Degree Name

Department

Mathematics

College

Physical and Mathematical Sciences

Defense Date

2024-07-10

Publication Date

2024-07-14

First Faculty Advisor

Dr. Tracianne B. Neilsen

First Faculty Reader

Dr. Mark N. Transtrum

Honors Coordinator

Dr. Davi Obata

Keywords

underwater acoustics, information geometry, model manifolds, transmission loss, VGS, parametrization

Abstract

In geoacoustic inversion, selecting an appropriate seabed parametrization, especially with an unknown number of sediment layers, is a challenge that is compounded by potential bias when establishing bounds in the parameter search space. One approach to addressing these issues is rooted in the techniques of Information geometry. Information geometry informs model selection and parameterization by quantifying which model parameters are informed by observational data. This paper provides an information geometric analysis of a shallow-water waveguide, where the acoustic properties of the lower half-space are derived from the viscous grain-shearing (VGS) model.

Specifically, we consider single-frequency transmission loss (TL) across a wide range of VGS parameters. By exploring the limits and boundaries of the geometric manifolds, particularly as parameters approach both low and high extremes, this approach allows for the determination of relative stiffness and sloppiness of model parameters and provides indications of parameter hierarchies and correlations. Results include slices of the model manifold and matrices of distances on a 16-dimensional model manifold, representing the absolute transmission loss for 16 different sediment types, providing insight into the relative impact of VGS parameters and the delineation of limiting regions. In doing so, this paper seeks to inform model selection and parameterization in geoacoustic inversion studies, leading to more efficient and interpretable models. [Work supported by the Office of Naval Research. Grant N00014-21-S-B001]