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


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.


Reflection full-waveform inversion full-waveform inversion misfit function 


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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.


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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

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