Wave Reflection and Refraction at the Interface of Triclinic and Liquid Medium

Document Type : Research Paper


Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India



A Mathematical model has been considered to study the reflection and refraction phenomenon of plane wave at the interface of an isotropic liquid medium and a triclinic (anisotropic) half-space. The incident plane qP wave generates three types of reflected waves namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) waves in the triclinic medium and one refracted P wave in the isotropic liquid medium. Expression of phase velocities of all the three quasi waves have been calculated. It has been considered that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation in anisotropic medium. Some specific relations have been established between directions of motion and propagation. The expressions for reflection coefficients of qP, qSV, qSH and refracted P waves with respect to incident qP wave are obtained. Numerical computation and graphical representations have been performed for the reflection coefficient of reflected qP, reflected qSV, reflected qSH and refraction coefficient of refracted P wave with incident qP wave.


[1] Achenbach J.D., 1976, Wave Propagation in Elastic Solids, North-Holland Publishing Company, New York.
[2] Keith C.M., Crampin S., 1977, Seismic body waves in anisotropic media, reflection and refraction at a plane surface, Geophysical Journal International 49: 181-208.
[3] Chattopadhyay A.,2004, Wave reflection and refraction in triclinic crystalline media, Archive of Applied Mechanics 73: 568-579.
[4] Chattopadhyay A.,2006, Wave reflection in triclinic crystalline media, Archive of Applied Mechanics 76: 65-74.
[5] Chattopadhyay A.,2007, Reflection for three dimensional plane waves in triclinic crystalline medium, Archive of Applied Mechanics 28(10): 1309-1318.
[6] Chattopadhyay A., Michel V.,2006, A model for spherical SH wave propagation in self-reinforced linearly elastic media, Archive of Applied Mechanics 75: 113-124.
[7] Carcione J.M., 2001, Wave Fields in Real Media, Wave Propagation in Anisotropic, an Elastic and Porous Media, Pergamon Press Inc.
[8] Crampin S.,1975, Distinctive particle motion of surface waves as a diagnostic of anisotropic layering, Geophysical Journal International 40: 177-186.
[9] Knott C.G.,1899, Reflection and refraction of elastic waves with seismological applications, The Philosophical Magazine 48: 64-97.
[10] Ditri J.J., Rose J.L., 1992, On the reflection of plane waves in transversely isotropic media, Journal of the Acoustical Society of America 92: 3003-3006.
[11] Singh S.J., Khurana S.,2002, Reflection of P and SV waves at the free surface of a monoclinic elastic half-space, Proceedings of the Indian Academy of Sciences 111: 401-412.
[12] Zilmer M., Gajewski D., Kashtan B.M.,1997, Reflection coefficients for weak anisotropic media, Geophysical Journal International, 129(2): 389-398,
[13] Chatterjee M., Dhua S., Chattopadhyay A., Sahu S.A., 2015, Reflection and refraction for three-dimensional plane waves at the interface between distinct anisotropic half spaces under initial stresses, International Journal of Geomechanics 16(4): 04015099.
[14] Paswan B., Sahu S. A., Chattopadhyay A.,2016, Reflection and transmission of plane wave through fluid layer of finite width sandwiched between two monoclinic elastic half-spaces, Acta Mechanica 227(12): 3687-3701.
[15] Singh P., Chattopadhyay A., Srivastava A., Singh A.K., 2018, Reflection and transmission of P-waves in an intermediate layer lying between two semi-infinite media, Pure and Applied Geophysics 175(12): 4305-4319.