مروری بر تحلیل دینامیکی و مدل‌سازی عددی گسل‌ها با استفاده از روش اجزای مرزی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری مهندسی ژئوتکنیک، گروه مهندسی عمران، دانشگاه رازی، کرمانشاه، ایران

2 استادیار، گروه مهندسی عمران، دانشگاه رازی، کرمانشاه، ایران

3 استاد، گروه مهندسی ژئوتکنیک لرزه‌ای، پژوهشگاه بین‌المللی زلزله‌شناسی و مهندسی زلزله، تهران، ایران

چکیده

یکی از روش ­های عددی در مکانیک محیط­ های پیوسته، روش المان مرزی (BEM) است. در این روش معادلات دیفرانسیلی حاکم به معادلات انتگرالی تبدیل و روی مرز مسئله اعمال خواهند شد. سپس مرز به قطعات مرزی تقسیم می­ شود و انتگرال­گیری عددی بر روی المان­ های مرزی انجام می­ شود که از حل آن می توان به جواب یکتای مسئله رسید. روش المان مرزی را می­ توان به‌راحتی بر روی مرز­های با هندسه پیچیده به کار برد. روش المان مرزی یا معادله انتگرال مرزی (BIEM)  یکی از روش‌های مدل‌سازی عددی است که کاربرد زیادی در شبیه ­سازی عددی دینامیک گسل­ ها دارد؛ نتایج آن دید وسیعی از فیزیک گسیختگی زلزله فراهم می­ کند. در این مقاله به‌مرور مدل‌سازی عددی گسل به روش المان مرزی پرداخته شده، و مطالعات انجام شده در زمینه مدل‌سازی عددی گسل به روش المان مرزی مورد بررسی قرار گرفته­ است. در نهایت نتایج به‌دست‌آمده به این‌گونه است که روش المان مرزی برای مسائل دارای مرزهای پیچیده همانند هندسه گسل و مسائل با مرز­های بی­کران مناسب است. همچنین می ­توان با استفاده از مدل‌سازی عددی به روش المان مرزی، لغزش رخ داده روی گسل و تغییر شکل­ های سطحی را به‌خوبی پیش ­بینی کرد.

کلیدواژه‌ها


  1. Beskos, D.E. (1987) Boundary element methods in dynamic analysis. Mech. Rev., 40, 1-23.
  2. Beskos, D.E. (1997) Boundary element methods in dynamic analysis: Part II (1986-1996). Mech. Rev., 50, 149-197.
  3. Bouchon, M. and Sa´nchez-Sesma, F.J. (2007) Boundary integral equations and boundary elements methods in elastodynamics. Geophys., 48, 157-189.
  4. Zhao, S. and Chao, D. (1995) Determination of the fault slip distribution of the 1976 Tangshan earthquake by the finite element method. Journal of Geodynamics19(2), 107-115.‏
  5. Trasatti, E., Kyriakopoulos, C., and Chini, M. (2011) Finite element inversion of DInSAR data from the Mw 6.3 L'Aquila earthquake, 2009 (Italy). Geophysical Research Letters38(8).‏
  6. Zhang, W., Iwata, T. & Irikura, K. (2006) Dynamic simulation of a dipping fault using a three‐dimensional finite difference method with nonuniform grid spacing. Journal of Geophysical Research: Solid Earth111(B5).‏
  7. Coates, R.T. and Schoenberg, M. (1995) Finite-difference modeling of faults and fractures. Geophysics, 60(5), 1514-1526.
  8. Okada, Y. (1985) Surface deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America75(4), 1135-1154.‏
  9. Okada, Y. (1992) Internal deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America82(2), 1018-1040.
  10. Thomas, A.L. (1993) Poly 3D: A Three-Dimensional, Polygonal Element, Displacement Discontinuity Boundary Element Computer Program with Applications to Fractures, Faults, and Cavities in the Earth's crust. Master's Thesis, to the Department of Geology, Stanford University.‏
  11. Maerten, F., Maerten, L., and Pollard, D.D. (2014) iBem3D, a three-dimensional iterative boundary element method using angular dislocations for modeling geologic structures. Computers and Geosciences72, 1-17.
