P. Borejko:

"A new solution for the acoustic pressure-field in a perfect wedge";

PAMM - Proceedings in Applied Mathematics and Mechanics,3(2003), 424 - 425.

A time domain analytical solution is presented for the acoustic pressure-field due to an impulsive point source in a liquid wedge with a rigid sloping bottom. The horizontal boundary of the wedge is a pressure-release surface. The wedge is isovelocity, and it is three-dimensional (3-D) in that the source and the receiver are not restricted to the plane perpendicular to the wedge apex.

This 3-D wedge with perfectly reflecting (i.e., impenetrable) boundaries, the 3-D perfect wedge, is the simplest theoretical model of a shallow water environment in which the ocean bottom has a constant slope, but it is inadequate in that it cannot account for acoustic penetration of the bottom typical for a real ocean floor.

In a perfect wedge, the acoustic field produced by a point source consists of two components: the diffraction field due to scattering at the apex, which under certain conditions vanishes [1], and the image field including the wave emitted by the source and a number of waves reflected off the wedge boundaries. These waves with spherical wave fronts propagate along the stationary time paths (the ray paths).

The repeated reflections from the sloping bottom introduce the curvature into the projection of the ray path onto the horizontal boundary, provided that the first segment of this path originating at the source has a cross-slope component. This path curvature in the horizontal is known as "horizontal, or bathymetric refraction" [2]. The ray path that leaves the source propagating up-slope may be turned around to reach the receiver propagating back down-slope. This change in propagation direction, known as "backscattering" [2], is due to multiple bottom reflections. The receiver can thus be reached along one of the two ray paths: the direct path or the indirect path which is turned around on approaching the apex. The image field in the wedge is thus three-dimensional, i.e., it depends on three spatial coordinates: the range (normal to the apex), the cross-range (parallel to the apex), and the depth coordinate.

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