Geodesic
Explicit solution of the inverse kinematic problem in the non-Herglotz case
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 20-29 
G. Ya. Beil'kin. Explicit solution of the inverse kinematic problem in the non-Herglotz case. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 9, Tome 78 (1978), pp. 20-29. http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a1/
@article{ZNSL_1978_78_a1,
     author = {G. Ya. Beil'kin},
     title = {Explicit solution of the inverse kinematic problem in the {non-Herglotz} case},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {20--29},
     year = {1978},
     volume = {78},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_78_a1/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The inverse kinematic problem is solved in the half space $R_+^{\nu+1}=\{(x,z)\mid z\geqslant0,\ x\in R^\nu\}$, $\nu\geqslant1$ under the assumption that the index of refraction can be represented in the form $$ n^2(x,z)=k^2(z)+\sum^\nu_{j=1}\Phi^2_j(x_j),\quad n_z<0. $$ The solution obtained is a generalization of the Herglotz–Wiechert formula. A formula is presented for the solution of the inverse kinematic problem in the general case of separation of variables in the eikonal equation.