Doppler effects in heterogeneous media with applications to ocean acoustic modeling

Doppler shift corrections to ocean acoustic signals are complicated by the multi-spatial-scale structure of the ocean medium, resulting in a multi-time-scale structure of the acoustic Green function. Repeated reflections and refractions lead in general to an infinite number of acoustic paths or modes, with different times of flight, connecting source and receiver. The rate of change of these flight times with source or receiver motion gives rise to Doppler shift corrections, and each acoustic path or mode has a different correction. A clean Doppler correction (in the sense of an observable coherent motion-induced frequency shift for each path or mode) is shown to emerge only when the medium is homogeneous along the direction of source or receiver motion, even when it is highly inhomogeneous in directions orthogonal to the motion. A very general quantitative theory for this correction is developed, encompassing earlier results in the literature, and presented in a form amenable to efficient numerical implementation in data processing.