Chuprov Invariant for Vector–Scalar Fields of Multipole Sources in Shallow Water

A computational and theoretical study of the properties of the well-known Chuprov waveguide invariant (CI) was carried out in a plane-parallel Pekeris waveguide. In contrast to earlier works, in which predominantly omnidirectional (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 are investigated. A differential equation has been obtained that makes it possible to fairly accurately calculate the CI values under different conditions of signal propagation and different depths of the sources and receivers. This makes it possible, in a simpler way than “total computer simulation,” to predict the invariance (stability) of the CI when both the hydrophysical conditions in the waveguide and the geometry of the experiment are varied. It is shown that the directivity of sources in the horizontal plane has virtually no effect on the properties of the CI, and the directivity in the vertical plane leads to a shift in the fan structure of the signal amplitude fields, but has little effect on the CI values. The properties of the fan structure change similarly when using vertical projections of the vibrational velocity vector: despite the fact that another analytical relation different from scalar fields is used to calculate the CI, the CI value is close to (1) at all frequencies and distances, except for those at which new modes or dislocations appear. At these frequencies and in these zones, alternating emissions with different signs and magnitudes occur. It is concluded that the stability of the CI allows the application of signal processing algorithms developed for scalar fields and nondirectional sources to vector–scalar fields generated, including with the use of directional sources.