Stress and Strain Accumulation Due to a Long Dip-Slip Fault Movement in an Elastic-Layer over a Viscoelastic Half Space Model of the Lithosphere-Asthenosphere System

Abstract

Most of the earthquake faults in North-East India, China, mid Atlantic-ridge, the Pacific seismic belt and Japan are found to be predominantly dip-slip in nature. In the present paper a dip-slip fault is taken situated in an elastic layer over a viscoelastic half space representing the lithosphere-asthenosphere system. A movement of the dip-slip nature across the fault occurs when the accumulated stress due to various tectonic reasons e.g. mantle convection etc., exceeds the local friction and cohesive forces across the fault. The movement is assumed to be slipping in nature, expressions for displacements, stresses and strains are obtained by solving associated boundary value problem with the help of integral transformation and Green’s function method and a suitable numerical methods is used for computation. A detailed study of these expressions may give some ideas about the nature of stress accumulation in the system, which in turn will be helpful in formulating an earthquake prediction programme.

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S. Sen and S. Debnath, "Stress and Strain Accumulation Due to a Long Dip-Slip Fault Movement in an Elastic-Layer over a Viscoelastic Half Space Model of the Lithosphere-Asthenosphere System," International Journal of Geosciences, Vol. 4 No. 3, 2013, pp. 549-557. doi: 10.4236/ijg.2013.43050.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] T. Maruyama, “Statical Elastic Dislocations in an Infinite and Semi-Infinite Medium,” Bull Earthquake Research Institute, Tokyo University, Tokyo, 1964.
[2] T. Maruyama, “On Two Dimensional Dislocations in an Infinite and Semi-Infinite Medium,” Bull Earthquake Research Institute, Tokyo University, Tokyo, 1966.
[3] J. C. Savage and L. M. Hastie, “Surface Deformation Associated with Dip Slip Faulting,” 1966.
[4] K. Rybicki, “The Elastic Residual Field of a Very Long Strike Slip Fault in the Presence of a Discontinuity,” Bulletin of the Seismological Society of America, Vol. 61, 1971, pp. 79-92.
[5] L. Mansinha and D. E. Smyllie, “The Displacement Fields of Inclined Faults,” Bulletin of the Seismological Society of America, Vol. 61, No. 5, 1971, pp. 1433-1440.
[6] R. Sato, “Stress Drop of Finite Fault,” Journal of Physics of the Earth, Vol. 20, 1972, pp. 397-407.
[7] S. J. Singh and M. Rosenman, “Quasi Static Deformation of a Viscoelastic Half-Space by a Displacement Dislocation,” Physics of the Earth and Planetary Interiors, Vol. 8, 1974, pp. 87-101.
[8] A. Nur and G. Mavko, “Post-Seismic Viscoelastic Rebound,” Science, Vol. 183, 1974, pp. 204-206.
[9] R. Sato and T. Yamashita, “Static Deformations in an Obliquely Layered Medium Part-II Dip-Slip Fault,” Journal of Physics of the Earth, Vol. 23, 1975, pp. 113-125.
[10] L. B. Freund and D. M. Barnett, “A Two-Dimensional Analysis of Surface Deformation Due to Dip-Slip Faulting,” Bulletin of Seismological Society of America, Vol. 66, No. 3, pp. 667-675.
[11] J. B. Rundle, “Viscoelastic Crustal Deformation by Finite Quasi-Static Sources,” Journal of the Geophysical Research, Vol. 83, No. B12, 1978, pp. 5937-5945.
[12] A. Mukhopadhyay, et al., “On Stress Accumulation near Finite Rectangular Fault,” Indian Journal of Meteorology, Hydrology and Geophysics (Mausam), Vol. 30, 1979, pp. 347-352.
[13] A. Mukhopadhyay, et al., “On Stress Accumulation and Fault Slip in Lithosphere,” Indian Journal of Meteorology, Hydrology and Geophysics (Mausam), Vol. 30, 1979, pp. 353-358.
[14] T. Iwasaki and R. Sato, “Strain Field in a Semi-Infinite Medium Due to an Inclined Rectangular Fault,” Journal of Physics of the Earth, Vol. 27, 1979, pp. 285-314.
[15] Cohen, “Post Seismic Viscoelastic Surface Deformations and Stress 1, Theoretical Considerations, Displacements and Strains Calculations,” Journal of Geophysical Research, Vol. 85, No. B6, 1980, pp. 3131-3150.
[16] S. Rani and S. J. Singh, “Static Deformation of a Uniform Half Space Due to a Long Dip-Slip Fault,” Geophysical Journal International, Vol. 109, 1992, pp. 469-476.
