Geodesic
Eeflection of space-time ray amplitudes from arbitrary moving boundary
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 72-88

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The problem of finding of the geometrical spreading for the space-time ray method in three-dimensional inhomogeneous medium with arbitary moving reflecting boundary is considered. A syatem of linear differential equations and initial conditions on reflecting boundary for geometrical spreading is obtained. It is proved that the problem can be solved under the natural conditions i) reflecting boundary is timelike, ii) incident ray doesa't touch the boundary. 
@article{ZNSL_1983_128_a7,
     author = {N. Ya. Kirpichnikova and M. M. Popov},
     title = {Eeflection of space-time ray amplitudes from arbitrary moving boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {72--88},
     publisher = {mathdoc},
     volume = {128},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a7/}
}
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N. Ya. Kirpichnikova; M. M. Popov. Eeflection of space-time ray amplitudes from arbitrary moving boundary. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 72-88. http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a7/