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Stratigraphic absorption compensation based on multiscale shearlet transform

  • Research Article - Applied Geophysics
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Abstract

Seismic waves propagating through viscoelastic media experience stratigraphic absorption and attenuation effects, which directly affect the imaging resolution in seismic exploration. Without stratigraphic absorption, the ratio of deep reflection energy to shallow reflection energy (attenuation ratio) is invariable at different frequencies. If a seismogram is decomposed into different frequency bands, these signals will show similar time–energy distributions. Therefore, the attenuation ratios should be similar across different frequency bands, except for frequency-variable weights. Nevertheless, the frequency-variable weights for different frequency bands can be obtained by benchmarking against the time–energy distributions of low-frequency information because the loss of low-frequency information is relatively insignificant. In this light, we obtained frequency-variable weights for different frequencies and established a stratal absorption compensation (SAC) model. The anisotropic basis of the shearlet enables nearly optimal representation of curved-shape seismic signals, and shearlets at different scales can represent signals for different frequency bands. Then, we combined the SAC model with the shearlet transform and established the new compensation method. As the signal and noise have different distributions in the shearlet domain, we selectively compensated the signals using a thresholding algorithm. Hence, it was possible to avoid noise enhancement. This is the prominent advantage of the proposed method over other compensation methods.

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References

  • Bai H, Li K (1999) Stratigraphic absorption based on time–frequency analysis. Oil Geophys Prospect 34(6):642–648 (in Chinese)

    Google Scholar 

  • Candès EJ, Donoho DL (2005a) Continuous curvelet transform: I. Resolution of the wavefront set. Appl Comput Harmonic Anal 19(2):162–197

    Article  Google Scholar 

  • Candès EJ, Donoho DL (2005b) Continuous curvelet transform: II. Discretization and frames. Appl Comput Harmonic Anal 19(2):198–222

    Article  Google Scholar 

  • Ferber R (2005) A filter bank solution to absorption simulation and compensation. SEG Tech Program Expand Abstr 24(1):2668

    Google Scholar 

  • Gao J, Ling Y, Zhou X, Mou YG (1996) Compensation for spherical divergence and absorption in time and frequency domain. Oil Geophys Prospect 31(6):856–866 (in Chinese)

    Google Scholar 

  • Guo K, Lim W, Labate D, Weiss G, Wilson E (2004a) Wavelets with composite dilations. Electron Res Announc Am Math Soc 10:78–87

    Article  Google Scholar 

  • Guo K, Lim W, Labate D, Weiss G, Wilson E (2004b) The theory of wavelets with composite dilations. In: Heil C (ed) Harmonic analysis and applications. Birkhäuser, Boston, pp 231–250

    Google Scholar 

  • Guo K, Lim W, Labate D, Weiss G, Wilson E (2006) Wavelets with composite dilations and their MRA properties. Appl Comput Harmonic Anal 20:231–249

    Article  Google Scholar 

  • Häuser S (2012) Fast finite Shearlet transform. arXiv:1202.1773

  • Herrmann FJ (2007) Recent developments in curvelet-based seismic processing. Seismic Laboratory for Imaging and Modeling, European Association of Geoscientists and Engineers, London. https://doi.org/10.3997/2214-4609.201405085

    Book  Google Scholar 

  • Herrmann FJ, Moghaddam P, Stolk CC (2008) Sparsity- and continuity-promoting seismic image recovery with curvelet frames. Appl Comput Harmonic Analsis 24(2):150–173

    Article  Google Scholar 

  • Lakshman H, Lim WQ, Schwarz H et al (2015) Image interpolation using shearlet based iterative refinement. Sig Process Image Commun 36:83–94

    Article  Google Scholar 

  • Li K, Li Y, Zhang X (2000) A method to compensate earth filtering based on wavelet packet. Chin J Geophys 43(4):542–549 (in Chinese)

    Article  Google Scholar 

  • Ling Y, Gao J, Zhang R (1997) Sand-dune Q absorption compensation based on 1-D elastic damping wave theory. Oil Geophys Prospect 32(6):795–803 (in Chinese)

    Google Scholar 

  • Liu X, Nian J, Liu H (2006) Generalized S-transform based on compensation for stratigraphic absorption of seismic attenuation. Geophys Prospect Petrol 45(1):9–14

    Google Scholar 

  • Liu C, Wang D, Wang T et al (2014) Random seismic noise attenuation based on the shearlet transform. Acta Petrol Sin 35(4):692–699 (in Chinese)

    Google Scholar 

  • Quan YL, Harris JM (1997) Seismic attenuation tomography using the frequency shift method. Geophysics 62(3):895–905

    Article  Google Scholar 

  • Saatcilar R, Coruh C (1999) Seismic Q estimations for lithological interpretation. SEG Tech Program Expand Abstr 14(1):1366

    Google Scholar 

  • Scott S, Taner MT, Treitel S (2006) Q estimation using Gabor–Morlet joint time–frequency analysis. In: SEG expanded abstracts, pp 2610–2614. https://doi.org/10.1190/1.2369829

  • Wang Y (2002) A stable and efficient approach of inverse Q filtering. Geophysics 67(2):657

    Article  Google Scholar 

  • Wang Y (2006) Inverse Q-filter for seismic resolution enhancement. Geophysics 71(3):v5l–v61

    Article  Google Scholar 

  • Wang D, Sun J, Meng D et al (2013) Absorption compensation based on curvelet transform. J Seism Explor 22(1):19–32

    Google Scholar 

  • Zhang G, Xiong X, Rong JJ, Cai ZD (2010) Stratum absorption and attenuation compensation based on improved generalized S transform. Oil Geophys Prospect 45(4):512–515 (in Chinese)

    Google Scholar 

  • Zhao S, Wang X, Wang J (1994) A simple frequency compensation method. Oil Geophys Prospect 29(2):231–235 (in Chinese)

    Google Scholar 

  • Zhou H, Qu G, Yang B (1994) New methods for calculating Q value using spectrum of seismic record. J Jilin Univ (Earth Sci Edn) 4:461–467 (in Chinese)

    Google Scholar 

Download references

Acknowledgements

We thank the ShearLab for sharing their codes available on the web. This research is supported by the Major Projects of the National Science and Technology of China (Grant No. 2016ZX05026-002-003), National Natural Science Foundation of China (No. 41374108), and Graduate Innovation Fund of Jilin University (No. 2017090).

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Correspondence to Deli Wang.

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Liu, C., Wang, D., Sun, J. et al. Stratigraphic absorption compensation based on multiscale shearlet transform. Acta Geophys. 66, 575–584 (2018). https://doi.org/10.1007/s11600-018-0156-8

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  • DOI: https://doi.org/10.1007/s11600-018-0156-8

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