## 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**

**Abstract:**

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