On the possibility of applying the reciprocity principle in the vector-scalar fields of mutipole sources in a waveguide

We study the applicability of the reciprocity principles in an underwater waveguide for the vector-scalar fields of multipole sources. We show analytically and numerically that multipole sources are divided into two groups according to this principle: in the first group, the sound pressure field and the horizontal projections of the vibration velocity vectors satisfy the reciprocity principle, while the vertical projections of these vectors do not. In the second group, the pressure and the horizontal projections of the vibration velocity vector do not satisfy the reciprocity principle, while their vertical projections do. We establish that the phase gradients and angles of arrival of signals in the vertical plane do not satisfy the reciprocity principle for the vector-scalar fields of volumetric sources with arbitrary directivity in the vertical plane.