Reflection and Transmission of Plane SH-Waves Through an Anisotropic Magnetoelastic Layer Sandwiched Between Two Semi-Infinite Inhomogeneous Viscoelastic Half-Spaces

Abstract

Reflection and transmission coefficients due to incident plane SH-waves at an anisotropic magnetoelastic layer sandwiched between two inhomogeneous viscoelastic half-spaces are obtained. The inhomogeneity in viscoelastic coefficients of the lower half-space is considered as quadratic, while that of the upper half-space is considered as exponential. The solutions for the layer and half-spaces are obtained analytically. The formulae for reflection and transmission coefficients are obtained for viscoelastic half-spaces subjected to continuity conditions of interfaces of an anisotropic magnetoelastic layer with viscoelastic half-spaces and Snell’s law. These coefficients are found to be the function of phase velocity, wave number, inhomogeneity, thickness of layer, and angle of incidence. Two special cases are considered. In case I, the problem is reduced to reflection and transmission in two viscoelastic half-spaces, whereas case II considers two isotropic half-spaces. Numerical computations are carried out for a specific model. The graphs are plotted for reflection and transmission coefficients against the angle of incidence and non-dimensional wave number for inhomogeneity parameters, the angle at which the wave crosses the magnetic field, the thickness of the layer, and frequency. In general, as the inhomogeneity parameter increases, the reflection and transmission coefficients decrease, while the angle at which the wave crosses the magnetic field, the thickness of the layer and frequency have systematic effects. The effect of angle of incidence on the reflection and transmission coefficients is not monotonic, but converges for an angle of incidence for all the parameters. Also, graphs are plotted for phase shift versus angle of incidence. The effects of inhomogeneity, the angle at which the wave crosses the magnetic field, thickness of the layer and frequency are considered. The phase shift exhibits a similar nature for these parameters.

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Acknowledgments

Authors Mr. S. Kumar and Miss S. Majhi are grateful to the Indian School of Mines, Dhanbad, India authorities for financial support in the form of a Research Fellowship and for providing us with the best facility. Authors are also thankful to the Editor and reviewers for their valuable comments and suggestions to improve the quality of the paper.

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Kumar, S., Pal, P.C. & Majhi, S. Reflection and Transmission of Plane SH-Waves Through an Anisotropic Magnetoelastic Layer Sandwiched Between Two Semi-Infinite Inhomogeneous Viscoelastic Half-Spaces. Pure Appl. Geophys. 172, 2621–2634 (2015). https://doi.org/10.1007/s00024-015-1048-3

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Key words

  • SH-waves
  • reflection and transmission coefficients
  • anisotropic magnetoelastic medium
  • Maxwell’s equation
  • viscoelastic coefficient