Geodesic
Algorithm for reconstruction of the elastic constants of an anisotropic layer lying in an isotropic horizontally stratified medium
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 20-51

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In the work the algorithm for numerical solving of the inverse problem for reconstruction of the elastic constants of an anisotropic (thinly stratified) layer is presented. In force of the basic restriction the algorithm allow us to reconstruct only part of the elastic constants. Conditions of symmetry for the trace of the direct problem solution on the surface was used together with usual form of the additional information (value of the direct problem solution on the surface). The numerical solution of the inverse problem was suggested to find in the frequency domain. The general statement of the inverse problem was decomposed to the series of the standard statements of inverse problems to reconstruct sequentially the part of the elastic constants. 
@article{SEMR_2007_4_a2,
     author = {A. L. Karchevsky},
     title = {Algorithm for reconstruction of the elastic constants of an anisotropic layer lying in an isotropic horizontally stratified medium},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {20--51},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a2/}
}
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A. L. Karchevsky. Algorithm for reconstruction of the elastic constants of an anisotropic layer lying in an isotropic horizontally stratified medium. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 20-51. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a2/