1887
Volume 54, Issue 2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

Reconstruction of missing seismic data is a critical procedure for subsequent applications like multiple wave suppression, wave-equation migration imaging and so on. In this paper, a fast, hyperparameter-free and sparse iterative spectral estimation approach is proposed for the reconstruction of two-dimensional seismic data of randomly missing traces. The proposed approach is based on the harmonic structure of the frequency slice of seismic data and the weighted covariance fitting criterion. Specifically, the method first iteratively estimates the spectrum of the frequency slice by solving a weighted covariance fitting problem. Then, the missing data is reconstructed by using the estimated spectrum and a linear minimum mean-squared error estimator. However, the spectral estimation depends on matrix-vector multiplications for each iteration, which has a high computational cost when the data increase to a large size. To solve this problem, a fast iterative technology is proposed by using an inverse fast Fourier transform, which fully exploits the Hermitian–Toeplitz structure of the covariance matrix and the exponential form of the steering vector and it significantly reduces the computational complexity. The proposed algorithm is hyperparameter-free, can provide super spectral resolution, and thus obtain better reconstruction performance. The experimental results of synthetic and real seismic data show that the proposed algorithm has higher reconstruction accuracy and lower computational complexity compared to other commonly used reconstruction algorithms.

© 2022 Australian Society of Exploration Geophysicists
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2023-03-04
2026-01-23

