arXiv subjects

Katherine C. Hegewisch

Publications and source records attributed to Katherine C. Hegewisch.

3 recordsLinked to original sources

arXiv2012

Constructing acoustic timefronts using random matrix theory

In a recent letter [Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering between acoustic modes due to sound speed fluctuations induced by the ocean's internal waves. The scattering exhibits a power-law decay as a function of the differences in mode numbers thereby generating a power-law, banded, random unitary matrix ensemble. This work gives a more complete account of that approach and extends the methods to the construction of an ensemble of acoustic timefronts. The result is a very efficient method for studying the statistical properties of timefronts at various propagation ranges that agrees well with propagation based on the parabolic equation. It helps identify which information about the ocean environment survives in the timefronts and how to connect features of the data to the surviving environmental information. It also makes direct connections to methods used in other disordered wave guide contexts where the use of random matrix theory has a multi-decade history.

math-ph↗

arXiv2011

Random matrix theory for underwater sound propagation

Ocean acoustic propagation can be formulated as a wave guide with a weakly random medium generating multiple scattering. Twenty years ago, this was recognized as a quantum chaos problem, and yet random matrix theory, one pillar of quantum or wave chaos studies, has never been introduced into the subject. The modes of the wave guide provide a representation for the propagation, which in the parabolic approximation is unitary. Scattering induced by the ocean's internal waves leads to a power-law random banded unitary matrix ensemble for long-range deep ocean acoustic propagation. The ensemble has similarities, but differs, from those introduced for studying the Anderson metal-insulator transition. The resulting long-range propagation ensemble statistics agree well with those of full wave propagation using the parabolic equation.

physics.ao-ph↗

arXiv2004

Ocean acoustic wave propagation and ray method correspondence: internal wave fine structure

Acoustic wave fields propagating long ranges through the ocean are refracted by the inhomogeneities in the ocean's sound speed profile. Intuitively, for a given acoustic source frequency, the inhomogeneities become ineffective at refracting the field beyond a certain fine scale determined by the acoustic wavelength. On the other hand, ray methods are sensitive to infinitely fine features. Thus, it is possible to complicate arbitrarily the ray dynamics, and yet have the wave field propagate unchanged. This feature raises doubts about the ray/wave correspondence. Given the importance of various analyses relying on ray methods, a proper model should, at a minimum, exclude all of the fine structure that does not significantly alter the propagated wave field when the correspondence to the ray dynamics is integral. We develop a simple, efficient, smoothing technique to be applied to the inhomogeneities - a low pass filtering performed in the spatial domain - and give a characterization of its necessary extent as a function of acoustic source frequency. We indicate how the smoothing improves the ray/wave correspondence, and show that the so-called ``ray chaos'' problem remains above a very low frequency (about 15-25 Hz).

physics.ao-ph↗