Deformation Field Produced by a Doublet Source in a Half-Space Model
محورهای موضوعی : Mechanics of Solids
1 - Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar-125001, India
2 - Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar-125001, India
کلید واژه: Elastic half-space, Standard linear solid, Kelvin, Maxwell, Viscoelastic,
چکیده مقاله :
Using Galerkin vector approach closed-form analytic expressions for the displacements and stresses caused by a doublet source buried in a homogenous, isotropic, perfectly elastic half-space have been obtained. Further, the viscoelastic deformation field has been obtained by applying the correspondence principle of linear viscoelasticity, assuming the medium to be elastic in dilatation and Kelvin, Maxwell, or SLS (Standard linear solid) type viscoelastic in distortion. The effect of Poisson’s ratio on the deformation field due to a doublet source is examined in elastic half-space. The effect of relaxation time on displacement and stress fields is studied due to a doublet source in viscoelastic half-space. The variation of the displacements and stresses with the epicentral distance is studied graphically using MATLAB software. Stresses for a doublet with axis parallel to x-axis attain minimum value for Poissonian half- space. Viscoelastic displacements and stresses attain maxima for the Maxwell model and minima for the Kelvin model.
[1] Singh S.J., Ben-Menahem A., 1969, Displacement and strain fields due to faulting in a sphere, Physics of the Earth and Planetary Interiors 2: 77-87.
[2] Singh S.J., 1970, Static deformation of a multilayered half-space by internal sources, Journal of Geophysical Research 75: 3257-3263.
[3] Singh S.J., Ben-Menahem A., Vered M., 1973, A unified approach to the representation of seismic sources, Proceedings of The Royal Society of London A 331: 525-551.
[4] Freund L.B., Barnett D.M., 1976, A two-dimensional analysis of surface deformation due to dip-slip faulting, Bulletin of the Seismological Society of America 66: 667-675.
[5] Aki K., Richards P.G., 1980, Quantitative Seismology: Theory and Methods, San Francisco.
[6] Stein S., Wysession M., 2003, An Introduction to Seismology, Earthquakes, and Earth Structure, Blackwell Publishing, Oxford.
[7] Okada Y., 1985, Surface deformation due to shear and tensile faults in a half-space, Bulletin of the Seismological Society of America 75: 1135-1154.
[8] Bonafede M., Dragoni M., Quareni F., 1986, Displacement and stress fields produced by a center of dilatation and by a pressure source in a viscoelastic half-space: application to the study of ground deformation and seismic activity at vampi flegeri, Geophysical Journal International 87: 455-485.
[9] Singh K., Singh S.J., 1989, Static and quasi-static deformation of a uniform half space by buried sources, Geophysical Journal International 27: 1-30.
[10] Roberts P.M., Phillips W.S., Fehler, M.C., 1992, Development of the active doublet method for measuring small velocity and attenuation changes in solids, Journal of the Acoustical Society of America 91: 3291.
[11] Horikawa H., 2001, Earthquake doublet in kagoshima, Japan: rupture of asperities in a stress shadow, Bulletin of the Seismological Society of America 91:112-127.
[12] Pandolfi D., Bean C.J., Saccorotti G., 2006, Coda wave interferometric detection of seismic velocity changes associated with the 1999 M = 3.6 event at Mt. vesuvius, Geophysical Research Letters 33: L06306.
[13] Wang R., Lorenzo-Martin F., Roth F., 2006, PSGRN/PSCMP- a new code for calculating co- and post-seismic deformation, geoid and gravity changes based on the viscoelastic-gravitational dislocation theory, Computer & Geosciences 32: 527-541.
[14] Lin C.H., Yeh Y.H., Ando M., 2008, Earthquake doublet sequences: evidence of static triggering in the strong convergent zones of taiwan, Terrestrial Atmospheric and Oceanic Sciences 19: 589-594.
[15] Lai K.Y., Chen Y.G., Wu Y.M., 2009, The 2005 Ilan earthquake doublet and seismic crisis in northeastern Taiwan: evidence for dyke intrusion associated with on-land propagation of the Okinawa Trough, Geophysical Journal International 179: 678-686.
[16] Kogan M.G., Vasilenko N.F., Frolov D.I., 2011, The mechanism of postseismic deformation triggered by the 2006-2007 great kurli earthquakes, Geophysical Research Letters 38: L06304.
[17] Donnera S., Ghodsb A., Krugera F., 2015, The Ahar-Varzeghan earthquake doublet (Mw 6.4 and 6.2) on 11 August 2012: Regional Seismic Moment Tensors and a Seismotectonic Interpretation, Bulletin of the Seismological Society of America 105: 791-807.
[18] Nissen E., Elliott J.R., Solan R.A., 2016, Limitations of rupture forecasting exposed by instantaneously triggered earthquake doublet, Nature Geoscience 9(4): 330-336.
[19] Verma N., and Singh K., 2020a, Deformation of two welded half-spaces caused by a centre of rotation source, Physics of the Earth and Planetary Interiors 299(106410): 1-12.
[20] Verma N., Singh K., 2020b, A comparative study of deformation field due to center of dilatation and center of rotation in a viscoelastic half-space model, Physics of the Earth and Planetary Interiors 299(106428), 1-7.
[21] Granik V.T., Ferrari M., 1993, Microstructural mechanics of granular media, Mechanics of Materials 15: 301-322.
[22] Ferrari M., Granik V.T., Imam A., Nadeau J., 1997, Advance in Doublet Mechanics, Springer.
[23] Sadd M.H., Dai Q.L., Parameswaran V., Shukla A., 2004a, Microstructural simulation of asphalt materials: modelling and experimental studies, Journal of Civil Engineering 16(2): 107-115.
[24] Mindlin R.D., Cheng D.H., 1950, Nuclei of strain in the semi-infinite solid, Journal of Applied Physics 21: 926-930.
[25] Mindlin R.D., 1936, Force at a point in the interior of a semi-infinite solid, Journal of Applied Physics 7: 195-202.
[26] Singh K., Singh S.J., 1990, Simple procedure for obtaining the quasi-static displacement, strains, and stresses in a viscoelastic half-space, Bulletin of the Seismological Society of America 80: 488-492.
