High-resolution time-frequency hilbert transform using sparsity-aware weighting function

Abstract

Instantaneous complex attributes that rely on conventional Hilbert transformation are normally susceptible to random noise and abrupt frequency variations in seismic signals. Moreover, conventional filtering methods diminish the spectral bandwidth needed to suppress noise when estimating seismic attributes. This has a significant impact on the resolution in thin-bed layers, which demand wide-band data to image properly. Therefore, in this paper, we address the noise and resolution problems in seismic attributes by applying a sparsity-aware weighting function that makes use of Geman-McClure and Laplace functions to a sparsity-based adaptive S-transform. The proposed filter not only suppresses the random noise but also increases the resolution of the Hilbert transform in the calculation of seismic attributes. Finally, to corroborate the superiority of the proposed method over some state-of-the-art approaches in synthetic and real data sets, the results are compared with the sparsity-based adaptive S-transform and the robust windowed Hilbert transform.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

References

  1. Ali A, Younas M, Ullah M, Hussain M, Toqeer M, Bhatti AS, Khan A (2019) Characterization of secondary reservoir potential via seismic inversion and attribute analysis: A case study. J Pet Sci Eng 178:272–293

    Article  Google Scholar 

  2. Andrade MCB, Porsani MJ, Ursin B (2018) Complex autoregressive time-frequency analysis: Estimation of time-varying periodic signal components. IEEE Signal Process Mag 35 (2):142– 153

    Article  Google Scholar 

  3. Boashash B (2015) Time-frequency signal analysis and processing: A comprehensive reference. Time-frequency signal analysis and processing. A Comprehensive Reference

  4. Castagna JP, Sun S, Siegfried RW (2003) Instantaneous spectral analysis: Detection of low-frequency shadows associated with hydrocarbons. Leading Edge 22(2):120–127

    Article  Google Scholar 

  5. Jones DL, Parks TW (1990) A high resolution data-adaptive time-frequency representation. IEEE Trans Acoust 38(12):2127– 2135

    Article  Google Scholar 

  6. Lamoureux MP, Gibson PC, Grossman JP, Margrave GF (2003) A fast, discrete gabor transform 423 via a partition of unity. J Fourier Anal Appl 72(6):W33–W43

    Google Scholar 

  7. Li J, Liu C, Zeng Z, Chen L (2015) GPR signal denoising and target extraction with the ceemd method. IEEE Geosci Remote Sens Lett 12(8):1615–1619

    Article  Google Scholar 

  8. Lima MVS, Ferreira TN, Martins WA, Diniz PSR (2014) Sparsity-aware data-selective adaptive filters. IEEE Trans Signal Process 62(17):4557–4572

    Article  Google Scholar 

  9. Lu WK, Zhang CK (2013) Robust estimation of instantaneous phase using a time-frequency adaptive filter. Geophysics 78(1):O1– O7

    Article  Google Scholar 

  10. Luo Y, Al-Dossary S, Marhoon M, Alfaraj M (2003) Generalized hilbert transform and its applications in geophysics. Lead Edge 22(3):198–202

    Article  Google Scholar 

  11. Natarajan BK (1995) Sparse approximate solutions to linear systems. SIAM J Comput 24 (2):227–234

    Article  Google Scholar 

  12. Radad M, Gholami A, Siahkoohi HR (2015) S-transform with maximum energy concentration: Application to non-stationary seismic deconvolution. J Appl Geophys 118:155–166

    Article  Google Scholar 

  13. Sattari H (2017) High-resolution seismic complex trace analysis by adaptive fast sparse s-transform. Geophysics 82(1):V51–V67

    Article  Google Scholar 

  14. Stockwell RG, Mansinha L, Lowe RP (1996) Localization of the complex spectrum: The S transform. IEEE Trans Signal Proc 44(4):998–1001

    Article  Google Scholar 

  15. Taner MT, Koehler F, Sheriff RE (1979) Complex seismic trace analysis. Geophys 44 (6):1041–1063

    Article  Google Scholar 

  16. Ville J (1948) Theorie et applications de la notion de signal analytique. Cables Trans 2(1):61–74

    Google Scholar 

  17. Wang X, Chen W, Zhu Z, Luo Y, Yang Y (2019) Robust seismic volumetric dip estimation combining structure tensor and multiwindow technology. IEEE Trans Geosci Remote Sens 57(1):395–405

    Article  Google Scholar 

  18. Xue W, Dai X, Zhu J, Luo Y, Yang Y (2019) A noise suppression method of ground penetrating radar based on eemd and permutation entropy. IEEE Geosci Remote Sens Lett 16(10):1625–1629

    Article  Google Scholar 

  19. Yazdanpanah H, Diniz PSR (2017) Recursive Least-Squares algorithms for sparse system modeling. In: IEEE International conference on acoustics, speech and signal processing (ICASSP) 2017, IEEE, pp 3879–3883

  20. Yazdanpanah H, Carini A, Lima MVS (2019) L0-norm adaptive Volterra filters. In: 27th European signal processing conference (EUSIPCO) 2019, pp 1–5

  21. Yuan S, Su Y, Wang T, Wang J, Wang S (2019) Geosteering phase attributes: A new detector for the discontinuities of seismic images. IEEE Geosci Remote Sens Lett 16(1):145–149

    Article  Google Scholar 

  22. Zhang J, Li Y, Wu N (2015) Noise attenuation for seismic data by hyperbolic-trace time-frequency peak filtering. IEEE Geosci Remote Sens Lett 12(3):601–605

    Article  Google Scholar 

Download references

Acknowledgements

The authors notably appreciate the funding of this study by the Brazilian Research Council, CNPq, with the grant number 141453/2016-8. Also, this study was financed in part by the São Paulo Research Foundation (FAPESP) grant #2015/22308-2. We especially thank Dr. Hossein Shomali for his constructive comments.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Mohsen Kazemnia Khakhki.

Ethics declarations

Conflict of Interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by: H. Babaie

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Khakhki, M.K., Moghaddam, P.P., Yazdanpanah, H. et al. High-resolution time-frequency hilbert transform using sparsity-aware weighting function. Earth Sci Inform (2021). https://doi.org/10.1007/s12145-021-00628-z

Download citation

Keywords

  • Sparsity-based adaptive S-transform
  • Window Hilbert transform
  • Adaptive weighting function