Normal-mode program with both the discrete and branch line contributions

In a stratified ocean model, in which the sound speed and density become constant as the depth coordinate becomes infinite, the pressure field can be represented as a finite sum of modes plus an integral superposition of modes. This later contribution is given by an integration around a branch cut. In this analysis the sound-speed and density profiles are partitioned in layers such that in each layer the square of the index of refraction can be approximated by a straight line and the density by a constant. The profile is terminated in a high-speed isovelocity half space. Using this profile, it is possible to express the depth-dependent portion of the pressure field in terms of Airy functions. Evaluation of the modal and branch line contributions shows that the branch integral can contribute significantly to the pressure field over a range equal to at least one water depth and in some cases to many water depths. Subject Classification: 30.20, 30.25.