Static deformation due to two-dimensional seismic sources embedded in an isotropic half-space in smooth contact with an orthotropic half-space

  • Authors

    • Yogita Godara DCRUST
    • Ravinder Kumar Sahrawat
    • Mahabir Singh
    2014-07-25
    https://doi.org/10.14419/gjma.v2i3.3005
  • Closed form analytical expressions for displacements and stresses at any point of a two-phase medium consisting of a homogeneous, isotropic, perfectly elastic half-space in smooth contact with a homogeneous, orthotropic, perfectly elastic half-space caused by two-dimensional seismic sources located in the isotropic half-space are obtained. The method consists of first finding the integral expressions for two half-spaces in smooth contact from the corresponding expressions for an unbounded medium by applying suitable boundary conditions at the interface and then evaluating the integrals analytically. Here, we discuss the horizontal and vertical displacements for vertical dip-slip fault numerically. Numerical computations indicate that the deformation field due to a source in an isotropic half-space in smooth contact with an anisotropic half-space may differ substantially from the deformation field when both the half-spaces are isotropic.

    Keywords: Isotropic Half-Space, Orthotropic Half-Space, Static-Deformation, Smooth Contact.

  • References

    1. Steketee, J.A., ''On Volterra's Dislocations in A Semi-infinite Elastic Medium'', Can. J. Phys., Vol. 36,1958a, 192-205 http://dx.doi.org/10.1139/p58-024.
    2. Stekettee, J.A,'' Some Geophysical Applications of the Elasticity Theory of Dislocations'', Can. J. Phys., vol. 36,1958b, 1168. 1198.
    3. Maruyama, T.,'' On two-dimensional elastic dislocations in an infinite and semi-infinite medium'', Bull. Earthq. Res. Inst., Univ. Tokyo, 44, 811-871, 1966.
    4. Freund, L. B. and D. M. Barnett,'' A two-dimensional analysis of surface deformation due to dip-slip Faulting'', Bull. Seismol. Soc. Am., 66, 667-675, 1976.
    5. Singh, S. J. and N. R. Garg,'' On the representation of two-dimensional seismic sources'', Acta Geophys. Pol., 34, 1-12, 1986.
    6. Singh, S. J., S. Rani, and N. R. Garg,'' Displacements and stresses in two welded half-spaces due to two- dimensional sources'', Phys. Earth. Planet. Inter 1991.
    7. Singh, S. J.,'' Static deformation of a transversely isotropic multilayered half-space by surface loads'', Phys. Earth Planet. Inter 42, 263-273, 1986. http://dx.doi.org/10.1016/0031-9201 (86)90029-4.
    8. Garg, N. R. and S. J. Singh,'' 2-D response of a transversely isotropic multilayered half-space due to surface Loads'', Indian J. Pure Appl. Maths., 18, 763-777, 1987.
    9. Pan, E.,'' Static response of a transversely isotropic and layered half-space to general surface loads'', Phys. Earth Planet. Inter., 54, 353-363, 1989a. http://dx.doi.org/10.1016/0031-9201 (89)90252-5.
    10. Pan, E.,'' Static response of a transversely isotropic and layered half-space due to general dislocation sources'', Phys. Earth Planet, Inter., 58, 103-117, 1989b. http://dx.doi.org/10.1016/0031-9201 (89)90046-0.
    11. Garg, N. R., S. J. Singh, and S. Manchanda,'' Static deformation of an orthotropic multilayered elastic half-space by two dimensional surface loads'', Proc. Ind. Acad. Sci. (Earth Planet. Sci.), 100, 205-218, 1991.
    12. Singh S. J., Rani S.,'' Static deformation due to two-dimensional seismic sources embedded in an isotropic half-space in welded contact with an orthotropic half-space'', J. Phys. Earth,39, 599-618, 1991. http://dx.doi.org/10.4294/jpe1952.39.599.
    13. Rani, S. et al.,''Static deformation due to dip-slip fault of finite width embedded in an isotropic half-space in welded contact with an orthotopic half space'', Sadhana Vol. 34, Part 6, pp. 887–902. Indian Academy of Sciences, 2009.
    14. Singh M. et al.,'' Static deformation of two half-spaces in smooth contact due to vertical tensile Fault'', Inter. J. Inn. Tec. Creat. Engg. 3, 17-30, 2013.
    15. Ben-Menahem, A. and S. J. Singh,'' Seismic Waves and Sources'', Springer-Verlag, New York, 1108 pp., 1981. http://dx.doi.org/10.1007/978-1-4612-5856-8.
    16. Rani, S., S. J. Singh, and N. R. Garg,'' Displacements and stresses at any point of a uniform half-space due to two-dimensional buried sources'', Phys. Earth Planet. Inter. 65, 276-286, 1991. http://dx.doi.org/10.1016/0031-9201 (91)90134-4.
  • Downloads

    Additional Files

  • How to Cite

    Godara, Y., Sahrawat, R. K., & Singh, M. (2014). Static deformation due to two-dimensional seismic sources embedded in an isotropic half-space in smooth contact with an orthotropic half-space. Global Journal of Mathematical Analysis, 2(3), 169-183. https://doi.org/10.14419/gjma.v2i3.3005