Where Do Lateral Waves Come from?

Abstract

Wave theory indicates that the first round from a point source reaching a point in the ocean (at a distance'many times the depth) is directed upward from the bottom at the critical angle and has the phase of a signal leaving the source at the critical angle, propagating just inside the bottom at the bottom speed, and exciting at the critical angle. Ordinary ray theory does not account for this field. A modified ray theory [A. A. Hudimac, J. Acoust. Soc. Am. 49, 77(A) (1971)] indicates that the errors of ray theory can be corrected by distributing simple sources in the bottom with density whose phase is that of the rays and whose magnitude is proportional to the Laplacian of the ray amplitude. The principal contribution to the rays ensonifying the observation points comes from the source distribution near the interface, below the observation points and toward the source. Sample calculations show that the resulting “diffraction” field is essentially that predicted by wave theory.