Backscattering in stratified time-dependent random media - CW and narrow-band pulse propagation

We consider backscattering in a random stratified medium where the wave-speed fluctuations depend on time and on the range coordinate, which is normal to the planes of stratification. For the limit where the correlation time is shorter than the mean scattering time, we first derive radiation-transport equations that govern the range evolution of the spectra of the ensemble-averaged forward- and back-propagating components of the field and their bichromatic coherence functions. The latter are governed by integro-differential equations that account for the broadening of the signal spectra due to the time dependence of the random fluctuations. When the correlation time is longer than both the period of the radiating signal and the travel time of a wavefront across a range correlation length, the spectrum of the radiation due to a monochromatic CW excitation remains confined to a narrow band over extensive ranges. This permits a quasi-monochromatic approximation, whereby the integro-differential equations produce ordinary differential equations that govern the quantities of interest. We use this approximation to track the power flux associated with the propagation of a narrow-band pulse.