## 7 Discussion  
In this paper, we considered the statistical problem of the behavior of the sound intensity of a low-frequency point source in a shallow-water homogeneous waveguide with randomly inhomogeneous liquid sediments of the bottom. The performed statistical modeling has shown that fluctuations in the speed of sound in the bottom sediments can lead to the effects of the appearance of strong fluctuations in the signal intensity at small distances from the source and a slowdown in the decay of the average intensity in the waveguide. Similar effects were previously established for random inhomogeneities in the speed of sound in the water layer with thermocline [16], which are usually caused by internal waves. In relation to the shelf zones of the Arctic basin, however, the nearly homogeneous speed of sound over the sea depth is typical, which reduces the relevance of studying the effect of the mechanism of internal waves on the propagation of sound in the shallow Arctic seas. At the same time, the diversity of the impedance characteristics of the bottom in this region and the significant lack of data on these characteristics translate the acoustic problem of signal propagation in the Arctic shelf into a statistical problem. In this formulation, the statistical analysis of the effect of fluctuations in the speed of sound in bottom sediments is partly a study that reflects the degree of our ignorance of the spatial varies in the bottom parameters at the waveguide regions where the sound signal propagates. The presented results of statistical modeling predict expectations regarding the intensity levels of the propagating signal in a shallow-water waveguide with a highly penetrable (in average) bottom. They clearly demonstrate the fast stochastization of the signal in such a waveguide with a simultaneous weakening of its intensity attenuation,which is associated with a decrease (in the statistical sense) in the leakage of acoustic energy into the bottom half-space. Just as in the case of fluctuations of the speed of sound in water, the magnitude of the described effects is determined by the average penetrability of the waveguide bottom and the horizontal scale \(L_{r}\) of the sediment inhomogeneities. The more reflective (\"rigid\" or \"soft\") the bottom is at a fixed \(L_{r}\), the less pronounced the described statistical effects become. The same is true for a decreasing \(L_{r}\) value for given parameters characterizing the degree of bottom rigidity. In terms of physics, the fact of a decrease in the transmission loss of sound can be explained by the appearance of local fluctuation waveguides along the propagation path, with varying degrees of focusing acoustic energy. The degree of focusing by these local fluctuation waveguides is determined by fluctuations of the imaginary parts of the eigenvalues \(\kappa_{m}(r)\). The larger the value of these imaginary parts \(\kappa_{m}(r)\), the more they fluctuate, and in the statistical mean, there is a decrease in the transmission loss of a signal. Here, we should refer to [36], in which the possibility of forming a fluctuation waveguide channeling the wave energy of a point source along random layers is theoretically shown for a random half-space of a layered medium. In works [29; 37; 38; 39; 40; 41; 42] for the statistical analysis of the influence of random inhomogeneities in water on the propagation of sound in a marine environment, a theory was developed that was called the diffusion approximation. It is based on assumptions that allow describing the effect of internal waves on acoustic fields in a deep ocean with an underwater sound channel. For a shallow sea, the main concern is to consistently take into account the sound losses caused by the bottom, and in the simulation, it is necessary to correctly calculate the random complex eigenvalues and eigenfunctions of the modes.