Reflection of waves from the boundary of a random elastic semi-infinite medium
In this paper the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities. Amplitude ratios have been obtained for various types of incident and reflected waves. It has been shown that an incidentSH orSV type of wave gives rise to reflectedSH, P andSV waves, the main components beingSH andP, SV in the respective cases. The reflected amplitudes have been calculated depending upon the randomness of the medium to the square of the small quantity ɛ, where ɛ measures the deviation of the medium from homogeneity. An incidentP-type wave produces mainly aP component and also a weakSH component to the order of ɛ2. The reflected amplitudes obtainable for elastic media are also altered by terms of the same order. The direction of the reflected wave is influenced by randomness in some cases.
Key wordsSmooth perturbation elastic waves reflection random medium
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- Bhattacharyya, R. K. (1986),On Wave Propagation in a Random Magneto-thermo-viscoelastic Medium, Indian J. Pure and Appl. Math.17 (5), 705–725.Google Scholar
- Bhattacharyya, R. K.,Wave Propagation in a Random Micropolar Elastic Medium (to be published).Google Scholar
- Chow, P. L. (1973),Thermoelastic Wave Propagation in a Random Medium and Some Related Problems, Int. J. Eng. Sci.11, 953.Google Scholar
- Karal, F. C., andKeller, J. B. (1964),Elastic, Electromagnetic and Other Waves in a Random Medium, J. Math. Phys.5 (4), 537–547.Google Scholar
- Keller, J. B. (1964),Stochastic Equations and Wave Propagation in Random Media, Proc. Sympos. Appl. Math.16, Am. Math. Soc., Providence, R.I. 145–170.Google Scholar
- Miklowitz, J.,The Theory of Elastic Waves and Waveguides (North-Holland Publishing Co., Amsterdam 1980).Google Scholar