Dispersion of Love wave in an isotropic layer sandwiched between orthotropic and prestressed inhomogeneous half-spaces

Rajneesh Kakar

doi:10.1590/1679-78251918

Abstract

An in-depth study has been carried out for the dispersion of Love waves in an isotropic elastic layer sandwiched between orthotropic and prestressed inhomogeneous elastic half-spaces. The inhomogeneities in density and rigidity of the lower half-space are space dependent and an arbitrary function of depth. Simple mathematical techniques are used to obtain dispersion relation for Love wave propagation in an isotropic layer. An extensive analysis is carried out through numerical computation to explore the effect of inhomogeneity and initial stress the lower half on the phase velocity of the Love waves. The numerical analysis of dispersion equation manifests that the phase velocity of the Love wave increases with the increase of stress parameter. The results further indicate that the inhomogeneity of the half space affect the wave velocity significantly. These results can be useful to study geophysical prospecting and understanding the cause and estimation of damage due to earthquakes.

Highlights

The deformation at any point of the medium is useful to analyze the deformation field around mining tremors and drilling into the crust of the earth
At the present time the usefulness of dislocation theory in seismology is restricted by the absence of detailed knowledge of either the tectonic stress which drives the system or the stress which resists slip on the fault plane and by the absence of detailed observations of deformation preceding, accompanying of dislocation theory to seismology lie in the mathematical theory but
An analytical approach is used to investigate the propagation of Love wave in a homogeneous isotropic layer of finite thickness between orthotropic and inhomogeneous half spaces

Summary

INTRODUCTION

The deformation at any point of the medium is useful to analyze the deformation field around mining tremors and drilling into the crust of the earth. Manna et al (2013) discussed propagation of Love wave in hetrogeneous elastic half-space and piezoelectric layer. Kundu et al (2013) discussed propagation of Love wave in porous rigid layer kept over prestressed half space. Ghorai et al (2010) showed the effect of rigid boundary on the propagation of Love wave in porous layer placed over an elastic half-space. Gupta et al (2013) proposed a mathematical model to study Love wave propagation in homogeneous and initially stressed hetrogeneous half-spaces. Kakar and Gupta (2014) studied Love waves in an intermediate heterogeneous layer lying in between homogeneous and inhomogeneous isotropic elastic half-spaces. The present paper deals with the study of propagation of Love wave in a sandwiched layer lying between orthotropic and inhomogeneous half spaces. It has been found that initial stress parameter, rigidity parameter and density parameter of the lower half-space affect the phase velocity of Love waves

Solution for the upper half-space

Solution for the lower half-space

BOUNDARY CONDITIONS

DISPERSION RELATIONS

NUMERICAL CALCULATIONS AND DISCUSSION

CONCLUSIONS