Shallow‐water propagation: The role of the branch‐line integral in the Pedersen‐Gordon model Free

Solutions to the wave equation for sound‐speed profiles which are terminated by an isospeed half‐space can be expressed as a sum of discrete modes plus a branch‐line integral (BLI). The BLI is often insignificant, but can be of great significance in duct propagation at frequencies near the cutoff freqency of the duct. In one example [D. C. Stickler, J. Acoust. Soc. Am. 57, 856–‐861 (1975)], the BLI dominated the mode contribution for ranges out to 30 km. The Pedersen‐Gordon normal‐mode model, on the other hand, terminates the profile with a “furry” half‐space in which the sound speed approaches zero as z^−1/2 as the depth (z) approaches infinity. The Pedersen‐Gordon model is applied to Stickler's shallow‐water duct, and the limit of the results for the sound field (based on only a mode sum), as the sound‐speed gradient in the half‐space (evaluated at its interface with the duct) approaches zero, is determined. This limit is found to be equal to Stickler's result for the sum of both the BLI and the mode contributions. The theoretical reasons for this equality are discussed.