘Shale anisotropic elastic modeling and seismic reflections’, J. Seism. Explor., 2016, 25, pp. 419432.
    24. 24)
      • 27. Naghizadeh, M., Sacchi, M.D.: ‘Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data’, Geophysics, 2010, 75, (6), pp. WB189WB202.
    25. 25)
      • 8. Telford, W.M., Telford, W.M., Geldart, L.P., et al: ‘Applied geophysics’ (Cambridge University Press, Melbourne, Australia, 1990), vol. 1.
    26. 26)
      • 63. Li, Q., Gao, J.: ‘Application of seismic data stacking in time–frequency domain’, IEEE Geosci. Remote Sens. Lett., 2014, 11, (9), pp. 14841488.
    27. 27)
      • 26. Liu, W., Cao, S., Liu, Y., et al: ‘Synchrosqueezing transform and its applications in seismic data analysis’, J. Seism. Explor., 2016d, 25, pp. 2744.
    28. 28)
      • 1. Nolet, G.: ‘Seismic tomography: with applications in global seismology and exploration geophysics’ (Springer Science and Business Media, Holland, 2012), vol. 5.
    29. 29)
      • 24. Chen, Y., Ma, J., Fomel, S.: ‘Double-sparsity dictionary for seismic noise attenuation’, Geophysics, 2016, 81, (2), pp. V103V116.
    30. 30)
      • 4. Yilmaz, O.: ‘Seismic data analysis: processing, inversion, and interpretation of seismic data’ (Society of Exploration Geophysicists, Tulsa, Okla, 2001).
    31. 31)
      • 46. Sacchi, M.D.: ‘F–x singular spectrum analysis’, CSPG CSEG CWLS Convention, 2009, pp. 392395.
    32. 32)
      • 49. Bekara, M., Van der Baan, M.: ‘Local singular value decomposition for signal enhancement of seismic data’, Geophysics, 2007, 72, (2), pp. V59V65.
    33. 33)
      • 53. Vidal, R., Favaro, P.: ‘Low rank subspace clustering (LRSC)’, Pattern Recognit. Lett., 2014, 43, pp. 4761.
    34. 34)
      • 30. Liu, W., Cao, S., Gan, S., et al: ‘One-step slope estimation for dealiased seismic data reconstruction via iterative seislet thresholding’, IEEE Geosci. Remote Sens. Lett., 2016, 13, pp. 14621466.
    35. 35)
      • 38. CandÃĺs, E.J., Donoho, D.L.: ‘Curvelets – a surprisingly effective nonadaptive representation for objects with edges’, in Schumaker, L., et al (Eds.): ‘Curve and surfaces’ (Vanderbilt University Press, Nashville, TN, 1999), pp. 105120.
    36. 36)
      • 10. Foster, D.J., Mosher, C.C.: ‘Suppression of multiple reflections using the radon transform’, Geophysics, 1992, 57, pp. 386395.
    37. 37)
      • 41. Lari, H.H., Gholami, A.: ‘Curvelet-TV regularized Bregman iteration for seismic random noise attenuation’, J. Appl. Geophysics, 2014, 109, pp. 233241.
    38. 38)
      • 65. Harrison, M.P.: ‘F–x linear prediction filtering of seismic images’, CREWES.
    39. 39)
      • 40. Neelamani, R., Baumstein, A.I., Gillard, D.G., et al: ‘Coherent and random noise attenuation using the curvelet transform’, Lead. Edge, 2008, 27, (2), pp. 240248.
    40. 40)
      • 12. Hampson, D.: ‘Inverse velocity stacking for multiple elimination’, J. Can. Soc. Explor. Geophys., 1986, 22, pp. 4455.
    41. 41)
      • 64. Zhang, Q.S., Jiang, J.J., Zhai, J.H., et al: ‘seismic random noise attenuation using modified wavelet thresholding’, Ann. Geophys., 2017, 59, (6), p. 0647.
    42. 42)
      • 67. Mousa, W.A., Al-Shuhail, A.A.: ‘Processing of seismic reflection data using MATLAB’, Synth. Lect. Signal Process., 2011, 5, (1), pp. 197.
    43. 43)
      • 43. Dutta, G., Schuster, G.T.: ‘Sparse least-squares reverse time migration using seislets’, SEG Tech. Program Expanded Abstr., 2015, pp. 42324237.
    44. 44)
      • 57. Hogben, L.: ‘Handbook of linear algebra’ (Chapman and Hall, Boca Raton, 2013).
    45. 45)
      • 56. CandÃĺs, E.J., Li, X., Ma, Y., et al: ‘Robust principal component analysis’, J. ACM, 2011, 58, (3), p. 11.
    46. 46)
      • 61. Davenport, M.A., Wakin, M.B.: ‘Analysis of orthogonal matching pursuit using the restricted isometry property’, IEEE Trans. Inf. Theory, 2010, 56, (9), pp. 43954401.
