Interference and Phase Invariants of Sound Fields

Abstract—The frequency-space amplitude and phase structure of the hydroacoustic source pressure fields in shallow water is analyzed. It is shown that the motion of a source or a receiver with a moderate velocity or the longitudinal arrangement of an extended multielement array results in formation of lines with a constant phase of the sound pressure that do not coincide with the intensity ridge lines. A differential equation that describes lines with the constant signal phase in the frequency-space region is derived and analyzed. It is shown that the parameter entering into the equation of the constant-phase lines almost does not change along this line. On this ground a notion of the phase invariant is introduced, which is compared to the notion of the interference invariant. They are shown to be stable under variation in the properties of the Pekeris waveguide, which, in the opinion of the authors, allows both invariants to be jointly or independently used in the data analysis to accumulate signal power along the lines under discussion for increasing the signal-to-noise ratio.