Geodesic
Boundary controls and quasiphotons in a~Riemannian manifold reconstruction problem via dynamical data
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 22, Tome 203 (1992), pp. 21-50

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The problem of reconstruction of a Riemannian manifold via it's dynamical Dirichlet to Newmann response operator is considered. The approach for solving the problem is based upon the boundary control theory method. The procedure of reconstruction uses nonstationary Gaussian beams (quasiphotons). The essential feature of the procedure is locality. The class of manifolds which may be reconstructed by this approach is described in terms of the boundary control theory. It includes for instance all analitical manifolds. 
@article{ZNSL_1992_203_a3,
     author = {M. I. Belishev and A. P. Katchalov},
     title = {Boundary controls and quasiphotons in {a~Riemannian} manifold reconstruction problem via dynamical data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {21--50},
     publisher = {mathdoc},
     volume = {203},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_203_a3/}
}
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M. I. Belishev; A. P. Katchalov. Boundary controls and quasiphotons in a~Riemannian manifold reconstruction problem via dynamical data. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 22, Tome 203 (1992), pp. 21-50. http://geodesic.mathdoc.fr/item/ZNSL_1992_203_a3/