Asymmetry analysis of beamforming time-delay for deep-water bottom reverberation

Reverberation is a key factor limiting the performance of active sonar in deep water, and its fine-scale spatiotemporal distribution characteristics represent a critical issue in underwater acoustics research. In a deep-water active detection experiment, a significant and stable asymmetry in the beam–time-delay distribution of reverberation is observed by using a towed line array combined with linear frequency-modulated (LFM) detection signals, and the underlying formation mechanisms are analyzed. First, based on ray theory, a deep-water bottom reverberation model is developed, which incorporates the array’s spatial attitude and Doppler shift, allowing for precise calculation of the propagation time of echoes from individual bottom scattering elements and enabling fine-scale reverberation simulation. Next, a comparison between theoretical models and experimental data demonstrates that the tilt angle of the array is the primary cause of the angular shift observed in the beam-delay diagram, while the Doppler shift induced by platform movement alters the peak response time after the LFM signal matched filtering, which is the key factor responsible for the asymmetric distribution of reverberation energy along the delay axis. Further analysis shows that the Doppler shift causes the bottom scattering region contributing to reverberation at a specific time to evolve from a concentric circular ring to an offset elliptical ring, with a horizontal distance deviation of up to several hundred meters. This study elucidates the combined effect of array attitude and Doppler shift on the beam-delay distribution of towed array reverberation, providing theoretical support for environmental sensing and parameter estimation.