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Effect of dry sandiness parameter and initial stress on the scattering of plane SH wave

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Abstract

The present paper is incorporated into a mathematical model of transmission and reflection of shear waves through the initially stressed dry sandy medium sandwiched between two initially stressed distinct orthotropic half-spaces. The formulae of transmission and reflection coefficients have been deduced for the propagation of SH waves in the described model subjected to certain boundary conditions applying Snell’s law and Cramer’s method. These coefficients are observed as a function of wave number, phase velocity, initial stress, rigidity, and dry sandiness coefficients. The concepts of energy partition, phase shift, conservation of energy, critical angle, and slowness section are introduced. Graphical approach has been carried out to accomplish a relation between reflection/refraction coefficient, phase shift, and energy ratio with an angle of incidence and wave number on the propagation of shear wave. The study reveals that sandiness parameter, initial stress, and wave number have a cogent respond to the scattering of shear wave that has been illustrated graphically.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology(ISM), Dhanbad, 826004, India

    Shishir Gupta,  Smita, Snehamoy Pramanik & Abhijit Pramanik

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  1. Shishir Gupta
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  2. Smita
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  3. Snehamoy Pramanik
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  4. Abhijit Pramanik
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Correspondence to Smita.

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Gupta, S., Smita, Pramanik, S. et al. Effect of dry sandiness parameter and initial stress on the scattering of plane SH wave. Arab J Geosci 11, 220 (2018). https://doi.org/10.1007/s12517-018-3536-0

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  • DOI: https://doi.org/10.1007/s12517-018-3536-0

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