Method of fault modelling
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1. The document discusses different methods of modeling fault geometry and slip, including analytical Green's function methods, dislocation theory, and forward and inverse modeling approaches. 2. It also describes the Coulomb software which models fault slip using inputs of fault length, width, dip angle, strike slip, and dip slip. 3. Finite element and boundary element methods are presented for relating observed displacement data to fault source parameters through systems of equations involving the fault geometry Green's function.
Method of fault modelling
- 1. Method of Modelling Kutubuddin ANSARI kutubuddin.ansari@ikc.edu.tr GNSS Surveying, GE 205 Lecture 12, May 22, 2015
- 2. The Geometry of the fault having parameters (length, width, depth, dip angle) can be given by analytically by Green function (G): 2 2 1 1 AL AW AL AW G d dη ξ= ∫ ∫ (Okada, 1985 &1992) Length Width DIP Slip Length(AL) Width(AW) Length Width cos sin x AL y d AW ξ η δ δ = − = + − (δ) Dislocation Theory
- 3. (P. Cervelli et. al 2001) S is Slip For Oblique Slip S= s.cosα + s.sinα d= sG(m) Relationship between dislocation field (d) and the fault geometry G(m)
- 4. Since the ruptured area is not a perfect finite rectangular and it contains error the Cervelli equation becomes Forward Modelling Approach d= sG(m)+ d-sG(m) 0 ˆ ˆ ˆd= sG(m) if ε ε ε = → where m=initial model parameter ˆ mod ˆ mod ˆ mod s slip error S Net slip d elled dislocaton field s el slip m el parameter rake of the netslip on the fault plane ε α = = = = = = =For Oblique Slip S= s.cosα + s.sinα
- 5. Coulomb Software Coulomb software is based on the Boundary Element Method (BEM). The inputs given to Coulomb are estimates of length, width, dip angle, strike slip and dip slip of the modelled fault plane as well as the co-ordinates of the trace of the fault plane. (Toda et al., 2010)
- 6. Coulomb Input File (Toda et al., 2010)
- 7. Coulomb Input File (Toda et al., 2010)
- 8. The relation between displacement field and the source geometry can be expressed by the following equation: ( ) ( ) d G m d sG m α = Where d= displacement vector m=source geometry (dislocation, length, width, depth, strike, dip) s=slip (P. Cervelli et al., 2001) Inverse Modelling
- 9. If we have observed data d1 , d2 , …dn and the Green function of each observation data are G1 , G2 , …Gn respectively, Then- 1 11 12 1 1 2 21 22 2 2 1 2 ......... ......... . . . . . . . . . ......... m m n n n nm m d G G G m d G G G m d G G G m = 1 1 11 12 1 1 2 21 22 2 2 1 2 ......... ......... . . . . . . . . . ......... m m m n n nm n m G G G d m G G G d m G G G d − = Least square approach
- 10. Cartesian Co-ordinate system (x,y,z) the half space occupied region z<0 if fault is located at (0,0,-d) the point force distribution can be given in following form . Finite Element Method μ, λ are lames constants
- 11. Thrust faults :- F1 and F2 will be horizontal and F3 will be vertical. Normal faults:- F2 and F3 will be horizontal and F1 will be vertical Strike-slip faults:- F1 and F3 will be horizontal and F2 will be vertical
- 13. ANSYS (Brick 8 node 185) element, White concentrated area is showing finite rectangular fault
- 14. Where Fi is acting force and ui and vi displacements of points and ki j are Stifness constants
- 15. At location of fault points