Abstract
The governing equations of an initially stressed rotating orthotropic dissipative medium are solved analytically to obtain the velocity equation which indicates the existence of two quasi-planar waves. The appropriate particular solutions in the half-space satisfy the required boundary conditions at the stress-free surface to obtain the expressions of the reflec-tion coefficients of the reflected quasi-P (qP) and reflected 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 and rotation parameter. The impact of initial stress and rotation parameters on the reflection coefficients is observed significantly.
Highlights
The Earth is considered as an elastic body with various additional parameters, e.g. porosity, initial stress, viscosity, dissipation, temperature, voids, diffusion, etc
The appropriate particular solutions in the half-space satisfy the required boundary conditions at the stress-free surface to obtain the expressions of the reflection coefficients of the reflected quasi-P and reflected quasi-SV waves in closed form for the incidence of qP and qSV waves
Following 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
The Earth is considered as an elastic body with various additional parameters, e.g. porosity, initial stress, viscosity, dissipation, temperature, voids, diffusion, etc. Various researchers studied the reflection and transmission problems at free surface, interfaces and in layered media [112]. The study of the reflection of plane waves in the presence of initial stresses and dissipation finds significant applications in various engineering fields. Following Biot [13] theory of incremental deformation, Selim [14] studied the reflection of plane waves at a free surface of an initially stressed dissipative medium. Singh and Arora [15] studied the reflection of plane waves from a free surface of an initially stressed transversely isotropic dissipative medium. We studied the problem on reflection of plane waves at a stress-free surface of an initially stressed rotating orthotropic dissipative solid half-space. The reflection coefficients of reflected waves are computed numerically to observe the effects of initial stress and rotation
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