IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-13742-6_13.html
   My bibliography  Save this book chapter

Pseudo-Differential Operator and Inverse Scattering of Multidimensional Wave Equation

In: Optimization and Regularization for Computational Inverse Problems and Applications

Author

Listed:
  • Hong Liu

    (Chinese Academy of Sciences, Key Laboratory of Petroleum Geophysics, Institute of Geology and Geophysics)

  • Li He

    (Chinese Academy of Sciences, Institute of Geology and Geophysics)

Abstract

The infra-structural feature of multidimensional inverse scattering for wave equation is discussed in this chapter. Previous studies on several disciplines pointed out that the basic frame of multidimensional inverse scattering for wave equation is much similar to the one-dimensional (1D) case. For 1D wave equation inverse scattering problem, four procedures are included, i.e., time-depth conversion, Z transform, 1D spectral factorization and conversion of reflection and transmission coefficient to the coefficient of wave equation. In multidimensional or in the lateral velocity varying situation, the conceptions of 1D case should be replaced by image ray coordinate, one-way wave operator, multidimensional spectral factorization based on Witt production and the plane wave response of reflection and transmission operator. There are some important basic components of multidimensional inverse scattering problem, namely, effective one-way operator integral representation, differential form of wave equation in ray coordinate, wide application of Witt product and the modern development of multidimensional spectral factorization. The example of spectrum factorization shows that the energy is well focused, which may benefit the velocity analysis and the pickup of the reflection coefficients.

Suggested Citation

  • Hong Liu & Li He, 2010. "Pseudo-Differential Operator and Inverse Scattering of Multidimensional Wave Equation," Springer Books, in: Yanfei Wang & Changchun Yang & Anatoly G. Yagola (ed.), Optimization and Regularization for Computational Inverse Problems and Applications, chapter 0, pages 301-325, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-13742-6_13
    DOI: 10.1007/978-3-642-13742-6_13
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-642-13742-6_13. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.