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P. Borejko:
"Some Characteristic Features of Pressure Records From a Point Source in a Shallow-Water Wedge Predicted by the Ray-Integral Solution";
in: "Proceedings of the Conference on New Concepts for Harbour Protection, Littoral Security and Shallow-Water Acoustic Communication", T. Akal et al. (ed.); Istanbul Ofset Basim Yayin A. S., Istanbul, 2005, (invited), 17 - 28.

The present investigation is undertaken with the aim of predicting some characteristics of the three-dimensional (3-D) acoustic pressure-field generated in a wedge-shaped shallow water by an impulse-excited point source.
A physical model offering an extensive insight into the intricacies of underwater sound propagation in a shallow water with a sloping bottom is a wedge of fluid overlying a rigid, fast-speed liquid, or fast-speed elastic substratum, where both the point source and the point receiver are placed in the wedge. A liquid wedge with a pressure-release horizontal surface and a rigid bottom (a perfect wedge) is the simplest model of such a shallow water environment, but it is inadequate in that it cannot account for acoustic penetration of the bottom typical for a real ocean floor. A liquid wedge with a pressure-release horizontal surface and a penetrable fast-speed bottom (a penetrable wedge) is a more realistic model for a sand-bottom (the case of a fast-speed liquid substratum) or a rock-bottom (the case of a fast-speed elastic substratum) ocean near a shoreline.
In this investigation, the generalized-ray-theory solution for the problem of 3-D propagation of sound in a penetrable wedge of fluid is developed to an operational stage which enables one to compute the actual pressure response curve, as recorded at a receiver-point, due to an arbitrary time variation of the pressure at the source-point.
In general, the acoustic field (the wave field) in a wedgelike domain consists of two components: the diffraction field due to scattering at the apex and the image field given by a sum of "partial wave-motions" including the wave-motion radiated from the source plus a finite number of wave-motions reflected off the wedge boundaries. The diffraction component of the field is ignored in the present solution, nevertheless the solution is exact for the image component of the field since the operational representation of the solution can be analyzed into a finite sum of "ray integrals" [single definite integrals (evaluated by applying the Cagniard method) amenable to numerical integration] and the operational interpretation of the solution shows that each ray integral has the physical significance of the partial wave-motion arriving at a receiver along a ray path. In the solution, the value of the pressure at a given observation time is then represented by one or more ray integrals.
Time records of the pressure are computed at five receivers, which are located at equal radial range in the horizontal plane from the source, but different orientation relative to the source, measured by the azimuth angle assuming values (directly down-slope), (obliquely down-slope), (directly cross-slope), (obliquely up-slope), and (directly up-slope). The arrival times of the partial waves propagating along various (direct and backscattered) paths are calculated at each receiver for the three substrata. It is found that the time interval between the first arrival and the ultimate arrival diminishes, and the pulses contributing to the response curve become more peaked, as the azimuth angle of the receiver increases.
For the rigid-bottom wedge, it is found that all backscattered pulses are significant at each receiver. For the fast-speed liquid-bottom wedge, it is found that, at each receiver, the source-pulse is preceded by the ground wave which is much weaker than the water wave, and the backscattered pulses are insignificant. For the fast-speed elastic-bottom wedge, it is found that, at each receiver, the backscattered pulses are significant, the ground-wave-response begins earlier than that in the fast-speed liquid-bottom wedge, and thus the pressure record separates out into distinct ground-wave and water-wave phases.

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