1887

Abstract

Summary

Seismic full waveform inversion (FWI) can be linearized by implementing a first-order Born approximation. However, this requires good a-priori knowledge of the background velocity. The problem of updating the background velocity in FWI can be handled by spatial scale separation of the velocity variations. Still, it is the Born approximation that decides which velocity scales can be considered as reflectivity which scale is the background.

We propose a new scale separation technique based on spatial derivatives of the velocity functions. Its incorporation into FWI results in a pre-conditioning scheme that is a scaled version of the Sobolev gradient. The per-iteration computational cost in applying this scaled Sobolev pre-conditioner is negligible. Sobolev gradients have been used in image processing to help convergence in non-linear problems. In our scaled version, the scaling parameters allow switching between different scales of velocity updates and thereby mitigating the non-linearity in FWI by initially switching to very low-wavenumber (background velocity) updates; small scale updates are included naturally during the later iterations. Numerical examples on the Marmousi models show the potential of the scaled Sobolev preconditioning.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.201601007
2016-05-30
2024-03-28
Loading full text...

Full text loading...

References

  1. Bunks, C., Saleck, F.M., Zaleski, S. and Chavent, G.
    [1995] Multiscale seismic waveform inversion. Geophysics, 60(5), 1457–1473.
    [Google Scholar]
  2. Neuberger, J.
    [1997] Sobolev Gradients and Differential Equations. No. 1670 in Lecture Notes in Computer Science. Springer.
    [Google Scholar]
  3. Pratt, R.G., Shin, C. and Hick, G.J.
    [1998] Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion. Geophysical Journal International, 133(2), 341–362.
    [Google Scholar]
  4. Renka, R.
    [2009] Image segmentation with a Sobolev gradient method. Nonlinear Analysis: Theory, Methods & Applications, 71(12), e774–e780.
    [Google Scholar]
  5. Renka, R.J.
    [2013] Nonlinear least squares and Sobolev gradients. Applied Numerical Mathematics, 65, 91–104.
    [Google Scholar]
  6. Sava, P. and Biondi, B.
    [2004] Wave-equation migration velocity analysis. I. Theory. Geophysical Prospecting, 52(6), 593–606.
    [Google Scholar]
  7. Symes, W.W.
    [1991] A differential semblance algorithm for the inverse problem of reflection seismology. Computers & Mathematics with Applications, 22(4), 147–178.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.201601007
Loading
/content/papers/10.3997/2214-4609.201601007
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