Geodesic
Dynamical inverse problem for the Lame type system (the BC-method)
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 218-259

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In the paper, for a Lame-type system, the inverse problem on recovering the fast and slow wave velocities from the boundary dynamical data (the response operator) is solved. The velocities are determined in the near-boundary domain, the depth of determination being proportional to the observation time. We use the BC-method, which is an approach to inverse problems based on their connections with boundary control theory. 
@article{ZNSL_2014_426_a13,
     author = {V. G. Fomenko},
     title = {Dynamical inverse problem for the {Lame} type system (the {BC-method)}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {218--259},
     publisher = {mathdoc},
     volume = {426},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a13/}
}
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V. G. Fomenko. Dynamical inverse problem for the Lame type system (the BC-method). Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 44, Tome 426 (2014), pp. 218-259. http://geodesic.mathdoc.fr/item/ZNSL_2014_426_a13/