Reflection of Plane Waves from a Free Surface of an Initially Stressed Transversely Isotropic Dissipative Medium

Baljeet Singh,Jyoti Arora

doi:10.4236/am.2011.29156

Abstract

The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the speeds of plane waves. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the expressions of the reflection coefficients of reflected quasi-P (qP) and quasi-SV (qSV) waves in closed form for the incidence of qP and qSV waves. A particular model is chosen for numerical computation of these reflection coefficients for a certain range of the angle of incidence. The numerical values of these reflection coefficients are shown graphically against the angle of incidence for different values of initial stress parameter. The impact of initial stress parameter on the reflection coefficients is observed significantly.

Highlights

We can not know the Earth completely by assuming mere an elastic body
The reflection of plane waves at free surface, interface and layers is important in estimating the correct arrival times of plane waves from the source
With the help of Biot [13] theory of incremental deformation, Selim [14] studied the reflection of plane waves at a free surface of an initially stressed dissipative medium

Summary

Introduction

If we consider various additional parameters, e.g. porosity, initial stress, viscosity, dissipation, temperature, voids, diffusion, etc., we can understand better the interior of the Earth. Various researchers studied the reflection and transmission problems at free surface, interfaces and in layered media [1,2,3,4,5,6,7,8,9,10,11,12]. The study of reflection of plane waves in the presence of initial stresses as well as dissipation is interesting. With the help of Biot [13] theory of incremental deformation, Selim [14] studied the reflection of plane waves at a free surface of an initially stressed dissipative medium. We studied the problem on reflection of plane waves at a stress-free surface of an initially stressed transversely isotropic solid half-space with dissipation. The reflection coefficients of reflected waves are computed numerically to observe the effect of initial stress

Formulation of the Problem and Solution

Reflection of Plane Waves from Free Surface

Numerical Example

Conclusions