  1. Caniven, Y., Dominguez, S., Soliva, R., Peyret, M., Cattin, R., and Maerten, F. (2017) Relationships between along-fault heterogeneous normal stress and fault slip patterns during the seismic cycle: Insights from a strike-slip fault laboratory model. Earth and Planetary Science Letters480, 147-157.‏
  2. Crouch, S.L. and Starfield, A.M. (1983) Boundary Element Methods in Solid Mechanics. Unwin Hyman,
  3. Mavko, G.M. (1982) Fault interaction near Hollister, California. Journal of Geophysical Research: Solid Earth87(B9), 7807-7816.
  4. Bilham, R. and King, G. (1989) The morphology of strike‐slip faults: Examples from the San Andreas Fault, California. Journal of Geophysical Research: Solid Earth94(B8), 10204-10216.
  5. Sempere, J.C. and Macdonald, K.C. (1986) Over-lapping spreading centers: Implications from crack growth simulation by the displacement discon-tinuity method. Tectonics5(1), 151-163.
  6. Olson, J. and Pollard, D.D. (1989) Inferring paleostresses from natural fracture patterns: A new method. Geology17(4), 345-348.‏
  7. Wu, H. and Pollard, D.D. (1995) An experimental study of the relationship between joint spacing and layer thickness. Journal of Structural Geology, 17(6), 887-905.‏
  8. Olson, J.E. and Pollard, D.D. (1991) The initiation and growth of en echelon veins. Journal of Structural Geology13(5), 595-608.
  9. Panji, M., Kamalian, M., Asgari Marnani, J., and Jafari, M.K. (2013) Transient analysis of wave propagations problems by half-plane BEM. Geophysical Journal International, 194, 1849-1865.
  10. Panji, M., Kamalian, M., Asgari Marnani, J., and Jafari, M.K. (2014a) Analyzing seismic convex topographies by a half-plane time-domain BEM. Geophysical Journal International, 197(1), 591-607.
  11. Panji, M., Kamalian, M., Asgari Marnani, J., and Jafari, M.K. (2014b) Antiplane seismic response from semi-sine shaped valley above embedded truncated circular cavity: a half-plane time-domain BEM. IJCE, 12(2), 193-206.
  12. Steketee, J.A. (1958) On Volterra's dislocations in a semi-infinite elastic medium. Canadian Journal of Physics.36(2), 192-205.‏
  13. Steketee, J.A. (1958) Some geophysical applications of the elasticity theory of dislocations. Canadian Journal of Physics36(9), 1168-1198.
  14. Chinnery, M.A. (1963) The stress changes that accompany strike-slip faulting. Bulletin of the Seismological Society of America53(5), 921-932.‏
  15. Chinnery, M.A. (1961) The deformation of the ground around surface faults. Bulletin of the Seismological Society of America51(3), 355-372.‏
  16. Maruyama, T. (1964) Statical elastic dislocations in an infinite and semi-infinite medium.  Earthq. Res. Inst.42, 289-368.‏
  17. Press, F. (1965) Displacements, strains, and tilts at teleseismic distances. Journal of Geophysical Research, 70(10), 2395-2412.‏
  18. Savage, J.C. and Hastie, L.M. (1966) Surface defor-mation associated with dip‐slip faulting. Journal of Geophysical Research71(20), 4897-4904.‏
  19. Savage, J.C. and Hastie, L.M. (1969) A dislocation model for the Fairview Peak, Nevada, earthquake. Bulletin of the Seismological Society of America, 59(5), 1937-1948.‏
  20. Smylie, L. and Mansinha, D.E. (1971) The Dis-placement Fields of Inclined Faults. Bulletin of the Seismological society of America61, 1433-1440.‏
  21. Davis, P.M. (1983) Surface deformation associated with a dipping hydrofracture. Journal of Geophysical Research: Solid Earth88(B7), 5826-5834.‏
  22. Ma, X.Q. and Kusznir, N.J. (1993) Modelling of near-field subsurface displacements for generalized faults and fault arrays. Journal of Structural Geology15(12), 1471-1484.‏
  23. Burgers, J. (1939) Internal strains in solids.  Acad. Science42, 293.‏
  24. Yoffe, E.H. (1960) The angular dislocation. Philo-sophical Magazine,5(50), 161-175.‏
  25. Eshelby, J.D., Bilby, B.A., Miller, K.J., and Willis, R. (Eds.) (1985) Fundamentals of Deformation and Fracture: Eshelby Memorial Symposium Sheffield 2-5 April 1984. Cambridge University Press.
