Abstract
The well studied, high-frequency Rayleigh waves polarized in a plane normal to a cross section of the surface of an inhomogeneous elastic body with phase speed close to the speed of transverse waves are generalized to the case of the time-dependent equations of elasticity. For the wave field uniform asymptotics are obtained in the form of space-time ray expansions of two types: with a real eikonal (for transverse waves diffracted at the surface) and with a complex eikonal (for a longitudinal wave damped away from the surface).
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V. M. Babich and N. Ya. Rusakova, “On the propagation of Rayleigh waves along the surface of an inhomogeneous, elastic body of arbitrary shape,” Zh. Vychisl. Mat. Mat. Fiz.,2, No. 4, 652–665 (1962).
I. V. Mukhina and I. A. Molotkov, “On the propagation of Rayleigh waves in an elastic half space,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 4, 3–8 (1967).
N. Ya. Kirpichnikova, “On the propagation of surface waves concentrated near rays in an inhomogeneous, elastic body,” Tr. MIAN,115, 114–130 (1971).
P. V. Krauklis and N. V. Tsepelev, “On the construction of high-frequency asymptotics of a wave field concentrated near the boundary of an elastic medium,” J. Sov. Math.,6, No. 5 (1976).
V. M. Babich and Z. A. Yanson, “On the propagation of Love waves along the surface of an elastic body of arbitrary shape,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 5, 17–27 (1985).
Z. A. Yanson, “Shortwave asymptotics of space-time creeping waves in elasticity theory,” J. Sov. Math.,38, No. 1 (1987).
V. M. Babich, “On the space-time ray method in the theory of elastic waves,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 2, 3–13 (1979).
P. V. Krauklis and N. V. Tsepelev, “Presurface waves in an inhomogeneous medium with an arbitrary smooth boundary,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 5, 3–10 (1973).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 168–183, 1986.
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Yanson, Z.A. Time-dependent waves of rayleigh type near the surface of an inhomogeneous elastic body. J Math Sci 50, 1785–1795 (1990). https://doi.org/10.1007/BF01097111
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DOI: https://doi.org/10.1007/BF01097111