J Seismol (2007) 11:235–258 DOI 10.1007/s10950-007-9050-6 ORIGINAL ARTICLE Shear waves at a corrugated interface between anisotropic elastic and visco-elastic solid half-spaces S. K. Tomar · Jatinder Kaur Received: 28 April 2006 / Accepted: 6 March 2007 / Published online: 9 May 2007 © Springer Science + Business Media B.V. 2007 Abstract Rayleigh’s method of approximation is employed to find out the reflection and trans- mission coefficients due to an incident plane SH wave at a corrugated interface between a laterally and vertically inhomogeneous anisotropic elastic solid half-space and a laterally and vertically inho- mogeneous isotropic visco-elastic solid half-space. The lateral and vertical inhomogeneities are de- scribed by the exponential variations of elastic parameters. The formulae of reflection and trans- mission coefficients are derived in closed form for the first-order approximation of the corrugation. The effects of the corrugation of the interface, the inhomogeneity, the anisotropy, the visco-elasticity and the frequency of the incident wave on these coefficients are studied analytically and numeri- cally for a specific model containing a periodic interface. The results of earlier workers have been reduced as particular cases from the present formulation. S. K. Tomar (B ) Department of Mathematics, Panjab University, Chandigarh-160 014, India e-mail: sktomar@yahoo.com J. Kaur Department of Mathematics, Guru Nanak Girls College, Santpura, Yamuna Nagar-135 001, Haryana, India Keywords Reflection · Transmission · SH-wave · Corrugation · Anisotropy · Inhomogeneity · Viscoelastic · Rayleigh’s method 1 Introduction The problems of reflection and transmission of seismic waves from the discontinuities present beneath the earth surface are of great help for understanding the internal structure of the Earth. They are also helpful in the detection of valu- able materials, such as minerals, oils and hydro- carbons, beneath the Earth surface. Accurate modeling procedures are needed to explore these materials. Keeping in view the fact that the earthquake-generated seismic waves encounter mountain basins, mountain roots and salt and ore bodies in their paths, it is doubtless to say that such irregularities do affect the reflection and transmission phenomena of seismic waves. Because the Earth does not behave as a per- fectly elastic body, to delineate the fine structure of the earth accurately, the imperfection of the elasticity of the earth materials like metals, con- crete, soil and mud cannot be disregarded. The attenuation of seismic waves with distance and of normal modes with time indicates the anelastic behaviour of the Earth. The general theory of visco-elasticity describes the linear behaviour of both elastic and anelastic materials and provides