In the present paper, it is shown that the dynamical boundary data (the response operator) that correspond to measurements on the boundary of a Riemannian manifold, do determine the distances (wave travel times) from the boundary points to an interior source with given semigeodesic coordinates. The procedure that finds these distances is in principle amenable to numerical realization. Bibliography: 4 titles.
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V. M. Babich and Y. S. Buldyrev, Short Wave-Length Diffraction Theory, Springer-Verlag, Berlin (1991).
M. I. Belishev, “Boundary control in reconstruction of manifolds and metrics (the BC method),” Inverse Probl., 13(5), R1-R45 (1997).
M. I. Belishev, “On the reconstruction of a Riemannian manifold via boundary data: the theory and plan of numerically testing,” Zap. Nauchn. Semin. POMI, 380, 8-30 (2010).
M. I. Belishev and M. N. Demchenko, “Time-optimal reconstruction of a Riemannian manifold via boundary electromagnetic measurements,” J. Inverse III-Posed Probl., 19, No. 2, 167-188 (2011).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 393 2011, pp. 29-45.
Translated by M. I. Belishev.
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Belishev, M.I. Determination of distances to a virtual source through dynamical boundary data. J Math Sci 185, 526–535 (2012). https://doi.org/10.1007/s10958-012-0936-7
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DOI: https://doi.org/10.1007/s10958-012-0936-7