  26. Barnett, D.M. (1985) The displacement field of a triangular dislocation loop. Philosophical Magazine,51(3), 383-387.
  27. Comninou, M. and Dundurs, J. (1975) The angular dislocation in a half space. Journal of Elasticity 5(3-4), 203-216.‏
  28. Aki, K. and Richards, P.G. (2002) Quantitative Seismology. 2nd Edition, University Science Books, Sausalito.
  29. Ida, Y. (1972) Cohesive force across the tip of a longitudinal-shear crack and Griffith’s specific surface energy. Geophys. Res., 77, 3796-3805.
  30. Jeyakumaran, M., Rudnicki, J.W., and Keer, L.M. (1992) Modeling slip zones with triangular dislocation elements. Bulletin of the Seismological Society of America82(5), 2153-2169.‏‏
  31. Price, E.J. and Bürgmann, R. (2002) Interactions between the Landers and Hector Mine, California, earthquakes from space geodesy, boundary element modeling, and time-dependent friction. Bulletin of the Seismological Society of America92(4), 1450-1469.‏
  32. Muller, J.R., Aydin, A., and Maerten, F. (2003) Investigating the transition between the 1967 Mudurnu Valley and 1999 Izmit earthquakes along the North Anatolian fault with static stress changes. Geophysical Journal International, 154(2), 471-482.‏
  33. Muller, J.R. and Aydin, A. (2004) Rupture progression along discontinuous oblique fault sets: implications for the Karadere rupture segment of the 1999 Izmit earthquake, and future rupture in the Sea of Marmara. Tectonophysics, 391(1-4), 283-302.‏
  34. Muller, J.R., Aydin, A., and Wright, T.J. (2006) Using an elastic dislocation model to investigate static Coulomb stress change scenarios for earthquake ruptures in the eastern Marmara Sea region, Turkey. Geological Society, London, Special Publications, 253(1), 397-414.‏
  35. Fielding, E.J., Wright, T.J., Muller, J., Parsons, B.E., and Walker, R. (2004) Aseismic deformation of a fold-and-thrust belt imaged by synthetic aperture radar interferometry near Shahdad, southeast Iran. Geology32(7), 577-580.‏
  36. Lovely, P.J., Pollard, D.D., and Mutlu, O. (2009) Regions of reduced static stress drop near fault tips for large strike-slip earthquakes. Bulletin of the Seismological Society of America99(3), 1691-1704.‏
  37. Fielding, E.J., Lundgren, P.R., Bürgmann, R., and Funning, G.J. (2009) Shallow fault-zone dilatancy recovery after the 2003 Bam earthquake in Iran. Nature458(7234), 64-68.‏
  38. Rigo, A., De Chabalier, J.B., Meyer, B., and Armijo, R. (2004) The 1995 Kozani-Grevena (northern Greece) earthquake revisited: an im-proved faulting model from synthetic aperture radar Geophysical Journal International, 157(2), 727-736.‏
  39. Muller, J.R. and Aydin, A. (2005) Using mechanical modeling to constrain fault geometries proposed for the northern Marmara Sea. Journal of Geophysical Research: Solid Earth110(B3).‏
  40. Akoglu, A.M., Cakir, Z., Meghraoui, M., Belabbes, S., El Alami, S.O., Ergintav, S., and Akyüz, H.S. (2006) The 1994–2004 Al Hoceima (Morocco) earthquake sequence: Conjugate fault ruptures deduced from InSAR. Earth and Planetary Science Letters252(3-4), 467-480.‏
  41. Marshall, S.T., Cooke, M.L., Owen, S.E. (2008) Effects of nonplanar fault topology and mechanical interaction on fault-slip distributions in the Ventura Basin, California. Bulletin of the Seismological Society of America98(3), 1113-1127.‏
  42. Dair, L. and Cooke, M.L. (2009) San Andreas fault geometry through the San Gorgonio Pass, California. Geology37(2), 119-122.‏
  43. Bürgmann, R., Schmidt, D., Nadeau, R.M., d'Alessio, M., Fielding, E., Manaker, D., and Murray, M.H. (2000) Earthquake potential along the northern Hayward fault, California. Science, 289(5482), 1178-1182.‏
  44. Schmidt, D.A., Bürgmann, R., Nadeau, R.M., and d'Alessio, M. (2005) Distribution of aseismic slip rate on the Hayward fault inferred from seismic and geodetic data. Journal of Geophysical Research: Solid Earth110(B8).‏
  45. Kreemer, C., Blewitt, G., and Maerten, F. (2006) Co‐and postseismic deformation of the 28 March 2005 Nias Mw 8.7 earthquake from continuous GPS data. Geophysical Research Letters33(7).
