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Geometry of Deformation

1

Geol341-Structural Geology Last Class- Contacts• Stratigraphic contacts

– Unconformities

• Primary Sedimentary Structures– Younging direction

• Intrusive contacts– Sills and dikes– Batholiths

• Folds– Anticlines, synclines, plunging folds

• Fault Contacts– Normal, thrust, strike-slip

Today• Kinematic Analysis• Deformation

– Rigid Body Deformation• Translation• Rotation• Displacement Vectors- Strain paths

– Non Rigid Body Deformation (Distortion)• Dilation- change in volume• Distortion- change in shape

Kinematic Analysis

• The study of the movements of rock during deformation

• Deformation= Change in shape, volume, or position of a body [due to an applied stress].

Dynamic Analysis

Deformation

• Translation

• Rotation

• Distortion– Dilation (volume change)

– Change in Shape• Simple Shear

• Pure Shear

Rigid Body

Non- Rigid Body

Rigid Body Deformation

• Particles in a body do not change relative positions

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Rigid Body Translation

Define frame of reference

Y

X

Yo+n

Xo+mXo

Yo m

n

Displacement vector

Vectors vs. Scalars

• Displacement vectors– Direction of movement

– Distance

Dike Intrusion Dike Intrusion

Finite Displacement Vectors

Dike Intrusion

Particle Path

vs.

Finite Displacement

Vectors

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Fault Striations- Last recorded motionFixed

Fault=displacement discontinuity

GPS Velocity

Field

Velocity Relative to North America

UNAVCO, 201510 mm/yr

mm/yr= km/my

Rigid Body RotationDefine frame of reference

Y

X

Displacement pathW

(Xo,Yo)

(X1,Y1)

X1=(CosW)Xo+(SinW)Yo

Y1=-(SinW)Xo+(CosW)Yo

Rotation Axis

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All Plate Motions are Rotations

v= ri sin Normal fault blocks rotate about horizontal axis

Non-Rigid Body Deformation

Distortion (Strain)

•Change in Volume (Dilation)

•Change in Shape

Homogeneous

vs.

Heterogeneous Deformation

Change in Volume (dilation)

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Volume increaseVein Fill

Volume DecreasePressure Solution

Strain Ellipse

Undeformed Deformed

Principal Strain Axes

Extension Quadrant

Shortening Quadrant

No change in length

Simple and Pure ShearPure Shear (Coaxial Strain)

Particle Paths

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Pure Shear

Deformed Quartzite

Boudinage

Strained Cobble Conglomerate

Simple Shear Strain

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Particle paths during strain

Fossen, 2010

SummarySimple Shear (non-coaxial)

•Like a deck of cards

•Long axis of ellipse rotates

•Lines parallel to shear plane do not change length

•Simple displacement field

•No volume change

•Square to parallelogram

Pure Shear (coaxial)

•Like sitting on a balloon

•No rotation of long axis

•All lines change length (almost)

•Complex displacement field

•No volume change

•Square to rectangle

Pure or Simple Shear?

Strain Field in a Shear Zone

From Ramsay and Hubert, 1983

Strain Ellipse (2D)

Undeformed Deformed

S3

S1

S1> S3

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Quantification of Strain 1

Longitudinal Strain = Elongation = e = (l1-lo)/ lo

Change in length over initial length

Values –1 to 1, often as a %

Shortening –

Extension +

Quantification of Strain 2

Stretch = s = l1/lo

Final length over initial length

Values 0 to Infinity

Shortening <1

Extension >1

e=-0.04 or -4%

e=-0.23 or -23%

32 km

6 km

Quantification of Non-Coaxial Strain

=Angle of shear

= Shear Strain = tan

(non dimensional)

Strain Markers

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Strain Markers- Oolites

From Ramsay and Hubert, 1983

Strain Markers- Fossils

Strained Trilobite

From Ramsay and Hubert, 1983

Strain Distribution in the AlpsMap View

From Ramsay and Hubert, 1983

Strain Distribution in the AlpsProfile View

From Ramsay and Hubert, 1983

Strain EllipsoidS3

S1

S2

Strain Axes= S1> S2 > S3

Major Minor axis

3D Strain

Cigars

Pancakes

S2/S3

S1/S2

S1>S2=S3

S1=S2>S3

No strain along 3rd

dimension

Oblate

Prolate

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Rock Fabrics and 3D Strain

From Ramsay and Hubert, 1983

Constriction

Flattening

LineationFoliation

Extension Quadrant

Shortening Quadrant

No change in length

Deformation Quadrants

Deformed dikes in metamorphic rock

From Ramsay and Hubert, 1983

x

y

Initial State

Pure Shear,No volume change, S1=1.5, horizontalS2= ?

2. Simple Shear,No volume change,Ψ = 45o

Sequential Deformation

Step 1

Step 2

Role of Strain Rate

• Strain Rate= rate of deformation

• Elongation/second

• Plate Motions are a few mm/yr

• If San Francisco is moving at 10 mm/yr relative to Fresno. What is the longitudinal strain rate?

Strain Rate Calculation

San Francisco

Fresno

L0

L110km

10 mm/yr = 10 km/My

L0 =300 kmL1= 310 Km

e= (L1-L0)/L0

e= 0.03

ê= strain rate= 0.03/My= 1 x 10-15/sec

Slow!

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Key Ideas• Strain = deformation = displacement +

change in shape

• Displacement fields

• Coaxial vs. Non-coaxial strain

• Strain ellipse, strain markers

• e= elongation (change in length/initial length)

• s= stretch (final length/initial length

• 3D strain - Constriction vs Flattening