Geodesic
Investigation of wave field in effective model of layered elastic-fluid medium
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 175-192

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For the medium consisting of alternating elastic and fluid layers, the effective model is constructed and investigated. This model is a special case of the Biot medium. The wave field is represented as Fourier and Mellin integrals. In the Mellin integral we replace contour of integration by a stationary contour. In the obtained expressions, we rearrange the integrals and calculate the inner integral. The external integral is equal to two residues. The corresponding poles are roots of two equations of fourth order. These roots are situated at the right half-plane and can be complex or real. The obtained representation for the wave field corresponds to the expressions derived by the method of Smirnov–Sobolev. 
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     author = {L. A. Molotkov and M. N. Perekareva},
     title = {Investigation of wave field in effective model of layered elastic-fluid medium},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {175--192},
     publisher = {mathdoc},
     volume = {332},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a11/}
}
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L. A. Molotkov; M. N. Perekareva. Investigation of wave field in effective model of layered elastic-fluid medium. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 175-192. http://geodesic.mathdoc.fr/item/ZNSL_2006_332_a11/