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In the present work, a mathematical modeling of propagation of Love waves in dry sandy layer under initial stress above anisotropic porous half-space under gravity is reported. The equation of motion for the Love wave has been formulated following Biot, using suitably chosen boundary conditions at the interface of sandy layer and porous halfspace under gravity. The dispersion equation of phase velocity of this proposed multilayer ground structure has been derived following the Whittaker function and its derivative, which is further expanded asymptotically, retaining the terms up to only the second degree for large argument due to small values of Biot's gravity parameter (varying from 0 to 1). The study reveals that the gravity and porosity of the porous half-space play important roles on the propagation of Love waves. It is observed that with the increase in gravitation parameter and porosity of the half-space, the phase velocity of the Love wave decreases, whereas the velocity of the waves increases for the increase in the value of the sandy parameter. The effects of these above-mentioned medium parameters for isotropic and anisotropic cases are studied on the propagation of Love waves, and their numerical results have been presented graphically.

In this paper, mathematical modeling of the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density under a rigid layer has been considered. The equation of motion has been formulated in the elastic medium using suitable boundary conditions. The frequency equation containing Whittaker's function for phase velocity due to torsional surface waves has been derived. The effect of rigid layer in the propagation of torsional surface waves in a transverse isotropic elastic medium with varying rigidity and density has been discussed. The numerical results have been shown graphically. It is observed that the influence of transverse and longitudinal rigidity and density of the medium have a remarkable effect on the propagation of the torsional surface waves. Frequency equations have also been derived for some particular cases, which are in perfect agreement with some standard results.

In this present context, mathematical modeling of the propagation of surface waves in a fluid saturated poro-elastic medium under the influence of initial stress has been considered using time dependent higher order finite difference method (FDM). We have proved that the accuracy of this finite-difference scheme is 2M when we use 2nd order time domain finite-difference and 2M-th order space domain finite-difference. It also has been shown that the dispersion curves of Love waves are less dispersed for higher order FDM than of lower order FDM. The effect of initial stress, porosity and anisotropy of the layer in the propagation of Love waves has been studied here. The numerical results have been shown graphically. As a particular case, the phase velocity in a non porous elastic solid layer derived in this paper is in perfect agreement with that of .

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