Geodesic
Wave propagation throgh a thin layer
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 20-29

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The short wave propagation through a thin layer is considered. The incident wave is described by its ray expansion. The boundary layer expansion method is used for obtaining results. The wave lenght and the thicknes of the layer are small parameters of the problem. 
@article{ZNSL_1988_173_a1,
     author = {V. M. Babich},
     title = {Wave propagation throgh a thin layer},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {20--29},
     publisher = {mathdoc},
     volume = {173},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a1/}
}
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V. M. Babich. Wave propagation throgh a thin layer. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 18, Tome 173 (1988), pp. 20-29. http://geodesic.mathdoc.fr/item/ZNSL_1988_173_a1/