Inclusion of elevation angle source directivity in the parabolic equation method

This paper addresses the modeling of sound propagation from a directional source using the parabolic equation (PE) method. The research was motivated by efforts to accurately predict aviation noise in complex propagation environments, with a focus on low frequency sound. Two methods of representing a directional source were developed for the unique form of the PE starting field. Both approaches recognize the elevation angle limitation of the PE method and the required resolution of vertical grid points in the PE starting field. These methods require only the directional function as input. Approach 1 calculates an aperture function with half-wavelength element spacing and uses the traditional Gaussian PE representation of a monopole to populate intermediate grid points. Approach 2 anticipates the starting field resolution and extends the vertical wave number spectrum of the directional function to allow use of straightforward inverse Fourier transform techniques. Both approaches produce accurate results within the valid PE elevation angle range for horizontal and vertical dipole radiation pattern examples, adequately controlling evanescent components of the acoustic field. However, Approach 2 is more direct and slightly more accurate. Therefore, it is identified as the preferred generalized source directivity starting field technique.