Range-dependent Waveguide Research Articles

Scattering matrix and boundary integral equation methods for long-range propagation in an acoustic waveguide with repeated boundary deformations

Boundary integral equation methods (BIEM) provide an accurate model for predicting the scattering of acoustic radiation from compact deformations of the walls of a waveguide. In numerical implementation, however, the denseness of the resulting coefficient matrix inhibits the modeling of scattering over very extensive deformations. It is shown how scattering matrix methods can be used to extend BIEM to allow for long-range propagation in a two-dimensional range-dependent waveguide. The extension to three-dimensional sources is also indicated.

Numerical implementation of a modal solution to a range-dependent benchmark problem

Numerical results are presented for a modal representation of sound propagation in a range-dependent waveguide with plane-parallel, perfectly reflecting boundaries. Range dependence in the waveguide is embedded in the sound speed that varies sinusoidally with depth and exponentially with range. The modal expansion is based on a conformal mapping technique, whereby the solution to the Helmholtz equation in a range-dependent waveguide is expressed in terms of a solution to a parabolic equation in a corresponding waveguide whose sound speed is constant in the mapped coordinates.

Ocean acoustic tomography based on adiabatic mode theory

A new method of ocean acoustic tomography is developed on the basis of adiabatic normal-mode theory. It is a full-wave method suitable for low frequency in a slowly varying range-dependent waveguide. The modal phase difference perturbations are proposed as data for inverting the sound-speed profile perturbation for a continuous-wave (cw) source. The modal travel time perturbations are proposed as data for a pulse source. It is shown that the ‘‘normalized depth structure,’’ as well as the ‘‘range-averaged strength parameter’’ (defined as the product of the effective horizontal scale and the maximum sound-speed perturbation), can be retrieved from the vertical slice modal tomography. A simulation example of inversion is presented to verify the basic ideas.

Adiabatic modes for up-slope propagation in a wedge-shaped ocean

Recent numerical studies of upslope propagation in a wedge-shaped ocean with penetrable bottom [F. Jensen and W. Kuperman, J. Acoust. Soc. Am. 67, 1564–1566 (1980)], have revealed that intermode coupling is negligible for small bottom slopes but that each range-dependent adiabatic trapped mode field is strongly perturbed when that mode passes through cutoff. This observation has revived interest in extending the description of an adiabatic mode field through the transition region from trapped to radiating [A.D. Pierce, J. Acoust. Soc. Am. Suppl. 1 69, S69 (1981)]. We present a procedure of inherent general validity for range-dependent waveguides whereby an initial ray-acoustic field undergoing multiple reflection is converted into local mode fields by Poisson summation. Before the conversion, a plane-wave spectrum is fitted to the ray family, and the resulting Poisson-transformed spectral integrals, after asymptotic evaluation by the stationary phase method, are found to produce the conventional adiabatic trapped modes downslope from their cutoff points. As mode cutoff is approached, the simple stationary phase procedure must be modified, and the transformed spectral integrals become “canonical integrals” that trace the transition of a mode uniformly from the trapped to the radiating (leaky) regime. Results are shown for the transition function and its connection to the trapped and leaky mode fields downslope and upslope from the cutoff region. [Work supported by ONR Ocean Acoustics Branch.]