1887
Volume 72, Issue 8
  • E-ISSN: 1365-2478

Abstract

Abstract

Missing data and random noise are prevalent issues encountered during the processing of acquired seismic data. Interpolation and denoising represent economical solutions to address these limitations. Recovering regularly missing traces is challenging because of the spatial aliasing, and the extra difficulty is compounded by the presence of noise. Hence, developing an effective approach to realize denoising and anti‐aliasing is important. Projection onto convex sets is an effective method for recovering missing seismic data that is typically used for processing data with a good signal‐to‐noise ratio. The computational attractiveness of the projection onto convex sets reconstruction approach is compromised by its slow convergence rate. In this study, we aimed to efficiently implement simultaneous seismic data de‐aliasing and denoising. We combined a discrete wavelet transform with a seislet transform to construct a hybrid wavelet transform. A new fast adaptive method based on the fast projection onto convex sets method was proposed to recover the missing data and remove random noise. This approach adjusts the projection operator and iterative shrinkage threshold operator. The result is influenced by the threshold value. We enhanced the processing accuracy by adopting an optimal threshold strategy. Synthetic and field data tests indicate the effectiveness of the proposed method.

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2024-09-15
2026-02-11
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References

  1. Abma, R. & Kabir, N. (2006) 3D interpolation of irregular data with a pocs algorithm. Geophysics, 71, E91–E97.
    [Google Scholar]
  2. Almadani, M., Waheed, U.B., Mascood, M. & Chen, Y.K. (2021) Dictionary learning with convolutional structure for seismic data denoising and interpolation. Geophysics, 86, V361–V374.
    [Google Scholar]
  3. Beck, A. & TeboulleM. (2009) A fast iterative shrinkage‐thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences, 2, 183–202.
    [Google Scholar]
  4. Bekara, M. & Baan, M.V.D. (2009) Random and coherent noise attenuation by empirical mode decomposition. Geophysics, 74, V89–V98.
    [Google Scholar]
  5. Cao, J.J. & Wang, B.F. (2015) An improved projection onto convex sets method for simultaneous interpolation and denoising. Chinese Journal of Geophysics (in Chinese), 58, 2935–2947.
    [Google Scholar]
  6. Carozzi, F. & Sacchi, M.D. (2019) Robust tensor‐completion algorithm for 5D seismic‐data reconstruction. Geophysics, 84, V97–V109.
    [Google Scholar]
  7. Chen, Y.K., Chen, K.L., Shi, P.D. & Wang, Y.Y. (2014) Irregular seismic data reconstruction using a percentile‐half‐thresholding algorithm. Journal of Geophysics and Engineering, 11, 65001.
    [Google Scholar]
  8. Ely, G., Aeron, S., Hao, N. & Kilmer, M.E. (2015) 5D seismic data completion and denoising using a novel class of tensor decompositions. Geophysics, 80, V83–V95.
    [Google Scholar]
  9. Fang, W.Q., Fu, L.H., Xu, W.T., Bian, A.F. & Li, H.W. (2023) CCNet‐5D: 5D convolutional neural network for seismic data interpolation. Geophysics, 88, V333–V344.
    [Google Scholar]
  10. Fomel, S. (2002) Applications of plane‐wave destruction filters. Geophysics, 67, 1946–1960.
    [Google Scholar]
  11. Fomel, S. (2003) Seismic reflection data interpolation with differential offset and shot continuation. Geophysics, 68, 733–744.
    [Google Scholar]
  12. Fomel, S. (2006) Towards the seislet transform. In: SEG annual meeting extended abstracts. Jacksonville, SEG. pp. 2847–2851a.
  13. Fomel, S. & Liu, Y. (2010) Seislet transform and seislet frame. Geophysics, 75, V25–V38.
    [Google Scholar]
  14. Galloway, E. & Sacchi, M.D. (2007) POCS method for seismic data reconstruction of irregularly sampled data. In: Abstract of 2007 CSPG‐CSEG convention, Calgary, Canada, 555.
    [Google Scholar]
  15. Gan, S., Wang, S., Chen, Y., Chen, X. & Chen, H. (2016) Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform. Journal of Applied Geophysics, 130, 194–208.
    [Google Scholar]
  16. Gao, J.J., Stanton, A., Naghizadeh, M., Sacchi, M.D. & Chen, X.H. (2013) Convergence improvement and noise attenuation considerations for beyond alias projection onto convex sets reconstruction. Geophysical Prospecting, 61, 138–151.
    [Google Scholar]
  17. Gholami, A. (2014) Non‐convex compressed sensing with frequency mask for seismic data reconstruction and denoising. Geophysical Prospecting, 62, 1389–1405.
    [Google Scholar]
  18. Gou, F.Y., Liu, C., Liu, Y., Feng, X. & Cui, F.Z. (2014) Complex seismic wavefield interpolation based on the Bregman iteration method in the sparse transform domain. Applied Geophysics, 11, 277–288.
    [Google Scholar]
  19. Greiner, T.A.L., Lie, J.E., Kolbjornsen, O., Evensen, A.K., Nilsen, E.H., Zhao, H. et al. (2022) Unsupervised deep learning with higher‐order total‐variation regularization for multidimensional seismic data reconstruction. Geophysics, 87, V59–V73.
