On the singularity index and the unfolding of the diffraction catastrophes

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Abstract

The caustics of high-frequency wave propagation may be classified using catastrophe theory. The wavefield in the vicinity of any caustic is described by the corresponding diffraction catastrophe. The singularity index, β, is a measure of the rate at which such a wavefield diverges as ω→∞ at the point where all control parameters and moduli are set equal to zero. It is shown that away from this point β also describes a balance between two different measures of the unfolding of the wavefield in each control direction, β = σnρ{variant}n. The indices σn and ρ{variant}n describe, respectively, the rate at which individual ray arrivals separate in time and decay as a function of control parameter.

Original languageEnglish (US)
Pages (from-to)107-110
Number of pages4
JournalWave Motion
Volume9
Issue number1
DOIs
StatePublished - Jan 1987

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ASJC Scopus subject areas

  • Modeling and Simulation
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Applied Mathematics

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