The prediction of the noise generated by en-route aircraft is gradually gaining in importance as the number of aircraft increases over the last few decades. While the studies of outdoor sound propagation have been focused on near ground propagation, the case when the sound source is high above the ground has not attracted much attention. At the same time there has been a lack of high-quality aircraft acoustic validation data sets that contain detailed acoustic, meteorology, and source-receiver position data. The DISCOVER-AQ data set, which was collected by Volpe in support of the Federal Aviation Administration (FAA), has greatly helped with studying the directivity and the Doppler effect in the comparison between simulation results and measurements.
To provide a more accurate prediction of en-route aircraft noise, we derived the analytic asymptotic solution of the sound field above a non-locally reacting ground due to a moving point source and a line source using the methods of the steepest descent and a Lorentz transform. The model predicts a much more accurate result for sound field above "soft" grounds, such as a snow-covered ground and sand-covered ground. At the same time, we derived a fast numerical algorithm based on Levin’s collocation for the prediction of the sound field in the presence of a temperature gradient, which can be applied to a wide range of acoustic problems involving integration. The achievements recorded in this thesis can be used to predict the sound field generated by aircraft, trains, and vehicles with a subsonic moving speed. In addition, the model can be used for detection and design of moving sound source.