Numerical simulations of parasitic folding in multilayers

1. Numerical simulations ofparasitic folding in multilayers SGM Bern, November 25, 2006 Marcel FrehnerStefan M. Schmalholz frehner@erdw.ethz.ch

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. ~1200m Mount RubinWestern Antarctica Picture courtesyof Chris Wilson Foliated MetagabbroVal Malenco; Swiss Alps Picture courtesy of Jean-Pierre Burg Motivation: Asymmetric parasitic folds on all scales

4. Motivation: The work by Hans Ramberg Ramberg, H.Geological Magazine1963: Evolution of drag folds

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. 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. Two-layer folds→ Example of numerical simulation • Resolution • 11’250 elements • 100’576 nodes

8. Two-layer folds→ After 40% shortening Strain ellipses coloured with: Bulkstrain Strain ellipses coloured with: Rotation angle

9. Two-layer folds→ Three regions of deformation Fold limb S Transition zone JFold hinge I

10. Absolute flattening Compression Shearing Flattening Two-layer folds→ Three deformation phases at fold limb 1 = Original distance Increasing shortening

11. Two-layer folds→ Observations I • 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 J S

12. Multilayer folds→ Example of numerical simulation • Viscositycontrast: 100 • Thickness ratioHthin:Hthick = 1:50 • Random initial perturbation onthin layers • Truly multiscale model • Number of thin layers in this example: 20 • Resolution: • 24‘500 elements • 220‘500 nodes

13. Multilayer folds→ Influence of number of thin layers 5 15 20 10

14. Multilayer folds→ Three deformation phases reformulated Amplitude of thin layers of thick layers

15. Multilayer folds→ Three deformation phases reformulated • Layer-parallel compression • No buckling of thick layers • Thin layers start to buckle anddevelop 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 layersleads to flattening normal to layers • Amplitudes of thin layers are decreased

16. Multilayer folds→ Similarity to two-layer folding

17. Multilayer folds→ Similarity to two-layer folding • Deformation of double layersystem is nearly independentof presence of multilayerstack in between 50% shortening: Black: Multilayer systemGreen: Two-layer system

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. Test for more complex geometry

20. Thank you