### 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 = σ_{n}ρ{variant}_{n}. The indices σ_{n} 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 language | English (US) |
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Pages (from-to) | 107-110 |

Number of pages | 4 |

Journal | Wave Motion |

Volume | 9 |

Issue number | 1 |

DOIs | |

State | Published - 1987 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics

### Cite this

**On the singularity index and the unfolding of the diffraction catastrophes.** / Brown, Michael G.

Research output: Contribution to journal › Article

*Wave Motion*, vol. 9, no. 1, pp. 107-110. https://doi.org/10.1016/0165-2125(87)90043-6

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TY - JOUR

T1 - On the singularity index and the unfolding of the diffraction catastrophes

AU - Brown, Michael G

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023163951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023163951&partnerID=8YFLogxK

U2 - 10.1016/0165-2125(87)90043-6

DO - 10.1016/0165-2125(87)90043-6

M3 - Article

AN - SCOPUS:0023163951

VL - 9

SP - 107

EP - 110

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

IS - 1

ER -