    [Google Scholar]
  20. Kaur, H., Pham, N. & Fomel, S. (2021) Seismic data interpolation using deep learning with generative adversarial networks. Geophysical Prospecting, 59, 307–326.
    [Google Scholar]
  21. Liu, C., Li, P., Liu, Y., Wang, D., Feng, X. & Liu, D.M. (2013) Iterative data interpolation beyond aliasing using seislet transform. Chinese Journal of Geophysics (in Chinese), 56(5), 1619–1627.
    [Google Scholar]
  22. Liu, L.N. & Ma, J.W. (2023) DL2: dictionary learning regularized with deep learning prior for simultaneous denoising and interpolation. Geophysics, 88, WA13–WA25.
    [Google Scholar]
  23. Liu, Y. & Fomel, S. (2010) OC‐seislet: seislet transform construction with differential offset continuation. Geophysics, 75, WB235–WB245.
    [Google Scholar]
  24. Liu, Y., Fomel, S. & Liu, C. (2015) Signal and noise separation in prestack seismic data using velocity‐dependent seislet transform. Geophysics, 80, WD117–WD128.
    [Google Scholar]
  25. Liu, Y., Zhang, P. & Liu, C. (2017) Seismic data interpolation using generalized velocity‐dependent seislet transform. Geophysical Prospecting, 65, 82–93.
    [Google Scholar]
  26. Liu, Y., Wu, G. & Zheng, Z.S. (2022) Seismic data interpolation without iteration using a t‐x‐y streaming prediction filter with varying smoothness. Geophysics, 87, V29–V38.
    [Google Scholar]
  27. Marfurt, K. (2006) Robust estimates of 3D reflector dip and azimuth. Geophysics, 71, P29–P40.
    [Google Scholar]
  28. Montefusco, L.B. & Papi, S. (2003) A parameter selection method for wavelet shrinkage denoising. BIT Numerical Mathematics, 43, 611–626.
    [Google Scholar]
  29. Naghizadeh, M. (2012) Seismic data interpolation and denoising in the frequency‐wavenumber domain. Geophysics, 77, V71–V80.
    [Google Scholar]
  30. Oboué, Y.A.S.I., Chen, W., Wang, H. & Chen, Y.K. (2021) Robust damped rank‐reduction method for simultaneous denoising and reconstruction of 5D seismic data. Geophysics, 86, V71–V89.
    [Google Scholar]
  31. O'Leary, D.P. & Hansen, P.C. (1993) The use of the l‐curve in the regularization of discrete ill‐posed problems. SIAM Journal on Scientific Computing, 14, 1487–1503.
    [Google Scholar]
  32. Oliveira, D.A.B., Ferreira, R.S., Silva, R. & Brazil, E.V. (2018) Interpolating seismic data with conditional generative adversarial networks. IEEE Geoscience and Remote Sensing Letters, 15, 1952–1956.
    [Google Scholar]
  33. Oliveira, D.A.B., Ferreira, R.S., Silva, R. & Brazil, E.V. (2019) Improving seismic data resolution with deep generative networks. IEEE Geoscience and Remote Sensing Letters, 16, 1929–1933.
    [Google Scholar]
  34. Oropeza, V. & Sacchi, M. (2011) Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics, 76, V25–V32.
    [Google Scholar]
  35. Rodriguez, I.V., Bonar, D. & Sacchi, M. (2012) Microseismic data denoising using a 3C group sparsity constrained time‐frequency transform. Geophysics, 77, V21–V29.
    [Google Scholar]
  36. Saad, O.M. & Chen, Y.K. (2020) Deep denoising autoencoder for seismic random noise attenuation. Geophysics, 85, V367–V376.
    [Google Scholar]
  37. Saad, O.M., Fomel, S., Abma, R. & Chen, Y.K. (2023) Unsupervised deep learning for 3D interpolation of highly incomplete data. Geophysics, 88, WA189–WA200.
    [Google Scholar]
  38. Stanton, A. & Sacchi, M.D. (2013) Vector reconstruction of multicomponent seismic data. Geophysics, 78, V131–V145.
    [Google Scholar]
  39. Trad, D. (2008) Five Dimensional Seismic Data Interpolation. In: SEG annual meeting extended abstracts. Las Vegas, SEG. pp. 978–982.
    [Google Scholar]
  40. Turquais, P., Asgedom, E.G., Söllner, W. & Gelius, L. (2018) Parabolic dictionary learning for seismic wavefield reconstruction across the streamers. Geophysics, 83, V263–V282.
    [Google Scholar]
  41. Wang, B.F., Wu, R.S., Chen, X.H. & Li, J.Y. (2015) Simultaneous seismic data interpolation and denoising with a new adaptive method based on dreamlet transform. Geophysical Journal Internal, 201, 1182–1194.
    [Google Scholar]
  42. Wang, Y. (2002) Seismic trace interpolation in the f‐x‐y domain. Geophysics, 67, 1232–1239.
    [Google Scholar]
  43. Wang, Y.F. (2007) Computational methods for inverse problems and their applications (in Chinese). Beijing: Higher Education Press.
    [Google Scholar]
  44. Wu, H., Zhang, B., Lin, T.F., Li, F.Y. & Lin, N.H. (2019) White noise attenuation of seismic trace by integrating variational mode decomposition with convolutional neural network. Geophysics, 84, V307–V317.
    [Google Scholar]
  45. Yang, P., Gao, J., & Chen, W. (2013) On analysis‐based two‐step interpolation methods for randomly sampled seismic data. Computers & Geosciences, 51, 449–461. https://doi.org/10.1016/j.cageo.2012.07.023
    [Google Scholar]
  46. Zhang, H. & Chen, X.H. (2013) Seismic data reconstruction based on jittered sampling and curvelet transform. Chinese Journal of Geophysics (in Chinese), 56, 1637–1649.
    [Google Scholar]
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