A normal mode theory of acoustic Doppler effects in the oceanic waveguide

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Abstract
This paper considers the problem of computing the acoustic field generated by a moving point source. In particular, the acoustic field is obtained in terms of the normal modes of a horizontally stratified ocean. The source motion is assumed to be uniform (unaccelerated), but is not restricted to a path radial to the receiver. The structure of the Fourier inversion integral is carefully analyzed and an evaluation is carried out by the method of stationary phase. The stationary phase point is explicitly computed as an expansion in powers of the ratio of the source speed to the mode group velocity. The resulting expression for the velocity potential is examined for Doppler effects for both instantaneous (modal) Doppler as well as Doppler determined by a finite bandwidth Fourier transform.

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