An exact representation of the image field in a perfect wedge

Abstract

A solution is presented for the image component of the three-dimensional (3-D) acoustic wave-field from an impulsive point source in a liquid wedge with impenetrable boundaries (mixed Dirichlet-Neumann) modeling shallow water over sloping bottom (shallow-water wedge). This exact and complete solution is in the form of a sum of partial waves including the pulse emitted from the source plus a finite number of pulses reflected off the wedge boundaries, and it is generally valid for all ranges and depths. The 3-D acoustic propagation effects in an impenetrable wedge are examined for range propagation when the receivers are located directly up-slope and down-slope of the source and at the source-point itself, and for cross-range propagation when the receivers are located directly cross-slope of the source. When the receiver recedes up-slope from the source, the duration of the pressure response is shortened, and the number of pulses arriving along the indirect ray paths (the backscattered pulses) decreases. When the receiver recedes down-slope from the source, the response duration is constant, and the number of backscattered pulses also decreases. As the source and the receiver separate in the cross-range-direction, the response duration is so shortened that the arrival of the last-arriving pulse approaches that of the first-arriving pulse in the limit (i.e., when the separation between the source and the receiver is “large” in the cross-range-direction), and the number of backscattered pulses remains constant.