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

Handle URI:
http://hdl.handle.net/10754/611780
Title:
The optimized gradient method for full waveform inversion and its spectral implementation
Authors:
Wu, Zedong; Alkhalifah, Tariq Ali ( 0000-0002-9363-9799 )
Abstract:
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.
KAUST Department:
Seismic Wave Analysis Group
Citation:
The optimized gradient method for full waveform inversion and its spectral implementation 2016, 205 (3):1823 Geophysical Journal International
Publisher:
Oxford University Press (OUP)
Journal:
Geophysical Journal International
Issue Date:
28-Mar-2016
DOI:
10.1093/gji/ggw112
Type:
Article
ISSN:
0956-540X; 1365-246X
Sponsors:
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 comments.
Additional Links:
http://gji.oxfordjournals.org/lookup/doi/10.1093/gji/ggw112
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorWu, Zedongen
dc.contributor.authorAlkhalifah, Tariq Alien
dc.date.accessioned2016-06-06T07:30:59Z-
dc.date.available2016-06-06T07:30:59Z-
dc.date.issued2016-03-28-
dc.identifier.citationThe optimized gradient method for full waveform inversion and its spectral implementation 2016, 205 (3):1823 Geophysical Journal Internationalen
dc.identifier.issn0956-540X-
dc.identifier.issn1365-246X-
dc.identifier.doi10.1093/gji/ggw112-
dc.identifier.urihttp://hdl.handle.net/10754/611780-
dc.description.abstractAt 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.en
dc.description.sponsorshipWe 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 comments.en
dc.language.isoenen
dc.publisherOxford University Press (OUP)en
dc.relation.urlhttp://gji.oxfordjournals.org/lookup/doi/10.1093/gji/ggw112en
dc.rightsThis article has been accepted for publication in Geophysical Journal International ©: The Authors 2016. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.en
dc.subjectNumerical solutionsen
dc.subjectFourier analysisen
dc.subjectInverse theoryen
dc.subjectTomographyen
dc.subjectWave propagationen
dc.titleThe optimized gradient method for full waveform inversion and its spectral implementationen
dc.typeArticleen
dc.contributor.departmentSeismic Wave Analysis Groupen
dc.identifier.journalGeophysical Journal Internationalen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorWu, Zedongen
kaust.authorAlkhalifah, Tariq Alien
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