Edge-Diffraction Impulse Responses Near Specular-Zone and Shadow-Zone Boundaries

Many methods for the computation of edge-diffraction impulse responses are based on the Biot-Tolstoy solution, an explicit, continuous-time expression for diffraction by an infinite wedge. This expression contains two singularities at the onset of the impulse response: one which is present for all source-receiver combinations, and a second which occurs only when a receiver moves across a specular-zone or shadow-zone boundary, i.e. a boundary where a geometrical-acoustics component has a discontinuity. For the calculation of discrete-time impulse responses, such a continuous-time analytical expression must be numerically integrated, and the singularities demand special attention. Svensson et al. [U. P. Svensson et al., J. Acoust. Soc. Am. 106, 2331-2344 (1999)] presented an analytic, secondary-source model of edge diffraction based on the Biot-Tolstoy expression in which the first singularity was eliminated by reformulating the expression as an integral along the edge. In this paper, analytical approximations for the model presented by Svensson et al. are described which address the second type of singularity and thus allow for accurate numerical computations for receivers at or near zone boundaries. Implementation details are also provided, along with example calculations.