[17] U. Ghosh, A. Mukhopadhyay and S. Sen, “On Two Interacting Creeping Vertical Surface-Breaking Strike-Slip Faults in a Two-Layered Model of Lithosphere,” Physics of the Earth and Planetary Interior, Vol. 70, 1992, pp. 119-129.
[18] J. W. Rudnicki and M. Wu, “Mechanics of Dip-Slip Faulting in an Elastic Half-Space,” Journal of the Geophysical Research, Vol. 100, No. B11, 1995, pp. 22,173-22,186.
[19] Y. Ting-To, J. B. Rundle and J. Fernandez, “Deformation Produced by a Rectangular Dipping Fault in a Viscoelastic Gravitational Layered Earth Model Part-II: Strike-Slip Fault-Strategy and Strength, Fortran Programs,” Computers and Geosciences, Vol. 22, No. 7, 1996, pp. 751-764.
[20] S. J. Singh, M. Punia and G. Kumari, “Deformation of a Layered Half-Space Due to a Very Long Dip-Slip Fault,” Proceedings of Indian National Science Academy, Vol. 63A, No. 3, 1997, pp. 225-240.
[21] J. C. Savage, “Displacement Field for an Edge Dislocation in Layered Half Space,” Journal of Geophysical Research, Vol. 103, No. B2, 1998, pp. 2439-2446.
[22] S. K. Tomar and Dhiman, “2D-Deformation Analysis of a Half-Space Due to a Very Long Dip-Slip Fault at Finite Depth,” Indian Academy Science (Earth Planet, Science), Vol. 112, No. 4, 2003, pp. 587-596.
[23] D. D. Oglesby, “The Dynamics of Strike-Slip Step Overs with Linking Dip-Slip Faults,” Bulletin of Seismological Society of America, Vol. 95, No. 5, 2005, pp. 1604-1622.
[24] C. Zhang, D. D. Oglesby and G. Xu, “Earthquake Nucleation on Dip-Slip Faults with Depth-Dependent Frictional Properties,” Journal of Geophysical Research, Vol. 111, No. 10, 2006, Article ID: B07303.
[25] M. Matsu’ura and R. Sato, “Static Deformation Due to Fault Spreading over Several Layers in Multi-Layered Medium Part-II-Strain and Tilt,” Journal of the Physics of the Earth, Vol. 23, No. 1, 1975, pp. 12-33.
[26] A. Mukhopadhyay, S. Sen and B. P. Paul, “On Stress Accumulation in a Viscoelastic Lithosphere Containing a Continuously Slipping Fault,” Bulletin Society of Earthquake Technology, Vol. 17, No. 1, 1980, pp. 1-10.
[27] A. Mukhopadhyay, S. Sen and B. P. Paul, “On Stress Accumulation near a Continuously Slipping Fault in a Two Layered Model of Lithosphere,” Bulletin Society of Earthquake Technology, Vol. 17, No. 4, 1980, pp. 29-38.
[28] M. Matsu’ura and R. Sato, “Static Deformation Due to Fault Spreading over Several Layers in Multi-Layered Medium Part-II-Strain and Tilt,” Journal of the Physics of the Earth, Vol. 23, No. 1, 1975, pp. 12-33.
[29] D. A. Spence and D. L. Turcotte, “An Elastostatic Deformation of a Uniform Half Space Due to a Long Dip-Slip Fault,” Geophysical Journal International, Vol. 109, 1976, pp. 469-476.
[30] S. Sen, S. Sarker and A. Mukhopadhyay, “A Creeping and Surface Breaking Long Strike-Slip Fault Inclined to the Vertical in a Viscoelastic Half-Space,” Mausam, Vol. 44, 1993, pp. 4365-4372.
[31] P. Segal, “Earthquake and Volcano Deformation,” Princeton University Press, Princeton, 2010.
[32] U. Ghosh and S. Sen, “Stress Accumulation near Buried Fault in Lithosphere-Asthenosphere System,” International Journal of Computing, Vol. 1, No. 4, 2011, pp. 786-795.
[33] S. G. Fuis, D. Scheirers, E. V. Langenheim, D. M. KohLer, “A New Perspective on the Geometry of the San Andreas Fault of South California and Relationship to Lithospheric Structure,” Bulletin of Seismological Society of America, Vol. 102, 2012, pp. 236-1251.
[34] P. Chift, J. Lin and U. Barcktiausen, “Marine and Petroleum Geology,” Vol. 19, 2002, pp. 951-970.
[35] S.-I. Karato, “Rheology of the Earth’s Mantle: A Historical Review Gondwana Research,” Vol. 18, No. 1, 2010, pp. 17-45.
[36] S. Sen and S. K. Debnath, “A Creeping Vertical Strike-Slip Fault of Finite Length in a Viscoelastic Half-Space Model of the Lithosphere,” International Journal of Computting, Vol. 2, No. 3, 2012, pp. 687-697.
[37] S. Sen and S. K. Debnath, “Long Dip-Slip Fault in a Viscoelastic Half-Space Model of the Lithosphere,” American Journal of Computational and Applied Mathematics, Vol. 2, No. 6, 2012, pp. 249-256.
[38] K. Aki and P. G. Richards, “Quantitative Seismology: Theory and Methods,” W. H. Freeman, San Francisco, 1980.

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