Non-Dispersive Approximations for Transient Ray Fields in an Inhomogeneous Medium

Abstract

Time-harmonic wave propagation in an inhomogeneously layered medium may be expressed in terms of ray integrals comprised of local spectral plane waves associated with particular rays. At high frequencies, the spectral wavenumber integrands are non-dispersive, and the resulting ray integrals can be inverted into the time domain to yield the transient response in closed form. Two principal methods, by Cagniard-DeHoop and by Chapman, have been developed to deal with the inversion. The former has limited scope and the latter, while more broadly applicable, restricts the spectral wavenumbers to be real. The two methods, which generate results of dissimilar appearance, can be embedded within a spectral theory that accommodates each and also more general problems by allowing real and complex spectral wavenumber contributions. The theory is described, and is illustrated for caustic forming ray species, for which the Cagniard-DeHoop method is inapplicable and the Chapman method less convenient.