On the singularity index and the unfolding of the diffraction catastrophes (Q1082859)

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, \(\beta\), is a measure of the rate at which such a wavefield diverges as \(\omega\to \infty\) at the point where all control parameters and moduli are set equal to zero. It is shown that away from this point \(\beta\) also describes a balance between two different measures of the unfolding of the wavefield in each control direction. \(\beta \sigma_ n\rho_ n\). The indices \(\sigma_ n\) and \(\rho_ n\) describe, respectively, the rate at which individual ray arrivals separate in time and decay as a function of control parameter.