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Full waveform inversion based on a local traveltime correction and zero-mean cross-correlation-based misfit function

  • Shiqi Dong
  • Liguo HanEmail author
  • Yong Hu
  • Yuchen Yin
Research Article - Applied Geophysics
  • 38 Downloads

Abstract

Full waveform inversion (FWI) suffers from the cycle skipping problem, because the observed data usually lack low-frequency components or due to errors in the wavelet estimation. In addition, the strong low-frequency non-zero-mean noise can have a large impact on FWI results. Thus, we propose a local waveform traveltime correction scheme to solve the situations when the observed data lack low-frequency components or when the estimation for the wavelet is incorrect. We use a sliding time window, which is used to decrease the traveltime differences between the calculated and observed data to increase the cross-correlation between them. Besides, we propose a zero-mean normalized cross-correlation misfit function to reduce the interference of the low-frequency non-zero-mean noise. Therefore, we propose new approaches to improve FWI results whether the observed data lack low-frequency components or the observed data are contaminated by the non-zero-mean low-frequency noise. Numerical examples on Marmousi model show the feasibility of a FWI based on the zero-mean normalized cross-correlation misfit function and a FWI based on the local traveltime correction method.

Keywords

FWI Local traveltime correction Zero-mean normalized cross-correlation 

Notes

Acknowledgments

We are grateful for the support of the National Natural Science Foundation of China (No.41674124).

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding authors state that there is no conflict of interest.

