تعیین میدان لغزش گسل‌های امتداد لغز به کمک روش‌های حل وارون

نویسندگان

دانشگاه تربیت مدرس

چکیده

در تحقیق حاضر، یک روش تئوری پیشنهاد میشود که در آن، با استفاده از روش گره مشترک که مبتنی بر روش عددی المان محدود است، مدلهای دو بعدی و سه بعدی از چند نوع گسل برای در نظر گرفتن ناپیوستگی و پیدا کردن میدان لغزش گسل‌ها ارائه شده است. روند حل مساله تا رسیدن به میدان لغزش گسل، شامل دو بخش حل مستقیم و حل معکوس می‌باشد. در حل مستقیم، با اعمال لغزش‌های یکنواخت معلوم در گسل، جابجایی‌های سطح زمین بدست آمده و صحت آن‌ها با نتایج تحلیلی مقایسه شده است. در بخش حل معکوس، با استفاده از روش گره مشترک، ماتریس‌های اپراتور گرین بدست آمده‌اند. برای منظور کردن ناپیوستگیها با این روش، فقط بردار بارگذاری اصلاح میشود و هیچ افزایشی در تعداد درجات آزادی اعمال نمیشود، و بنابراین ماتریس سختی کل سیستم بدون تغییر میماند. درنهایت، برای پیدا کردن رژیم لغزش گسل و تعیین ناحیه قفل‌شده، بعد از رفع تکینگی ماتریس‌های اپراتور گرین، حل معکوس بدست می آید. صحت سنجی‌ مدل‌های حل معکوس نیز نتایج قابل قبولی را نشان می‌دهند، که حاکی از تعیین ناحیه قفل‌شده گسلها با دقت قابل‌قبول هستند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Determination of slippage field of strike-slip faults using inverse solution methods

چکیده [English]

In this paper, a theoretical approach is proposed, in which spatial distribution of the strength of interplate coupling between two faces of strike-slip faults is investigated in detail through the inverse analysis of synthesized geodetic data. Synthesized (or available) geodetic data representing free surface movements is implemented to determine the solution of undertaken inverse problem that computes slippage vectors’ rates. Analytical approaches for treatment of faults in crustal deformation analysis involve some limitations. One important limitation of these methods is idealization of uniform dislocation on a rectangular fault plane in a uniform medium or half space. In fact, the real source is more complex than that supposed in these models and thus only the first-order aspects of the source characteristics can be evaluated from a uniform dislocation model. Isotropic and homogeneous material properties are the main assumptions of these methods. The Finite Element Method (FEM) on the other hand, allows easy treatment of complex boundary shape (interface zone) and internal variations of material properties. The FEM can simulate source geometry flexibly, and is also able to regard geological regimes and various layered structures. The standard equations of inverse problems offer a straightforward way for finding slippage vectors at two faces of the considered fault. One of the new aspects of the current study is evaluation of Green’s Operator Matrix (GOM) by means of FEM. This concept enables us to overcome all limitations of traditional inverse methods. In other words, the Green’s functions are not only functions of interface’s geometry, but are also functions of some other parameters like far-field boundary conditions, and geological structures (various material properties) which are not regarded in the traditional analytical inversion analysis. To implement fault sliding in a continuum-based FEM program, Split Node Technique (SNT) as a simple and efficient method is applied. This method does not increase the number of Degree Of Freedom (DOF) and the global stiffness matrix of system remains unchanged, which is the major advantage of this method. Furthermore, no net forces or moments are induced on the finite element mesh. This method is a direct approach and does not need any iteration, which is a common feature of other methods (e.g., contact problem techniques, or interface/joint elements). The initial idea of SNT for simple one-dimensional element is developed to 2D and 3D domains in the present research. How to find the Green’s functions by the FEM? By applying unit slippage vectors in each DOF of the interface nodes, we can determine corresponding component of the GOM. As other common inversion problems, singularity of coefficient matrix is the main problem. This problem particularly emerges if the number of DOFs is too large. The numerical procedure does not fail algorithmically, however it returns a set of slippage vectors that are wrong, even though direct substitution back into the original equations results in acceptable free-surface deformations. Singular Value Decomposition (SVD) diagnoses precisely what the problem is. In some cases, SVD will not only diagnose the problem, it will also solve it. The approach in current research is based on kinematic modeling of seismological problem. In other words, we only investigate fault movement, not causes of the occurred movement. In this research, both forward and inverse steps are considered to completely solve the problem. The forward step is performed by applying the slip along the fault’s faces and determining the displacement at the ground surface. This step is done using the FEM, whose results are compared with the analytical ones to verify the forward step. In the inverse solution on the other hand, our goal is to reach fault slip field using of surface displacement obtained from the first step as input data. Here, using this technique, 2D and 3D models of different types of strike-slip faults are presented in elastic mode for splitting purposes. The final step is to verify the inverse solution obtained for all models, from which the coupled zones of the considered faults are determined with acceptable accuracies.

