Martin A. Mazur
Kenneth E. Gilbert
Appl. Res. Lab. and the Graduate Prog. in Acoust., Penn State Univ., P.O. Box 30, State College, PA 16804
In classical ray tracing, eigenrays are determined by a ``shooting'' approach whereby the launch angles of rays are varied until the rays intersect the receiver. In nonseparable range-dependent environments, the ray paths computed by conventional methods are sometimes chaotic, thereby putting a fundamental limit on the accuracy of ray tracing. Previous researchers [M. D. Collins and W. A. Kuperman, ``Overcoming ray chaos,'' J. Acoust. Soc. Am. 95, 3167--3170 (1994)] have suggested that ray chaos can be overcome by recasting the problem in terms of Fermat's principle of minimum propagation time. The problem then becomes amenable to so-called ``direct methods'' of optimization theory. For the specialized duct investigated by Collins and Kuperman we have easily found eigenrays using a simple Rayleigh--Ritz method for directly minimizing the travel time integral. The structure of the ray equations for the duct suggests, however, that the numerical instability may actually be due to ``stiffness'' rather than chaos. To investigate chaos independently of numerical issues such as stiffness, we consider several nonseparable, range-dependent ducts with known piecewise analytic ray solutions. Results obtained from a shooting method and from Fermat's principle for several such ducts are presented and discussed. [Work supported by ONR.]