Chuprov invariant for vector-scalar fields of multipole sources in a shallow sea

Abstract

A computational and theoretical study of the properties of the well-known waveguide invariant S.D. Chuprova (IC) was carried out in a plane-parallel Pekeris waveguide. Unlike earlier works, in which predominantly non-directional (monopole) sources were used as a source, and sound pressure fields (scalar fields) were studied, in this work not only scalar, but also vector fields formed in the waveguide by directional - combined multipole sources with directivity in both horizontal and vertical planes. A differential equation has been obtained that makes it possible to fairly accurately calculate the IC values under different conditions of signal propagation and different depths of sources and receivers. This makes it possible, in a simpler way than “full computer modeling,” to predict the invariance (stability) of the IC when varying both the hydrophysical conditions in the waveguide and the geometry of the experiment. It is shown that the directionality of sources in the horizontal plane has virtually no effect on the properties of the IC, and the directionality in the vertical plane leads to a shift in the fan structure of the signal amplitude fields, but has little effect on the IC values. The properties of the fan structure change in a similar way when using vertical projections of the oscillatory velocity vector - despite the fact that another analytical relation, different from scalar fields, is used to calculate the IC, the IC value is close to (+1) at all frequencies and distances, except those at which new modes or dislocations arise. At these frequencies and in these zones, alternating emissions with different signs and magnitudes occur. It is concluded that the stability of IC allows the application of signal processing algorithms developed for scalar fields and non-directional sources to vector-scalar fields generated, including using directional sources.