Prediction of Target-Induced Multipath Interference Acoustic Fields in Shallow-Sea Ideal Waveguides and Statistical Characteristics of Waveguide Invariants

The acoustic scattering of targets in shallow-sea waveguides exhibits complex features such as multipath propagation and intricate echo components, with its acoustic field properties remaining incompletely understood. This study employs a hybrid method combining normal modes and scattering functions to numerically model the acoustic scattering of targets in waveguide channels. We analyze the coupling mechanisms of multipath acoustic waves and derive precise predictive formulas for the bright–dark interference fringe patterns in range–frequency spectra based on the physical mechanisms governing acoustic field interference. By tracking the peak trajectories of these interference fringes in range–frequency spectra, we investigate the variations of the waveguide invariant with frequency, range, and depth, revealing statistical patterns of the waveguide invariant in target–waveguide coupled scattering fields under different water depths. The results demonstrate that, under constant channel conditions, waveguide properties exhibit a weak correlation with target material characteristics. In shallow water environments, waveguide invariant values display broader distributions with higher probability density peaks, whereas increasing water depth progressively narrows the distribution range and monotonically reduces the peak magnitudes of the probability density function. Experimental validation via scaled elastic target echo testing confirms the observed trends of waveguide invariant variation with water depth.