Narrow Results

The requirement by modern navies to predict sonar performance in shallow water, whether for use in research, planning or operations, led to an initiative for the validation of reverberation models in the form of two Reverberation Modeling Workshops at the University of Texas at Austin in November 2006 and May 2008 [J. S. Perkins and E. I. Thorsos, Update on the reverberation modeling workshops, J. Acoust. Soc. Am.126 (2009) 2208]. The problem considered here (Problem XI, from the 2006 workshop) requires the computation of reverberation versus time in a Pekeris waveguide with Lambert scattering from the seabed. Results from eigenray, normal mode and (hybrid) continuum methods are presented and compared for the time window 0.05s to 1000s after pulse transmission. Approximate analytical solutions are used to provide insight into the expected behavior of the reverberation and establish regimes of validity of numerical models. In situations where the regimes of validity of different methods coincide, the solutions of models applying these methods overlap. The overlapping solutions agree with each other within ±0.3dB. Their purpose is to provide a baseline against which future model improvements can be assessed and quantified.

The eigenfunctions of the modified Helmholtz operator have no orthogonality in a bounded domain with a perfectly matched layer (PML), which makes it difficult to calculate the coordinates under two different local bases when the marching algorithm is applied. In this paper, we derive the conjugate eigenfunctions of the operator and discuss the cross orthogonality between the eigenfunctions and their conjugate eigenfunctions. On the other hand, we derive a simple formula for calculating the coordinates under the local base. The numerical results indicate that this method is effective.

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.