Geodesic
One method of computation of wave fields in layered elastic media
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 154-171

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The method of computation of wave fields propagated in layered elastic media is proposed. All multiple reflected waves of $P$ and $S$ types are calculated. The method is based on summing of the cinematical and dynamical analogies. 
@article{ZNSL_1990_186_a15,
     author = {N. S. Smirnova},
     title = {One method of computation of wave fields in layered elastic media},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {154--171},
     publisher = {mathdoc},
     volume = {186},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a15/}
}
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N. S. Smirnova. One method of computation of wave fields in layered elastic media. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 154-171. http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a15/