Geodesic
On the matrix method for slightly heterogeneous layered acoustical media
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 105-115

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The matrix method is generalized for slightly geterogeneous layered acoustical media. This approach enables one to find the reflection and transmission coefficients for several layers, and to investigate normal modes in a layered waveguide. 
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     author = {L. A. Molotkov and N. A. Razumovskii},
     title = {On the matrix method for slightly heterogeneous layered acoustical media},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--115},
     publisher = {mathdoc},
     volume = {128},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a11/}
}
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L. A. Molotkov; N. A. Razumovskii. On the matrix method for slightly heterogeneous layered acoustical media. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 13, Tome 128 (1983), pp. 105-115. http://geodesic.mathdoc.fr/item/ZNSL_1983_128_a11/