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A NOTE ON SCATTERING OPERATOR SYMBOLS FOR ELLIPTIC WAVE PROPAGATION

Kim, Jeong-Hoon

  • Published : 2002.04.01

Abstract

The ill-posed elliptic wave propagation problems can be transformed into well-posed initial value problems of the reflection and transmission operators characterizing the material structure of the given model by the combination of wave field splitting and invariant imbedding methods. In general, the derived scattering operator equations are of first-order in range, nonlinear, nonlocal, and stiff and oscillatory with a subtle fixed and movable singularity structure. The phase space and path integral analysis reveals that construction and reconstruction algorithms depend crucially on a detailed symbol analysis of the scattering operators. Some information about the singularity structure of the scattering operator symbols is presented and analyzed in the transversely homogeneous limit.

Keywords

wave splitting;invariant imbedding;Feynman path integral;Weyl composition equation;pseudodifferential operator symbol;singularity

References

  1. Harmonic analysis in Phase Space G.B.Folland
  2. J.Acoust.Soc.Am. v.81 Factorization and path integration of the Helmholtz equation: Numerical algorithms L.Fishman;J.J.McCoy;S.C.Wales https://doi.org/10.1121/1.394542
  3. Techniques and Applications of Path Integration L.S.Schulman
  4. J.Math.Anal.Appl. v.95 Obtaining scattering kernels using invariant imbedding J.Corones;R.Krueger https://doi.org/10.1016/0022-247X(83)90115-4
  5. Commun.Pure Appl.Math. v.32 The Weyl calculus of pseudo-differential operators L.Hormander https://doi.org/10.1002/cpa.3160320304
  6. IMA J.Appl.Math. v.62 Reflected pulses from a refractive random medium at grazing incidence J.H.Kim https://doi.org/10.1093/imamat/62.3.263
  7. Commun.Pure Appl.Math. v.4 The W.K.B. approximations as the first term of a geometrical-optical series H.Bremmer https://doi.org/10.1002/cpa.3160040111
  8. J.Math.Phys. v.27 Direct and inverse scattering in the time domain for a dissipative wave equation. Ⅲ. Scattering operators in the presence of a phase velocity mismatch G.Kristensson;R.Krueger
  9. Wave Motion v.14 Exact and approximate solutions of the Helmholtz, Weyl composition equation in scalar wave propagation L.Fishman https://doi.org/10.1016/0165-2125(91)90037-O
  10. Wave Spitting with Applications to Wave Propagation and Inverse Scattering V.H.Weston;J.P.Corones;L.Fishman;J.J.McCoy
  11. Pseudodifferential Operators M.E.Taylor