Modified Ray Theory in the Presence of a Boundary.
WOODS HOLE OCEANOGRAPHIC INSTITUTION MASS
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The modified ray theory based on Generalized WKB solutions to a two turning point problem for an unbounded medium having a maximum in sound velocity has been extended to include a pressure release surface and rigid boundary at the maximum. This modified ray theory, unlike ordinary ray theory, predicts a frequency dependent phase change which varies continuously for the transition from normal incidence rays to rays which reverse far from the boundary. The behavior of this phase, and in turn its derivative, gives rise to a frequency dependent beam displacement for ray bundles. The results have the same form as for the unbounded problem but with an additional important contribution. These beam displacement phenomena can have the consequence of introducing caustics or convergence zones where none exist according to ordinary ray representations and distorting caustics and shadow zones in a frequency dependent way when they do exist in the ordinary ray picture. Numerical results for simple velocity profiles characteristic of the ocean indicate that these frequency dependent diffraction effects can be significant for frequencies on the order of 50 Hz. Author