Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T10:15:34.396Z Has data issue: false hasContentIssue false
  • English
  • Français

Reflection/refraction of SH-waves at a corrugated interface between two different anisotropic and vertically heterogeneous elastic solid half-spaces

Published online by Cambridge University Press:  17 February 2009

Rajneesh Kumar ,
Sushil K. Tomar  and
Asha Chopra
Rajneesh Kumar
Affiliation:
Department of Mathematics, Kurukshetra University, Kurukshetra 136 119, India.
Sushil K. Tomar
Affiliation:
Mathematics Department, Panjab University, Chandigarh 160 014, India; e-mail: [email protected].
Asha Chopra
Affiliation:
Department of Mathematics, Kurukshetra University, Kurukshetra 136 119, India.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the reflection and transmission of SH-waves at a corrugated interface between two different anisotropic, heterogeneous elastic solid half-spaces. Both the media are assumed to be transversely isotropic and vertically heterogeneous. Rayleigh's method is followed and expressions for the reflection and transmission coefficients are obtained in closed form for the first-order approximation of the corrugation. It is found that these coefficients depend on corrugation and are affected by the anisotropy and heterogeneity of the media. Numerical computations for a particular model have been performed.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 3 , January 2003 , pp. 447 - 460
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Abubakar, I., “Reflection and refraction of plane SH-waves at irregular interfaces”, J. Phys. Earth 10 (1962) 1–14, 15–20.CrossRefGoogle Scholar
[2]Abubakar, I., “Scattering of plane elastic waves at rough surfaces”, Proc. Cambridge Phil. Soc. 58 (1962) 136–157.CrossRefGoogle Scholar
[3]Asano, S., “Reflection and refraction of elastic waves at a corrugated boundary surface. I The case of SH-wave”, Bull. Earthq. Res. Inst., Tokyo Univ. 38 (1960) 177–197.Google Scholar
[4]Asano, S., “Reflection and refraction of elastic waves at a corrugated boundary surface. Part II”, Bull. Earthq. Res. Inst., Tokyo Univ. 39 (1961) 367–466.Google Scholar
[5]Asano, S., “Reflection and refraction of elastic waves at a corrugated boundary surface”, Bull. Seismol. Soc. Amer. 56 (1966) 201–221.CrossRefGoogle Scholar
[6]Crampin, S., “A review of wave motion in anisotropic and cracked elastic media”, Wave Motion 3 (1981) 343–391.CrossRefGoogle Scholar
[7]Daley, p. F. and Hron, F., “Reflection and transmission coefficients for transversely isotropic media”, Bull. Seismol. Soc. Amer. 67 (1977) 661–675.CrossRefGoogle Scholar
[8]Dunkin, J. W. and Eringen, A. C., “The reflection of elastic waves from the wavy boundary of half-space”, in Proc. 4th US National Congress on Appl. Mech., (University of California, Berkeley, 1962) 143–160.Google Scholar
[9]Gupta, R. N., “Reflection of plane waves from a linear transition layer in liquid media”, Geophysics 30 (1965) 122–132.CrossRefGoogle Scholar
[10]Mandal, B., “Reflection and transmission properties of elastic waves on a plane interface for general anisotropic media”, J. Acoust. Soc. Amer. 90 (1991) 1106–1118.CrossRefGoogle Scholar
[11]Musgrave, M. J. P., “Reflection and refraction of plane elastic waves at a plane boundary between allotropic media”, Geophys. J. Roy. Astron. Soc 2 (1960) 406–418.CrossRefGoogle Scholar
[12]Pao, Y., “Elastic waves in solids”, J. Appl. Mech. 50 (1983) 1151–1164.CrossRefGoogle Scholar
[13]Rokhlin, S. I., Bolland, T. K. and Adler, L., “Reflection and refraction of elastic waves on a plane interface for generally anisotropic media”, J. Acoust. Soc. Amer. 79 (1986) 906–918.CrossRefGoogle Scholar
[14]Sato, R., “The reflection of elastic waves on a corrugated surface”, J. Seismol. Soc. Japan 8 (1955) 8–22.Google Scholar
[15]Savarensky, E., Seismic waves (Mir, Moscow, 1975).Google Scholar
[16]Singh, B. M., Singh, S. J. and Chopra, S. D., “Reflection and refraction of SH-waves at the plane boundary between two laterally and vertically heterogeneous solids”, Acta Geophysica Polonica 24 (1978) 209–216.Google Scholar
[17]Thapliyal, V., “Reflection of SH-waves from an anisotropic transition layer”, Bull. Seismol. Soc. Amer. 64 (1974) 1979–1991.CrossRefGoogle Scholar
[18]Tomar, S. K. and Saini, S. L., “Reflection and refraction of SH-waves at a corrugated interface between two two-dimensional transversely isotropic half-spaces”, J. Phys. Earth 45 (1997) 347–362.CrossRefGoogle Scholar