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A theory of reverberation and related first-order scattered fields, developed earlier by the author, is now extended to include the often critical effects of absorption in the medium, multiple specular reflections, and nonzero velocity gradients . As before, a combination of field and ray theory is used to obtain typical scattered and reflected waveforms; a spatial and temporal ensemble of random point scatterers is embedded in the now inhomogeneous medium and the handling of complex geometries is emphasized. Also as before, the effects of the scattering mechanism are described in generality by linear time-varying filter responses. A general vertical velocity gradient is postulated, which may be approximated by contiguous linear velocity profiles. Propagation characteristics for the latter are obtained in detail, including expressions for ray path lengths and delays for arbitrary beam orientations. A useful operator formalism is developed, which assists in determining the principal contributions to the received return when different modes of propagation e.g., convergence zone (CVZ), bottom bounce (BB), surface duct (SD), etc., are employed. Platform and scatterer Doppler are included, as well as arbitrary apertures and beam patterns. Specific waveform results for the important cases of narrow-band signal excitation are given, in addition to the general broad-band theory developed for both bistatic and monostatic reception. A number of models of possible scatterer response are also included, for both physical and biological applications in oceanography.