Journal of Theoretical and Computational Acoustics

This tutorial demonstrates the use of information geometry tools in analyzing environmental parameter sensitivities in underwater acoustics. Sensitivity analyses quantify how well data can constrain model parameters, with application to inverse problems like geoacoustic inversion. A review of examples of parameter sensitivity methods and their application to problems in underwater acoustics is given, roughly grouped into “local” and “non-local” methods. Local methods such as Fisher information and Cramér-Rao bounds have important connections to information geometry. Information Geometry combines the fields of information theory and differential geometry by interpreting a model as a Riemannian manifold, known as the model manifold, that encodes both local and global parameter sensitivities. As an example, 2-dimensional model manifold slices are constructed for the Pekeris waveguide with sediment attenuation, for a vertical array of hydrophones. This example demonstrates how effective, reduced-order models emerge in certain parameter limits, which correspond to boundaries of the model manifold. This example also demonstrates how the global structure of the model manifold influences the local sensitivities quantified by the Fisher information matrix. This paper motivates future work to utilize information geometry methods for experimental design and model reduction applied to more complex modeling scenarios in underwater acoustics.

The parabolic equation method is the most effective approach for solving wave propagation problems in environments with strong vertical variations and gradual horizontal variations. This approach efficiently provides accurate solutions for problems involving sloping fluid-fluid interfaces, sloping solid-solid interfaces, and sloping solid boundaries. There remains a need for improvement for the case of sloping fluid-solid interfaces. The most promising approach to date is the combination of a single-scattering approximation and the treatment of part of the fluid layer as a solid layer with low shear speed. This is a singular perturbation, which results in rapid oscillations near the interface between the low-speed layer and the true solid layer. It is demonstrated here that the rapid oscillations may be eliminated by using slip conditions at the interface between the low-speed layer and the true solid layer. Stability problems were encountered when attempting to directly implement the slip conditions, but this problem was resolved by using an equivalent condition involving the normal derivative of the tangential displacement. This progress does not fully resolve the case of the sloping fluid-solid interface. There remains a need to find a vertical interface condition that is compatible with the slip conditions and that provides accurate results for problems involving sloping fluid-solid interfaces.

The deep-water sound multipath arrivals and interference striation patterns not only vary with range and depth but also with frequency. The first two cases can be solved using a ray-mode method in the high-frequency limit. However, this method may cause unsatisfactory results in treating low-frequency sounds (as low as tens of Hertz) because of the Wentzel-Kramers-Brillouin (WKB) high-frequency approximation assumption. To overcome this problem, the authors exploited phase information to modify the ray parameters, such as the propagation range, the time delay, and the group velocity. Following that, a waveguide invariant (WI) expression was derived to address low-frequency sound interference problems. Numerical investigations demonstrated that the physical mechanism of the frequency dependence of the multipath arrivals and interference striation patterns could be better understood using this modified ray-mode method. In addition, the influence of bottom sound speed on multipath interference structures is also considered.

This work deals with a coupled acoustic problem involving a compressible fluid and a poroelastic material contained in a cavity whose walls are all rigid except for the top, where a flexible plate is placed. The fluid is described utilizing its acoustic pressure, whereas, for the plate, the Naghdi shell model is used. The mechanical behaviour of the absorbing layer attached to the plate is described by using the Biot-Allard model, where the governing equations are written in the displacement-based formulation. The main novelty of this work lies in addressing the coupling between the plate and the poroelastic medium using the Reissner-Mindlin formulation for the Naghdi’s shell model and the displacement-based formulation for the Biot-Allard model. A comprehensive three-dimensional analysis is performed, comparing numerical and experimental results and showing the advantages of using the Biot-Allard poroelastic model in combination with the Naghdi shell model to predict the in-plane displacements of the plate structure over other fluid-equivalent formulations, such as the Allard-Champoux model.

Rayleigh scattering from a spherical object located near a planar rigid boundary at distances smaller than the wavelength is calculated. Low frequency analysis reduces a scattering problem to a sequence of potential problems. An analytical solution based on expansion in spherical solid harmonics and the use of addition theorem is presented. Analytical perturbation approach is validated by comparison with numerical calculations. The velocity of the center of the particle and the scattering amplitude are determined. In the lowest order in wavenumber, the scattering amplitude is expressed in terms of the monopole and dipole components. In contrast to the behavior of a bubble, under the same conditions, dipole oscillations of the particle in the direction normal to the boundary are not excited and the monopole component of the scattering amplitude does not depend on the location of the particle relative to the boundary.

The problem of investigating the nonlinear acoustic waves in stepped acoustic resonators is treated theoretically. A perturbation scheme that combines the method of multi-scale expansion yields a set of coupled nonlinear ordinary differential equations for deriving an analytical model to describe the resonant oscillations. The nonlinear sound pressure in stepped resonator is predicted with accuracy up to the second-order terms of a small-amplitude parameter $𝜀$. The pressure amplitudes and waveforms at the closed end of stepped resonators with different size parameters are investigated by the derived analytical model and qualitatively compared with the measured results in experiment. The qualitative comparison of calculated and measured results shows good agreement. The results suggest that the sound pressure generated in stepped resonators with different size parameters may be very different. Not all stepped resonators can generate high-amplitude and low-distortion standing waves. The derived analytical model can be used to qualitatively study the nonlinear acoustic waves in stepped acoustic resonators and design suitable tube dimensions for resonant macrosonic synthesis.