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Application of ray theory to the problem of long-range propagation of explosive sound in a layered liquid

DEPARTMENT OF APPLIED MATHEMATICS, THE WEIZMANN INSTITUTE, REHOVOT, Israel

Abstract

In order to test the applicability of ray theory even to extremely large ranges, we have applied it to the problem of determining the exact shape of the pressure pulse received at a range r equal to 460 times the depth of the layer H, in the case of an explosion in a layered liquid. The time variation of the pressure at the source was assumed to be given by a Heaviside unit function. Comparison is made with a previous solution of this problem which was obtained, for the identical conditions, by the use of the normal mode theory. The exact ray-theory solution exhibits the well-known characteristic features of a ground wave followed by a dispersive water wave, but the pattern of the received pressure pulse is more ruffled than in the normal mode solution, in which the higher modes, as well as branch-line integrals, were neglected. The applicability of ray theory to long-range propagation is made feasible by virtue of the mutual cancellation at long ranges of all but a group of the last-arriving rays.