Ray Doppler approximation on the stationary phase point of normal mode model about acoustic field generated by moving point source

The well-known method of computing the acoustic field generated by a moving source obtained by Hawker no longer applies if the source velocity is not small enough. An approach is presented to find the stationary phase point of the normal mode model in order to solve the problem of modeling underwater acoustics field excited by the aircraft. The method bases on Doppler frequency of virtual source determined by ray acoustics theory, and combined with normal mode theory. More accurate stationary phase point than Hawker's solution is found. Numerical results are presented to illustrate the validity of the presented algorithm.