Torsional surface wave propagation in an initially stressed non-homogeneous layer over a non-homogeneous half-space

It is of great interest to study torsional surface wave propagation in an initially stressed non-homogeneous layer over a non-homogeneous half-space. The method of separation of variables is applied to find the displacement field. It is well known in the literature that the earth medium is not at all initial stress free and homogeneous throughout, but it is initially stressed and non-homogeneous. Keeping these things in mind, we have discussed propagation of torsional surface wave in an initially stressed non-homogeneous layer over a non-homogeneous half-space. It has been observed that the inhomogeneity parameter and the initial stress play an important role for the propagation of torsional surface wave. It has been seen that as the non-homogeneity parameter in the layer increases, the velocity of torsional surface wave also increases. Similarly as the non-homogeneity parameter in the half-space increases, the velocity of torsional surface wave increases. The initial stresses P present in the inhomogeneous layer also have effect in the velocity of propagation. It has been observed that an increase in compressive initial stresses decreases the velocity of torsional surface wave.