Environmental perturbation of ocean waveguide eigenmodes

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Explicit forms are derived for the coupling matrix that relates perturbations in environmental parameters to resulting perturbations in the trapped acoustic modal eigenfunctions in the ocean waveguide [Kuperman etal., J. Acoust. Soc. Am. 89, 125–133 (1991); Desaubies etal., J. Acoust. Soc. Am. 80, 1148–1160 (1986)]. Special consideration is paid to the continuity conditions across the ocean/bottom interface. The perturbation is carried out with respect to frequency, ocean depth, sound-speed profile, and density distribution. Density is included to account for stratification in the bottom, and to estimate scattering from internal gravity waves near the thermocline. The matrix elements are expressed in terms of inner products of the unperturbed eigenfunctions with environmental perturbations. The results give straightforwardly the perturbations in eigenvalues (i.e., the horizontal component of the local wave vector for each mode). Applying the results to the variation of eigenmodes with horizontal position in the ocean, one finds separate terms for bathymetric (bottom slope) and oceanographic (water column) contributions. Results are related to the determination of horizontal ray paths of the trapped modes in global scale ocean acoustic experiments, and to the inversion of group arrival time data.