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References

  1. Bagaini, C., and U.Spagnolini. 1993. Common shot velocity analysis by shot continuation operator. SEG Technical Program Expanded Abstracts12 no. 1: 673–676.
     [Google Scholar]
  2. Bolondi, G., E.Loinger, and F.Rocca. 1982. Offset continuation of seismic sections. Geophysical Prospecting30: 813–828.
     [Google Scholar]
  3. Cadzow, J.A.1988. Signal enhancement-a composite property mapping algorithm. IEEE Transactions on Acoustics, Speech, and Signal Processing36 no. 3: 49–62.
     [Google Scholar]
  4. Cai, S., X.Y.Shi, and H.B.Zhu. 2017. Direction-of-arrival estimation and tracking based on a sequential implementation of C-SPICE with an off-grid model. Sensors17 no. 12: 2718–2729.
     [Google Scholar]
  5. Cao, J.J., Z.C.Cai, and W.Q.Liang. 2020. A novel thresholding method for simultaneous seismic data reconstruction and denoising. Journal of Applied Geophysics177: 1–10.
     [Google Scholar]
  6. Chemingui, N., and B.Biondi. 1996. Handing the irregular geometry in wide-azimuth surveys. SEG Technical Program Expanded Abstracts15 no. 1: 32–35.
     [Google Scholar]
  7. Chen, K., and M.D.Sacchi. 2015. Robust reduced-rank filtering for erratic seismic noise attenuation. Geophysics80 no. 1: V1–V11.
     [Google Scholar]
  8. Crawley, S., R.Clapp, and J.Claerbout. 1999. Interpolation with smoothly nonstationary prediction-error filters. SEG Technical Program Expanded Abstracts no.18: 1154–1157.
  9. Fang, W.Q., L.H.Fu, M.Zhang, and Z.M.Li. 2021. Seismic data interpolation based on U-net with texture loss. Geophysics86 no. 1: V41–V54.
     [Google Scholar]
  10. Fomel, S., and Y.Liu. 2010. Seislet transform and seislet frame. Geophysics75 no. 3: V25–V38.
     [Google Scholar]
  11. Gülünay, N.2003. Seismic trace interpolation in the Fourier transform domain. Geophysics68 no. 1: 355–369.
     [Google Scholar]
  12. Hennenfent, G., and F.Herrmann. 2008. Simply denoise: wavefield reconstruction via jittered undersampling. Geophysics73 no. 3: V19–V28.
     [Google Scholar]
  13. Jia, Y.N., S.W.Yu, and J.W.Ma. 2018. Intelligent interpolation by Monte Carlo machine learning. Geophysics83 no. 3: V83–V97.
     [Google Scholar]
  14. Kabir, M.M.N., and D.J.Verschuur. 1995. Restoration of missing offsets by parabolic Radon transform. Geophysical Prospecting43: 347–368.
     [Google Scholar]
  15. Karlsson, J., W.Rowe, L.Z.Xu, G.Glentis, and J.Li. 2013. Fast missing-data IAA with application to notched spectrum SAR. IEEE Transactions on Aerospace and Electronic Systems50 no. 2: 959–971.
     [Google Scholar]
  16. Liu, B., and M.D.Sacch. 2004. Minimum weighted norm interpolation of seismic records. Geophysics69 no. 6: 1560–1568.
     [Google Scholar]
  17. Liu, Q., L.H.Fu, and M.Zhang. 2021. Deep-seismic-prior-based reconstruction of seismic data using convolutional neural networks. Geophysics86 no. 6: V131–V142.
     [Google Scholar]
  18. Liu, Q., L.H.Fu, M.Zhang, and W.J.Zhang. 2020. Two-dimensional seismic data reconstruction using patch tensor completion. Inverse Problems and Imaging14 no. 6: 985–1000.
     [Google Scholar]
  19. Liu, Y., and S.Fomel. 2010. OC-seislet: seislet transform construction with differential offset continuation. Geophysics75 no. 6: WB235–WB245.
     [Google Scholar]
  20. Ma, J.W.2013. Three-dimensional irregular seismic data reconstruction via low-rank matrix completion. Geophysics78 no. 5: V181–V192.
     [Google Scholar]
  21. Naghizadeh, M., and M.D.Sacchi. 2009. f–x adaptive seismic trace interpolation. Geophysics74 no. 1: V9–V16.
     [Google Scholar]
  22. Naghizadeh, M., and M.D.Sacchi. 2010. Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data. Geophysics75: 6. WB189–WB202.
     [Google Scholar]
  23. Oropeza, V., and M.D.Sacchi. 2011. Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics76 no. 3: V25–V32.
     [Google Scholar]
  24. Oropeza, V.E.2010. The singular spectrum analysis method and its application to seismic data denoising and reconstruction, PhD diss., University of Alberta.
  25. Park, H.R., and J.Li. 2015. Sparse covariance-based high resolution time delay estimation for spread spectrum signals. Electronics Letters51 no. 3: 155–157.
     [Google Scholar]
  26. Park, J., J.Choi, S.Seol, J.Byun, and Y.Kim. 2021. A method for adequate selection of training data sets to reconstruct seismic data using a convolutional U-Net. Geophysics86 no. 3: V375–V388.
     [Google Scholar]
  27. Peng, X., X.W.Li, C.C.Wang, J.J.Zhu, L.Liang, H.Q.Fu, Y.N.Du, Z.F.Yang, and Q.H.Xie. 2019. SPICE-Based SAR tomography over forest areas using a small number of P-band airborne F-SAR images characterized by non-uniformly distributed baselines. Remote Sensing11 no. 8: 975–992.
