Arrival time and angle fluctuations of sea-surface forward scattering

The properties of the sound field, which is scattered from the sea surface, must be considered in any system that uses surface-reflected acoustic waves. In this paper, the probability density functions (PDFs) for time and the angle of arrival of the acoustic wave scattered from the sea surface are proposed. The trajectories of the emitted rays that reach the receiver are obtained by using the sea surface elevation and slope and the positions of the source and receiver. In this approach, the phenomenon of shadowing, which plays an important role in small grazing angles, is taken into account. The shadowing effect causes some parts of the sea surface to be shadowed by other parts. To show the validity of the proposed approach, the results are compared with experimental data and the arrival time and angle fluctuations obtained from a ray-tracing model with realistic one-dimensional sea surface boundaries. Also, it is shown that the standard deviation of the received angle fluctuations in this model is in close agreement with the experimental results reported in the literature. The importance of this model is that the PDFs of the arrival angle and time are presented theoretically, considering the shadowing effect.