1887

Abstract

Summary

The use of optimal transport distances has been recently promoted to mitigate cycle skipping issues in full waveform inversion. This distance is convex with respect to shifted patterns between compared data. This is the reason why it has attracted interest for full waveform inversion as the convexity with respect to time shifts can be seen as a proxy for the convexity with respect to wave velocities. The main difficulty for the application of optimal transport to seismic data is related to their non positivity: the optimal transport theory is developed for the comparison of positive quantities. We present a review of the strategies proposed to overcome this issue, and explain their limitations. They are either not adapted for the comparison of realistic data, or lose the convexity property. On this basis, we propose a novel approach based on a graph space interpretation of the seismic traces. Synthetic and observed traces are seen as point clouds in a 2D space (the graph space), which are compared using a 2D optimal transport technique. This strategy overcomes the positivity issue while preserving the convexity property. An application of this strategy on the Marmousi 2 model illustrates its interest for mitigating cycle skipping.

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/content/papers/10.3997/2214-4609.201801031
2018-06-11
2024-03-28
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References

  1. Engquist, B. and Froese, B.D.
    [2014] Application of the Wasserstein metric to seismic signals. Communications in Mathematical Science, 12(5), 979–988.
    [Google Scholar]
  2. Métivier, L., Brassier, R., Mérigot, Q., Oudet, E. and Virieux, J.
    [2016a] Measuring the misfit between seismograms using an optimal transport distance: Application to full waveform inversion. Geophysical Journal International, 205, 345–377.
    [Google Scholar]
  3. [2016b] An optimal transport approach for seismic tomography: Application to 3D full waveform inversion. Inverse Problems, 32(11), 115008.
    [Google Scholar]
  4. Qiu, L., Ramos-Martinez, J., Valenciano, A., Yang, Y. and Engquist, B.
    [2017] Full-waveform inversion with an exponentially encoded optimal-transport norm. In: SEG Technical Program Expanded Abstracts 2017. 1286–1290.
    [Google Scholar]
  5. Virieux, J., Asnaashari, A., Brassier, R., Métivier, L., Ribodetti, A. and Zhou, W.
    [2017] An introduction to Full Waveform Inversion. In: Grechka, V and Wapenaar, K. (Eds.) Encyclopedia of Exploration Geophysics, Society of Exploration Geophysics, R1–1–R1–40.
    [Google Scholar]
  6. Yang, Y. and Engquist, B.
    [2017] Analysis of optimal transport and related misfit functions in full-waveform inversion. In: SEG Technical Program Expanded Abstracts 2017. 1291–1296.
    [Google Scholar]
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