The evolution of vertical spatial coherence with range from source

Abstract

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 30 and 40 m and signals were recorded on a moored receiving system consisting of two 1.4 m long vertical line arrays (VLA) centered at depths 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 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 deg vertical arrival angle. The coherence also increases with r* reflecting the change in modal structure.