Dislocation Theory

Kutubuddin ANSARIkutubuddin.ansari@ikc.edu.tr

GNSS Surveying, GE 205

Lecture 11, May 13, 2015

Length

Wid

th

DIP Angle

Slip

FaultRake Fault 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

Top Depth

Length

Wid

thBottom Depth

Earth Surface

( ) Bottom Depth Top DepthSin Dip AngleWidth

Strike-Slip Fault

•  The movement of blocks along a fault is horizontal.

•Rake zero (0o )

Fault plane solution of strike-slip Earthquake

Slip

•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

Dip-Slip Fault

•  The movement of blocks along a fault is vertical.

•Rake zero (90o )

Slip

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.

Dip-Slip Fault

Normal Fault

Thrust Fault

Reverse Fault

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

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

11

2

1 tan sin2 ( )

1 cos sin2 ( )

x

y

qG IR R qR

yq qG IR R R

are arbitrary constants1 2 3, , , , , ,R p y d I I I (Okada, 1985)

31 sin cos

2xqG IR

1

11 cos tan sin cos

2 ( )yyqG I

R R qR

Strike Slip case

Dip Slip case

(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)

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

India fixed-velocity field

Modelled velocity

ResultsSingle dislocation model

' '1 11 11

' '2 21 21

1 2

' '1 1

( ) ( )( ) ( )

. . .

. . .

. . .( ) ( )n n n

d G m G md G m G m

s s

d G m G m

Two dislocation model

Three dislocation model

Modelled velocity

Case Length (Km) Width (Km)

Bottom Depth

Top Depth

Dip Angle

Reverse 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)

240.95115.18

24± 325± 3

3± 0.25± 0.3

5± 0.510± 0.3

19±111

30

3 73 (Fault 1)73 (Fault 2)73 (Fault 3)

149.16200.70286.71

16± 0.216± 0.521± 4

3± 0.22± 0.31± 0.2

5± 0.14± 0.14± 0.5

20± 181

610

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 faultW= Width of finite rectangular faults = slip

10 0log ( ) 6.071.5w

MM Nm

Moment Magnitude

Moment magnitude Mw comes from seismic moment Mo

μ = 3x1010 N/m2

L=200 kmW= 100 kms = 10 mmMO= μsLWMo=(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

1810log (6 10 ) 6.07

1.5wM Nm

1810

10

log (6 10 ) 6.071.5

log(6) 18log (10) 6.071.5

0.778+18 6.071.5

6.448

w

w

w

w

M

M

M

M Nm