Reflection and refraction of SH-waves at a corrugated interface between two laterally and vertically heterogeneous viscoelastic solid half-spaces

Reflection and transmission coefficients due to incident plane SH-waves at a corrugated interface between two isotropic, laterally and vertically heterogeneous visco-elastic solid half spaces are obtained. The density and complex rigidity of each medium are considered to vary along horizontal and vertical directions. Closed form expressions of reflection and transmission coefficients are derived using Rayleigh’s method of approximation. These coefficients are found to be the function of corrugation, heterogeneity, angle of incidence, angle between propagation and attenuation vectors and visco-elasticity of the media. Numerical computations are made for a specific model to study the nature of dependence of these coefficients. Variations of reflection and transmission coefficients for the first order of approximation of the corrugation versus angle of incidence, corrugation and angle between propagation and attenuation vectors are computed and depicted graphically. Comparison is made between these coefficients in viscoelastic media and in uniform elastic media. The problems investigated earlier by Asano [Bull. Earthq. Res. Inst. 38 (1960) 177], Singh et al. [Acta Geophys. Pol. XXVI (1978) 209], Kaushik and Chopra [Geophys. Res. Bull. 18 (1980) 111] and Gupta [Geophys. Trans. 33 (1987) 89] have been reduced as particular cases.