The Waveguide Invariant Close to the Deep-Water Bottom

Waveguide invariant, denoted by β, describes the dispersive nature of the underwater acoustic waveguide. In most range-independent shallow-water waveguides β≈1, whereas β is no longer constant in deep water and is more appropriately described by a distribution. This paper investigates the characteristic of β close to the deep-water bottom. The adiabatic normal mode theory is used to analyze β resulting from the bottom-bounce dominated acoustic field qualitatively. Then, the Wentzel–Kramers–Brillouin approximation with bottom reflection phase shift and the dominance of the acoustic field by groups of modes are employed to amend the original waveguide invariant theory. The interference between the phase-compensated dominant modal groups is calculated to obtain the value of β and analyze the distribution in the two-dimensional spectrum of the interference pattern. For a typical deep-water waveguide, both qualitative and quantitative analyses indicate that β≈1 when close to the bottom instead of a distribution. Simulation and experiment data demonstrate that the interference between phase-compensated dominant modal groups produces particular structure in the two-dimensional spectrum resulting from β being approximately equal to 1. The characteristic of β proposed in this paper has potential application in remote ranging the underwater acoustic source in deep water, which is verified using experimental data.