Summary
A problem of reflection and transmission of a plane SH-wave incident at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space is investigated. Rayleigh's method of approximation is applied to derive the reflection and transmission coefficients for the first and second order approximation of the corrugation. The expressions for reflection and transmission coefficients for the first order approximation of the corrugation are obtained in closed form for a special type of interface, and the energy partition relation is derived. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of elastic properties of the half-spaces and also of the angle of incidence. Numerical examples illustrating the effects of the sandiness, the anisotropy, the corrugation of the interface, the frequency, and the angle of the incidence on the coefficients are presented.
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S. Asano (1960) ArticleTitleReflection and refraction of elastic waves at a corrugated boundary surface, Part I: The case of incidence of SH-wave Bull. Earthqu. Res. Inst. 38 117–197 Occurrence Handle115796
S. Asano (1961) ArticleTitleReflection and refraction of elastic waves at a corrugated boundary surface, Part II Bull. Earthq. Res. Inst. 39 367–466 Occurrence Handle147043
S. Asano (1966) ArticleTitleReflection and refraction of elastic waves at a corrugated interface Bull. Seismol. Soc. Am. 56 201–221
I. Abubakar (1962) ArticleTitleScattering of plane elastic waves at rough surfaces Proc. Camb. Phil. Soc. 58 136–157 Occurrence Handle0104.41503 Occurrence Handle151038 Occurrence Handle10.1017/S030500410003629X
I. Abubakar (1962) ArticleTitleReflection and transmission of plane SH-waves at irregular interfaces J. Phys. Earth 10 1–14
I. Abubakar (1962) ArticleTitleReflection and refraction of plane SH-waves at irregular interfaces J. Phys. Earth 10 15–20
Dunkin, J. W., Eringen, A. C.: The reflection of elastic waves from the wavy boundary of a half-space. Proceedings of the 4th U. S. National Congress on Applied Mechanics, University of California Press, Berkeley, pp. 143–160 (1962).
L. M. Salvin B. Wolf (1970) ArticleTitleScattering of Love waves in a surface layer with an irregular boundary for the case of a rigid underlying half space Bull. Seismol. Soc. Am. 60 859–877
J. H. Sumner H. Deresiewicz (1972) ArticleTitleWaves in an elastic plate with an irregular boundary Pure and Appl. Geophys. 96 106–112 Occurrence Handle10.1007/BF00875633
R. N. Gupta (1965) ArticleTitleReflection of plane waves from a linear transition layer in liquid media Geophysics 30 122–132 Occurrence Handle10.1190/1.1439528
S. K. Gupta (1965) ArticleTitleReflection and refraction from curved interfaces: model-study Geophys. Prospect. 26 82–96 Occurrence Handle10.1111/j.1365-2478.1978.tb01578.x
S. Gupta (1965) ArticleTitleReflection and transmission of SH-waves in laterally and vertically heterogeneous media at an irregular boundary Geophys. Trans. 33 89–111
R. Zhang M. Shinozuka (1996) ArticleTitleEffects of irregular boundaries in a layered half-space on seismic waves J. Sound Vibr. 195 1–16 Occurrence Handle10.1006/jsvi.1996.0400
S. K. Tomar S. L. Saini (1997) ArticleTitleReflection and refraction of SH-waves at a corrugated interface between two dimensional transversely isotropic half spaces J. Phys. Earth 45 347–362
S. K. Tomar J. Kaur (2003) ArticleTitleReflection and refraction of SH-waves at a corrugated interface between two laterally and vertically heterogeneous anisotropic elastic half spaces Earth Planet Space 55 531–547
J. Kaur S. K. Tomar V. P. Kaushik (2005) ArticleTitleReflection and refraction of SH-waves at a corrugated interface between two laterally and vertically heterogeneous viscoelastic solid half-spaces Int. J. Solids Struct. 42 3621–3643 Occurrence Handle10.1016/j.ijsolstr.2004.11.014 Occurrence Handle1119.74450
M. J. P. Musgrave (1977) ArticleTitleReflection and refraction of plane elastic waves at a plane boundary between aleotropic media Geophys. J. Royol Astron. Soc. 2 406–418
E. G. Henneke (1965) ArticleTitleReflection-refraction of stress waves at a plane boundary between anisotropic media J. Acoust. Soc. Am. 51 210–217 Occurrence Handle10.1121/1.1912832
P. F. Daley F. Hron (1977) ArticleTitleReflection and transmission coefficients for transversely isotropic media Bull. Seis. Soc. Am. 67 661–676
S. L. Saini S. J. Singh (1977) ArticleTitleEffect of anisotropy on the reflection of SH-waves at an interface Geophys. Res. Bull. 15 67–73
C. M. Keith S. Crampin (1977) ArticleTitleSeismic body waves in anisotropic media: Reflection and refraction at a plane interface Geophys. J. Royol Astron. Soc. 49 181–208
S. I. Rokhlin T. K. Bolland L. Adler (1986) ArticleTitleReflection and refraction of elastic waves on a plane interface between two generally anisotropic media J. Acoust. Soc. Am. 79 906–918 Occurrence Handle10.1121/1.393764
B. Mandal (1977) ArticleTitleReflection and transmission properties of elastic wave on a plane interface for general anisotropic media J. Acoust. Soc. Am. 90 1106–1118 Occurrence Handle10.1121/1.402300
A. Ruger (1977) ArticleTitleP-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry Geophys. 62 713–722 Occurrence Handle10.1190/1.1444181
S. K. Chakraborty A. Chandra (1984) ArticleTitleReflection and refraction of plane SH-waves at the boundary of dry sandy layer and anisotropic elastic medium Acta Geophys. Polonica 32 69–79
L. Rayleigh (1977) ArticleTitleOn the dynamical theory of gratings Proc. Roy. Soc. Lond. A 79 399–416
Sobczyk, K.: Fundamental study in engineering 6, Stochastic wave propagation, Ch. 5. Institute of Fundamental Technological Research, Warsaw, Poland 1985.
W. H. Weiskopff (1945) ArticleTitleStresses in soils under foundation J. Franklin Inst. 239 445–465 Occurrence Handle10.1016/0016-0032(45)90189-X Occurrence Handle12030
B. K. Kar A. K. Pal V. K. Kalyani (1986) ArticleTitlePropagation of Love waves in an irregular dry sandy layer Acta Geophys. Polonica. 34 157–170
E. Savarensky (1975) Seismic waves Mir Publication Moscow
J. D. Achenbach (1973) Wave propagation in elastic solids, Ch. 5 North-Holland Amsterdam New York
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Tomar, S.K., Kaur, J. SH-waves at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space. Acta Mechanica 190, 1–28 (2007). https://doi.org/10.1007/s00707-006-0423-7
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DOI: https://doi.org/10.1007/s00707-006-0423-7