  46. Zhang, L., Wu, J.C., Ge, L.L., Ding, X.L., and Chen, Y.L. (2008) Determining fault slip distri-bution of the Chi-Chi Taiwan earthquake with GPS and InSAR data using triangular dislocation Journal of Geodynamics, 45(4-5), 163-168.‏
  47. Cheng, L.W., Lee, J.C., Hu, J.C., and Chen, H.Y. (2009) Coseismic and postseismic slip distribution of the 2003 Mw = 6.5 Chengkung earthquake in eastern Taiwan: Elastic modeling from inversion of GPS data. Tectonophysics466(3-4), 335-343.‏
  48. Willemse, E.J. and Pollard, D.D. (2000) 'Normal fault growth: evolution of tipline shapes and slip distribution'. In: Aspects of Tectonic Faulting, Springer, Berlin, Heidelberg, 193-226.
  49. Willemse, E.J., Pollard, D.D., and Aydin, A. (1996) Three-dimensional analyses of slip distributions on normal fault arrays with consequences for fault scaling. Journal of Structural Geology, 18(2-3), 295-309.‏‏
  50. Willemse, E.J. (1997) Segmented normal faults: Correspondence between three‐dimensional mecha-nical models and field data. Journal of Geophysical Research: Solid Earth102(B1), 675-692.‏
  51. Crider, J.G. (2001) Oblique slip and the geometry of normal-fault linkage: mechanics and a case study from the Basin and Range in Oregon. Journal of Structural Geology23(12), 1997-2009.‏
  52. Maerten, L., Willemse, E.J., Pollard, D.D., and Rawnsley, K. (1999) Slip distributions on inter-secting normal faults. Journal of Structural Geology, 21(3), 259-272.‏
  53. Maerten, L. (1999) Mechanical Interaction of Intersecting Normal Faults: Theory, Field Examples and Applications. Ph.D. Thesis, Stanford University, Stanford, CA.
  54. Martel, S.J. and Boger, W.A. (1998) Geometry and mechanics of secondary fracturing around small three‐dimensional faults in granitic rock. Journal of Geophysical Research: Solid Earth, 103(B9), 21299-21314.‏
  55. Kattenhorn, S.A., Aydin, A., and Pollard, D.D. (2000) Joints at high angles to normal fault strike: an explanation using 3-D numerical models of fault-perturbed stress fields. Journal of Structural Geology22(1), 1-23.‏
  56. Bourne, S.J. and Willemse, E.J. (2001) Elastic stress control on the pattern of tensile fracturing around a small fault network at Nash Point, UK. Journal of Structural Geology23(11), 1753-1770.‏
  57. Soliva, R., Maerten, F., Petit, J.P., and Auzias, V. (2010) Field evidences for the role of static friction on fracture orientation in extensional relays along strike-slip faults: comparison with photoelasticity and 3-D numerical modeling. Journal of Structural Geology32(11), 1721-1731.‏
  58. Bai, T., Maerten, L., Gross, M.R., and Aydin, A. (2002) Orthogonal cross joints: do they imply a regional stress rotation? Journal of Structural Geology24(1), 77-88.‏
  59. Crider, J.G. and Pollard, D.D. (1998) Fault linkage: Three‐dimensional mechanical interaction between echelon normal faults. Journal of Geophysical Research: Solid Earth103(B10), 24373-24391.
