The caustics of high-frequency wave propagation may be classified using catastrophe theory. This paper examines the transient wave fields in the vicinity of the elliptic, hyperbolic, and parabolic umbilic catastrophes. Analytical results are presented which describes the time-dependent wave field due to an impulsive source on and at large distances in each control direction away from the most singular point of each of these transient wave fields as each control parameter is independently varied. These results are compared to previously derived results on the transient wave fields in the vicinity of the cuspoid catastrophes (the cuspoid and umbilic catastrophes have coranks 1 and 2, respectively). The transient wave fields in the vicinity of the cuspoid and umbilic catastrophes differ with regard to the temporal structure of the wave field on the most singular point of each catastrophe, the manner in which these temporal structures unfold, and the phase shifts which individual rays undergo as a result of touching one of the catastrophes.

High Frequency and Pulse Scattering investigates high frequency and pulse scattering, with emphasis on the phenomenon of echoes from objects. Geometrical and catastrophe optics methods in scattering are discussed, along with the scattering of sound pulses and the ringing of target resonances. Caustics and associated diffraction catastrophes are also examined. Comprised of two chapters, this volume begins with a detailed account of geometrically based approximation methods in scattering theory, focusing on waves transmitted through fluid and elastic scatterers and glory scattering; surface ray representations of scattering by shells and other smooth objects; and caustics and associated diffraction catastrophes. The second chapter deals with the relation between sound pulses and the vibrational spectra of elastic submerged objects. The theory of the scattering of sound pulses from elastic and impenetrable objects is described, together with the theory of surface wave pulses. Target resonances and the singularity expansion method are also analyzed. This book will be of interest to physicists.

Advances in Imaging and Electron Physics merges two long-running serials--Advances in Electronics and Electron Physics and Advances in Optical & Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.