The optimized gradient method for full waveform inversion and its spectral implementation

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26 Scopus citations


At the heart of the full waveform inversion (FWI) implementation is wavefield extrapolation, and specifically its accuracy and cost. To obtain accurate, dispersion free wavefields, the extrapolation for modelling is often expensive. Combining an efficient extrapolation with a novel gradient preconditioning can render an FWI implementation that efficiently converges to an accurate model. We, specifically, recast the extrapolation part of the inversion in terms of its spectral components for both data and gradient calculation. This admits dispersion free wavefields even at large extrapolation time steps, which improves the efficiency of the inversion. An alternative spectral representation of the depth axis in terms of sine functions allows us to impose a free surface boundary condition, which reflects our medium boundaries more accurately. Using a newly derived perfectly matched layer formulation for this spectral implementation, we can define a finite model with absorbing boundaries. In order to reduce the nonlinearity in FWI, we propose a multiscale conditioning of the objective function through combining the different directional components of the gradient to optimally update the velocity. Through solving a simple optimization problem, it specifically admits the smoothest approximate update while guaranteeing its ascending direction. An application to the Marmousi model demonstrates the capability of the proposed approach and justifies our assertions with respect to cost and convergence.
Original languageEnglish (US)
Pages (from-to)1823-1831
Number of pages9
JournalGeophysical Journal International
Issue number3
StatePublished - Mar 28 2016

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank KAUST for its support and the SWAG group for the
collaborative environment. We also thank the editor Jean Virieux
and two anonymous reviewers for their fruitful suggestions and


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