  60. Soliva, R., Benedicto, A., and Maerten, L. (2006) Spacing and linkage of confined normal faults: importance of mechanical thickness. Journal of Geophysical Research: Solid Earth, 111(B1).‏
  61. Savage, H.M. and Cooke, M.L. (2003) Can flat-ramp-flat fault geometry be inferred from fold shape?: A comparison of kinematic and mechanical folds. Journal of Structural Geology25(12), 2023-2034.‏
  62. Bellahsen, N., Fiore, P.E., and Pollard, D.D. (2006) From spatial variation of fracture patterns to fold kinematics: A geomechanical approach. Geophy-sical Research Letters33(2).‏
  63. White, I.R. and Crider, J.G. (2006) Extensional fault-propagation folds: Mechanical models and observations from the Modoc Plateau, northeastern California. Journal of Structural Geology, 28(7), 1352-1370.‏
  64. Allward-Fiore, P. (2006) 3D Characterization and Mechanics of Brittle Deformation in Thrust Fault Related Folds. D. Thesis, Stanford University, CA, USA.‏
  65. Mynatt, I., Hilley, G.E., and Pollard, D.D. (2007) Inferring fault characteristics using fold geometry constrained by Airborne Laser Swath Mapping at Raplee Ridge, Utah. Geophysical Research Letters, 34(16).‏
  66. Shackleton, J.R. and Cooke, M.L. (2007) Is plane strain a valid assumption in non-cylindrical fault-cored folds? Journal of Structural Geology29(7), 1229-1240.‏
  67. Hilley, G.E., Mynatt, I., and Pollard, D.D. (2010) Structural geometry of raplee ridge monocline and thrust fault imaged using inverse boundary element modeling and ALSM data. Journal of Structural Geology32(1), 45-58.‏
  68. Griffith, W.A. and Cooke, M.L. (2004) Mechanical validation of the three-dimensional intersection geometry between the Puente Hills blind-thrust system and the Whittier fault, Los Angeles, California. Bulletin of the Seismological Society of America94(2), 493-505.‏
  69. Olson, E.L. and Cooke, M.L. (2005) Application of three fault growth criteria to the Puente Hills thrust system, Los Angeles, California, USA. Journal of Structural Geology27(10), 1765-1777.‏
  70. Brankman, C.M. and Aydin, A. (2004) Uplift and contractional deformation along a segmented strike-slip fault system: the Gargano Promontory, southern Journal of Structural Geology, 26(5), 807-824.‏
  71. Resor, P.G. (2003) Deformation Associated with Continental Normal Faults. Doctoral dissertation, Stanford University.‏
  72. Grant, J.V. and Kattenhorn, S.A. (2004) Evolution of vertical faults at an extensional plate boundary, southwest Iceland. Journal of Structural Geology, 26(3), 537-557.‏
  73. Soliva, R., Benedicto, A., Schultz, R.A., Maerten, L., and Micarelli, L. (2008) Displacement and interaction of normal fault segments branched at depth: Implications for fault growth and potential earthquake rupture size. Journal of Structural Geology30(10), 1288-1299.‏
  74. Meigs, A.J., Cooke, M.L., and Marshall, S.T. (2008) Using vertical rock uplift patterns to constrain the three-dimensional fault configuration in the Los Angeles Basin. Bulletin of the Seismological Society of America98(1), 106-123.‏
  75. Maerten, F., Resor, P., Pollard, D., and Maerten, L. (2005) Inverting for slip on three-dimensional fault surfaces using angular dislocations. Bulletin of the Seismological Society of America, 95(5), 1654-1665.‏
  76. Johnson, K.M. and Segall, P. (2004) Imaging the ramp–décollement geometry of the Chelungpu fault using coseismic GPS displacements from the 1999 Chi-Chi, Taiwan earthquake. Tectonophysics, 378(1-2), 123-139.
  77. ‏Tselentis, G.A. and Gkika, F. (2005) Boundary element slope instability modeling of Corinth Canal, Greece due to nearby fault activation. WIT Transactions on the Built Environment, 78.
  78. Maerten, L., Gillespie, P., and Pollard, D.D. (2002) Effects of local stress perturbation on secondary fault development. Journal of Structural Geology, 24(1), 145-153.
  79. Childs, C., Watterson, J., and Walsh, J.J. (1995) Fault overlap zones within developing normal fault systems. Journal of the Geological Society152(3), 535-549.