Download - Dislocation Theory
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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
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Top Depth
Length
Wid
thBottom Depth
Earth Surface
( ) Bottom Depth Top DepthSin Dip AngleWidth
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Strike-Slip Fault
• The movement of blocks along a fault is horizontal.
•Rake zero (0o )
Fault plane solution of strike-slip Earthquake
Slip
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•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
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Dip-Slip Fault
• The movement of blocks along a fault is vertical.
•Rake zero (90o )
Slip
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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.
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Dip-Slip Fault
Normal Fault
Thrust Fault
Reverse Fault
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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
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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
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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
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(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)
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Consider the case we have observed data d1, d2, ……. dn and the Green function of each observation data are G1, G2, ……. Gn respectively, Then:
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India fixed-velocity field
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Modelled velocity
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ResultsSingle dislocation model
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' '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
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Three dislocation model
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Modelled velocity
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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
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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
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10 0log ( ) 6.071.5w
MM Nm
Moment Magnitude
Moment magnitude Mw comes from seismic moment Mo
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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
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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