کلیدواژه‌ها [English]

  • Fault
  • Discontinuity
  • Finite Element Method
  • Split node technique
  • Green’s operator
  • Coupled zone
بحرانی، ا. ح. و خاجی، ن.، 1389، ماتریس عملگرهای تابع گرین گسل‌های درون صفحه‌ای، م. فیزیک زمین و فضا، 36(1)، 69-59.
خاجی، ن.، 1383،کاربرد روش گره مشترک برای مدل‌سازی ناپیوستگیها در محیط پیوسته، م. فنی و مهندسی مدرس، دوره 15، بهار، 37-49.
خاجی، ن. و هیگاشیهارا، ه.، 1384، دیدگاهی نوین در مدل‌سازی عددی تغییرشکل‌های پوسته زمین، قسمت اول: نظریه، م. فنی و مهندسی مدرس، 19، بهار، 30-13.
 
Chinnery, M. A., 1961, The deformation of the ground around surface faults, Bulletin of the Seismological Society of America, 51, 355-372.
Eterovic, A. L. and Bathe, K. J., 1991, On the treatment of inequality constraints arising from contact condition in finite element analysis, Computers and Structures, 40, 203-209.
Farahani, A., Wijeyewickrema, A. C. and Ohmachi, T., 2006, Effects of soft soil deformations on buried structures due to fault dislocation, Center for Urban Earthquake Engineering (CUEE), Tokyo, 1-6.
Freund, L. B. and 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.
Goodman, R. E., Taylor, R. L. and Brekke, T. L., 1968, A model for the mechanics of jointed rock, Journal of Soil Mechanics and Foundations Division ASCE, 99, 637-659.
Hamidi, M. and Khaji, N., 2011, Accurate boundary conditions for finite element modeling of movyement field within Iran tectonic plate, Proceedings of the 6th International Conference on Seismology and Earthquake Engineering, SEE6, Tehran, Iran.
Hasan, W. M. and Voila, E., 1997, Use of the singular value decomposition method to detect ill-conditioning of structural identification problems, Computers and Structures, 63, 267-275.
Hermann, L. R., 1978, Finite element analysis of contact problems, Journal of Engineering

Mechanics Division ASCE., 104, 1043-1059.
Khanmirza, E., Khaji, N. and Majd, V. J., 2011, Model updating of multistory shear buildings for simultaneous identification of mass, stiffness and damping matrices using two different soft-computing methods, Expert Systems with Applications, 38, 5320-5329.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., 1992, Numerical recipe in Fortran 77, The Art of Scientific Computing,  Edition, Cambridge University Press.
Tomar, S. K. and Dhiman, N. K., 2003, 2-D Deformation analysis of a half space due to a long dip-slip fault at finite depth, Proceedings of the Indian Academy of Sciences, Earth and Planetary Sciences, 112. 587-596.
Rani, S. and Bala, N., 2006, 2-D deformation of two welded half-spaces due to a blind dip-slip fault, Journal of Earth System Science, 115, 277-287.
Rani, S. and Bala, N., 2013, Deformation of a two-phase medium due to a long buried strike-slip fault, Natural Science, 5, 1078-1083.
Poulios, K., and Renard, Y., 2015, An unconstrained integral approximation of large sliding frictional contact between deformable solids, Computers and Structures, 153, 75-90.
Zhao, G.-F., 2015, Modelling 3D jointed rock masses using a lattice spring model, International Journal of Rock Mechanics and Mining Sciences, 78, 79-90.
Wang, D. Y., Zhang, Z. N., Zheng, H. and Ge, X. R., 2013, Propagation of interactive parallel flat elliptical cracks inclined to shear stress, Theoretical and Applied Fracture Mechanics, 63-64, 18-31.