Ray-based description of shadow zone arrivals

Field experiments and numerical simulation show that due to scattering from internal-wave-induced sound speed perturbations, the sound energy at megameter ranges penetrates well below the unperturbed timefront, i.e., into the geometric shadow. Shadow zone arrivals form continuations of cusps of the timefront. In the present paper, this effect is analyzed using a stochastic ray theory derived for statistical description of chaotic rays. Probability density functions for parameters of perturbed rays, including those penetrating into the shadow zone, are evaluated analytically. This made it possible to derive analytical estimates for a vertical extent of shadow zone arrivals and for a coarse-grained distribution of sound energy in the shadow zone. It is shown that the lengths of cusp extensions into the shadow zone grow with range r as r(1/2). A known estimate for the spread of timefront segments in the presence of internal waves is applied for obtaining a criterion of nonoverlapping of the cusp continuations. These results are derived for steep rays whose grazing angles at the sound channel axis exceed 5°.