Sumit Kumar Vishwakarma

Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space

Abstract In the present paper, the dispersion equation which determines the velocity of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space has been obtained. The dispersion equation obtained is in agreement with the classical result of Love wave when the initial stresses and inhomogeneity parameters are neglected. Numerical results analyzing the dispersion equation are discussed and presented graphically. The result shows that the initial stresses have a pronounced influence on the propagation of torsional surface waves. It has also been shown that the effect of density, directional rigidities and non-homogeneity parameter on the propagation of torsional surface waves is prominent.

Existence of torsional surface waves in an earth’s crustal layer lying over a sandy mantle

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.

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

Abstract 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.

Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface

In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.

Propagation of torsional surface waves in an inhomogeneous layer over an initially stressed inhomogeneous half-space

This paper has been framed to study the propagation of torsional surface waves in an inhomogeneous layer of finite thickness over an initially stressed inhomogeneous half-space. Rigidity, density and initial stress of the half-space are assumed to have linear variation, and in layers linear variation in rigidity and density are also considered. It has been observed that the inhomogeneity parameter and the initial stress play an important role for the propagation of the torsional surface wave. The method of separation of variables is applied to find the displacement field. The dispersion equation of phase velocity is derived. The velocities of torsional waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed. As a particular case it has been seen that the dispersion equation is in agreement with the classical result of the Love wave when the initial stresses and inhomogeneity parameters are neglected.

Torsional Wave Propagation in a Substratum over a Dry Sandy Gibson Half-Space

AbstractThe propagation of torsional surface waves in a transversely isotropic substratum lying over a dry sandy gibson half-space in the presence of initial stress (compressive and tensile) and gravity have been studied analytically and computed numerically. The dispersion equation has been derived in a closed form. The effect of various inhomogeneity parameters on the torsional wave propagation has been exhibited by means of graphs. The influence of initial stress (compressive and tensile), Biot’s gravity parameter, and the sandy parameter have also been shown on the phase velocity of the torsional surface wave. Dispersion equations are in perfect agreement with the standard results when derived for some particular cases. Graphical user interface software has been developed to generalize the effect of various parameter discussed.

Influence of rigid boundary on the love wave propagation in elastic layer with void pores

In this paper, a mathematical model for Love wave propagation in a porous elastic layer under a rigid boundary resting over a poro-elastic half-space has been developed. The study shows that such a medium transmits two types of Love waves. The first front depends on the change in volume fraction of the pores whereas the second front depends upon the modulus of rigidity of the elastic matrix of the medium and is the same as the Love wave in an elastic layer over an elastic half-space. It is observed that the first front is many times faster than the shear wave in the medium with void pores due to the change in the volume fraction of the pores and is significant.

Torsional wave propagation in a self-reinforced medium sandwiched between a rigid layer and a viscoelastic half space under gravity

Abstract The present paper constitutes the study of torsional surface wave propagation in a self-reinforced layer resting over a gravitating viscoelastic half space. The layer has an inhomogeneity of linear type associated with the rigidity and density of the medium. Dispersion equation has been obtained in the terms of HypergeometricU and LaguerreL function. The dispersion equation reduces to a classical form when the inhomogeneity of the layer, gravity and viscosity of the half space vanishes. The influence of various parameters has been depicted by means of graphs for both reinforced and reinforcement free medium.

On Love Wave Frequency Under the Influence of Linearly Varying Shear Moduli, Initial Stress, and Density of Orthotropic Half-Space

The present work studies Love wave propagation in an inhomogeneous anisotropic layer superimposed over an inhomogeneous orthotropic half-space under the influence of rigid boundary plane. The layer exhibits inhomogeneity which varies quadratically with depth, whereas the half-space has inhomogeneity in the shear moduli, density, and initial stress which varies linearly downward. The frequency equation is deduced in the closed form. It has been found that the dispersion equation is a function of phase velocity, wave number, inhomogeneity parameters, and initial stress. To analyze the result more profoundly, numerical simulation and graphical illustrations have been effectuated to depict the pronounced impact of the affecting parameters on the phase velocity of Love wave. As a special case, the procured dispersion relations have been found in well agreement with the standard Love wave equation.

Behaviour of Torsional Surface Wave in a Homogeneous Substratum over a Dissipative Half Space

The present paper studies the propagation of torsional surface wave in a homogeneous isotropic substratum lying over a viscoelastic half space under the influence of rigid boundary. Dispersion relation has been obtained analytically in a closed form. The effect of internal friction, rigidity, wave number and time period on the phase velocity has been studied numerically. Dispersion equation thus obtained match perfectly with the classical dispersion equation of Love wave when derived as a particular case.