A STATISTICAL THEORY OF REVERBERATION AND SIMILAR FIRST-ORDER SCATTERED FIELDS. I. WAVEFORMS AND THE GENERAL PROCESS,
MIDDLETON (DAVID) CONCORD MASS*
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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 non-separable, statistical space-time operators, by which the signal source and the receiver are coupled to one another, as well as to the point-scatterers.
- Statistics and Probability