method of fault modelling

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Method of Modelling Kutubuddin ANSARI [email protected] GNSS Surveying, GE 205 Lecture 12, May 22, 2015

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Page 1: Method of fault modelling

Method of Modelling

Kutubuddin [email protected]

GNSS Surveying, GE 205

Lecture 12, May 22, 2015

Page 2: Method of fault modelling

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 d

(Okada, 1985 &1992)

Length

Wid

th

DIP

Slip

Length(AL) Wid

th(A

W)

Length

Wid

th

cos sinx ALy d AW

(δ)

Dislocation Theory

Page 3: Method of fault modelling

(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)

Page 4: Method of fault modelling

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)

0ˆ ˆ ˆd= sG(m)

if

where

m=initial model parameter

ˆ modˆ modˆ mod

s slip

errorS Net slip

d elled dislocaton fields el slipm el parameter

rake of the netslip on the fault plane

For Oblique Slip

S= s.cosα + s.sinα

Page 5: Method of fault modelling

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)

Page 6: Method of fault modelling

Coulomb Input File (Toda et al., 2010)

Page 7: Method of fault modelling

Coulomb Input File (Toda et al., 2010)

Page 8: Method of fault modelling

The relation between displacement field and the source geometry can be expressed by the following equation:

( )( )

d G md sG m

Where d= displacement vectorm=source geometry (dislocation, length, width, depth, strike, dip)s=slip

(P. Cervelli et al., 2001)

Inverse Modelling

Page 9: Method of fault modelling

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 md G G G m

d G G G m

11 11 12 1 1

2 21 22 2 2

1 2

.........

.......... . .. . .. . .

.........

m

m

m n n nm n

m G G G dm G G G d

m G G G d

Least square approach

Page 10: Method of fault modelling

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

Page 11: Method of fault modelling

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

Page 12: Method of fault modelling
Page 13: Method of fault modelling

ANSYS (Brick 8 node 185) element, White concentrated area is showing finite rectangular fault

Page 14: Method of fault modelling

Where Fi is acting force and ui and vi displacements of points and ki

j are Stifness constants

Page 15: Method of fault modelling

At location of fault points

Page 16: Method of fault modelling