Amplitude–Phase Structure of the Sound Field in the Deep Sea

Amplitude-phase characteristics of sound pressure (SP) in the deep ocean is analytically and numerically investigated under summer conditions. To this end, analytical relations are obtained, which allow calculating and comparing space–frequency structure characteristics of water, leaky, and trapped modes, as well as of the SP field formed by the mode sum. The calculations are performed using the modified Wentzel–Kramers–Brillouin approximation. It is shown that modes of different types dominate at different distances, and this enables describing structure variability of both the amplitude and the phase distribution of the SP field in different zones with a different mode composition. It is found that in the field based on the sum of all modes the mode properties more distinctly manifested at various distances are of those modes which dominate at these distances. As a consequence, space–frequency structures of SP amplitudes are substantially different in different zones. But, due to stability of phase gradients in zones of interference maxima, phase surfaces coincide in shape for all types of modes, all frequencies, and almost all distances. Some difference is only observed for leaky modes in the near-field zone. Numerical values of effective phase velocities of the summed field depend, as expected, on phase velocities of modes of various types and on their “extinction” rate, and they are appreciably different in different zones. This should be taken into account during direction finding and estimation of noise source coordinates.