Full text loading...
-
Mitigating Non-linearity in Full Waveform Inversion by Scaled Sobolev Pre-conditioning
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 78th EAGE Conference and Exhibition 2016, May 2016, Volume 2016, p.1 - 5
Abstract
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.