Horizontal-longitudinal coherence of bottom-received acoustic field in deep water with an incomplete channel

Horizontal-longitudinal coherence, a key parameter characterizing the spatial variability of the acoustic field, provides important guidance for array design. This study investigates the horizontal-longitudinal coherence of low-frequency (50 Hz) bottom-received acoustic fields in deep water featuring an incomplete sound channel at a depth of approximately 1700 m. Based on ray theory, the variations of the horizontal-longitudinal coherence coefficient with source–receiver distance and longitudinal separation are analyzed. The results reveal distinct oscillatory behavior in the horizontal-longitudinal coherence coefficient as functions of both distance and separation. Specifically, intra-cluster interference primarily governs the range-dependent variation, whereas the energy distribution among ray clusters and their mutual interference jointly determine the oscillation period and amplitude with respect to longitudinal separation. In regions of constructive intra-cluster interference, transmission loss is low. When acoustic energy is concentrated within a single constructive ray cluster, the horizontal-longitudinal coherence coefficient remains high (≥ 0.707). When energy is distributed across two clusters, inter-cluster interference induces periodic oscillations in the horizontal-longitudinal coherence coefficient between 0.4 and 1.0. In regions of destructive intra-cluster interference, the received energy is dispersed across three to four clusters, and asynchronous phase differences among these clusters cause the horizontal-longitudinal coherence coefficient to decrease rapidly—to approximately 0.4—within 10 wavelengths, without subsequent recovery. Experimental observations agree well with numerical simulations, validating the generality of these patterns.