Inquisitive Analysis of the Point Source Effect on Propagation of SH Wave Through an Orthotropic Crustal Layer

Document Type : Research Paper


Department of Applied Mathematics, IIT(ISM) Dhanbad, India


The occurrence of SH wave propagation under the effect of a point source in an orthotropic substratum lying over a heterogeneous orthotropic half space is deliberated in the prospect of a devastating earthquake. The quadratic alteration is acknowledged for density and shear modulus which is hypothesized to be a function of depth. The method of Green's function and transformation technique contributes to obtain the dispersion equation and dispersion curves. An effort has been accomplished to demonstrate the classical equation of Love wave followed from dispersion equation.  “Mathematica” software is applied to depict the graphics. Graphics are designed to show the effect of heterogeneous parameters corresponding to density and shear modulus. Dispersion equation is obtained considering the case that the displacement and stress are continuous at the interface. The present work is an attempt to express the behavior of SH wave in an orthotropic medium under the effect of point source.


[1] Biot M.A., 1956, Mechanics of Incremental Deformation, Wiley, New York.
[2] Bullen K.E., 1940, The problem of the earth density variation, Bulletin of Seismological Society of America 30(3): 235-250.
[3] Chattopadhyay A., Singh A.K., 2011, Effect of point source and heterogeneity on the propagation of magnetoelastic elastic wave in a monoclinic medium, International Journal of Engineering Science and Technology 3(2): 68-83.
[4] Chattopadhyay A., Gupta S., Kumari P., Sharma V.K., 2012, Effect of point source and heterogeneity on the propagation of SH waves in a viscoelastic layer over a viscoelastic half space, Acta Geophysica 6(1): 112-139.
[5] Covert E.D., 1958, Approximate calculation of Green's function for built up bodies, Journal of Mathematical Physics 37(1-4): 58-65.
[6] Colquitt D.J., Columbi A., Craster R.V., Roux P., Guennear, S.R.L., 2017, Seismic manufactures: Sub wavelength resonators and Rayleigh wave interaction, Journal of the Mechanics and Physics of Solids 99: 379-393.
[7] Dinckal C., On the mechanical and elastic properties of anisotropic engineering materials based upon harmonic representation, Proceedings of the World Congress on Engineering, London, U.K.
[8] Deresiewich H., 1962, A note on Love wave in a homogeneous crust overlying an inhomogeneous substratum, Bulletin of Seismological Society of America 52(3): 639-645.
[9] Ewing M., Jardetzsky W.S., Press F., 1957, Elastic Waves in Layered Media, MC Graw Hill, New York.
[10] Gubbins D., 1990, Seismology and Plate Tectonics, Cambridge University Press, Cambridge, UK.
[11] Kakar R., 2015, Dispersion of love wave in an isotropic layer sandwiched between an orthotropic and prestressed inhomogeneous half spaces, Latin American Journal of Solids and Structures 12(10): 1934-1949.
[12] Kundu S., Gupta S., Vaishnav P.K., Manna S., 2016, Propagation of love waves in a heterogeneous medium over an inhomogeneous half space under the effect of point source, Journal of Vibration and Control 22(5): 1-12.
[13] Kundu S., Gupta S., Manna S., 2014, SH type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi infinite media, Meccanica 49(3): 749-758.
[14] Mavco G., Conceptual overview of Rock and fluid factors that impact seismic velocity and impedance, Standard Rock Physics Laboratory.
[15] Sevostianov I., Kachanov M., 2008, On approximate symmetries of the elastic properties and elliptic orthotropy, International Journal of Engineering Science 46(3): 211-223.
[16] Vlaar N.J., 1966, The field from an SH point source in a continuously layered inhomogeneous half space, Bulletin of the Seismological Society of America 56(6): 1305-1315.
[17] Vaishnav P.K., 2017, Torsional surface wave propagation in anisotropic layer sandwiched between heterogeneous half space, Journal of Solid Mechanics 9(1): 213-224.
[18] Vavryčuk V., 2008, Velocity, attenuation and quality factor in anisotropic viscoelastic media: A perturbation approach, Geophysics 73(5): 63-73.
[19] Watanabe K., Payton R.G., 2002, Green's function for SH wave in a cylindrically monoclinic material, Journal of Mechanics Physics of Solids 50(11): 2425-2439.