On the Dependence of Acoustic Modes on Media Parameters in the Pekeris-Airy Waveguide

A waveguide consisting of an isospeed water layer overlying a halfspace with a sound speed gradient is considered. The dependence of horizontal wavenumbers of normal modes in such a waveguide on the sound frequency, water depth and geoacoustic parameters of the bottom are investigated. It is shown that these dependencies are described by ordinary differential equations that can be solved numerically at very low computational cost providing a substantial increase in the efficiency of broadband modelling of sound propagation. The explicit formulae for the derivatives of horizontal wavenumbers with respect to the bottom parameters can be also used in dispersion-based geoacoustic inversion methods. This approach can be extended to the case of a waveguide consisting of several layers of Airy-type media. We also propose a new and concise proof that the spectrum of the Sturm-Liouville problem from which the modes are found for this waveguide is purely discrete.