Phase space representation of sound field excited by a noise source in underwater acoustic waveguide

The analysis of the field excited in a waveguide by a point noise source is performed using the phase space representation of this field given by the distribution of its amplitude in the depth-angle-time space. The transition from the traditional description of the field amplitude as a function of depth and time to phase space representation is performed using the coherent state expansion developed in quantum mechanics. In this paper, the correlation function of noise signals arriving at different points of the phase plane depth-angle is investigated. Numerical simulation data show that measurements of signal correlations in phase space, performed with the help of a receiving vertical antenna, can be used as input data in solving the problem of source localization and reconstruction of unknown parameters of the sound speed profile. It is shown that in phase space there is an analog of the classical interference pattern observed in the distribution of sound intensity in the distance-frequency plane. The slopes of striations in this interference pattern, as in the conventional one, are given by the Chuprov waveguide invariant.