Advertisement

Applied Geophysics

, Volume 14, Issue 3, pp 407–418 | Cite as

Reflection full-waveform inversion using a modified phase misfit function

  • Chao Cui
  • Jian-Ping Huang
  • Zhen-Chun Li
  • Wen-Yuan Liao
  • Zhe Guan
Seismic inversion
  • 72 Downloads

Abstract

Reflection full-waveform inversion (RFWI) updates the low- and highwavenumber components, and yields more accurate initial models compared with conventional full-waveform inversion (FWI). However, there is strong nonlinearity in conventional RFWI because of the lack of low-frequency data and the complexity of the amplitude. The separation of phase and amplitude information makes RFWI more linear. Traditional phase-calculation methods face severe phase wrapping. To solve this problem, we propose a modified phase-calculation method that uses the phase-envelope data to obtain the pseudo phase information. Then, we establish a pseudophase-information-based objective function for RFWI, with the corresponding source and gradient terms. Numerical tests verify that the proposed calculation method using the phase-envelope data guarantees the stability and accuracy of the phase information and the convergence of the objective function. The application on a portion of the Sigsbee2A model and comparison with inversion results of the improved RFWI and conventional FWI methods verify that the pseudophase-based RFWI produces a highly accurate and efficient velocity model. Moreover, the proposed method is robust to noise and high frequency.

Keywords

Reflection full-waveform inversion full-waveform inversion misfit function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The authors wish to thank the SWPI group in the China University of Petroleum (East China) for financial support and discussions. J.P. Huang was supported by the Tai Shan Science Foundation through The Excellent Youth Scholars program.

