Complex ray methods for acoustic interaction at a fluid–fluid interface

The development of a systematic method for finding the reflected and transmitted fields due to a point source in the presence of a plane, penetrable interface is presented. This approach is based on the classical method of steepest descent, but the plane-wave reflection and transmission coefficients are allowed to influence the location of the saddle points and their steepest descent paths. As a consequence, saddle points are, in general, complex, and complicated processes such as the reflected lateral wave field and the evanescent field in the bottom are incorporated in the saddle point formulation. The geometric interpretation of the saddle point criterion is derived in terms of eigenrays and their characteristics, from which expressions are obtained for the ray displacement upon reflection and transmission. Summaries of the eigenray structure of the reflected and transmitted fields are given for low-frequency situations.