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Mathematical Geosciences

, Volume 51, Issue 4, pp 419–436 | Cite as

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

  • Sanjeev A. SahuEmail author
  • Kamlesh K. Pankaj
  • Shreeta Kumari
Article
  • 75 Downloads

Abstract

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.

Keywords

SH-wave Finite difference method Courant number Initial stress Dispersion equation 

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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  • Sanjeev A. Sahu
    • 1
    Email author
  • Kamlesh K. Pankaj
    • 1
  • Shreeta Kumari
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)DhanbadIndia

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