STATIONARY-PHASE FOR SUMMATIONS

The geometrical, or ''ray'' approach to high-frequency wave fields is well known. Using the method of stationary phase, the ray terms can be shown to arise as the leading-order solution of an exact integral for mulation for the wave field. However, this analysis cannot be applied directly when the problem geometry is cylindrical or circular, and the integral is replaced by a summation. Instead the sum must first be co nverted into an integral by the rather cumbersome means of a Watson tr ansformation. Here an intuitive and concise extension of the method of stationary phase, which may be applied directly to summations, is pre sented, and the validity of the approach is confirmed using the Watson transformation. (C) 1996 Acoustical Society of America.