Modal Perturbation Theory in the Case of Bathymetry Variations in Shallow-Water Acoustics

Perturbations of acoustic normal modes by bathymetry variations in a shallow-water waveguide are considered. The problem is reduced to the case of a potential perturbation for the stationary Schrodinger equation. The derivatives of the modal functions and eigenvalues with respect to water depth are formally calculated. Applications of such derivatives in sound propagation models based on the normal mode theory are discussed. It is shown that the computational cost associated with the sound pressure field computation in a range-dependent waveguide can be reduced by a factor of 5-10 by using the proposed formulas. DOI 10.1134/S1061920821020102