Modeling of seismic data in the downward continuation approach

C.C. Stolk, Maarten V. de Hoop

    Research output: Contribution to journalArticleAcademicpeer-review

    49 Citations (Scopus)

    Abstract

    Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The high-frequency part of the wavefield in the background medium is described by a geometrical optics representation. It can also be described by a one-way wave equation. Based on this we derive a downward continuation operator for seismic data. This operator solves a pseudodifferential evolution equation in depth, the so-called double-square-root equation. We consider the modeling operator based on this equation. If the rays in the background that are associated with the reflections due to the perturbation are nowhere horizontal, the singular part of the data is described by the solution to an inhomogeneous double-square-root equation.
    Original languageUndefined
    Pages (from-to)1388-1406
    Number of pages19
    JournalSIAM journal on applied mathematics
    Volume65
    Issue number4
    DOIs
    Publication statusPublished - 26 Apr 2005

    Keywords

    • Seismic modeling microlocal analysis double-square-root equation
    • EWI-13982
    • double-square-root equation
    • seismic modeling
    • IR-53450
    • microlocal analysis
    • MSC-35R30
    • METIS-226232
    • MSC-86A15

    Cite this

    Stolk, C.C. ; de Hoop, Maarten V. / Modeling of seismic data in the downward continuation approach. In: SIAM journal on applied mathematics. 2005 ; Vol. 65, No. 4. pp. 1388-1406.
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    title = "Modeling of seismic data in the downward continuation approach",
    abstract = "Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The high-frequency part of the wavefield in the background medium is described by a geometrical optics representation. It can also be described by a one-way wave equation. Based on this we derive a downward continuation operator for seismic data. This operator solves a pseudodifferential evolution equation in depth, the so-called double-square-root equation. We consider the modeling operator based on this equation. If the rays in the background that are associated with the reflections due to the perturbation are nowhere horizontal, the singular part of the data is described by the solution to an inhomogeneous double-square-root equation.",
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    Modeling of seismic data in the downward continuation approach. / Stolk, C.C.; de Hoop, Maarten V.

    In: SIAM journal on applied mathematics, Vol. 65, No. 4, 26.04.2005, p. 1388-1406.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Modeling of seismic data in the downward continuation approach

    AU - Stolk, C.C.

    AU - de Hoop, Maarten V.

    PY - 2005/4/26

    Y1 - 2005/4/26

    N2 - Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The high-frequency part of the wavefield in the background medium is described by a geometrical optics representation. It can also be described by a one-way wave equation. Based on this we derive a downward continuation operator for seismic data. This operator solves a pseudodifferential evolution equation in depth, the so-called double-square-root equation. We consider the modeling operator based on this equation. If the rays in the background that are associated with the reflections due to the perturbation are nowhere horizontal, the singular part of the data is described by the solution to an inhomogeneous double-square-root equation.

    AB - Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth background. The discontinuities are contained in the medium perturbation. The high-frequency part of the wavefield in the background medium is described by a geometrical optics representation. It can also be described by a one-way wave equation. Based on this we derive a downward continuation operator for seismic data. This operator solves a pseudodifferential evolution equation in depth, the so-called double-square-root equation. We consider the modeling operator based on this equation. If the rays in the background that are associated with the reflections due to the perturbation are nowhere horizontal, the singular part of the data is described by the solution to an inhomogeneous double-square-root equation.

    KW - Seismic modeling microlocal analysis double-square-root equation

    KW - EWI-13982

    KW - double-square-root equation

    KW - seismic modeling

    KW - IR-53450

    KW - microlocal analysis

    KW - MSC-35R30

    KW - METIS-226232

    KW - MSC-86A15

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    DO - 10.1137/S0036139904439545

    M3 - Article

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    SP - 1388

    EP - 1406

    JO - SIAM journal on applied mathematics

    JF - SIAM journal on applied mathematics

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