Geodesic
The sound field generated by a~source moving in the inhomogeneous layer on the homogeneous halfspace
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 16, Tome 156 (1986), pp. 35-48

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In the paper the formulae for the amplitudes and instantaneous frequency of sound waves generated bу moving source are proposed. The formulae are derived by the use of the space-time ray method and the method of two-scale expansion (the method of horizontal rays and vertical modes). 
@article{ZNSL_1986_156_a3,
     author = {V. S. Buldyrev},
     title = {The sound field generated by a~source moving in the inhomogeneous layer on the homogeneous halfspace},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {35--48},
     publisher = {mathdoc},
     volume = {156},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a3/}
}
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V. S. Buldyrev. The sound field generated by a~source moving in the inhomogeneous layer on the homogeneous halfspace. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 16, Tome 156 (1986), pp. 35-48. http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a3/