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Geometry of Deformation 1

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Geometry of Deformation 1 9/8/2016 Geol341-Structural Geology Last Class- Contacts • Stratigraphic contacts – Unconformities Geometry of • Primary Sedimentary Structures – Younging direction Deformation • Intrusive contacts – Sills and dikes – Batholiths 1 • Folds – Anticlines, synclines, plunging folds • Fault Contacts – Normal, thrust, strike-slip Today Kinematic Analysis • Kinematic Analysis • Deformation • The study of the movements of rock during – Rigid Body Deformation deformation • Translation • Rotation • Displacement Vectors- Strain paths • Deformation= Change in shape, volume, or – Non Rigid Body Deformation (Distortion) position of a body [due to an applied stress]. • Dilation- change in volume • Distortion- change in shape Dynamic Analysis Deformation Rigid Body Deformation • Translation • Particles in a body do not change relative • Rotation Rigid Body positions • Distortion – Dilation (volume change) Non- Rigid Body – Change in Shape • Simple Shear • Pure Shear 1 9/8/2016 Rigid Body Translation Vectors vs. Scalars Define frame of reference • Displacement vectors Y – Direction of movement – Distance Yo+n n Yo m Displacement vector Xo Xo+m X Dike Intrusion Dike Intrusion Finite Displacement Vectors Dike Intrusion Particle Path vs. Finite Displacement Vectors 2 9/8/2016 Fault Striations- Last recorded motion Fixed Fault=displacement discontinuity GPS Velocity Rigid Body Rotation Field Define frame of reference Y (Xo,Yo) Velocity Relative to North Displacement America W path (X1,Y1) mm/yr= km/my X Rotation X1=(CosW)Xo+(SinW)Yo 10 mm/yr UNAVCO, 2015 Axis Y1=-(SinW)Xo+(CosW)Yo 3 9/8/2016 All Plate Motions are Rotations v= r sin i Normal fault blocks rotate about horizontal axis Non-Rigid Body Deformation Distortion (Strain) •Change in Volume (Dilation) •Change in Shape Change in Volume (dilation) Homogeneous vs. Heterogeneous Deformation 4 9/8/2016 Volume increase Volume Decrease Vein Fill Pressure Solution Strain Ellipse Extension Quadrant No change in Principal Strain Axes length Shortening Quadrant Undeformed Deformed Pure Shear (Coaxial Strain) Simple and Pure Shear Particle Paths 5 9/8/2016 Pure Shear Deformed Quartzite Strained Cobble Conglomerate Boudinage Simple Shear Strain 6 9/8/2016 Particle paths during strain Fossen, 2010 Summary Pure or Simple Shear? Simple Shear (non-coaxial) Pure Shear (coaxial) •Like a deck of cards •Like sitting on a balloon •Long axis of ellipse rotates •No rotation of long axis •Lines parallel to shear plane do •All lines change length not change length (almost) •Simple displacement field •Complex displacement field •No volume change •No volume change •Square to parallelogram •Square to rectangle Strain Ellipse (2D) Strain Field in a Shear Zone S3 S1 S1>S3 Undeformed Deformed From Ramsay and Hubert, 1983 7 9/8/2016 Quantification of Strain 1 Quantification of Strain 2 Stretch = s = l1/lo Longitudinal Strain = Elongation = e = (l1-lo)/ lo Final length over initial length Change in length over initial length Values 0 to Infinity Values –1 to 1, often as a % Shortening <1 Shortening – Extension >1 Extension + e=-0.04 or -4% 6 km e=-0.23 or -23% 32 km Quantification of Non-Coaxial Strain Markers Strain =Angle of shear = Shear Strain = tan (non dimensional) 8 9/8/2016 Strain Markers- Oolites Strain Markers- Fossils Strained Trilobite From Ramsay and Hubert, 1983 From Ramsay and Hubert, 1983 Strain Distribution in the Alps Strain Distribution in the Alps Map View Profile View From Ramsay and Hubert, 1983 From Ramsay and Hubert, 1983 3D Strain No strain along 3rd Strain Ellipsoid dimension S 3 Cigars S /S S1=S2>S3 S1 1 2 S2 S1>S2=S3 Strain Axes= S >S >S 1 2 3 Prolate Pancakes Major Minor axis S2/S3 Oblate 9 9/8/2016 Rock Fabrics and 3D Strain Extension Quadrant Constriction No change in length Foliation Lineation Shortening Flattening Quadrant Deformation Quadrants From Ramsay and Hubert, 1983 Sequential Deformation Deformed dikes in metamorphic rock Initial State y Step 1 Pure Shear, No volume change, S1=1.5, horizontal Step 2 x S2= ? 2. Simple Shear, No volume change, Ψ = 45o From Ramsay and Hubert, 1983 Role of Strain Rate Strain Rate Calculation 10 mm/yr = 10 km/My • Strain Rate= rate of deformation L =300 km • Elongation/second 0 L1= 310 Km • Plate Motions are a few mm/yr e= (L -L )/L 10km L 1 0 0 1 e= 0.03 • If San Francisco is moving at 10 mm/yr San Francisco L relative to Fresno. What is the longitudinal 0 ê= strain rate= 0.03/My strain rate? = 1 x 10-15/sec Fresno Slow! 10 9/8/2016 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 11.
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