Seismic amplitude recovery with curvelets

P.P. Moghaddam, F.J. Herrmann, C.C. Stolk

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    Abstract

    A non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness and continuity constraints is proposed. The applied formalism explores curvelets as a directional frame that, by their sparsity on the image, and their invariance under the imaging operators, allows for a stable recovery of the amplitudes. Our method is based on the estimation of the normal operator in the form of an 'eigenvalue' decomposition with curvelets as the 'eigenvectors'. Subsequently, we propose an inversion method that derives from estimation of the normal operator and is formulated as a convex optimization problem. Sparsity in the curvelet domain as well as continuity along the reflectors in the image domain are promoted as part of this optimization. Our method is tested with a reverse-time 'wave-equation' migration code simulating the acoustic wave equation.
    Original languageUndefined
    Title of host publicationExtended Abstracts, EAGE 69th Conference & Exhibition
    Place of PublicationHouten
    PublisherEAGE Publications BV
    PagesP172
    Number of pages4
    ISBN (Print)978-90-73781-54-2
    Publication statusPublished - 2007
    EventExtended Abstracts, EAGE 69th Conference & Exhibition - London
    Duration: 11 Jun 200714 Jun 2007

    Publication series

    Name
    PublisherEAGE Publications BV
    Number1

    Conference

    ConferenceExtended Abstracts, EAGE 69th Conference & Exhibition
    Period11/06/0714/06/07
    Other11-14 June 2007

    Keywords

    • EWI-11573
    • IR-64534
    • METIS-245860

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