References

  1. Alkhalifah T (2016) Full-model wavenumber inversion: an emphasis on the appropriate wavenumber continuation. Geophysics 81:R89–R98.  https://doi.org/10.1190/geo2015-0537.1 CrossRefGoogle Scholar
  2. Alkhalifah T, Choi Y (2014) From tomography to full-waveform inversion with a single objective function. Geophysics 79:R55–R61.  https://doi.org/10.1190/geo2013-0291.1 CrossRefGoogle Scholar
  3. Bai J, Yingst D, Bloor R, Leveille J (2014) Viscoacoustic waveform inversion of velocity structures in the time domain. Geophysics 79:R103–R119.  https://doi.org/10.1190/geo2013-0030.1 CrossRefGoogle Scholar
  4. Biondi B, Symes WW (2004) Angle-domain common-image gathers for migration velocity analysis by wavefield-continuation imaging. Geophysics 69:1283–1298.  https://doi.org/10.1190/1.1801945 CrossRefGoogle Scholar
  5. Bishop TN et al (1985) Tomographic determination of velocity and depth in laterally varying media. Geophysics 50:903–923.  https://doi.org/10.1190/1.1441970 CrossRefGoogle Scholar
  6. Bozdağ E, Trampert J, Tromp J (2011) Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements. Geophys J Int 185:845–870.  https://doi.org/10.1111/j.1365-246X.2011.04970.x CrossRefGoogle Scholar
  7. Bunks G, Saleck FM, Zaleski S, Chavent G (1995) Multiscale seismic waveform inversion. Geophysics 60:1457–1473.  https://doi.org/10.1190/1.1443880 CrossRefGoogle Scholar
  8. Chen G, Chen S, Wu R-S (2015) Full Waveform Inversion in time domain using time-damping filters. SEG Tech Program Expanded Abstr.  https://doi.org/10.1190/segam2015-5878658.1 CrossRefGoogle Scholar
  9. Chi B, Dong L, Liu Y (2014) Full waveform inversion method using envelope objective function without low frequency data. J Appl Geophys 109:36–46.  https://doi.org/10.1016/j.jappgeo.2014.07.010 CrossRefGoogle Scholar
  10. Chi B, Dong L, Liu Y (2015) Correlation-based reflection full-waveform inversion. Geophysics 80:R189–R202.  https://doi.org/10.1190/geo2014-0345.1 CrossRefGoogle Scholar
  11. Choi Y, Alkhalifah T (2011) Source-independent time-domain waveform inversion using convolved wavefields: application to the encoded multisource waveform inversion. Geophysics 76:R125–R134.  https://doi.org/10.1190/geo2010-0210.1 CrossRefGoogle Scholar
  12. Choi Y, Alkhalifah T (2012) Application of multi-source waveform inversion to marine streamer data using the global correlation norm. Geophys Prospect 60:748–758.  https://doi.org/10.1111/j.1365-2478.2012.01079.x CrossRefGoogle Scholar
  13. Choi Y, Alkhalifah T (2015) Unwrapped phase inversion with an exponential damping. Geophysics 80:R251–R264.  https://doi.org/10.1190/geo2014-0498.1 CrossRefGoogle Scholar
  14. Choi Y, Alkhalifah T (2018) Time-domain full-waveform inversion of exponentially damped wavefield using the deconvolution-based objective function. Geophysics 83:R77–R88.  https://doi.org/10.1190/geo2017-0057.1 CrossRefGoogle Scholar
  15. Datta D, Sen MK (2016) Estimating a starting model for full-waveform inversion using a global optimization method. Geophysics 81:R211–R223.  https://doi.org/10.1190/geo2015-0339.1 CrossRefGoogle Scholar
  16. Engquist B, Froese BD, Yang Y (2016) Optimal transport for seismic full waveform inversion. Commun Math Sci 14:2309–2330.  https://doi.org/10.4310/CMS.2016.v14.n8.a9 CrossRefGoogle Scholar
  17. Fomel S (2007) Local seismic attributes. Geophysics 72:A29–A33.  https://doi.org/10.1190/1.2437573 CrossRefGoogle Scholar
  18. Gauthier O, Virieux J, Tarantola A (1986) Two-dimensional nonlinear inversion of seismic waveforms: numerical results. Geophysics 51:1387–1403.  https://doi.org/10.1190/1.1442188 CrossRefGoogle Scholar
  19. Guo Q, Alkhalifah T (2017) Elastic reflection-based waveform inversion with a nonlinear approach. Geophysics 82:R309–R321.  https://doi.org/10.1190/geo2016-0407.1 CrossRefGoogle Scholar
  20. Hale D (2006) Fast local cross-correlations of images. SEG Tech Program Expanded Abstr.  https://doi.org/10.1190/1.2370185 CrossRefGoogle Scholar
  21. Hu W (2014) FWI without low frequency data-beat tone inversion. SEG Tech Program Expanded Abstr.  https://doi.org/10.1190/segam2014-0978.1 CrossRefGoogle Scholar
  22. Hu Y, Han L, Xu Z, Zhang F, Zeng J (2017) Adaptive multi-step full waveform inversion based on waveform mode decomposition. J Appl Geophys 139:195–210.  https://doi.org/10.1016/j.jappgeo.2017.02.017 CrossRefGoogle Scholar
  23. Hu Y, Han L, Zhang P, Ge Q (2018) Time-frequency domain multi-scale full waveform inversion based on adaptive non-stationary phase correction. EAGE Tech Program Ext Abstr.  https://doi.org/10.3997/2214-4609.201800891 CrossRefGoogle Scholar
  24. Justice JH et al (1989) Acoustic tomography for enhancing oil recovery. Lead Edge 8:12–19.  https://doi.org/10.1190/1.1439605 CrossRefGoogle Scholar
  25. Krebs JR, Anderson JE, Hinkley D, Neelamani R, Lee S, Baumstein A, Lacasse MD (2009) Fast full-wavefield seismic inversion using encoded sources. Geophysics 74:WCC177–WCC188.  https://doi.org/10.1190/1.3230502 CrossRefGoogle Scholar
  26. Lailly P (1983) The seismic inverse problem as a sequence of before stack migrations. In: Conference on inverse scattering: theory and application, pp 206–220Google Scholar
  27. Lee KH, Kim HJ (2003) Source-independent full-waveform inversion of seismic data. Geophysics 68:2010–2015.  https://doi.org/10.1190/1.1635054 CrossRefGoogle Scholar
  28. Li Y, Choi Y, Alkhalifah T, Li Z, Zhang K (2018) Full-waveform inversion using a nonlinearly smoothed wavefield. Geophysics 83:R117–R127.  https://doi.org/10.1190/geo2017-0312.1 CrossRefGoogle Scholar
  29. Lian S, Yuan S, Wang G, Liu T, Liu Y, Wang S (2018) Enhancing low-wavenumber components of full-waveform inversion using an improved wavefield decomposition method in the time-space domain. J Appl Geophys 157:10–22.  https://doi.org/10.1016/j.jappgeo.2018.06.013 CrossRefGoogle Scholar
  30. Liu Y, Teng J, Xu T, Wang Y, Liu Q, Badal J (2016) Robust time-domain full waveform inversion with normalized zero-lag cross-correlation objective function. Geophys J Int 209:106–122.  https://doi.org/10.1093/gji/ggw485 CrossRefGoogle Scholar
  31. Liu Q, Peter D, Tape C (2019) Square-root variable metric based elastic full-waveform inversion—part 1: theory and validation. Geophys J Int 218:1121–1135.  https://doi.org/10.1093/gji/ggz188 CrossRefGoogle Scholar
  32. Luo Y, Schuster GT (1991) Wave-equation traveltime inversion. Geophysics 56:645–653.  https://doi.org/10.1190/1.1443081 CrossRefGoogle Scholar
  33. Mikesell TD, Malcolm AE, Yang D, Haney MM (2015) A comparison of methods to estimate seismic phase delays: numerical examples for coda wave interferometry. Geophys J Int 202:347–360.  https://doi.org/10.1093/gji/ggv138 CrossRefGoogle Scholar
  34. Pan W, Huang L (2018) Elastic-wave-equation traveltime tomography in anisotropic media using differential measurements of long-offset data. SEG Tech Program Expand Abstr 2018:5233–5237.  https://doi.org/10.1190/segam2018-2997226.1 CrossRefGoogle Scholar
  35. Pratt RG, Shin C, Hicks GJ (1998) Gauss–Newton and full Newton methods in frequency-space seismic waveform inversion. Geophys J Int 133:341–362.  https://doi.org/10.1046/j.1365-246X.1998.00498.x CrossRefGoogle Scholar
  36. Sajeva A, Aleardi M, Stucchi E, Bienati N, Mazzotti A (2016) Estimation of acoustic macro models using a genetic full-waveform inversion: applications to the Marmousi model. Geophysics 81:R173–R184.  https://doi.org/10.1190/geo2015-0198.1 CrossRefGoogle Scholar
  37. Schuster GT, Wang X, Huang Y, Dai W, Boonyasiriwat C (2011) Theory of multisource crosstalk reduction by phase-encoded statics. Geophys J Int 184:1289–1303.  https://doi.org/10.1111/j.1365-246X.2010.04906.x CrossRefGoogle Scholar
  38. Shin C, Ho Cha Y (2009) Waveform inversion in the Laplace–Fourier domain. Geophys J Int 177:1067–1079.  https://doi.org/10.1111/j.1365-246X.2009.04102.x CrossRefGoogle Scholar
  39. Shin C, Min D-J (2006) Waveform inversion using a logarithmic wavefield. Geophysics 71:R31–R42.  https://doi.org/10.1190/1.2194523 CrossRefGoogle Scholar
  40. Sun B, Alkhalifah T (2019) Adaptive traveltime inversion. Geophysics 84:U13–U29.  https://doi.org/10.1190/geo2018-0595.1 CrossRefGoogle Scholar
  41. Symes WW, Carazzone JJ (1991) Velocity inversion by differential semblance optimization. Geophysics 56:654–663.  https://doi.org/10.1190/1.1443082 CrossRefGoogle Scholar
  42. Tarantola A (1984) Linearized inversion of seismic reflection data. Geophys Prospect 32:998–1015.  https://doi.org/10.1111/j.1365-2478.1984.tb00751.x CrossRefGoogle Scholar
  43. Virieux J, Operto S (2009) An overview of full-waveform inversion in exploration geophysics. Geophysics 74:WCC1–WCC26.  https://doi.org/10.1190/1.3238367 CrossRefGoogle Scholar
  44. Wang G, Yuan S, Wang S (2019) Retrieving low-wavenumber information in FWI: an efficient solution for cycle skipping. IEEE Geosci Remote Sens Lett 16:1125–1129.  https://doi.org/10.1109/lgrs.2019.2892998 CrossRefGoogle Scholar
  45. Warner M, Guasch L (2014) Adaptive waveform inversion: theory. SEG Tech Program Expand Abstr.  https://doi.org/10.1190/segam2014-0371.1 CrossRefGoogle Scholar
  46. Wu R-S, Luo J, Wu B (2014) Seismic envelope inversion and modulation signal model. Geophysics 79:WA13–WA24.  https://doi.org/10.1190/geo2013-0294.1 CrossRefGoogle Scholar
  47. Xu S, Wang D, Chen F, Zhang Y, Lambare G (2012) Full waveform inversion for reflected seismic data. EAGE Tech Program Ext Abstr.  https://doi.org/10.3997/2214-4609.20148725 CrossRefGoogle Scholar
  48. Yang H, Han L, Zhang F, Sun H, Bai L (2016) Full waveform inversion without low frequency using wavefield phase correlation shifting method. J Seism Explor 25:45–55Google Scholar
  49. Yuan S, Wang S, Luo Y, Wei W, Wang G (2019) Impedance inversion by using the low-frequency full-waveform inversion result as an a priori model. Geophysics 84:R149–R164.  https://doi.org/10.1190/geo2017-0643.1 CrossRefGoogle Scholar
  50. Zhang P, Han L, Xu Z, Zhang F, Wei Y (2017) Sparse blind deconvolution based low-frequency seismic data reconstruction for multiscale full waveform inversion. J Appl Geophys 139:91–108.  https://doi.org/10.1016/j.jappgeo.2017.02.021 CrossRefGoogle Scholar
  51. Zhang Z, Alkhalifah T, Wu Z, Liu Y, He B, Oh J (2019) Normalized nonzero-lag crosscorrelation elastic full-waveform inversion. Geophysics 84:R1–R10.  https://doi.org/10.1190/geo2018-0082.1 CrossRefGoogle Scholar
  52. Zhou B, Greenhalgh SA (2003) Crosshole seismic inversion with normalized full-waveform amplitude data. Geophysics 68:1320–1330.  https://doi.org/10.1190/1.1598125 CrossRefGoogle Scholar
  53. Zhu H, Fomel S (2016) Building good starting models for full-waveform inversionusing adaptive matching filtering misfit. Geophysics 81:U61–U72.  https://doi.org/10.1190/geo2015-0596.1 CrossRefGoogle Scholar

Copyright information

© Institute of Geophysics, Polish Academy of Sciences & Polish Academy of Sciences 2019

Authors and Affiliations

  1. 1.College of Geo-Exploration Science and TechnologyJilin UniversityChangchunChina

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