Thesis Abstract 

A Development of Various Techniques for Investigating Ray Chaos in Underwater
Acoustic Propagation

Martin Alois Mazur 
Ph.D.; August 1998 
The Pennsylvania State University 
Kenneth E. Gilbert, Thesis Advisor


Acoustic ray tracing techniques are important for the study and solution of
underwater acoustic propagation problems. Recently, it has been discovered 
that ray tracing over long distances is generally subject to the phenomenon of
chaos. Where chaos exists, the calculation of ray paths is extremely sensitive
to the initial data, and the number of ray paths connecting two points grows 
rapidly with the distance separating the points. In this thesis, various 
techniques for investigating ray chaos are developed and evaluated. First, 
direct optimization methods are developed. Direct methods are useful for 
finding at least some of the ray paths connecting two points under chaotic 
conditions when conventional methods can fail. Direct methods are developed for
ray propagation in continuous media and ray propagation with discrete 
transitions. Next, phase screen techniques are developed. Phase screen 
techniques provide a valuable theoretical link between the wave and ray 
regimes. Phase screen techniques are useful practically as a means of speeding
up and simplifying the analysis of ray tracing in continuous media. They can 
also be used to study propagation problems that are inherently discrete. 
Finally, phase screen methods are applied to chaotic ray propagation in random
media. Phase screen techniques are employed to reduce a continuous random 
medium to a medium with discrete transitions. Analytic results are obtained 
for the discrete problem that characterize the chaotic behavior of the ray 
paths. The results are compared to known results for continuous media. 
Conditions on the spacing of the phase screens required to reproduce the 
results of the continuous case are derived.