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2 results

  • 3 - Reflection and Transmission of Plane Waves

  • Edward S. Krebes, University of Calgary
  • Book:
    Seismic Wave Theory
    Published online:
    15 March 2019
    Print publication:
    28 March 2019, pp 112-151

  • Summary

    This chapter covers the mathematical theory of how plane waves are reflected by boundaries or interfaces separating solid layers in the subsurface and how they are transmitted through them. Reflections off the Earth's surface are also discussed. The equations describing the physical boundary conditions that incident, reflected, and transmitted waves must satisfy are derived. The calculation of reflection and transmission coefficients, which give the amplitudes of reflected and transmitted waves, is covered.Polarity reversals and phase changes are discussed. Critical angles, which are related to the total internal reflection of incident waves, are studied. This is followed by coverage of the calculation of the amount of seismic wave energy that is reflected and transmitted, reflection and transmission of waves from liquid–liquid, liquid–solid, and rigid boundaries, and approximate formulas for reflection and transmission coefficients.

  • Reflection coefficients and energy ratios in a micropolar thermoelastic medium without energy dissipation

  • Baljeet Singh
  • Journal:
    The ANZIAM Journal / Volume 48 / Issue 3 / January 2007
    Published online by Cambridge University Press:
    17 February 2009, pp. 433-447
    • Article
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  • The linear governing equations of a micropolar thermoelastic medium without energy dissipation are solved to show the existence of four plane waves in a two-dimensional model. The expressions for velocities of these plane waves are obtained. The boundary conditions at the free surface are used to obtain a system of four nonhomogeneous equations. These equations are solved numerically for a particular model to obtain reflection coefficients for the incidence of coupled longitudinal displacement and coupled transverse microrotational waves. These reflection coefficients as well as the energy ratios are computed and are shown graphically with the angle of incidence in the presence and absence of thermal effects.