The self-focusing effect of nondirected acoustic emission in layered media

Abstract

If an acoustic field from a nondirected pointed source is located in a layered medium, for example, in an aquatic medium, and a halfinfinite space with a bottom, we apply one physical model of the medium or another. Most frequently, the Pekeris waveguide model is used. Two principally different model approaches are possible to solve the boundary prob� lem: the selfconjugate approach (classic) described in (1-3) and the nonselfconjugate approach (general) described in (4). A comparison of these two model solutions was performed in (4), which showed their significant difference in the description of the acoustic field in the boundary layer and near the symmetry axis of the system point source, i.e., the layered medium in the halfspace. In the selfconjugate model formulation, the spec� trum of eigenvalues of the transversal operator corre� sponding to the Pekeris boundary problem is real, which is interpreted as a lack of emission losses in the system waveguide-halfspace. However, imaginary sources appear in the solution, which are distributed along the symmetry axis in the halfspace. These sources, precisely, simulate emission into the half� space at zero power flux through the impedance inter� face waveguide-halfspace. This provides unidirec� tional (phase synchronism) wave motion along the impedance interface and satisfies conditions of local continuity of the field by the pressure and normal component of the oscillation velocity (conditions of ( p, vz) continuity) at the boundary. In the nonselfconjugate model approach, emit� ted waves of the complex spectrum of the transversal operator appear as do the converging response waves, which provide a positive definiteness of the power flux through the impedance interface. However, the total wave motion appears opposite, out of phase, while conditions of ( p, vz)�continuity are satisfied only on average. A real focusing zone formed by converging response waves appears on the symmetry axis as a con� sequence of emitted waves in the total solution. The appearance of converging response waves is explained by the fact that these waves, together with diverging waves, form a field of the standing wave type in the close zone to the emitter and on the symmetry axis, which plays the role of an absolutely rigid boundary where the radial component of the oscillating velocity should turn to zero. The objective of this work is to analyze the acous� tic field focusing effect in the near zone of the emitter immediately at the symmetry axis in a halfspace on the example of the Pekeris model problem and to study its practical application in the investigation of the sea bottom structure using the methods of acous� tic profiling.