Geodesic
Determination of distances to virtual source from dynamical boundary data
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 29-45 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the paper, we show that the dynamical boundary data (the response operator), which correspond to the measurements at the boundary of a Riemannian manifold, do determine the distances (wave travel times) from the boundary points to an interior source with a given semi-geodesic coordinates. The procedure, which determines these distances, is in principle available for numerical realization. 
@article{ZNSL_2011_393_a3,
     author = {M. I. Belishev},
     title = {Determination of distances to virtual source from dynamical boundary data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {29--45},
     year = {2011},
     volume = {393},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a3/}
}
TY  - JOUR
AU  - M. I. Belishev
TI  - Determination of distances to virtual source from dynamical boundary data
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2011
SP  - 29
EP  - 45
VL  - 393
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a3/
LA  - ru
ID  - ZNSL_2011_393_a3
ER  - 
%0 Journal Article
%A M. I. Belishev
%T Determination of distances to virtual source from dynamical boundary data
%J Zapiski Nauchnykh Seminarov POMI
%D 2011
%P 29-45
%V 393
%U http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a3/
%G ru
%F ZNSL_2011_393_a3
M. I. Belishev. Determination of distances to virtual source from dynamical boundary data. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 29-45. http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a3/

[1] V. M. Babich, V. S. Buldyrev, Asisptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, Moskva, 1972 | MR

[2] M. I. Belishev, “Boundary control in reconstruction of manifolds and metrics (the BC method)”, Inverse Problems, 13:5 (1997), R1–R45 | DOI | MR | Zbl

[3] M. I. Belishev, “O rekonstruktsii rimanova mnogoobraziya po granichnym dannym: teoriya i plan chislennogo eksperimenta”, Zap. nauchn. semin. POMI, 380, 2010, 8–30 | MR

[4] M. I. Belishev, M. N. Demchenko, “Time-optimal reconstruction of Riemannian manifold via boundary electromagnetic measurements”, J. Inverse and Ill-Posed Problems, 19:2 (2011), 167–188 | DOI | MR | Zbl