### Reflection and transmission of quasi-P waves through an orthotropic layer sandwiched between two half-spaces

#### Abstract

In this paper, the reflection and transmission of a qP wave through an orthotropic elastic layer sandwiched between two orthotropic elastic half-spaces is investigated. The main aim is to derive the expressions in closed-form of the reflection and transmission coefficients. These expressions have been obtained by using the transfer matrix for an orthotropic layer. Based on the obtained expressions, some numerical examples are carried out to examine the dependence of the reflection and transmission coefficients on the incident angle, the wave frequency and the ratio of mass densities.

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W. M. Ewing and W. S. Jardetzky. Waves in layered media. McGraw-Hill, New York, (1957).

L. Brekhovskikh. Waves in layered media. Academic Press, New York, second edition, (1976).

L. M. Brekhovskikh and O. A. Godin. Acoustics of layered media, Vol. 10. Springer, Berlin, (2013).

A. Ben-Menahem and S. J. Singh. Seismic waves and sources. Springer-Verlag, New York, (1981).

A. H. Nayfeh. Wave propagation in layered anisotropic media: With application to composites, Vol. 39. NorthHolland Pub. Co., (1995).

R. D. Borcherdt. Viscoelastic waves in layered media. Cambridge University Press, New York, (2009).

A. Chattopadhyay and S. Choudhury. The reflection phenomena of P-waves in a medium of monoclinic type. International Journal of Engineering Science, 33, (2), (1995), pp. 195–207. doi:10.1016/0020-7225(94)00055-o.

M. Chatterjee, S. Dhua, S. A. Sahu, and A. Chattopadhyay. Reflection in a highly anisotropic medium for three-dimensional plane waves under initial stresses. International Journal of Engineering Science, 85, (2014), pp. 136–149. doi:10.1016/j.ijengsci.2014.08.010.

S. I. Rokhlin, T. K. Bolland, and L. Adler. Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media. The Journal of the Acoustical Society of America, 79, (4), (1986), pp. 906–918. doi:10.1121/1.393764.

A. Chattopadhyay, S. Saha, and M. Chakraborty. Reflection and transmission of shear waves in monoclinic media. International Journal for Numerical and Analytical Methods in Geomechanics, 21, (7), (1997), pp. 495–504. doi:10.1002/(sici)1096-9853(199707)21:7<495::aidnag884>3.0.co;2-a.

A. Chattopadhyay and Rajneesh. Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium. Acta Geophysica, 54, (3), (2006), pp. 239–249. doi:10.2478/s11600-006-0022-y.

A. Chattopadhyay, P. Kumari, and V. K. Sharma. Reflection and refraction at the interface between distinct generally anisotropic half spaces for three-dimensional plane quasi-P waves. Journal of Vibration and Control, 21, (3), (2015), pp. 493–508. doi:10.1177/1077546313488615.

S. Kumar, P. C. Pal, and S. Majhi. Reflection and transmission of plane SH-waves through an anisotropic magnetoelastic layer sandwiched between two semi-infinite inhomogeneous viscoelastic half-spaces. Pure and Applied Geophysics, 172, (10), (2015), pp. 2621–2634. doi:10.1007/s00024-015-1048-3.

B. Paswan, S. A. Sahu, and A. Chattopadhyay. Reflection and transmission of plane wave through fluid layer of finite width sandwiched between two monoclinic elastic half-spaces. Acta Mechanica, 227, (12), (2016), pp. 3687–3701. doi:10.1007/s00707-016-1684-4.

P. Kumari, V. K. Sharma, and C. Modi. Reflection/refraction pattern of quasi-(P/SV) waves in dissimilar monoclinic media separated with finite isotropic layer. Journal of Vibration and Control, 22, (11), (2016), pp. 2745–2758. doi:10.1177/1077546314548911.

P. C. Vinh, V. T. N. Anh, and N. T. K. Linh. On a technique for deriving the explicit secular equation of Rayleigh waves in an orthotropic half-space coated by an orthotropic layer. Waves in Random and Complex Media, 26, (2), (2016), pp. 176–188. doi:10.1080/17455030.2015.1132859.

T. T. Tuan and T. N. Trung. The dispersion of Rayleigh waves in orthotropic layered half-space using matrix method. Vietnam Journal of Mechanics, 38, (1), (2016), pp. 27–38. doi:10.15625/0866-7136/38/1/6191.

S. J. Singh and S. Khurana. Reflection and transmission of P and SV waves at the interface between two monoclinic elastic half-spaces. Proceedings National Academy of Sciences India Section A, 71, (4), (2001), pp. 305–320.

J. Achenbach. Wave propagation in elastic solids, Vol. 16. North-Holland Publishing Company, Amsterdam-New York-Oxford, (1973).

T. C. T. Ting. Anisotropic elasticity: Theory and applications, number 45. Oxford University Press, New York, (1996).

DOI: https://doi.org/10.15625/0866-7136/10807

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