Geodesic
Determination of a wave field in a laterally inhomogeneous medium from boundary data
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 55-68

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We deal with the Cauchy problem for a perturbed wave equation in the half-plane with data given on a part of the space-time boundary. The equation in consideration describes a wave process in a laterally inhomogeneous medium. We propose a reconstruction algorithm, which is applicable to the problem of determining nonstationary wave field from boundary data arising in geophysics. 
@article{ZNSL_2019_483_a3,
     author = {M. N. Demchenko},
     title = {Determination of a wave field in a laterally inhomogeneous medium from boundary data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {55--68},
     publisher = {mathdoc},
     volume = {483},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a3/}
}
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M. N. Demchenko. Determination of a wave field in a laterally inhomogeneous medium from boundary data. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 55-68. http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a3/