12.005 Lecture Notes 18
Dislocation in Elastic Halfspace Model of the Earthquake Cycle
Interseismic: Slip below depth D
εxy
5 10 15
-15 -10 -5
X/D
y
-3
0
Displacement
3
X/D
Strain
Figure 18.1
Figure by MIT OCW.
Coseismic: Region above D “catches up”
εxy
5
-15 -10 -5
y
-3
0
X/D
Figure 18.2
Figure by MIT OCW.
3
10 15
X/D
Displacements from Earthquakes, Fault Slip, etc
Consider a strike-slip fault with displacement S, independent of depth – A screw
“dislocation” – i.e., a slip discontinuity. Original ring (dashed) becomes helix (solid).
2
x3
ce
rfa
Su ault
f
Fault
displacement S
1
D
o
ati
c
o
sl
s
Di axi
x2
n
S/2
S/2
x1
Figure 18.3. Section across a mathematical model of a transcurrent fault.
Figure by MIT OCW.
“Dislocations” are used to describe defects in crystals, as well as fault motions. A crystal
disrupted by a screw dislocation is shown in the figure below.
7
8
9
10
6
b*
5
1
4
3
2
Figure by MIT OCW.
Figure 18.4. A screw dislocation in a cubic lattice constitutes a deformation that is
out of the plane of atoms illustrated. The two atoms denotes by solid circles are
essentially part of a second plane. The Burgers circuit indicated by the numbered
steps naturally moves into this second plane. Therefore in order to close the
circuit the Burgers vector b* must be perpendicular to the plane of atoms shown.
Types:
Edge
Screw
Figure 18.5
Figure by MIT OCW.
b*
1
2
3
10
4
9
5
8
7
6
1
2
3
10
4
9
5
8
7
6
Figure 18.6 Side view of an edge dislocation in a cubic lattice.
Figure by MIT OCW.
Dislocation motion helps crystals deform (don’t all have to slip at one time). Also helps
Earth deform!
C
B
D
S
E
A
Figure 18.7 A dislocation.
Figure by MIT OCW.
b
C
B
C
A
A
E
E
E
E
b
S
S
B
S
S
Figure 18.8 Upper group: Slip by propagation of an edge dislocation EE. Lower
group: Slip by propagation of a screw dislocation SS.
Figure by MIT OCW.
Displacement (meters)
2
1
0
0
2
4
6
8
10
Distance from fault (km) NE
Figure 18.9 Displacement as a function of distance from a transcurrent fault.
Figure by MIT OCW.