Deep learning can be used to help reconstruct low frequencies in seismic data, and to directly infer velocity models in simple cases. In order to succeed with deep learning, a good training set of velocity models is critical. We present a new way to design random models that are statistically similar to a given guiding model. Our approach is based on shuffling the coefficients of a wavelet packet decomposition (WPD) of the guiding model, allowing us to replicate realistic textures from a synthetic model. We generate realistically random models from the BP 2004 and Marmousi II models for neural network training, and utilize the trained network to extrapolate low frequencies for the SEAM model. We apply full-waveform inversion to the extrapolated data to understand the limitations of our approach.


Article metrics loading...

Loading full text...

Full text loading...


  1. Aravkin, A.Y., Van Leeuwen, T., Burke, J.V. and Herrmann, F.J.
    [2011] A Nonlinear Sparsity Promoting Formulation and Algorithm for Full Waveform Inversion. In: 73rd EAGE Conference and Exhibition Incorporating SPE EUROPEC 2011.
    [Google Scholar]
  2. Araya-Polo, M., Jennings, J., Adler, A. and Dahlke, T.
    [2018] Deep-Learning Tomography. The Leading Edge, 37(1), 58–66.
    [Google Scholar]
  3. Christophe, E., Mailhes, C. and Duhamel, P.
    [2008] Hyperspectral Image Compression: Adapting SPIHT and EZW to Anisotropic 3-D Wavelet Coding. IEEE Trans. Image Proc., 17(12), 2334–2346.
    [Google Scholar]
  4. Daubechies, I.
    [1992] Ten Lectures on Wavelets, SIAM.
  5. 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:1704.04861.
  6. Laine, A. and Fan, J.
    [1993] Texture Classification by Wavelet Packet Signatures. IEEE Trans. Pattern Analysis Machine Intelligence, 15(11), 1186–1191.
    [Google Scholar]
  7. Lin, Y., Abubakar, A. and Habashy, T.M.
    [2012] Seismic Full-Waveform Inversion Using Truncated Wavelet Representations. In: SEG Tech. Progr. Expanded Abstracts 2012, Society of Exploration Geophysicists, 1–6.
    [Google Scholar]
  8. 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?
    [Google Scholar]
  9. Ovcharenko, O., Kazei, V., Peter, D., Zhang, X. and Alkhalifah, T.
    [2018] Low-Frequency Data Extrapolation Using a Feed-Forward ANN. In: 80th EAGE Conference and Exhibition 2018.
    [Google Scholar]
  10. Ray, A., Kaplan, S., Washbourne, J. and Albertin, U.
    [2017] Low Frequency Full Waveform Seismic Inversion within a Tree Based Bayesian Framework. Geophys. J. International, 212(1), 522–542.
    [Google Scholar]
  11. Sun, H. and Demanet, L.
    [2018] Low Frequency Extrapolation with Deep Learning. In: SEG Tech. Progr. Expanded Abstracts 2018, Society of Exploration Geophysicists, 2011–2015.
    [Google Scholar]
  12. Taubman, D.S. and Marcellin, M.W.
    [2002] JPEG2000: Standard for Interactive Imaging. Proc. IEEE, 90(8), 1336–1357.
    [Google Scholar]
  13. Wu, Y., Lin, Y. and Zhou, Z.
    [2018] InversionNet: Accurate and Efficient Seismic Waveform Inversion with Convolutional Neural Networks. In: SEG Tech. Progr. Expanded Abstracts 2018, Society of Exploration Geophysicists, 2096–2100.
    [Google Scholar]

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error