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A theory of reverberation and related first-order scattered fields is developed, based on the assumption of weak inhomogeneities (i.e., primary scattering only), and a consequent representation in terms of Poisson point processes in space and time. Both surface and volume reverberation are included, separately and together, for general geometries, source and receiver at the same and different locations, and arbitrary transmitting and receiving apertures. A combination of field- and ray-theory is employed to obtain a characteristic scattered waveform, where the inhomogeneous medium is replaced by a homogeneous and isotropic one in which a spatially and temporally random ensemble of point scatterers is embedded. The effects of the scattering mechanism are described generally by a linear, time-varying filter response. The medium itself is seen to be dispersive and is represented by a set of linear (statistical) space-time operators, by which the signal source and the receiver are coupled to one another, as well as to the point scatterers. Broadband as well as narrowband signals and reverberation are included in the model, which is capable of handling general apertures, illuminating signals, doppler of the scatterers, multiple sources and receivers (overlapping beams), and a characteristic time-varying scatter mechanism, that reveals in detail the inherent nonstationarity of the reverberation. Shadowing effects of "rough" surfaces are included, and a variety of important special results, such as the case of narrowband excitation, and simple (time- and frequency-independent) scattering, are also described. The emphasis is on broadband (frequency-dependent) structures, and their associated space-time operators, by which the system as a whole is represented, and with the help of which one can apply the general methods of statistical communication theory to the central problems of signal processing for detection, communication, and classification, in an environment dominate- - d by reverberation or clutter and analogous signal-dependent noise processes.