Torsional surface wave dispersion in pre-stressed dry sandy layer over a gravitating anisotropic porous half-space

Abstract

The present paper discusses the dispersion of torsional surface wave in a pre-stressed dry sandy layer over an anisotropic porous half-space under the influence of gravity. The inhomogeneity has been expected as hyperbolic variation in the sandy layer. The mathematical analysis of the problem has been dealt with the asymptotic expansion of Whittaker function and its derivative. The dispersing mathematical statement acquired is in concurrence with the conventional consequence of Love wave in a homogeneous layer over a homogeneous half space when the upper limit plane is thought to be traction free. The velocities of torsional waves are ascertained numerically as a component of kH and introduced in various graphs, where k is the wave number and H is the thickness of the sandy layer. The numerical expression gives the scaffold between displaying results and field application. The impact of non-homogeneity in modulus of rigidity, stress, density, and porosity have been portrayed by the method for numerical data and graphs. The study reveals that the torsional surface wave propagates in an initially stressed dry sandy layer over a gravitating anisotropic porous half-space. It is additionally watched that the vicinity of gravity field builds the speed of the torsional surface wave. This work may be valuable to comprehend the way of seismic wave proliferation amid quake in the considered media.