Geodesic
The second approximation of the ray method for calculation of the intensity of the wave front in isotropic
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 79-94

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This paper continues the series of the precedent papers devoted to elaboration of algorithms for calculation of the second and next terms of the ray series for the vector of longitudinal displacements in isotropic nonhomogeneous elastic media in the case of the dimension 2.5. 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. 
@article{ZNSL_1997_239_a6,
     author = {N. Ya. Kirpichnikova},
     title = {The second approximation of the ray method for calculation of the intensity of the wave front in isotropic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {79--94},
     publisher = {mathdoc},
     volume = {239},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a6/}
}
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N. Ya. Kirpichnikova. The second approximation of the ray method for calculation of the intensity of the wave front in isotropic. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 79-94. http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a6/