Geodesic
The direct dynamical problem of seismics for horizontally stratified media
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 23-61

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A method of numerical solving the elasticity system for horizontal stratified anisotropic media is presented. The algorithm uses a relation between a system of differential equation of second order and a differential matrix Riccati equation which admits a solution in an analytical form in the each layer. The proposed numerical method differs from known methods and can be applied for horizontal stratified media of any type. 
@article{SEMR_2005_2_a2,
     author = {A. L. Karchevsky},
     title = {The direct dynamical problem of seismics for horizontally stratified media},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {23--61},
     publisher = {mathdoc},
     volume = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a2/}
}
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A. L. Karchevsky. The direct dynamical problem of seismics for horizontally stratified media. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 23-61. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a2/