     [Google Scholar]
  28. Ronen, J.1987. Wave equation trace interpolation. Geophysics52 no. 7: 973–984.
     [Google Scholar]
  29. Sacchi, M.D., T.J.Ulrych, and C.J.Walker. 1998. Interpolation and extrapolationusing a high-resolution discrete Fourier transform. IEEE Transactions on Signal Processing46 no. 1: 31–38.
     [Google Scholar]
  30. Sayed, A.2003. Fundamentals of adaptive filtering. New York: Wiley.
  31. Schaeffer, H., and S.Osher. 2013. A low patch-rank interpretation of texture. Siam Journal on Imaging Sciences6 no. 1: 226–262.
     [Google Scholar]
  32. Sen, S., S.Kainkaryam, C.Ong, and A.Sharma. 2019. Interpolation of regularly sampled pre-stack seismic data with self-supervised learning. SEG Technical Program Expanded Abstracts. 3974–3978.
  33. Shang, X.L., J.Li, and P.Stoica. 2021. Weighted SPICE algorithms for Range-Doppler imaging using one-bit automotive radar. IEEE Journal of Selected Topics in Signal Processing15 no. 4: 1041–1054.
     [Google Scholar]
  34. Spitz, S.2012. Seismic trace interpolation in the f–x domain. Geophysics56 no. 6: 785–794.
     [Google Scholar]
  35. Stoica, P., J.Li, and J.Ling. 2009. Missing data recovery via a nonparametric iterative adaptive approach. IEEE Signal Processing Letters16 no. 4: 241–244.
     [Google Scholar]
  36. Stoica, P., P.Babu, and J.Li. 2011a. New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data. IEEE Transactions on Signal Processing 59 no. 1: 35–47.
  37. Stoica, P., P.Babu, and J.Li. 2011b. SPICE: A sparse covariance-based estimation method for array processing. IEEE Transactions on Signal Processing 59 no. 2: 629–638.
  38. Trad, D.2009. Five-dimensional interpolation: recovering from acquisition constraints. Geophysics74 no. 6: V123–V132.
     [Google Scholar]
  39. Trad, D.O., T.J.Ulrych, and M.D.Sacchi. 2002. Accurate interpolation with highresolution time-variant Radon transforms. Geophysics67 no. 2: 644–656.
     [Google Scholar]
  40. Wang, B.F., N.Zhang, W.K.Lu, and J.L.Wang. 2019. Deep-learning-based seismic data interpolation: A preliminary result. Geophysics84 no. 1: 11–20.
     [Google Scholar]
  41. Wang, J., J.W.Ma, B.Han, and Y.F.Cheng. 2015. Seismic data reconstruction via weighted nuclear-norm minimization. Inverse Problems in Science and Engineering23 no. 1: 277–291.
     [Google Scholar]
  42. Wang, Q., Y.T.Shen, L.H.Fu, and H.W.Li. 2020. Seismic data interpolation using deep internal learning. Exploration Geophysics51 no. 6: 683–697.
     [Google Scholar]
  43. Xu, S., Y.Zhang, D.Pham, and G.Lambaré. 2005. Antileakage Fourier transform for seismic data regularization. Geophysics70 no. 4: V87–V95.
     [Google Scholar]
  44. Xue, M., L.Z.Xu, and J.Li. 2011. IAA spectral estimation: fast implementation using the Gohberg–Semencul factorization. IEEE Transactions on Signal Processing59 no. 7: 3251–3261.
     [Google Scholar]
  45. Zhang, H., X.H.Chen, and L.Y.Zhang. 2017. 3D simultaneous seismic data reconstruction and noise suppression based on the curvelet transform. Applied Geophysics14 no. 1: 87–95.
     [Google Scholar]
  46. Zhang, Q.L., H.Abeida, M.Xue, W.Rowe, and J.Li. 2012. Fast implementation of sparse iterative covariance-based estimation for source localization. Journal of the Acoustical Society of America131 no. 2: 1249–1259.
     [Google Scholar]
  47. Zhang, Y., A.Jakobsson, Y.Zhang, Y.Huang, and J.Yang. 2018a. Wideband sparse reconstruction for scanning radar. IEEE Transactions on Geoscience and Remote Sensing 56 no. 10: 6055–6068.
  48. Zhang, H., S.Diao, H.Yang, G.Huang, X.Chen, and L.Li. 2018b. Reconstruction of 3D non-uniformly sampled seismic data along two spatial coordinates using non-equispaced curvelet transform. Exploration Geophysics 49 no. 6: 906–921.
  49. Zhang, W.J., L.H.Fu, M.Zhang, and W.T.Cheng. 2020. 2-D seismic data reconstruction via truncated nuclear norm regularization. IEEE Transaction on Geoscience and Remote Sensing58 no. 9: 6336–6343.
     [Google Scholar]
  50. Zheng, Y., L.T.Liu, and X.D.Yang. 2019. SPICE-ML algorithm for direction-of-arrival estimation. Sensors20 no. 1: 119–130.
     [Google Scholar]
/content/journals/10.1080/08123985.2022.2114828
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Fast hyperparameter-free spectral approach for 2D seismic data reconstruction
Exploration Geophysics 54, 174 (2023); https://doi.org/10.1080/08123985.2022.2114828
/content/journals/10.1080/08123985.2022.2114828
/content/journals/10.1080/08123985.2022.2114828
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  • Article Type: Research Article
Keyword(s): minimum mean-squared error; Seismic data reconstruction; spectral estimation; weighted covariance fitting criterion

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