Theory of sound propagation from a moving source in a three-layer Pekeris waveguide

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Abstract
A theory is developed for the acoustic field in a three-layer waveguide, representing the atmosphere, shallow ocean and sediment. The unaccelerated source is moving horizontally in the atmosphere. Two solutions are presented. The first, for a line source normal to the direction of travel, is a single wavenumber integral yielding the two-dimensional (2-D) field in each layer; and the second, for a point source, is a double wavenumber integral for the 3-D field in each layer. In both cases, the moving-source dispersion relationship for the three-layer environment is derived. From the 2-D dispersion relation, asymmetries fore and aft of the source, due to source motion, are shown to exist in the field in all three layers. In the water column, complex Doppler effects modify asymmetrically the effective depth of the channel and hence also the mode shapes. Evidence of the fore-aft modal asymmetry appears in the high-resolution spectrum of the field in the channel, which exhibits several sharp peaks on either side of the unshifted frequency, each associated with an up- or downshifted mode. A numerical evaluation of the 3-D solution provides a graphic illustration of the asymmetrical character of the field in all three layers.

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