1887

Abstract

Summary

The least squares L2 norm is susceptible to local minima if the low wavenumber components of the initial model are not accurate, and this happens often with data corresponding to salt bodies. Deconvolution of the predicted and observed data offers an extended comparison, which is more global. The matching filter calculated from the deconvolution has energy focussed at zero-lag, like a Dirac delta function, when the velocity model is accurate, and the predicted data matches the observed one. We utilize a framework for designing a misfit function by measuring the Wasserstein distance W2 between the resulting matching filter and a representation of the Dirac delta function based on the optimal transport theory. Unlike data, the matching filter can be easily transformed into a distribution satisfying the requirement of the optimal transport theory. This optimal transport between two distributions leads to minimizing the least squares difference of the mean and variance of the distributions. If the objective for the matching filter is a Dirac delta function, i.e., with both zero mean and variance, the optimization reduces to the adaptive waveform inversion (AWI) misfit. Along with a total variation constraint, this method can invert for the BP model with high accuracy.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201900878
2019-06-03
2021-04-16
Loading full text...

Full text loading...

References

  1. Engquist, B. and Froese, B.
    [2014] Application of the Wasserstein metric to seismic signals. Communications in Mathematical Sciences, 9(1), no. 1, 79–88.
    [Google Scholar]
  2. Luo, S. and Sava, P.
    [2011] A deconvolution based objective function for wave equation inversion. SEG Technical Program Expanded Abstracts, 2788–2792.
    [Google Scholar]
  3. 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, 205(1), no. 1, 345–377.
    [Google Scholar]
  4. Olkin, I. and Pukelsheim, F.
    [1982] The distance between two random vectors with given dispersion matrices. Linear Algebra and its Applications, 48, 257–263.
    [Google Scholar]
  5. Sun, B. and Alkhalifah, T.
    [2018a] The application of an optimal transport to a preconditioned data matching function for robust waveform inversion. SEG Technical Program Expanded Abstracts.
    [Google Scholar]
  6. [2018b] Mitigate Cycle Skipping In FWI: A Generalized Instanatenous Travel-Time Approach. 80th EAGE Conference and Exhibition.
    [Google Scholar]
  7. [2019] A robust waveform inversion using a global comparison of modeled and observed data. The Leading Edge, accepted.
    [Google Scholar]
  8. Villani, C.
    [2003] Topics in optimal transportation, Graduate studies in mathematics:. American Mathematical Society, 58, 1–145.
    [Google Scholar]
  9. Warner, M. and Guasch, L.
    [2016] Adaptive waveform inversion: Theory. Geophysics, 81(6), no. 6, R429–R445.
    [Google Scholar]
  10. Yang, Y., Engquist, B., Sun, J. and Hamfeldt, B.F.
    [2018] Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion. Geophysics, 83(1), no. 1, R43–R62.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201900878
Loading
/content/papers/10.3997/2214-4609.201900878
Loading

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