Geodesic
Space-time caustic of elastic short wave field
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 147-161

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A smooth caustic of space-time rays is considered. The points of tangency of caustic with the rays are only first order everywhere. The analytical expression of wave field in the neighbourhood of a caustic is obtained. 
@article{ZNSL_1981_117_a9,
     author = {N. Ya. Kirpichnikova},
     title = {Space-time caustic of elastic short wave field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {147--161},
     publisher = {mathdoc},
     volume = {117},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a9/}
}
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N. Ya. Kirpichnikova. Space-time caustic of elastic short wave field. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 147-161. http://geodesic.mathdoc.fr/item/ZNSL_1981_117_a9/