Normal mode theory: The role of the branch‐line integral in Pedersen–Gordon type models Available to Purchase

The acoustic field at the cutoff frequency of a shallow water channel described by Stickler [J. Acoust. Soc. Am. 57, 856–861 (1975)] is calculated using the Pedersen–Gordon normal mode model. As the (negative) sound‐speed gradient in the terminal layer approaches zero, the values of the acoustic field at various positions are found to approach well defined limits. These limits are in excellent agreement with the corresponding values obtained by Stickler for the same profile terminated by an iso‐speed layer. Stickler’s calculation included a significant Branch Line Integral (BLI) contribution, whereas the present calculation does not, although it does include the first mode of the first family, and many modes of the second family, of ‘‘Freehafer’’ modes. This agreement demonstrates that, as argued by Freehafer, there is no BLI in the solution of the wave equation for a stratified half‐space that has a free surface, a piecewise analytic sound‐speed profile, and a sound speed that approaches zero at infinite distance from the surface.