Geodesic
About propagation of seismic waves in block elastic-fluid media.~I
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 230-253

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In the paper the approach of averaging block elastic-fluid media is proposed and the effective model for block medium in which every cell consists of three elastic blocks and one fluid block is constructed. The investigation of the model equations is shown that in this model two longitudinal waves and one wave with a concave front propagate. The limited cases when the fluid block is narrowed down to a point or when the fluid block occupies the whole cell are considered in the paper. 
@article{ZNSL_2003_297_a13,
     author = {L. A. Molotkov},
     title = {About propagation of seismic waves in block elastic-fluid {media.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {230--253},
     publisher = {mathdoc},
     volume = {297},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a13/}
}
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L. A. Molotkov. About propagation of seismic waves in block elastic-fluid media.~I. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 230-253. http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a13/