On the solution of the problem of low-frequency acoustic signal propagation in a shallow-water waveguide with three-dimensional random inhomogeneities

Based on the local mode method, the problem of the propagation of tonal acoustic signals of a frequency f < 1 kHz in a shallow water waveguide typical for the shelf zones of an ocean is considered in the presence of three-dimensional random fluctuations of the sound speed in the water column. Three-dimensional linear acoustics equations with random coefficients are reformulated into causal equations of the first order, for which, by analogy with the two-dimensional case, the solution can be written in quadratures in a convenient exponential representation. As applied to the problem of fluctuations of the speed of sound in a waveguide, a solution is written in the one-way propagation approximation (forward scattering), on the basis of which it is possible to perform statistical modeling. In the particular case, an example illustrating the statistical calculations of the average transmission loss of the signal frequency of 500 Hz is presented.