Articles written in Journal of Earth System Science
Volume 115 Issue 2 April 2006 pp 257-265
Modified Christoffel equations are derived for three-dimensional wave propagation in a general anisotropic medium under initial stress. The three roots of a cubic equation define the phase velocities of three quasi-waves in the medium. Analytical expressions are used to calculate the directional derivatives of phase velocities. These derivatives are, further, used to calculate the group velocities and ray directions of the three quasi-waves in a pre-stressed anisotropic medium. Effect of initial stress on wave propagation is observed through the deviations in phase velocity, group velocity and ray direction for each of the quasi-waves. The variations of these deviations with the phase direction are plotted for a numerical model of general anisotropic medium with triclinic/ monoclinic/orthorhombic symmetry
Volume 118 Issue 6 December 2009 pp 677-687
In a pre-stressed anisotropic elastic medium, three types of quasi-waves propagate along an arbitrary direction. In general, none of the waves is truly longitudinal. The present study finds the specific directions in a pre-stressed anisotropic elastic medium along which longitudinal waves may propagate. This paper demonstrates how the propagation of longitudinal waves is affected by various pre-stresses present in the medium. The study establishes the explicit expressions defining the existence and propagation of longitudinal waves in pre-stressed anisotropic elastic medium. These expressions involve not only the direction and elastic stiffness of the medium, but also the prestresses present in the medium. Changes in conditions for the existence of longitudinal waves in orthotropic, monoclinic and triclinic anisotropies are discussed in detail. The most important part of the paper is a practical aspect suggested to calculate the specific directions for the existence of longitudinal waves in pre-stressed anisotropic elastic medium. In this approach, only those parameters are used that can be observed by the receiver in a geophysical experiment of wave propagation. The existence of longitudinal waves has been shown graphically using a numerical example for three types of anisotropic symmetries in elastic medium.