Arch Appl Mech (2014) 84:235–245 DOI 10.1007/s00419-013-0796-8 ORIGINAL Sanjeev A. Sahu · Pradeep K. Saroj · Nidhi Dewangan SH-waves in viscoelastic heterogeneous layer over half-space with self-weight Received: 5 May 2013 / Accepted: 10 October 2013 / Published online: 29 October 2013 © Springer-Verlag Berlin Heidelberg 2013 Abstract The effect of gravity, heterogeneity and internal friction on propagation of SH-waves (horizontally polarised shear waves) in viscoelastic layer over a half-space has been studied. Using the method of separation of variables, dispersion equation has been obtained and used to recover the damped velocity of SH-waves. Both the real and imaginary parts of dispersion equation are in well agreement with the classical Love wave equation. It has been observed that heterogeneity of the medium affects the velocity profile of SH-wave significantly. Some other peculiarities have been observed and discussed in our study. Keywords SH-wave · Viscoelastic · Gravity · Internal friction · Heterogeneity 1 Introduction The earth is considered to be a layered elastic medium with a variation in density and rigidity in constituent’s layers. The study of body waves in a half-space is important to seismologists due to its possible applications in geophysical prospecting and in understanding the cause and estimation of damage due to earthquakes. In seismological studies, the phenomenon ‘liquefaction’ denotes a state in which solid deposit of sands inside the ground is transformed into a state of suspension, so that they behave as a viscous liquid. Studies of wave propagation in the earth stratum under loads have been done with assumption that the earth behaves to a first approximation as an ideal elastic or viscoelastic material. The theory of viscoelasticity is of great importance in the broad field of solid mechanics and particularly in seismology, exploration geophysics, etc. Geophysical studies reveal the fact that the interior of earth, similar to the outer, is layered. To study the effect of viscoelasticity in wave propagation, some attempts have been done earlier. Several papers have been published on the propagation of seismic waves in elastic medium with different types of inhomogeneity. Bhattacharya [1] pointed out some possible exact solution of SH-wave equation for inhomogeneous media. Cooper [2], Shaw and Bugl [3], Schoenberg [4], Borcherdt [5], Kaushik and Chopra [6], Gogna and Chander[7] and Romeo [8] have studied the propagation of SH-waves in viscoelastic media. The propagation of waves in a homogeneous viscoelastic layer overlying a viscoelastic medium was studied by Kanai [9]. Lockett [10] discussed the reflection and refraction of waves in viscoelastic materials. Cerveny [11] studied the propagation of SH-waves in viscoelastic media with and without heterogeneity. Chattopadhyay et al. [12] S. A. Sahu (B ) · P. K. Saroj · Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, Jharkhand, India E-mail: maths.sngv@gmail.com Tel.: +91-326-2235917 Fax: +91-326-2296563 N. Dewangan St. Guru Ghasidas Govt. PG college, Kurud, Chhattisgarh, India