Lines of equal phases and phase invariant in the sound field of the deep sea

The spatial-frequency characteristics of the amplitudes and phases of sound pressure in the deep sea have been studied. Analytical relationships have been obtained that allow one to calculate and compare the amplitude-phase structures of water, leaky and trapped modes, as well as the sound pressure field formed by the sum of the modes. The calculations have been performed using the modified WKB (Wentzel–Kramers–Brillouin) approximation. It has been shown that in the deep sea, as in the shallow sea, there are stable lines of equal phases along which, under certain conditions, coherent summation of complex Fourier components is possible. To describe the lines of equal phases, a differential equation has been obtained that uses the phase invariant, already studied in the shallow sea, as a basic parameter. This has made it possible to study the properties of the phase invariant corresponding to water, leaky and trapped modes in all zones of the sound field for the deep sea as well. It is established that at different distances in the field constructed from the sum of all modes, invariant properties are manifested, first of all, those modes that dominate at these distances. It is shown that the leaky modes formed in the near illumination zone and in the shadow zone, formed by steep rays reflected from the bottom, have invariant properties only at large distances from the source. Water and trapped modes have invariant properties in full and at all distances. Recommendations are given on the use of equal phase lines and the phase invariant in processing experimental data and modeling.

deep sea, distributions of amplitudes and phases of water, leaky and trapped modes, as well as total sound pressure at different distances and frequencies, equal phase lines, phase invariant, accumulation of signal power