A Numerical Approach for Solution of Aseismic Ground Deformation Problems

Subhash Chandra Mondal^1, , Sanjay Sen² and Suma Debsarma²

¹Department of Mathematics, Umeschandra College, FC-129, Sector-III, Salt Lake, Kolkata-7000106, India

²Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata-700009, India

Cite this paper:
Subhash Chandra Mondal, Sanjay Sen and Suma Debsarma. A Numerical Approach for Solution of Aseismic Ground Deformation Problems. Journal of Geosciences and Geomatics. 2018; 6(1):27-34. doi: 10.12691/jgg-6-1-4

Abstract

Numerical techniques based on the finite difference scheme with discontinuity have been developed for problems associated with aseismic ground deformation in seismically active regions. We stress upon the applicability of such numerical techniques in solving problems in geodynamics. A long strike-slip fault is considered in a viscoelastic half space representing the lithosphere-asthenosphere system. The fault undergoes a sudden movement under the action of tectonic forces induced by mantle convection. The resulting boundary value problems have been solved with the help of numerical technique, based on a finite difference scheme with appropriate boundary conditions, developed for the purpose. The numerical techniques developed here can be modified for more general deformation problems where analytical methods become very complicated.

Keywords:
elliptic boundary value problem finite difference scheme with discontinuity aseismic ground deformation strike slip fault linearly viscoelastic medium

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References:

[1]	Debnath, P., Sen, S., “Creeping Movement across a Long Strike- Slip Fault in a Half Space of Linear Viscoelastic Material Representing the Lithosphere-Asthenosphere System”, Frontiers in Science 2014, 4(2): 21-28.
[2]	Debnath, P., Sen, S., “A Vertical Creeping Strike Slip Fault in a Viscoelastic Half Space under the Action of Tectonic Forces Varying with Time”, IOSR Journal of Mathematics (IOSR-JM), e-ISSN:2278-5728, p-ISSN:2319-765X. Volume 11, Issue 3 Ver. I (May-Jun, 2015), pp 105-114.
[3]	Ghosh, U., Mukhopadhyay, A., Sen, S. (1992), “On two interacting creeping vertical surface-breaking strike-slip fault in a two-layered model of the lithosphere”, Physics of the Earth and Planetary Interiors, 70, pp. 119-129 .
[4]	Mukhopadhyay, A. et.al. (1979a), “On stress accumulating near finite fault”. Indian journal of meteorology, Hydrology and Geophysics. (Mousam), Vol. 30, pp. 347-352. (with B.B. Pal and S. Sen).
[5]	Mukhopadhyay, A. et.al. (1979b), “On stress accumulating and fault slip in the lithosphere”. Indian journal of meteorology, Hydrology and Geophysics. (Mousam ), Vol. 30, pp. 353-358.
[6]	Segall, P., Earthquake and Volcano Deformation, Princeton University Press, Princeton and Oxford, 1954.
[7]	Jain, M. K., Iyengar, S. R. K., Jain, R. K. , Computational methods for Partial Differential Equation, Wiley Eastern Limited, 4835/24, Ansari Road, Daryaganj, New Delhi- 110002, 1994.
[8]	Ghods, A.,Mir, M., “Analysis of rectangular thin plates by using finite difference method”, Journal of Novel Applied Sciences, 2014JNAS Journal-2014-3-3/260-267.
[9]	Shashkov, M., Conservative Finite-Difference Methods on General Grids, CRC Press, Inc., 1996.
[10]	Catlhes III, L.M., The viscoelasticity of the Earths mantle, Princeton University Press, Princeton, N.J, 1975.15
[11]	Chandru, M. et. al. (2017), “A Numerical Method for Solving Boundary and Interior Layers Dominated Parabolic Problem with Discontinuous Convection coefficient and Source Terms”, Differential Equations and Dynamical System, pp 1-22,
[12]	Chift, P., Lin, J., Barcktiausen, U., “Evidence of low flexural rigidity and low viscosity lower continental crust during continental break-up in the South China Sea”, Marine and Petroleum Geology: 19, 951-970, 2002.
[13]	Das, P., “A higher order difference method for singularly perturbed parabolic partial differential equation”, Journal of Difference Equation and Applications, Vol- 24, 2018-Issue 3, Page 452-477.
[14]	I. Farago, Cs. Gaspar, Numerical methods to the solution of partial differential equations with hydrodynamic applications, Technical University, Budapest, 1983. [study material, not published].
[15]	Karato. S.I. (July, 2010), “Rheology of the Earths mantle”, A historical review of Gondwana Research, vol-18, issue-1, pp. 17-45.
[16]	Mao, D., “A treatment of Discontinuities in Shock-Capturing Finite Difference Methods”, Journal of Computational Physics 92, 3422-445 (1991).
[17]	Mao, D., “A treatment of Discontinuities for Finite Difference Methods”, Journal of Computational Physics 103, 359-369 (1992).
[18]	Maruyama, T. (1966). “On two dimensional dislocation in an infinite and semi-infinite medium”. Bull. Earthquake Res. Inst., Tokyo Univ., 44, part 3, pp. 811-871.
[19]	Rybicki, K. (1971), “The elastic residual field of a very long strike-slip fault in the presence of a discontinuity”. Bull. Seis. Soc. Am., 61, 79-92.