1) The document discusses different types of faults including strike-slip, dip-slip, and oblique-slip faults. It defines key parameters used to describe faults like length, width, dip angle, slip, and rake. 2) Equations are provided to calculate the geometry of faults using Green's functions which relate the dislocation field (displacement) to fault parameters. 3) The document gives an example of inverting GPS data using a single, two, and three dislocation models to model displacement from faults. Model parameters like length, width, depth and slip are estimated.

1. Dislocation Theory
Kutubuddin ANSARI
kutubuddin.ansari@ikc.edu.tr
GNSS Surveying, GE 205
Lecture 11, May 13, 2015

3. Length
Width
DIP Angle
Slip
Fault
RakeFault is a planar
fracture or discontinuity
in a volume of rock,
across which there has
been significant
displacement along the
fractures as a result of
rock mass movement.
DIP Angle (δ )
Rake (ψ)
Depth

4. Top Depth
Length
Width
Bottom Depth
Earth Surface
( )
Bottom Depth Top Depth
Sin Dip Angle
Width
−
=

5. Strike-Slip Fault
• The movement of
blocks along a fault is
horizontal.
•Rake zero (0o
)
Fault plane
solution of
strike-slip
Earthquake
Slip

6. •If the block on the far side of
the fault moves to the left,
the fault is called Left-lateral
(sinistral) Fault.
•If the block on the far side moves
to the right, the fault is called
Right-lateral (dextral) Fault.
Strike-Slip Fault

7. Dip-Slip Fault
• The movement of
blocks along a fault is
vertical.
•Rake zero (90o
)
Slip

8. Dip-Slip Fault
•If the hanging wall moves
downward relative to the footwall,
the fault is called Normal
(extensional) Fault.
•If the hanging wall moves upward
relative to the footwall, the fault is
called Reverse Fault. Reverse
faults indicate compressive
shortening of the crust.
• Reverse fault having dip angle less
than 450
is called Thrust Fault.

9. Dip-Slip Fault
Normal Fault
Thrust Fault
Reverse Fault

10. Oblique-Slip Fault
•A fault which has a
component of dip-slip and
a component of strike-slip
is termed an oblique-slip
fault.
• Rake will be (0 < ψ >90)
Slip

11. 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

12. 1
1
2
1
tan sin
2 ( )
1 cos
sin
2 ( )
x
y
q
G I
R R qR
yq q
G I
R R R
ξ ξη
δ
π η
δ
δ
π η η
−
  
= − + +  ÷
+   
 
= − + + + + 
%
are arbitrary constants
1 2 3, , , , , ,R p y d I I I%%
(Okada, 1985)
3
1
sin cos
2
x
q
G I
R
δ δ
π
 
=− −  
1
1
1
cos tan sin cos
2 ( )
y
yq
G I
R R qR
ξη
δ δ δ
π ξ
− 
= − + − + 
Strike Slip case
Dip Slip case

13. (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)

14. Consider the case we have observed data d1, d2, ……. dn
and the Green function of each observation data are G1, G2,
……. Gn respectively, Then:

15. India fixed-velocity
field

16. Modelled velocity

17. Results Single dislocation model

18. ' '
1 11 11
' '
2 21 21
1 2
' '
1 1
( ) ( )
( ) ( )
. . .
. . .
. . .
( ) ( )n n n
d G m G m
d G m G m
s s
d G m G m
    
    
    
    
= +     
    
    
    
          
Two dislocation model

19. Three dislocation model

20. Modelled velocity

21. Case Length (Km) Width
(Km)
Bottom
Depth
Top
Depth
Dip
Angle
Rever
se Slip
Strike
Slip
1 73 (Fault 1) 115.18 25± 2 5±0.3 10± 1 15± 1 0
2 79 (Fault 1)
73 (Fault 2)
240.95
115.18
24± 3
25± 3
3± 0.2
5± 0.3
5± 0.5
10± 0.3
19±1
11
3
0
3 73 (Fault 1)
73 (Fault 2)
73 (Fault 3)
149.16
200.70
286.71
16± 0.2
16± 0.5
21± 4
3± 0.2
2± 0.3
1± 0.2
5± 0.1
4± 0.1
4± 0.5
20± 1
8
1
6
1
0

23. Richter magnitude scale
The Richter magnitude scale (Richter scale)
assigns a magnitude number to quantify the
energy released by an earthquake.
Seismic moment = μ* slip*rupture area
MO= μ*s*A
MO= μ*s*L*W
μ = shear modulus of the crust (approx 3x1010
N/m2
)
L= Length of finite rectangular fault
W= Width of finite rectangular fault
s = slip

24. 10 0log ( )
6.07
1.5
w
M
M Nm= −
Moment Magnitude
Moment magnitude Mw comes from seismic moment Mo

25. μ = 3x1010
N/m2
L=200 km
W= 100 km
s = 10 mm
MO= μsLW
Mo=(3x1010
)x(10 x10-3
)x (200 x 103
)x(100 x 103
)
Mo=(3x1010
)x(10-2
)x (2 x 105
)x(1x105
)
Mo=6x1018
Example
18
10log (6 10 )
6.07
1.5
wM Nm
×
= −

26. 18
10
10
log (6 10 )
6.07
1.5
log(6) 18log (10)
6.07
1.5
0.778+18
6.07
1.5
6.448
w
w
w
w
M
M
M
M Nm
×
= −
+
= −
= −
=