Spectral and modal representations of the Doppler-shifted field in ocean waveguides

A simple spectral representation is derived for the Doppler-shifted field in general stratified waveguides, including those with elastic bottoms and ice covers. By transforming the field representation for a moving, finite bandwidth source into the moving receiver’s frame of reference, a spectral integral representation is obtained for the dynamic transfer functions, which may then be transformed into time domain responses by standard Fourier synthesis. The spectral representation of the Doppler-shifted field is more general than earlier modal formulations since it is not based on any assumptions concerning the invariance of mode shapes, and it properly accounts for modal cutoff effects. However, it will be demonstrated that its approximate modal expansion is consistent with earlier modal formulations. The spectral formulation has been implemented in an existing wave-number integration code, and applied to illustrate the fundamental physics of the source/receiver dynamics in stratified waveguides. Examples include moving source/receivers in shallow water, and the acoustic emission produced by propagating ice fractures in the Arctic.