# Can we quantitatively go from LPO fabrics to deformation ...

Relating Lattice Preferred Orientation to Deformational Process using Statistical Analysis of Symmetry in Orientation Distribution Space Can we quantitatively relate LPO fabrics to deformation symmetry? Christopher Thissen Mark Brandon Yale University Symmetry in Quartz LPOs n=101114 Can we improve on the skeleton diagram approach by

making quantitative estimates about the fabric symmetry? caxes a-axes Thigpen et al., 2010 Quantitative Links between LPO and Deformation Symmetry Curies Symmetry Principle The symmetry of the effect is at least as great as the symmetry of the cause. So: The symmetry of the LPO is at least as high as the symmetry of the factors causing LPO and is usually directly related Foliation (S)

L Curie, 1894 Quantitative Links between LPO and Deformation Symmetry Girdle of rotation axes Uniaxial Quartz c-axes Orthorhombic Quartz c-axes

Monoclinic Quartz c-axes Initial Distribution Z Final Orientation Distribution Z [100] X [010]

X [001] X X ABOVE: Consider a monomineralic rock with an initial random orientation distribution of a hypothetical cubic mineral, with a single slip system, with slip in the (001) plane in the [100] direction. The initial stereograms for [100], [010], and [001] would all look the same, like the example above. LEFT: The three stereograms show the

orientation distribution for the three axis directions [100], [010], and [001] after a coaxial deformation with strain directions X, Y, and Z. 5 Quantifying Symmetry Searching for Symmetry Operators [100] Z X X X

[001] [010] Black: Original Distribution Blue: Rotated Distribution (rotation at 000,00) X Good Fit Poor Fit Quantifying Symmetry Searching for Symmetry Operators [100] Z

X X X [001] [010] Black: Original Distribution Blue: Rotated Distribution (rotation at N) X Good Fit Poor Fit Quantifying Symmetry

Searching for Symmetry Operators Z Z Z X X X [100] Z [001]

[010] Black: Original Distribution Blue: Rotated Distribution (rotation at 045, 00) X Good Fit Poor Fit Quantifying Symmetry Searching for Symmetry Operators Z Z Z

[100] Z X X X [010] [001] Black: Original Distribution Blue: Rotated Distribution (rotation at 045, 00) X Good Fit

Poor Fit Quantifying Symmetry Searching for Symmetry Operators Z Z [001] [010] Z X Good Fit X

X X [100] Z Poor Fit Quantifying Symmetry Searching for Symmetry Operators The orientation of each crystal can be characterized by three rotation angles, called Euler Angles. The Euler angles can be used to define a 3D space in which each crystal orientation is represented by a point. Engler and Randle, 2010

Quantifying Symmetry Searching for Symmetry Operators 0 50 Reduced Chi^2 Value Quantifying Symmetry Synthetic Olivine Example N=500 [100] 0

50 Reduced Chi^2 Value [010] [001] Quantifying Symmetry Synthetic Olivine Example N=500 [100] [010]

[001] Rotation Axes 0 50 Reduced Chi^2 Value Quantifying Symmetry Synthetic Olivine Example N=500 [100] [010]

[001] Rotation Axes 0 50 Reduced Chi^2 Value Quantifying Symmetry Moine Thrust Mylonites Law, 2010 Quantifying Symmetry Moine Thrust Mylonites Law, 2010

Quantifying Symmetry Moine Thrust Mylonites MT-07-21 n=10,000 caxes a-axes 14 4 Thigpen, et al., 2010 Conclusions We can statistically quantify the symmetry of LPO fabrics using Chi^2 in Euler space The goal is to quantify the type of symmetry

present and the symmetry orientation and relate this to the deformation

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