A HAMILTON SOLVER FOR FINDING MODAL EIGENVALUES

A method is proposed for finding the normal mode eigenvalues in shallow water waveguide. We transform the problem determining eigenvalues in complex wave number plane into solving a "true" one dimensional Hamilton system. Simulations are performed, the result agrees very well with that calculated by the normal mode program KrakanC.

A real frequency, complex wave-number analysis of leaking modes

Leaking-mode dispersion and attenuation is computed for two single-layer models. Roots of the dispersion relation are obtained in the complex wave-number plane, using real frequency as the independent variable. At low frequencies the root loci on the (+, +) sheet determine the fundamental propagating mode plus a series of attenuated standing-wave modes in the vicinity of the source. As frequency increases, the complex roots on all four sheets migrate through the wave-number plane, producing (successively) organ-pipe modes, PL modes, and normal modes. For higher frequencies, the modes exhibit a tendency to couple with pure P- (and S-) type motion in the wave guide. These effects are related to similar phenomena which occur for the case of the free elastic plate. Results are also calculated for a six-layer continental model. Here the pseudo-modes on the (+, −) sheet noted by Cochran et al. (using real wave-number analysis) are found to be decoupled P- and S-related modes whose phase-velocity curves freely intersect one another when frequency is assumed real.