Acta Applicandae Mathematica

, Volume 67, Issue 2, pp 117–171 | Cite as

Wave Field Decomposition in Anisotropic Fluids: A Spectral Theory Approach

  • B. Lars G. Jonsson
  • Maarten V. de Hoop

Abstract

An extension of directional wave field decomposition in acoustics from heterogenous isotropic media to generic heterogenous anisotropic media is established. We make a connection between the Dirichlet-to-Neumann map for a level plane, the solution to an algebraic Riccati operator equation, and a projector defined via a Dunford–Taylor type integral over the resolvent of a nonnormal, noncompact matrix operator with continuous spectrum.

In the course of the analysis, the spectrum of the Laplace transformed acoustic system's matrix is analyzed and shown to separate into two nontrivial parts. The existence of a projector is established and using a generalized eigenvector procedure, we find the solution to the associated algebraic Riccati operator equation. The solution generates the decomposition of the wave field and is expressed in terms of the elements of a Dunford–Taylor type integral over the resolvent.

directional wave field decomposition wave splitting spectral reduction acoustic anisotropy generalized eigenvalue problem algebraic Riccati operator equation Dirichlet-to-Neumann maps generalized vertical wave number operators generalized vertical slowness 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • B. Lars G. Jonsson
    • 1
  • Maarten V. de Hoop
    • 2
  1. 1.Department of Electromagnetic TheoryRoyal Institute of TechnologyStockholmSweden
  2. 2.Center for Wave PhenomenaColorado School of MinesGoldenUSA

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