1aAO6. Second-order analysis of eigenray displacement: When does Fermat's principle apply?

Session: Monday Morning, May 13

Time: 9:20

Author: B. Edward McDonald
Author: Michael D. Collins
Location: Naval Res. Lab., Washington, DC 20375
Author: Ira B. Bernstein
Location: Yale Univ., New Haven, CT 06520


In the ocean sound channel multiple eigenrays, each possessing stationary travel time, may connect two fixed points. In a highly structured propagation environment, how does one determine if the travel time of a given eigenray is a local minimum (Fermat's principle), maximum, or saddle point with respect to ray parameters? A second-order analysis of the travel time integral along an eigenray is carried out to reveal conditions determining the nature of the stationarity. In three dimensions, the problem reduces to a second-order differential/diadic eigenvalue equation along the ray. In two dimensions, it becomes a scalar Sturm--Liouville eigenvalue problem. An analytic example is given in which both maximum and minimum travel time eigenrays exist. Conditions for ray chaos in the analytic example are derived and related to the occurrence of maximum travel time eigenrays. [Work supported by NRL.]

from ASA 131st Meeting, Indianapolis, May 1996