Geodesic
Point source waves near the interface between elastic and liquid media
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 39, Tome 379 (2010), pp. 47-66 
N. Ya. Kirpichnikova. Point source waves near the interface between elastic and liquid media. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 39, Tome 379 (2010), pp. 47-66. http://geodesic.mathdoc.fr/item/ZNSL_2010_379_a2/
@article{ZNSL_2010_379_a2,
     author = {N. Ya. Kirpichnikova},
     title = {Point source waves near the interface between elastic and liquid media},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {47--66},
     year = {2010},
     volume = {379},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_379_a2/}
}
TY  - JOUR
AU  - N. Ya. Kirpichnikova
TI  - Point source waves near the interface between elastic and liquid media
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 47
EP  - 66
VL  - 379
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_379_a2/
LA  - ru
ID  - ZNSL_2010_379_a2
ER  - 
%0 Journal Article
%A N. Ya. Kirpichnikova
%T Point source waves near the interface between elastic and liquid media
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 47-66
%V 379
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_379_a2/
%G ru
%F ZNSL_2010_379_a2

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Combined surface waves are under consideration, they can be presented as a combination of whispering gallery waves (concentrated near the boundary in the layer of width $O(\omega^{-2/3})$ for $\omega\to\infty$, where $\omega$ is a frequency) and standard surface waves (exponentially decaying moving away from the interface boundary with parameter proportional to $\omega$), or waves oscillating when going away from the boundary. Those waves are obtained near the boundary $z=0$ of inhomogeneous elastic medium $z>0$ (propagation velocities $a(z)$ and $b(z)$) and inhomogeneous liquid (velocity in the liquid is $a_0(z)$). In the latter case there are wave fields propagating with phase velocity close to the velocities of Stonely and Rayleigh, and also close to velocities $a_0$, $b$ and $a$ on the interface boundary. Bibl. 10 titles.

[1] L. M. Brekhovskikh, Volny v sloistykh sredakh, Izd-vo AN SSSR, 1956

[2] L. M. Brekhovskikh, “O poverkhnostnykh volnakh v tverdom tele”, Akust. zh. AN SSSR, 12:3 (1966), 374–376

[3] L. M. Brekhovskikh, “O poverkhnostnykh volnakh v tverdom tele, uderzhivaemykh kriviznoi granitsy”, Akust. zh. AN SSSR, 13:4 (1967), 541–555

[4] I. V. Mukhina, I. A. Molotkov, “O rasprostranenii voln Releya v uprugom poluprostranstve, neodnorodnom po dvum koordinatam”, Izv. AN SSSR. Fizika Zemli, 1967, no. 4, 3–8

[5] I. A. Molotkov, “Vozbuzhdenie voln Releya i Stonli”, Zap. nauchn. semin. LOMI, 17, 1970, 168–183 | MR | Zbl

[6] I. A. Molotkov, P. V. Krauklis, “Smeshannye poverkhnostnye volny na granitse uprugoi sredy i zhidkosti”, Izv. AN SSSR. Fizika Zemli, 1971, no. 8, 3–11

[7] N. Ya. Kirpichnikova, “O rasprostranenii sosredotochennykh vblizi luchei poverkhnostnykh voln v neodnorodnom uprugom tele proizvolnoi formy”, Trudy Matem. in-ta im. V. A. Steklova, 115, 1971, 114–130 | MR | Zbl

[8] M. A. Leontovich, V. A. Fok, “Reshenie zadachi o rasprostranenii elektromagnitnykh voln vdol poverkhnosti Zemli po metodu parabolicheskogo uravneniya”, Zhurn. eksperim. i teor. fiziki, 16:7 (1946), 557–573 | MR | Zbl

[9] R. N. Buchal, J. B. Keller, “Boundary layer problems in diffraction theory”, J. Comm. Pure Appl. Math., 13:1 (1960), 85–114 | DOI | MR | Zbl

[10] V. M. Babich, N. Ya. Kirpichnikova, Metod pogranichnogo sloya v zadachakh difraktsii, Izd-vo Leningr. un-ta, L., 1974 | MR