Geodesic
Doppler effect in the motion of a source and a refractive surface
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 17, Tome 165 (1987), pp. 52-58 Cet article a éte moissonné depuis la source Math-Net.Ru

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The space-time ray-tracing method is used to derive equations for the instantaneous frequency and instantaneous wave vector of a wave radiated by a moving source in a time-dependent inhomogeneous medium and reflected from a moving surface. 
@article{ZNSL_1987_165_a6,
     author = {N. S. Grigor'eva},
     title = {Doppler effect in the motion of a source and a refractive surface},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {52--58},
     year = {1987},
     volume = {165},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_165_a6/}
}
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N. S. Grigor'eva. Doppler effect in the motion of a source and a refractive surface. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 17, Tome 165 (1987), pp. 52-58. http://geodesic.mathdoc.fr/item/ZNSL_1987_165_a6/