**Abstract:**

For extremely high frequencies, the geometrical theory of diffraction is probably a sufficient, if not necessary, method to carry out predictions of scattering from ellipsoids or objects of more complicated structures for ka values on the order of a few hundred to tens of thousands. It is possible to extend the Helmholtz integral expression to the problem of ellipsoids near an ocean bottom by making use of a Green's function with a reflection coefficient that characterizes the bottom. In carrying out the integral expressions, saddle point methods were experimented with to determine the reflected signal, and the Maggi transformation and principles from differential geometry to reduce the diffraction integral over the shadow side of the object to line an integral at the illuminated shadow region of demarcation. The latter two devices are necessary due to time constraints in evaluating surface integrals for ultra-high frequencies. Examples are presented. [Work sponsored by ONR, the Naval Res. Lab., and the Univ. of New Orleans.]

ASA 133rd meeting - Penn State, June 1997