This paper aims to study the dispersion of torsional surface waves in a crustal layer being sandwiched between a rigid boundary plane and a sandy mantle. In the mantle, rigidity and initial stress vary linearly while density remains constant. Dispersion relation has been deduced in a closed form by means of variable separable method in the form of Whittaker function. The velocity equation for isotropic layer over a homogeneous half-space has been obtained which coincides with the standard result of Love wave under the effect of rigid boundary.

The present work illustrates a theoretical study on the effect of rigid boundary for the propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. It is believed that the inhomogeneity in the half space arises due to hyperbolic variation in shear modulus and density whereas the layer has linear variation in shear modulus and density. The dispersion equation has been obtained in a closed form by using Whittaker’s function, which shows the variation of phase velocity with corresponding wave number. Numerical results show the dispersion equations, which are discussed and presented by means of graphs. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close resemblance. It is also observed that, for a layer over a homogeneous half space, the velocity of torsional waves does not coincide with that of Love waves in the presence of the rigid boundary, whereas it does at the free boundary. Graphical user interface (GUI) software has been developed using MATLAB 7.5 to generalize the effect of various parameter discussed.

The present paper is concerned with the propagation of torsional surface waves in an initially stressedanisotropic porous layer sandwiched between homogeneous and non-homogeneous half-space. We assumethe quadratic inhomogeneity in rigidity and density in the lower half-space and irregularity is taken inthe form of rectangle at the interface separating the layer from the lower half-space. The dispersionequation for torsional waves has been obtained in a closed form. Velocity equation is also obtained inthe absence of irregularity. The study reveals that the presence of irregularity, initial stress, porosity,inhomogeneity and anisotropy factor in the dispersion equation approves the significant effect of theseparameters in the propagation of torsional waves in porous medium. It has also been observed that fora uniform media, the velocity equation reduces to the classical result of Love wave.

The propagation of SH wave in a heterogeneous initially stressed viscoelastic layer lying over a heterogeneous initially stressed orthotropic half-space due to a point source is analysed mathematically. The dispersion equation of SH wave is obtained for the propagation of SH wave in a specified model. The method of Green’s function and Fourier transformation is incorporated to obtain the dispersion equation. The curves of dispersion equation are sketched for various values of heterogeneous parameters and initial stress on angular frequency, phase velocity and damping velocity in respect of wave number. The dispersion equation is derived for some special cases which reduces to the classical equation of Love-type wave. The present study reveals the effect of heterogeneous parameter and initial stress associated with both viscoelastic and orthotropic media.