Geodesic
Diffraction of surface SV-waves on the line of elastic parameters discontinuity
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 77-105

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The set of diffraction problems on elastic surface waves of vertical polarization (SV-waves) from a line of elastic parameters jump is under consideration. The reflected and transmitted wave fields expressions are obtained by means of the parabolic equation method. The corresponding transformation coefficients are found for the reflection and transmission. 
@article{ZNSL_2007_342_a3,
     author = {N. Ya. Kirpichnikova},
     title = {Diffraction of surface {SV-waves} on the line of elastic parameters discontinuity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--105},
     publisher = {mathdoc},
     volume = {342},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_342_a3/}
}
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N. Ya. Kirpichnikova. Diffraction of surface SV-waves on the line of elastic parameters discontinuity. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 36, Tome 342 (2007), pp. 77-105. http://geodesic.mathdoc.fr/item/ZNSL_2007_342_a3/