1Geometry of Deformation2Geol341/342-Structural GeologyOutline• Strain Ellipse• Coaxial vs Non Coaxial Strain• Quantifying Strain– Angular Shear– Stretch– Elongation • Stain Markers- Strain Fields•3D Strain– Constriction vs. Flattening• Strain RatesDeformation• Translation• Rotation• Distortion– Dilation– Coaxial Strain– Non-Coaxial StrainRigid BodyNon- Rigid BodyNon-Coaxial and Coaxial StrainCoaxial StrainNon-Coaxial Strain2SummaryNon-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 parallelogramCoaxial•Like sitting on a balloon•No rotation long axis •All lines change length (almost)•Complex displacement field•No volume change•Square to rectangleStrain Field in a Shear ZoneFrom Ramsay and Hubert, 1983Strain EllipsoidS3S1S2Strain Axes= S1>S2 >S3Major Minor axisStrain Ellipse (2D)UndeformedDeformedS3S1S1>S3Quantification of Coaxial StrainLongitudinal Strain = Elongation = e = (l1-lo)/ loChange in length over initial lengthValues –1 to 1, often as a %Shortening –Extension +Stretch = s = l1/loFinal length over initial lengthValues 0 to InfinityShortening <1Extension >1Quantification of Non-Coaxial StrainΨ=Angle of shearγ= Shear Strain = tan Ψ(non dimentional)3Strain MarkersStrain Markers- OolitesFrom Ramsay and Hubert, 1983Strain Markers- FossilsStrained TrilobiteFrom Ramsay and Hubert, 1983Strain Distribution in the AlpsMap ViewFrom Ramsay and Hubert, 1983Strain Distribution in the AlpsProfile ViewFrom Ramsay and Hubert, 19833D Strain CigarsPancakesS2/S3S1/S2S1>S2=S3S1=S2>S3No strain along 3rddimension4Rock Fabrics and 3D StrainFrom Ramsay and Hubert, 1983ConstrictionFlatteningLineationFoliationExtension QuadrantShortening QuadrantNo change in lengthDeformation QuadrantsDeformed dikes in metamorphic rockFrom Ramsay and Hubert,