Modeling of SH-Wave Propagation in a Pre-stressed Highly Anisotropic Layered Structure

The present study presents the propagation of horizontally polarized shear waves (SH-waves) in highly anisotropic layered media under the effect of horizontal and vertical initial stresses. Following Biot’s theory of incremental stresses, the present problem has been formulated. The dispersion equation has been derived using the Thomson–Haskell matrix method. Closed form expressions for phase and group velocities have been obtained using finite difference schemes. Also, the stability condition of using this finite difference scheme has been achieved. Substantial influence of the Courant number (stability ratio), tensile and compressive stress on both phase and group velocities has been observed and depicted through graphs.