Geodesic
About propagation of seismic waves in block elastic-fluid media.~II
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 254-271

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The two-dimensional medium consisting of alternating elastic and fluid blocks along the $x$ and $z$ axes is considered. For this block medium, the effective model described by a system of equations is constructed by the method of matrix averaging. The investigation of these equations of this model permits to separate two body waves from the wave field, to draw their fronts, and to write the expressions of their velocities along the axes. The effective model is considered in the cases, when the block medium turns into a layered elastic-fluid medium, when all blocks are of the same size, and when elastic or fluid medium occupies whole volume. 
@article{ZNSL_2003_297_a14,
     author = {L. A. Molotkov},
     title = {About propagation of seismic waves in block elastic-fluid {media.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {254--271},
     publisher = {mathdoc},
     volume = {297},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a14/}
}
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L. A. Molotkov. About propagation of seismic waves in block elastic-fluid media.~II. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 32, Tome 297 (2003), pp. 254-271. http://geodesic.mathdoc.fr/item/ZNSL_2003_297_a14/