Evaluation of shadow-zone fields by uniform asymptotics and complex rays

This article presents the theory and numerical results of a new method for evaluating fields in ray-theory shadow zones. The travel time and pressure of ray theory are computed using complex ray parameters. With the use of these quantities, the amplitude and phase of the field, associated with each ray-theory caustic, are evaluated by uniform asymptotics. The complex conjugate properties of shadow-zone rays allow uniform asymptotics to be expressed in terms of only one ray arrival. At large distances into the shadow zone the uniform asymptotics has been reduced to geometric acoustics. The complex ray theory is developed utilizing the analytic continuation of the two real rays which form the caustic boundary of the shadow zone. Explicit steps for numerical calculations are given. Numerical calculations are presented for a bilinear sound speed model of the deep ocean. Results agree well with those obtained by other methods. For some receivers the entire shadow zone has been bridged with a continuous solution connecting the two caustic structures which bound the zone. Various properties of the shadow- zone fields are illustrated by the examples. Among the most surprising is the existence of a ray solution with the real parameter in the middle of the shadow zone. Another example is a ray solution with real travel time within the shadow zone, where the uniform asymptotic formulation for a two-ray system diverges.