In underwater acoustics or more precisely in shallow water propagation, the determination of the modes propagating in the water duct is critical. Several approaches in solving the propagation problem in an acousto-elastic environment have been discussed. The first approach which is the most widely used is the KRAKEN normal mode program which divides the environment into layers. Recently another model called ORCA based on Airy function solutions was proposed. While KRAKEN uses the secant method for finding modes, ORCA uses a special mode finding algorithm which improves its robustness. But difficulties still remain because of the presence of branch line integrals. For example, ORCA requires the use of false bottoms which complicate the mode solution. A new root finder for KRAKEN which makes the code more robust is presented in this paper. It is based on winding number integrals and does not require the use of false bottoms. Consequently robust and accurate solutions of the depth-dependent wave equation can be obtained. In addition to this new root finder, a simple modofication of the characteristic equation is used to find the modes which are closed to a branch points. Some examples of the behaviour as a function of frequency of a mode which is closed to a branch point will be presented.
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