Abstract

A general analytic theory of reverberation has been constructed for the common cases of a weakly turbulent medium, where surface and volume scattering are represented by collections of independent point scatterers obeying suitable Poisson laws in space [Middleton, IEEE Trans. Inform. Theory (July 1967)]. The scattering portions of each medium are described by characteristic position-dependent stochastic linear and time-varying filters, to which are assigned a hierarchy of basic structures. The result is a combined physical-phenomenological model that uses wave theory to determine the form of typical scattered waves, and ray theory to incorporate them into the governing geometry. The intractably complex scatter boundary conditions are embodied in the statistical filter. Frequency-selective apertures, general geometries, and signals are also incorporated. The theory can readily be extended to include nonzero velocity gradients, absorption, and discrete multipath phenomena. Initial experiments show good to excellent quantitative agreement (Kincaid and Rustay, General Electric Co.), including predicted volume and surface effects and spectral broadening caused by inherent doppler of the scatterers. [Work supported by the Office of Naval Research.]

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