Geodesic
Coefficients of reflection and refraction in the case of elastic-fluid systems
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 154-167

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Processes of reflection and refraction are investigated in the case of a vertically layered elastic-fluid system. Special matrices characterizing the layers, the boundaries, and the entire system are introduced to find the refraction coefficients. By means of these matrices general formulas for the refraction coefficients are obtained, and the matrix method is generalized to elastic-fluid systems. 
@article{ZNSL_1976_62_a12,
     author = {L. A. Molotkov},
     title = {Coefficients of reflection and refraction in the case of elastic-fluid systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {154--167},
     publisher = {mathdoc},
     volume = {62},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a12/}
}
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L. A. Molotkov. Coefficients of reflection and refraction in the case of elastic-fluid systems. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 8, Tome 62 (1976), pp. 154-167. http://geodesic.mathdoc.fr/item/ZNSL_1976_62_a12/