On torsional surface wave in dry sandy crust laid over an inhomogeneous half space

Abstract

An in-depth investigation has been carried out for the propagation of torsional surface waves in a dry sandy layer over an inhomogeneous half space. Both medium are assumed to be under compressive initial stress. The inhomogeneities that arise due to slow variation in rigidity and density in the lower half space is taken as an arbitrary function of depth. Using WKB approximation a closed form dispersion relation of torsional surface wave in the sandy layer has been formulated in terms of the arbitrary bounded functions. This dispersion equation is further employed to study the polynomial and exponential variation in rigidity and density of the half-space. An extensive analysis is carried out through numerical computation to explore the effect of inhomogeneity, initial stress, sandiness and thickness of the layer on the phase velocity of the torsional surface waves. The analysis of dispersion equation manifests the decline of phase velocity in the presence of sandy parameter as well as by increase in thickness of the sandy layer. The results further indicate that the initial stress of both the medium and the inhomogeneity of the half space affect the wave velocity significantly.