Ray-based analysis of the interference striation pattern in an underwater acoustic waveguide

In some underwater acoustic waveguides with specially selected sound speed profiles striations or fringes of the interference pattern are determined by a single parameter \beta\ called the waveguide (or Chuprov) invariant. In the present paper it is shown that an analytical description of fringes may be possible in a waveguide with an arbitrary sound speed profile. A simple analytical expression is obtained for smooth lines formed by local maxima of the interference pattern. This result is valid at long enough ranges. It is derived proceeding from a known relation connecting the differences of ray travel times and the action variables of ray paths.