Torsional wave propagation in non-homogeneous layer between non-homogeneous half-spaces

The study of surface wave in a layered medium has their possible application in geophysical prospecting. In the present work, dispersion equation for torsional wave in an inhomogeneous isotropic layer between inhomogeneous isotropic half-spaces has been derived. Two cases are discussed separately for torsional wave propagation in inhomogeneous layer between homogeneous and non-homogeneous half-spaces, respectively. Further, two possible modes for torsional wave propagation are obtained in case of inhomogeneous layer sandwiched between non-homogeneous half-spaces. Closed form solutions for displacement in the layer and half-spaces are obtained in each case. The study reveals that the layer width, layer inhomogeneity, frequency of inhomogeneity, as well as inhomogeneity in the half-space has significant effect on the propagation of torsional surface waves. Displacement and implicit dispersion equation for torsional wave velocities are expressed in terms of Heun functions and their derivatives. Effects of inhomogeneity on torsional wave velocity are also discussed graphically by plotting the dimensionless phase velocity against dimensionless and scaled wave number for different values of inhomogeneity parameter. Copyright (c) 2012 John Wiley & Sons, Ltd.