    47. 47)
      • 47. Oropeza, V., Sacchi, M.D.: ‘Simultaneous seismic data and reconstruction via multichannel singular spectrum analysis’, Geophysics, 2011, 76, (3), pp. V25V32.
    48. 48)
      • 42. Gan, S., Wang, S., Chen, Y., et al: ‘Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform’, J. Appl. Geophys., 2016, 130, pp. 194208.
    49. 49)
      • 39. Vossen, R.V., Curtis, A., Laake, A., et al: ‘Surface-consistent deconvolution using reciprocity and waveform inversion’, Geophysics, 2006, 71, (2), pp. V19V30.
    50. 50)
      • 58. Cai, J.F., Candès, E.J., Shen, Z., et al: ‘A singular value thresholding algorithm for matrix completion’, SIAM J. Optim., 2010, 20, (4), pp. 19561982.
    51. 51)
      • 59. Quesada, J., Rodriguez, P.: ‘September. Automatic vehicle counting method based on principal component pursuit background modeling’. IEEE Int. Conf. on Image Processing (ICIP), 2016, pp. 38223826.
    52. 52)
      • 11. Verschuur, D.J., Berkhout, A., Wapenaar, C., et al: ‘Adaptive surface-related multiple elimination’, Geophysics, 1992, 57, (9), pp. 11661177.
    53. 53)
      • 44. Kaplan, S.T., Sacchi, M.D., Ulrych, T.J., et al: ‘Sparse coding for data-driven coherent and incoherent noise attenuation’. 79th Annual Int. Meeting, SEG, Expanded Abstracts, 2009, pp. 33273331.
    54. 54)
      • 37. Chakraborty, A., Okaya, D.: ‘Frequency-time decomposition of seismic data using wavelet-based methods’, Geophysics, 1995, 60, (6), pp. 19061916.
    55. 55)
      • 32. Fomel, S., Liu, Y.: ‘Seislet transform and seislet frame’, Geophysics, 2010, 75, (3), pp. V25V38.
    56. 56)
      • 34. Chen, Y.: ‘Fast dictionary learning for noise attenuation of multidimensional seismic data’, Geophys. J. Int., 2017, 209, pp. 2131.
    57. 57)
      • 28. Zu, S., Zhou, H., Chen, Y., et al: ‘A periodically varying code for improving deblending of simultaneous sources in marine acquisition’, Geophysics, 2016, 81, (3), pp. V213V225.
    58. 58)
      • 33. Cai, J., Huang, S., Ji, H., et al: ‘Data-driven tight frame construction and image denoising’, Appl. Comput. Harmon. Anal., 2013, 37, pp. 89105.
    59. 59)
      • 35. AllenJ, B.: ‘Short term spectral analysis, synthetic and modification by discrete Fourier transform’, IEEE Trans. Acoust. Speech Signal Process., 1977, 25, (3), pp. 235238.
    60. 60)
      • 16. Deng, P., Chen, Y., Zhang, Y., et al: ‘Weighted stacking of seismic AVO data using hybrid AB semblance and local similarity’, J. Geophys. Eng., 2016, 13, (2), p. 152.
    61. 61)
      • 21. Canales, L.: ‘Random noise reduction’. 54th Annual Int. Meeting of the Society of Exploration Geophysicists, 1984, pp. 525527.
    62. 62)
      • 13. Liu, G.C., Chen, X.H., Li, J.Y., et al: ‘Seismic noise attenuation using nonstationary polynomial fitting’, Appl. Geophys., 2011, 8, (1), pp. 1826.
    63. 63)
      • 36. Mallat, S.G.: ‘A wavelet tour of signal processing: the sparse way’ (Academic, Orlando, FL, USA, 2009).
    64. 64)
      • 55. Chan, T.S.T., Yang, Y.H.: ‘Polar n-complex and n-bicomplex singular value decomposition and principal component pursuit’, IEEE Trans. Signal Process., 2016, 64, (24), pp. 65336544.
    65. 65)
      • 48. Abma, R., Kabir, N.: ‘3D interpolation of irregular data with a POCS algorithm’, Geophysics, 2006, 71, (6), pp. E91E97.
    66. 66)
      • 3. Steeples, D.W., Miller, R.D.: ‘January. Seismic reflection methods applied to engineering, environmental, and ground-water problems’. Symp. on the Application of Geophysics to Engineering and Environmental Problems, Society of Exploration Geophysicists, 1988, pp. 409461.
    67. 67)
      • 20. Tian, Y., Li, Y., Lin, H., et al: ‘A sparse NMF-SU for seismic random noise attenuation’, IEEE Geosci. Remote Sens. Lett., 2013, 10, (3), pp. 607611.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-spr.2017.0556
Loading

Related content

content/journals/10.1049/iet-spr.2017.0556
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading