Eigenfrequencies of an underwater acoustic resonator formed due to horizontal refraction over a circular bottom depression

The problem of sound propagation in an area of a shallow sea with a circular bottom depression is considered. Such depression can be considered a resonator admitting a specific class of eigenstates that have vertical profiles corresponding to normal modes and horizontal structure of whispering gallery waves. A method for computing eigenfrequencies corresponding to such eigenstates is proposed and the estimation of their respective quality factors is discussed. The relation of these eigenstates to quasistationary states from quantum mechanics is highlighted, and the connection between their quality factors and the classically forbidden quantum gap is established. A simple numerical algorithm for computing eigenfrequencies and their decay factors for a given frequency band is proposed and illustrated on the case of a cylindrical depression.