Low-frequency data proved to be crucial for robust full-waveform inversion (FWI) applications. However, acquiring those data in the field is a challenging and costly task. Deep neural networks can be trained to extrapolate missing low frequencies, but no optimal network configuration exists. Therefore, the search for an acceptable network architecture is a tedious empirical task whose outcome heavily affects the performance of the application. Here, we propose and utilize transfer learning to reduce the computational efforts otherwise spent on an optimal architecture search and an initial network training. We re-train the light-weight MobileNet convolutional network to infer low-frequency data from a frequency-domain representation of the individual shot-gathers, which leads to an efficient, yet accurate inference of low frequencies according to wavenumber theory. In particular, we show that the extrapolated 0.25 - 1 Hz from 2–4.5 Hz data are accurate enough for acoustic FWI on part of the original BP 2004 model and the Marmousi II model of double scale. We bridge the gap between the 1 Hz predicted and the 2 Hz modeled data by the application of a Sobolev space norm regularization.


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  1. Billette, F. and Brandsberg-Dahl, S.
    [2005] The 2004 BP velocity benchmark. In: 67th EAGE Conference & Exhibition.
    [Google Scholar]
  2. Bourgeois, A., Bourget, M., Lailly, P., Poulet, M., Ricarte, P. and Versteeg, R
    . [1991] Marmousi, model and data. The Marmousi Experience, 5–16.
    [Google Scholar]
  3. Bunks, C., Saleck, F.M., Zaleski, S. and Chavent, G
    . [1995] Multiscale seismic waveform inversion. Geophysics, 60(5), 1457–1473.
    [Google Scholar]
  4. Deng, J., Dong, W., Socher, R., Li, L.J., Li, K. and Fei-Fei, L.
    [2009] Imagenet: A large-scale hierarchical image database. In: ComputerVisionand Pattern Recognition, 2009. CVPR2009. IEEE Conference on. Ieee, 248–255.
    [Google Scholar]
  5. Goodfellow, I., Bengio, Y. and Courville, A
    . [2016] Deep learning, 1.
    [Google Scholar]
  6. Gray, S.H
    . [2016] Seismic imaging. In: Encyclopedia of Exploration Geophysics, Society of Exploration Geophysicists, S1–1.
    [Google Scholar]
  7. Howard, A.G., Zhu, M., Chen, B., Kalenichenko, D., Wang, W., Weyand, T.
    , Andreetto, M. and Adam, H. [2017] Mobilenets: Efficient convolutional neural networks for mobile vision applications. arXiv preprint arXiv:1704.04861.
    [Google Scholar]
  8. Hu, W
    . [2014] FWI without low frequency data-beat tone inversion. In: SEG Technical Program Expanded Abstracts 2014, Society of Exploration Geophysicists, 1116–1120.
    [Google Scholar]
  9. Huang, J., Rathod, V., Sun, C., Zhu, M., Korattikara, A., Fathi, A., Fischer, I., Wojna, Z., Song, Y., Guadarrama, S. et al.
    [2017] Speed/accuracy trade-offs for modern convolutional object detectors. In: IEEE CVPR, 4.
    [Google Scholar]
  10. Jin, Y., Hu, W., Wu, X. and Chen, J
    . [2018] Learn low wavenumber information in FWI via deep inception based convolutional networks. In: SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2091–2095.
    [Google Scholar]
  11. Kalita, M., Kazei, V.
    , Choi, Y. and Alkhalifah, T. [2018] Regularized full-waveform inversion with automated salt-flooding. Geophysics, submitted.
    [Google Scholar]
  12. Kazei, V. and Alkhalifah, T
    . [2018] Waveform inversion for orthorhombic anisotropy with P waves: feasibility and resolution. Geophysical Journal International, 213(2), 963–982.
    [Google Scholar]
  13. Kazei, V., Kalita, M. and Alkhalifah, T.
    [2017] Salt-body Inversion with Minimum Gradient Support and Sobolev Space Norm Regularizations. In: 79th EAGE Conference and Exhibition2017.
    [Google Scholar]
  14. Ovcharenko, O., Kazei, V., Peter, D. and Alkhalifah, T
    . [2017] Neural network based low-frequency data extrapolation. In: 3rd SEG FWI workshop: What are we getting?, Society of Exploration Geophysicists.
    [Google Scholar]
  15. . [2018a] Variance-based model interpolation for improved full-waveform inversion in the presence of salt bodies. Geophysics, 83(5), 1–60.
    [Google Scholar]
  16. Ovcharenko, O., Kazei, V., Peter, D., Zhang, X. and Alkhalifah, T.
    [2018b] Low-Frequency Data Extrapolation Using a Feed-Forward ANN. In: 80th EAGE Conference and Exhibition2018.
    [Google Scholar]
  17. Sun, H. and Demanet, L
    . [2018] Low frequency extrapolation with deep learning. In: SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2011–2015.
  18. Virieux, J. and Operto, S
    . [2009] An overview of full-waveform inversion in exploration geophysics. Geophysics, 74, WCC1–WCC26.
  19. Wang, R. and Herrmann, F
    . [2016] Frequency down extrapolation with TV norm minimization. In: SEG Technical Program Expanded Abstracts 2016, Society of Exploration Geophysicists, 1380–1384.
    [Google Scholar]

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