Volume reverberation and target echo calculations using normal modes

A shallow-water model for calculating boundary reverberation using normal modes and ray-mode analogies has been previously reported. The authors describe extensions for handling target echo, and volume reverberation within the water column and subbottom. The equations and sample results are presented for a shallow-water environment. As specific examples, subbottom reverberation is compared to boundary reverberation using Lambert's rule; and, the effects of time spreading on target echo and signal excess are illustrated.