Application of the equivalent source method to outdoor directional sound sources

Abstract

Many outdoor sound sources, such as aircraft and moving ground vehicles, exhibit directional sound radiation patterns that can be measured in the far field. However, this information is insufficient for specifying a source function that can be used in propagation algorithms. The equivalent source method (ESM) allows one to reconstruct an equivalent distribution of point sources having a given far-field radiation pattern. In this research, the application of the ESM to spatially complex radiation patterns, similar to those of actual helicopters, is studied in detail. Two algorithms for the source reconstruction are developed for arbitrarily complex radiation patterns. The first algorithm reconstructs three-dimensional source distributions that may not, however, be convenient for initializing calculations withparabolic equations. The second algorithm is designed for the two-dimensional parabolic equations and reconstructs strictly vertical source distributions having a given radiation pattern over a limited range of elevation angles. Some practical aspects of the measured data, such as outliers, data incompleteness, and phase loss in sound level measurements are also studied and recommendations are provided for mitigating their adverse effects on source reconstruction.