Application of the equivalent source method to directional noise sources

Prediction of noise levels at long ranges from such sources as flying aircraft or moving ground vehicles is an important practical problem. When terrain, wind, and atmospheric effects are taken into account, this problem cannot be solved analytically, and, thus, numerical solutions are required. There are several numerically efficient algorithms to solve the problem, but, typically, all of them are designed for an omnidirectional point source. Such specification is inadequate for complex and extended sources exhibiting directional radiation patterns. Thus, a method for incorporating directional sound sources into propagation algorithms is needed. This paper describes the equivalent source method (ESM), which enables reconstruction of a compact point-source distribution reproducing a given, arbitrarily complicated, radiation pattern in the far field. The ESM is demonstrated using an asymmetrical surrogate aircraft radiation pattern. Application of the ESM to parabolic equation algorithms is also considered. Some issues of acquisition of input data, such as outliers and data incompleteness, and their adverse effect on source reconstruction are also discussed.