Influence of Heterogeneity on Rayleigh Wave Propagation in an Incompressible Medium Bonded Between Two Half-Spaces

Document Type: Research Paper


Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India


The present investigation deals with the propagation of Rayleigh wave in an incompressible medium bonded between two half-spaces. Variation in elastic parameters of the layer is taken linear form. The solution for layer and half-space are obtained analytically. Frequency equation for Rayleigh waves has been obtained. It is observed that the heterogeneity and width of the incompressible medium has significant effect on the phase velocity of Rayleigh waves. Some particular cases have been deduced. Results have been presented by the means of graph. Also the findings are exhibited through graphical representation and surface plot.


[1] Rayleigh L., 1885, On waves propagating along the plane surface of an elastic solid, Proceedings of the Royal Society of London, Series A 17: 4-11.
[2] Bullen K.E., 1947, An Introduction to the Theory of Seismology, Cambridge University Press.
[3] Ewing W.M., Jardetzky W.S., Press F., 1957, Elastic Waves in Layered Media, McGraw-Hill, New York.
[4] Love A.E.H., 1944, A Treatise on the Mathematical Theory of Elasicity, Dover Publication, New York.
[5] Stonely R., 1924, Elastic waves at the surface of separation of two solids (transverse waves in an internal stratum), Proceedings of the Royal Society of London.
[6] Stonely R., 1926, The effect of ocean on Rayleigh waves, Monthly Notices of the Royal Astronomical Society 1: 349-356.
[7] Biot M.A., 1952, The interaction of Rayleigh and Stonely waves in ocean bottom, Bulletin of the Seismological Society of America 42: 81-92.
[8] Tolstoy I., 1954, Dispersive properties of fluid layer over lying a semi-infinite elastic solid, Bulletin of the Seismological Society of America 44: 493-512.
[9] Abubaker I., Hudson J.A., 1961, Dispersive properties of liquid overlying an aelotropic half-space,The Royal Astronomical Society 5: 218-229.
[10] Carcoine J.M., 1992, Rayleigh waves in isotropic viscoelastic media, Geophysical Journal International 108:453-464.
[11] Destrade M., 2001, Surface waves in orthotropic incompressible materials, Acoustical Society of America 110(2): 837.
[12] Rudzki M.P., 2003, On the propagation of an elastic surface wave in a transversely isotropic medium, Journal of Applied Geophysics 54: 185-190.
[13] Vinh P.C., Ogden R.W., 2004, Formulas for Rayleigh wave speed in orthotropic elastic solids, Archives of Mechanics 56(3): 247-265.
[14] Singh J., Kumar R., 2013, Propagation of Rayleigh waves due to the presence of a rigid barrier in a shallow ocean, International Journal of Engineering and Technology 5(2): 917-924.
[15] Gupta I.S., 2013, Propagation of Rayleigh waves in a prestressed layer over a prestressed half-space, Frontiers in Geotechnical Engineering 2(1): 16-22.
[16] Vinh P.C., Anh V.T.N., Thanh V.P., 2014, Rayleigh waves in an isotropic elastic half-space coated by a thin isotropic elastic layer with smooth contact, Wave Motion 51: 496-504.
[17] Pal P.C., Kumar S., Bose S., 2015, Propagation of Rayleigh waves in anisotropic layer overlying a semi-infinite sandy medium, Ain Shams Engineering Journal 6(2): 621-627.
[18] Gupta I.S., Kumar A., 2014, Propagation of Rayleigh wave over the pre-stressed surface of a heterogeneous medium, Proceeding of 59th Congress of ISTAM.
[19] Kakar R., Kakar S., 2013, Rayleigh waves in non-homogeneous granular medium, Journal of Chemical, Biological and Physical Sciences 3(1): 464-478.
[20] Dutta S., 1963, Rayleigh waves in a two layer heterogeneous medium, Bulletin of the Seismological Society of America 53(3): 517-526.
[21] Singh B., 2014, Wave propagation in an incompressible transversely isotropic thermoelastic solid, Meccanica 50:1817-1825.
[22] Vinh P.C., Link N.T.K., 2013, Rayleigh waves in an incompressible elastic half-space overlaid with a water layer under the effect of gravity, Meccanica 48: 2051-2060.
[23] Singh B., 2013, Rayleigh wave in an initially stressed transversely isotropic dissipative half-space, Journal of Solid Mechanics 5(3): 270-277.
[24] Kakar R., 2015, Rayleigh waves in a homogeneous magneto-thermo voigt-type viscoelastic half-space under initial surface stresses, Journal of Solid Mechanics 7(3): 255-267.