The evolution of vertical spatial coherence with range from source
Peter H. Dahl, Dajun tang, and Jee Woong Choi

Vertical spatial coherence for shallow water propagation at frequencies 1-10 kHz is studied as function of range (50 to 5000 m), as part of the Shallow-Water 2006 program that took place off the coast of New Jersey in August 2006 in waters 80 m deep. An acoustic source was deployed from the R/V Knorr at depths from 30 and 40 m and signals were recoreded on a moored receiving system consisting of two 1.4 m long vertical line arrays (VLA) centered at tepths 25 and 50 m. At all ranges, spatial coherence, Γ (normalized spatial correlation), is locally stationary and depends on element vertical separation d up to the maximum kd (59) afforded by the VLA, where k is the acoustic wave number. For range normalized by depth, r*, less than about 10, Γ is oscillatory, with non-zero imaginary part, reflecting the inclusion of multipaths for which no single path dominates. For r* greater than 10, Γ tends to exhibit a monotonic decay with kd and the imaginary part vanishes reflecting symmetry about 0° vertical arrival angle. The coherence also increases with r* reflecting the change in modal structure.

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