Geol342-Structural Geology
Today
Geometry of
Deformation
• Deformation
– Rigid Body Deformation
• Translation
• Rotation
• Displacement Vectors- Strain paths
– Non Rigid Body Deformation (Distortion)
• Dilation- change in volume
• Distortion- change in shape
Deformation
Deformation
• Change in shape, volume, or position of a
body [due to an applied stress].
• Translation
• Rotation
Rigid Body
• Distortion
– Dilation
– Coaxial Strain
– Non-Coaxial Strain
Non- Rigid Body
Dike Intrusion
Rigid Body Translation
Define frame of reference
Y
Yo+n
n
Yo
m
Displacement
vector
Xo
Xo+m
X
1
Dike Intrusion
Dike Intrusion
Finite
Displacement
Vectors
Displacement
Path
vs.
Displacement
Vectors
Fault Striations- Last recorded motion
Fixed
Southern California GPS Velocity Field
Velocity
Relative to
North
America
Fault=displacement discontinuity
2
All Plate Motions are Rotations
Rigid Body Rotation
Define frame of reference
Y
(Xo,Yo)
W
Displacement
path
(X1,Y1)
X
Rotation
Axis
X1=(CosW)Xo+(SinW)Yo
Y1=-(SinW)Xo+(CosW)Yo
v= ω ri sin Θ
Motion with respect to what?
Non-Rigid Body Deformation
Distortion (Strain)
•Change in Volume (Dilation)
•Change in Shape
Homogeneous
vs.
Heterogeneous
Deformation
3
Strain Ellipse
Principal Strain Axes
Undeformed
Deformed
Coaxial Strain
Non-Coaxial and Coaxial Strain
Non-Coaxial Strain
4
Summary
Strain Field in a Shear Zone
Non-Coaxial
Coaxial
•Like a deck of cards
•Like sitting on a balloon
•Long axis of ellipse rotates
•No rotation long axis
•Lines parallel to shear plane
do not change length
•All lines change length
(almost)
•Simple displacement field
•Complex displacement field
•No volume change
•No volume change
•Square to parallelogram
•Square to rectangle
Quantification of Coaxial Strain 1
Longitudinal Strain = Elongation = e = (l1-lo)/ lo
Change in length over initial length
Values
–1 to 1, often as a %
Shortening –
Extension +
From Ramsay and Hubert, 1983
Quantification of Coaxial Strain 2
Stretch = s = l1/lo
Final length over initial length
Values 0 to Infinity
Shortening <1
Extension >1
5
Quantification of Non-Coaxial
Strain
Ψ=Angle of shear
e=-0.04 or -4%
6 km
γ= Shear Strain = tan Ψ
e=-0.23 or -23%
(non dimensional)
32 km
Strain Markers- Oolites
Strain Markers
From Ramsay and Hubert, 1983
Strain Markers- Fossils
Strain Ellipsoid
S2
Strained Trilobite
S1
S3
Strain Axes= S1> S2 > S3
Major
Minor axis
From Ramsay and Hubert, 1983
6
3D Strain
Rock Fabrics and 3D Strain
No strain along 3rd
dimension
Constriction
Cigars
Foliation
S1=S2>S3
S1/S2
Lineation
Flattening
S1>S2=S3
Prolate
Pancakes
S2/S3
Oblate
From Ramsay and Hubert, 1983
7