# Compressed wavefield extrapolation with curvelets

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 Title: Compressed wavefield extrapolation with curvelets Author: Lin, Tim T. Y.; Herrmann, Felix J. Subject Keywords Helmholtz operator;compressed sensing;wavefield extrapolation;eigenfunctions;curvelets;incoherent;compressed processing;compressed wavefield extrapolation Issue Date: 2007 Publicly Available in cIRcle 2008-03-20 Publisher Society of Exploration Geophysicists Citation: Herrmann, Felix J., Lin, Tim T.Y. 2007. Compressed wavefield extrapolation with curvelets. SEG 77th Annual Meeting and Exposition. 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. Affiliation: Earth and Ocean Sciences, Dept. of (EOS), Dept of URI: http://hdl.handle.net/2429/607 Peer Review Status: