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Scattering of plane elastic waves at rough surfaces. I

Published online by Cambridge University Press:  24 October 2008

Iya Abubakar
Iya Abubakar
Affiliation:
St Catherine's CollegeCambridge
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Abstract

An approximate solution of the two-dimensional problem of reflexion of plane harmonic P and S V waves by an irregular boundary is obtained using a modification of Rice's perturbation method of approximation on the assumption that the curvature of the surface is everywhere small. The case of a periodic surface is treated in more detail. It is found that the reflected waves are composed of specularly reflected waves and various diffracted waves, propagating in both horizontal directions if the wavelength of the incident waves is long compared with that of the surface. If the wavelength of incident distortional waves is long compared with that of the surface, the amplitudes of some of the scattered waves decrease exponentially with depth. In general the phases of the waves change on reflexion and the phase angles of the reflected waves are functions of the wavelength of the corrugation and the angle of incidence. It is verified, in the case of zero angle of incidence, that the energy going into the scattered radiation is obtained at the expense of the energy of the specularly reflected waves.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 1 , January 1962 , pp. 136 - 157
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Brekhovskikh, L. M.Ž. Eksper. Teoret. Fiz. 23 (1952), 275.Google Scholar
(2)Ewing, W. M., Jardetzky, W. S. and Press, F.Elastic waves in layered medium, 1st ed. (New York, 1957).Google Scholar
(3)Kupradze, V. D.Fundamental problems in the mathematical theory of diffraction, 1st ed. (Leningrad and Moscow, 1935).Google Scholar
(4)Miles, J. W.J. Acoust. Soc. Amer. 26 (1954), 191.CrossRefGoogle Scholar
(5)Mindlin, I. A.Dokl. Akad. Nauk SSSR, 27 (1940), no. 9.Google Scholar
(6)Rayleigh, . Lord. The theory of sound, 2nd ed., vol. 2 (London, 1896).Google Scholar
(7)Rayleigh, . Lord. Proc. Roy. Soc. London Ser. A, 79 (1907), 399.Google Scholar
(8)Rice, S. O.Comm. Pure Appl. Math. 4 (1951), 351.CrossRefGoogle Scholar
(9)Sato, R.Zisin Ser. II, 8, no. 1, 8.Google Scholar
(10)Sezawa, K.Bull. Earthquake Res. Inst. Tokyo, 7 (1929), 437.Google Scholar
(11)Sherman, D. I.Dokl. Akad. Nauk SSSR, 48 (1945), no. 9.Google Scholar
(12)Skuridin, G. A.Izv. Akad. Nauk SSSR. Ser. Geofiz. 2 (1957), 36.Google Scholar
(13)Sokolnikoff, I. S.Mathematical theory of elasticity, 2nd ed. (New York, 1956).Google Scholar