Elimination of branch cuts from the normal-mode solution using gradient half spaces

Abstract

A method for eliminating the branch cuts and branch line integrals from the normal-mode solution to the range-invariant acoustic wave equation has been developed and implemented. In the usual normal-mode formulation, evaluation of the vertical wave number in the ocean waveguide’s lower half space involves a square root operation and gives rise to a branch point at the critical angle. When the Pekeris cut is chosen, energy steeper than the critical angle is represented by leaky modes, and lateral-wave energy near the critical angle is represented by the branch line integral. When a mode lies near the branch cut, the branch line integral can be significant at all ranges. Branch line integrals are cumbersome to compute, and, for range-dependent problems, cannot be included in adiabatic and coupled-mode algorithms. By inserting small attenuation and sound-speed gradients in the lower half space, the plane-wave solution is replaced by an Airy function solution, the branch point is eliminated, the Pekeris branch cut is replaced by a series of modes, and the leaky modes become bounded at infinite depth. Implementation of and example calculations using this approach using the normal-mode model ORCA are given.