Fast coupled-mode approximation for broad-band pulse propagation in a range-dependent ocean

An approximation method is proposed for the prediction of broad-band acoustic signals propagating in range-dependent ocean environments. The method is based on the one-way coupled-mode approach and uses second-order frequency expansions of eigenvalues, eigenfunctions, and coupling coefficients about the central frequency of the source. Exploiting analytic expressions for the frequency derivatives of eigenvalues and eigenfunctions, their frequency behavior over the source bandwidth is described from the solution of the vertical eigenvalue problem at the central (reference) frequency. The expansion obtained for the coupling coefficients enables their approximate evaluation at frequencies other than central in terms of reference quantities and, thus, bypasses the need for evaluative eigenfunctions in the intermediate range segments for these frequencies. The method is applied to a 600-km range-dependent section from the Thetis-2 tomography experiment in the western Mediterranean sea. A sufficient degree of accuracy is obtained, particularly for the low- and intermediate-order modes, corresponding to the intermediate and late part of the arrival pattern in the time domain. The approximation is faster by two orders of magnitude than the exact broad-band coupled-mode calculation.