A statistical theory of reverberation and similar first-order scattered fields--IV: Statistical models

The earlier theory (Parts I and II) is extended to include the determination of various important statistics of the reverberation process under the broadened conditions of and using the results for the scattered and reflected fields developed in Part III. The new conditions involve nonzero velocity gradients, absorbing media, and multiple reflections, as well as the usual Doppler, general signals and apertures, and mono- and bistatic operation. Of principal interest are the mean return (specular reflection), the mean intensity, and the covariance of these generally nonstationary processes, following reception by the receiving aperture. These we determine under the basic Poisson assumptions of primarily independent single scattering, as before. Also of major importance are the auto- and cointensity spectra associated with the various second-order statistics. General relations for these and higher order moments are indicated. The quasi-stationary cases of "short" narrow-band signals occur in many practical operational situations and are treated here in detail, under a variety of general and special conditions, appropriate to both oceanographic and general communication applications (e.g., detection and classification). The development of our quasi-phenomenological model (Parts I-IV) concludes with a critique of the role of the Poisson assumption of independent scatterers in both volume and surface scatter and a short account of possible and needed extensions of the present "macroscopic" theory to one that is fully physical at the "microscopic" level as well.