Propagation of Torsional Surface Waves under the Effect of Irregularity and Initial Stress

Shishir Gupta,Dinesh K Majhi,Sumit K Vishwakarma,Santimoy Kundu

doi:10.4236/am.2011.212207

Abstract

The present paper has been framed to study the influence of irregularity, initial stress and porosity on the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. The irregularity has been taken in the half-space in the form of a parabola. It is observed that torsional sur- face waves propagate in this assumed medium. In the absence of irregularity the velocity of torsional surface wave has been obtained. Further, it has been seen that for a layer over a homogeneous half space, the velo- city of torsional surface waves coincides with that of Love waves.

Highlights

The study of surface waves in a half-space is important to seismologists due to its possible applications in Geophysical prospecting and in understanding the cause and estimation of damage due to earthquakes
The present paper has been framed to study the influence of irregularity, initial stress and porosity on the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface
It is observed that torsional surface waves propagate in this assumed medium

Summary

Introduction

The study of surface waves in a half-space is important to seismologists due to its possible applications in Geophysical prospecting and in understanding the cause and estimation of damage due to earthquakes. Under the assumption of dynamic coupling between solid and fluid mass, Biot [10] has developed the mathematical theory for the propagation of elastic waves in a fluid saturated porous medium Based on this theory, many problems of surface waves in poro-elastic materials have been studied in the past years by Buckingham, M. The study of wave propagation in elastic medium with different irregularities is of great importance to seismologists as well as to geophysicists to understand and predict the seismic behavior at the different margins of earth. The present paper discusses the possibility of existence of torsional surface wave in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. Parabolic irregularity is mostly found in the earth so the present study can help the seismologists to understand and predict the seismic behaviour at different margins of the earth

Formulation of the Problem

Solution for Porous Layer

L2d N P where q2

Solution for Non-Homogeneous Elastic Half Space

Case III

Numerical Computation and Discussion