Geodesic
Effect of inhomogeneity of the medium on the directivity of the simplest sources of elastic waves
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 77-87

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The initial data for the first correction term of the ray expansion of a longitudinal wave excited by a point center of expansion are found by the boundary-layer method. The same is done for a transverse wave from a center of rotation. 
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     author = {A. P. Kiselev},
     title = {Effect of inhomogeneity of the medium on the directivity of the simplest sources of elastic waves},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--87},
     publisher = {mathdoc},
     volume = {140},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a7/}
}
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A. P. Kiselev. Effect of inhomogeneity of the medium on the directivity of the simplest sources of elastic waves. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 14, Tome 140 (1984), pp. 77-87. http://geodesic.mathdoc.fr/item/ZNSL_1984_140_a7/