Narrow-band pulse propagation in a one-dimensional stratified random medium

Abstract

In the stratified random medium considered here, the spatially fluctuating wave speed and refractivity vary only in the range direction, which is normal to the planes of stratification. To treat backscattering in such a medium, it is convenient to split the field into forward- and backward-propagating components, and derive coupled equations that govern the range evolution of the statistical moments of these components. The derivation entails an ensemble-averaging operation, which is here predicated on the key assumption that the two components, which are incident from opposite directions on a differential range slab, are statistically independent of the refractivity fluctuations within that slab. The assumption is justifiable when the fluctuations exhibit a sufficiently rapid time dependence. This procedure is used to derive equations for the bichromatic coherence of the two field components, which are then solved to determine the evolution of the power flux associated with the propagation of a signal due to a planar narrow-band pulse incident on a semi-infinite scattering slab. It is shown that the pulse signal is attenuated exponentially in the range direction, on the so-called ‘‘localization’’ scale, while the scattered power forms echo pulses which are gradually attenuated until all the incident pulse energy is reflected back out of the slab.