Statistical characteristics of a wave propagating through a layer with random irregularities

Statistical characteristics of a wave propagating through a layer with random irregularities are investigated by a simulation procedure. The investigation is carried out within the geometrical optics approximation in its validity range. It is shown that when the irregular layer is a long distance from the source and observer, a significant role in the formation of eikonal (phase path) fluctuations is then played by trajectory fluctuations in regions of the propagation medium, free from irregularities before and after the irregular layer. With these variations taken into account, which are neglected in conventional perturbation theory, we obtained approximate expressions for the dispersion and the correlation function of the eikonal. We investigate the behaviour of the eikonal dispersions, the angles and correlation functions of the eikonal and field for different disturbances of the medium, and for different distances of the receiver and transmitter from the layer boundaries.