1887
  1. Home
  2. Conferences
  3. Conference Proceedings
  4. 78th EAGE Conference and Exhibition 2016
  5. Conference paper

Abstract

Summary

Conventional full waveform inversion based on the L2 norm is known to suffer from cycle skipping. Numerous techniques have been promoted to face this long term issue, relying on modifications of the function which measures the discrepancy between observed and predicted data. In this study, we propose to measure this discrepancy through the solution of an optimal transport problem. Instead of proceeding to a sample-by-sample comparison of the seismic signal, this offers the possibility to perform a global comparison of the data, taking into account the spatial and time coherency of the predicted and observed shot gathers. The optimal transport problem is reformulated as a non-smooth convex optimization problem, which can be solved efficiently through proximal splitting techniques. As for other modifications of the misfit function, the optimal transport distance is integrated naturally in the FWI workflow through a modification of the adjoint source term. This modified adjoint source is simply the solution of the optimal transport problem. A 2D time-domain acoustic application on the Marmousi 2 model is presented. We show how the sensitivity to the accuracy of the initial model can be reduced using the optimal transport distance.

© EAGE Publications BV
Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201601534
2016-05-30
2024-04-24

  • From This Site

    /content/papers/10.3997/2214-4609.201601534
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Adams, J.C.
    [1989] MUDPACK: Multigrid portable FORTRAN software for the efficient solution of linear elliptic partial differential equations. Applied Mathematics and Computation, 34(2), 113–146.
     [Google Scholar]
  2. Combettes, P.L. and Pesquet, J.C.
    [2011] Proximal Splitting Methods in Signal Processing. In: Bauschke, H.H., Burachik, R.S., Combettes, P.L., Elser, V., Luke, D.R. and Wolkowicz, H. (Eds.) Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer Optimization and Its Applications, 49, Springer New York, 185–212.
     [Google Scholar]
  3. Guasch, L. and Warner, M.
    [2014] Adaptive Waveform Inversion - FWI Without Cycle Skipping - Applications. In: 76th EAGE Conference and Exhibition 2014.
     [Google Scholar]
  4. Lellmann, J., Lorenz, D., Schönlieb, C. and Valkonen, T.
    [2014] Imaging with Kantorovich–Rubinstein Discrepancy. SIAM Journal on Imaging Sciences, 7(4), 2833–2859.
     [Google Scholar]
  5. Luo, S. and Sava, P.
    [2011] A deconvolution-based objective function for wave-equation inversion. SEG Technical Program Expanded Abstracts, 30(1), 2788–2792.
     [Google Scholar]
  6. Luo, Y. and Schuster, G.T.
    [1991] Wave-equation traveltime inversion. Geophysics, 56(5), 645–653.
     [Google Scholar]
  7. Ma, Y. and Hale, D.
    [2013] Wave-equation reflection traveltime inversion with dynamic warping and full waveform inversion. Geophysics, 78(6), R223–R233.
     [Google Scholar]
  8. Métivier, L., Brossier, R., Mérigot, Q., Oudet, E. and Virieux, J.
    [2016] Measuring the misfit between seismograms using an optimal transport distance: Application to full waveform inversion. Geophysical Journal International, in press.
     [Google Scholar]
  9. Plessix, R.E.
    [2006] A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167(2), 495–503.
     [Google Scholar]
  10. Symes, W.W.
    [2008] Migration velocity analysis and waveform inversion. Geophysical Prospecting, 56, 765–790.
     [Google Scholar]
  11. Villani, C.
    [2003] Topics in optimal transportation. Graduate Studies In Mathematics, Vol. 50, AMS.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201601534
Loading
Overcoming Cycle Skipping in FWI - An Optimal Transport Approach
Conference Proceedings 2016, 1 (2016); https://doi.org/10.3997/2214-4609.201601534
/content/papers/10.3997/2214-4609.201601534
/content/papers/10.3997/2214-4609.201601534
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

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