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Pseudo-Differential Operator and Inverse Scattering of Multidimensional Wave Equation

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Optimization and Regularization for Computational Inverse Problems and Applications

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.

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Author information

Authors and Affiliations

  1. Key Laboratory of Petroleum Geophysics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    Hong Liu

  2. Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    Li He

Authors
  1. Hong Liu
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  2. Li He
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Editor information

Editors and Affiliations

  1. Key Laboratory of Petroleum Geophysics Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

    Yanfei Wang  & Changchun Yang  & 

  2. Department of Mathematics Faculty of Physics, Lomonosov Moscow State University, Moscow, 119991, Russia

    Anatoly G. Yagola

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© 2010 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Liu, H., He, L. (2010). Pseudo-Differential Operator and Inverse Scattering of Multidimensional Wave Equation. In: Wang, Y., Yang, C., Yagola, A.G. (eds) Optimization and Regularization for Computational Inverse Problems and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13742-6_13

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