The variation of frequency F as a function of wave number K and the associated spectral transfer function are computed for different modes in a complex oceanic wave-guide. The model consists of a fluid layer resting upon a three-layer elastic half-space. The layers and the half-space are homogeneous.
The comparison of theoretical results with measured power spectra for two records taken in the Pacific Ocean shows qualitative agreement stressing strongly the role of the leaking compressional organ-pipe modes which are not continuations of normal modes beyond cutoff frequency.
The mathematical procedure consists in the integration of the second-minor propagator equation of Gilbert and Backus (1966). The determinant representing the secular function is computed directly rather than by summing the products of its elements. This improves both accuracy and computing time. The integration can be reduced to that of a third-order nonlinear differential system which, for K = 0, splits into two Riccati equations.
The (F, K)-diagram corresponding to every mode is obtained by a technique based on properties of similar diagrams for simple oceanic and continental structures.