Geodesic
On computation of the second term of the ray method for the vector of longitudinal displacements in isotropic nonhomogeneous elastic media
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 24, Tome 218 (1994), pp. 25-43

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This paper continues the series of the precedent papers devoted to elaboration of algorithms for computation of the second and next terms of the ray series for the vector of longitudinal displacements in isotropic nonhomogeneous elastic media. The method, proposed in this paper, essentially differs from used earlier ones. This method is based on expansions of the amplitudes, the eikonal and the given task parameters into series with respect to coordinates transversal to the direction of propagation of the considered waves. The comparison of the methodses of computation of the correction terms of the ray expansios for the vector of longitudinal displacements is carried out. Bibliography: 10 titles. 
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     author = {N. Ya. Kirpichnikova},
     title = {On computation of the second term of the ray method for the vector of longitudinal displacements in isotropic nonhomogeneous elastic media},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {25--43},
     publisher = {mathdoc},
     volume = {218},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_218_a3/}
}
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N. Ya. Kirpichnikova. On computation of the second term of the ray method for the vector of longitudinal displacements in isotropic nonhomogeneous elastic media. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 24, Tome 218 (1994), pp. 25-43. http://geodesic.mathdoc.fr/item/ZNSL_1994_218_a3/