Abstract
A theory relating the phase rate of low-frequency cw signals to the range rate between the source and receiver is presented. A key component of this theory is the parabolic approximation, which was introduced into underwater acoustics by Tappert. It is shown that, after shifting the received signal to the base band, the leading-order behavior of the residual phase rate is simply equal to the product of a typical wavenumber in the water column and the source–receiver range rate. This result holds true even for situations where the acoustic field magnitude clearly displays a complicated multimodal (or multipath) interference pattern. The theory is supported by a variety of experimental measurements obtained in a broad range of ocean environments. These include deep- and shallow-water situations, range-independent and range-dependent cases, and short- and long-range scenarios. Implications of the theory for phase tracking and localization of quasi-cw sources are also discussed. [Work supported by ONR.]
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