References

  1. Alan, R. L., 1988, Fourth-order finite-difference P-SV seismograms: Geophysics, 53(11), 1425–1436.CrossRefGoogle Scholar
  2. Bozdağ, E., Trampert, J., and Tromp, J., 2011, Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements: Geophys. J. Int., 185(2), 845–870.CrossRefGoogle Scholar
  3. Bunks, C., Saleck, F. M., Zaleski, S., et al., 1995, Multiscale seismic waveform inversion: Geophysics, 60(5), 1457–1473.CrossRefGoogle Scholar
  4. Chi, B., Dong, L., and Liu, Y., 2015, Correlation-based reflection full-waveform inversion: Geophysics, 80(4), 189–202.CrossRefGoogle Scholar
  5. Choi, Y., and Alkhalifah, T., 2011, Frequency-domain waveform inversion using the unwrapped phase: 81th Annual International Meeting, SEG, Expanded Abstracts, 2576–2580.Google Scholar
  6. Choi, Y., and Alkhalifah, T., 2013, Frequency-domain waveform inversion using the phase derivative: Geophys. J. Int., 195(3), 1904–1916.CrossRefGoogle Scholar
  7. Choi, Y., and Alkhalifah, T., 2015, Unwrapped phase inversion with an exponential damping: Geophysics, 80(5), 251–264.CrossRefGoogle Scholar
  8. Di, N. C., Shipp, E. R. and Singh, S., 1999, Fast traveltime tomography and analysis of real data using semiautomated picking procedure: 69th Annual International Meeting, SEG, Expanded Abstracts, 1414–1417.Google Scholar
  9. Dong, L. G., Chi, B. X., Tao, J. X., et al., 2013, Objective function behavior in acoustic full-waveform inversion: Chinese Journal Geophysics, 56(10), 3445–3460.Google Scholar
  10. Fichtner, A., Kennett, B. L. N., Igel, H., et al., 2008, Theoretical background for continental- and global-scale full-waveform inversion in the time–frequency domain: Geophys. J. Int., 175(2), 665–685.CrossRefGoogle Scholar
  11. Fichtner, A., and Trampert, J., 2011, Hessian kernels of seismic data functionals based upon adjoint techniques: Geophys. J. Int., 185(2), 775–798.CrossRefGoogle Scholar
  12. Hale, D., 2013, Dynamic wraping of seismic images: Geophysics, 78(2), S105–S115.CrossRefGoogle Scholar
  13. Huang, C., Dong, L. G., and Chi, B. X., 2015, Elastic envelope inversion using multicomponent seismic data with filtered-out low frequency: Applied Geophysics, 12(3), 362–377.CrossRefGoogle Scholar
  14. Huang, J. P., Yang, Y., Li, Z. C., et al., 2014, Comparative study among implementations of several free-surface boundaries with perfectly matched layer conditions: Acta Seismologica Sinica, 36(5), 964–977.Google Scholar
  15. Luo, J. R., and Wu, R. S., 2015, Seismic envelope inversion: reduction of local minima and noise resistance: Geophysical Prospecting, 63(3), 597–614.CrossRefGoogle Scholar
  16. Luo, J. R., Wu, R. S., and Gao, F. C., 2016, Time-domain full-waveform inversion using instantaneous phase with damping: 86th Annual International Meeting, SEG, Expanded Abstracts, 1472–1476.Google Scholar
  17. Ma, Y., and Hale, D., 2013, Wave-equation reflection traveltime inversion with dynamic wraping and fullwaveform inversion: Geophysics, 78(6), R223–R233.CrossRefGoogle Scholar
  18. Mora, P., 1989, Inversion = migration + tomography: Geophysics, 54(12), 1575–1586.CrossRefGoogle Scholar
  19. Plessix, R. É., 2006, A review of the adjoint-state method for computing the gradient of a functional with geophysical applications: Geophys. J. Int., 167(2), 495–503.CrossRefGoogle Scholar
  20. Plessix, R. É., 2013, A pseudo-time formulation for acoustic full waveform inversion: Geophys. J. Int., 192(2), 613–630.CrossRefGoogle Scholar
  21. Pratt, R. G., 1999, Seismic waveform inversion in the frequency domain-Part 1: Theory and verification in a physical scale model: Geophysics, 64(3), 888–901.CrossRefGoogle Scholar
  22. Shin, C., and Min, D. J., 2006, Waveform inversion using a logarithmic wavefield: Geophysics, 71(3), R31–R42.CrossRefGoogle Scholar
  23. Snieder, R., Xie, M. Y., Pica, A., et al., 1989, Retrieving both the impedance contrast and background velocity: A global strategy for the seismic reflection problem: Geophysics, 54(8), 991–1000.CrossRefGoogle Scholar
  24. Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49(8), 1259–1266.CrossRefGoogle Scholar
  25. Tejero, J. C. E., Dagnino, D., Sallares, V., et al., 2015, Comparative study of objective functions to overcome noise and bandwidth limitations in full waveform inversion: Geophys. J. Int., 203(1), 632–645.CrossRefGoogle Scholar
  26. Virieux, J., and Operto, S., 2009, An overview of fullwaveform inversion in exploration geophysics: Geophysics, 74(6), WCC1–WCC26.CrossRefGoogle Scholar
  27. Wang, H., Singh, S. C., Audebert, F., et al., 2015, Inversion of seismic refraction and reflection data for building longwavelength velocity models: Geophysics, 80(2), 81–93.CrossRefGoogle Scholar
  28. Wu, R. S., Luo, J., and Wu, B., 2014, Seismic envelope inversion and modulation signal model: Geophysics, 79(3), WA13–WA24.CrossRefGoogle Scholar
  29. Xu, S., Wang, D., Chen, F., et al., 2012, Inversion on reflected seismic wave: 82nd Annual International Meeting, SEG, Expanded Abstracts, 1–7.Google Scholar
  30. Zhou, W., Brossier, R., Operto, S., et al., 2015, Full waveform inversion of diving & reflected waves for velocity model building with impedance inversion based on scale separation: Geophys. J. Int., 202(3), 1535–1554.CrossRefGoogle Scholar

Copyright information

© Editorial Office of Applied Geophysics and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Chao Cui
    • 1
    • 2
  • Jian-Ping Huang
    • 1
    • 2
  • Zhen-Chun Li
    • 1
    • 2
  • Wen-Yuan Liao
    • 3
  • Zhe Guan
    • 4
  1. 1.School of GeosciencesChina University of Petroleum (East China)QingdaoChina
  2. 2.Laboratory for Marine Mineral ResourcesQingdao National Laboratory for Marine Science and TechnologyQingdaoChina
  3. 3.Department of Mathematics and StatisticsUniversity of CalgaryAlbertaCanada
  4. 4.Department of Earth ScienceRice UniversityHoustonUSA

Personalised recommendations