Interference and phase structure of the low-frequency vector-scalar field in shallow water for variable reception or transmission depths

Abstract

Relations for calculating the amplitude and phase characteristics of sound pressure and orthogonal projections of the vibration velocity vector and phase gradient in shallow water have been derived. Dependences of the effective phase velocity of equivalent plane wave, orthogonal projections of the gradient of sound pressure phase, and projections of the vibration velocity vector on the transmitter (or receiver) depth are calculated for different frequencies and location depths of receivers (and transmitters). It is found that the horizontal projections of the vibration velocity vector and phase gradient satisfy the reciprocity principle whereas their vertical projections do not obey this principle. Therefore, the characteristics of the vertical components must be studied independently with variation in their transmission or reception depth. It is shown that, for low frequencies and variable transmitter or receiver depth, the effective phase velocities in interference maxima exceed generally the speed of sound in water by 5-15% or even more. Some recommendations on the use of sound field characteristics in the regions of maximum sound pressure for solving problems of direction finding and signal detection are formulated. The behavior of the characteristics of arrival angles of equivalent plane wave with variation in the transmission or reception depth are investigated.