Sound propagation from a point time-harmonic source in a stratified water layer lying over an elastic solid half-space is investigated. It is assumed that the sound speed in the layer is less than the shear speed in the solid bottom, and that it increases with the depth. Numerical examples are given which show that the dependence of the wave field on the range between the source and the receiver can sharply change the character under rather small variations of the frequency. Namely, for some particular frequencies, the sound amplitude shows a periodical dependence on the range, while for other frequencies there is no periodicity. A theoretical explanation of this phenomenon is given in a mathematical development using the normal modes theory and high-frequency asymptotic approximations. The dispersion phase curves are found to have “quasi-intersections,” i.e., small domains where two adjacent curves almost intersect. The corresponding frequencies are called the “specific” frequencies. For any nonspecific frequency, there isoneinterface Stoneley(=Scholte)mode, whilst for each specific frequency there aretwomodes of the Stoneley type with close phase velocities. The periodicity of the field is a result of interference in the two Stoneley modes.