The misfit function of the conventional Full Waveform Inversion (FWI) based on the L2 norm is a strong nonlinear optimization problem and it may easily fall into a local minimum. In addition, the conventional FWI misfit function also needs an accurate source wavelet and a high signal-to-noise ratio (SNR) seismic data. These restrictions constraint the application of FWI in the real field seismic data processing. In this abstract, the misfit function of normalized energy spectrum is proposed to alleviate the strong nonlinear problem for the FWI method and reduce the dependence of high SNR seismic data and source wavelet. It is to match the normalized energy spectrum of recorded and synthetic data with the frequency distribution, which ignores the waveform and phase oscillation characteristics. Numerical examples show that the normalized energy spectrum FWI (NESFWI) results are better than the normalized FWI (NFWI) results in some areas, such as constructing a good initial velocity model, noise immunity, and source wavelet independence.


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  1. Chi, B., Dong, L., Liu, Y.
    , 2014. Full waveform inversion method using envelope objective function without low frequency data. J Appl Geophys109, 36–46.
    [Google Scholar]
  2. Choi, Y., Alkhalifah, T.
    , 2012. Application of multi-source waveform inversion to marine streamer data using the global correlation norm. Geophys Prospect60, 748–758.
    [Google Scholar]
  3. Hu, Y., Han, L.G., Xu, Z., Zhang, F.J., Zeng, J.W.
    , 2017. Adaptive multi-step Full Waveform Inversion based on Waveform Mode Decomposition. J Appl Geophys139, 195–210.
    [Google Scholar]
  4. 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. Geophysical Journal International209, 106–122.
    [Google Scholar]
  5. Métivier, L., Brossier, R., Mérigot, Q., Oudet, E., Virieux, J.
    , 2017. Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion. Geophysical Journal International205, 332–364.
    [Google Scholar]
  6. Shin, C., Ha, W.
    , 2017. Accumulated energy norm for full waveform inversion of marine data. J Appl Geophys147, 91–101.
    [Google Scholar]
  7. Wu, R.-S., Luo, J., Wu, B.
    , 2014. Seismic envelope inversion and modulation signal model. Geophysics79, WA13–WA24.
    [Google Scholar]

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