1. SGM Bern 11/25/2006 Marcel Frehner 1 Numerical simulations of parasitic folding in multilayers SGM Bern, November 25, 2006 Marcel Frehner Stefan M. Schmalholz frehner@erdw.ethz.ch

2. SGM Bern 11/25/2006 Marcel Frehner 2 Outline  Motivation  Method  Two-layer folds  3 regions of deformation  3 deformation phases  Multilayer folds  3 deformation phases reformulated  Similarity to two-layer folds  Conclusions

3. SGM Bern 11/25/2006 Marcel Frehner 3 Motivation: Asymmetric parasitic folds on all scales Mount Rubin Western Antarctica Picture courtesy of Chris Wilson ~1200m Foliated Metagabbro Val Malenco; Swiss Alps Picture courtesy of Jean-Pierre Burg

4. SGM Bern 11/25/2006 Marcel Frehner 4 Motivation: The work by Hans Ramberg Ramberg, H. Geological Magazine 1963: Evolution of drag folds

5. SGM Bern 11/25/2006 Marcel Frehner 5 Motivation  Asymmetric parasitic folds are used in field studies  Problem:  Conditions for their development are not thoroughly studied  Why become parasitic folds asymetric?  Goal:  Understanding of the strain history and the development of multilayer folds  Quantify necesary conditions for the development of asymetric parasitic folds

6. SGM Bern 11/25/2006 Marcel Frehner 6 Method  Self-developed finite element (FEM) program  Incompressible Newtonian rheology  2D  Dimensionless formulation  Pure shear boundary conditions  Modelled area: Half wavelength of fold  Viscosity contrast: 100  Sinusoidal initial perturbation

7. SGM Bern 11/25/2006 Marcel Frehner 7 Two-layer folds → Example of numerical simulation  Resolution  11’250 elements  100’576 nodes

8. SGM Bern 11/25/2006 Marcel Frehner 8 Two-layer folds → After 40% shortening Strain ellipses coloured with: Bulk strain Strain ellipses coloured with: Rotation angle

9. SGM Bern 11/25/2006 Marcel Frehner 9 Two-layer folds → Three regions of deformation Fold limb S Transition zone J Fold hinge I

10. SGM Bern 11/25/2006 Marcel Frehner 10 Two-layer folds → Three deformation phases at fold limb Increasing shortening 1 = Original distance CompressionShearingFlattening Absolute flattening

11. SGM Bern 11/25/2006 Marcel Frehner 11 Two-layer folds → Observations  Three regions of deformation  Fold hinge, layer-parallel compression only  Fold limb  Transition zone, complicated deformation mechanism  Three deformation phases at fold limb  Layer-parallel compression  Shearing without flattening  Flattening normal to the layers S I J

12. SGM Bern 11/25/2006 Marcel Frehner 12 Multilayer folds → Example of numerical simulation  Viscosity contrast: 100  Thickness ratio H thin :H thick = 1:50  Random initial perturbation on thin layers  Truly multiscale model  Number of thin layers in this example: 20  Resolution:  24‘500 elements  220‘500 nodes

13. SGM Bern 11/25/2006 Marcel Frehner 13 Multilayer folds → Influence of number of thin layers 5 10 15 20

14. SGM Bern 11/25/2006 Marcel Frehner 14 Multilayer folds → Three deformation phases reformulated Amplitude of thin layers of thick layers

15. SGM Bern 11/25/2006 Marcel Frehner 15 Multilayer folds → Three deformation phases reformulated  Layer-parallel compression  No buckling of thick layers  Thin layers start to buckle and develop symmetric fold stacks  Shearing without flattening  Buckling of thick layers causes shearing between them  Folds of multilayer stack become asymmetric  Flattening normal to layers  Increased amplification of thick layers leads to flattening normal to layers  Amplitudes of thin layers are decreased

16. SGM Bern 11/25/2006 Marcel Frehner 16 Multilayer folds → Similarity to two-layer folding

17. SGM Bern 11/25/2006 Marcel Frehner 17 Multilayer folds → Similarity to two-layer folding  Deformation of double layer system is nearly independent of presence of multilayer stack in between 50% shortening: Black: Multilayer system Green: Two-layer system

18. SGM Bern 11/25/2006 Marcel Frehner 18 Conclusions  Deformation history between a two-layer system at the fold limb can be divided into three phases  Layer parallel compression  Shearing without flattening  Flattening normal to layers  Thin layers develop vertical symmetric fold-stacks during first phase; They deform passively afterwards (like in the double layer case)  Whether fold-stacks survive the flattening phase is due to their amplitude at the point of buckling initiation of the thick layers  A bigger number of thin layers amplifies faster  Deformation of a two-layer system is nearly independent of the presence or absence of a multilayer stack in between

19. SGM Bern 11/25/2006 Marcel Frehner 19 Test for more complex geometry

20. SGM Bern 11/25/2006 Marcel Frehner 20 Thank you