# Compressed wavefield extrapolation with curvelets

 dc.contributor.author Lin, Tim T. Y. dc.contributor.author Herrmann, Felix J. dc.date.accessioned 2008-03-20T18:36:17Z dc.date.available 2008-03-20T18:36:17Z dc.date.issued 2007 dc.identifier.citation Herrmann, Felix J., Lin, Tim T.Y. 2007. Compressed wavefield extrapolation with curvelets. SEG 77th Annual Meeting and Exposition. en dc.identifier.uri http://hdl.handle.net/2429/607 dc.description.abstract An \emph {explicit} algorithm for the extrapolation of one-way wavefields is proposed which combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in {3-D}. By using ideas from \emph{compressed sensing}'', we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume{,} thereby reducing the size of the operators. According {to} compressed sensing theory, signals can successfully be recovered from an imcomplete set of measurements when the measurement basis is \emph{incoherent} with the representation in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can successfully be extrapolated in the modal domain via a computationally cheaper operatoion. A proof of principle for the compressed sensing'' method is given for wavefield extrapolation in {2-D}. The results show that our method is stable and produces identical results compared to the direct application of the full extrapolation operator. en dc.format.extent 2684048 bytes dc.format.mimetype application/pdf dc.language.iso eng en dc.publisher Society of Exploration Geophysicists en dc.subject Helmholtz operator en dc.subject compressed sensing en dc.subject wavefield extrapolation en dc.subject eigenfunctions en dc.subject curvelets en dc.subject incoherent en dc.subject compressed processing en dc.subject compressed wavefield extrapolation en dc.title Compressed wavefield extrapolation with curvelets en dc.type text en dc.type.text conference Paper en dc.description.affiliation Earth and Ocean Sciences, Dept. of (EOS), Dept of en dc.description.reviewstatus en dc.rights.copyright Herrmann, Felix J. en
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