1. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 1 Numerical simulations of parasitic folding and strain distribution in multilayers EGU Vienna, April 17, 2007 Marcel Frehner Stefan M. Schmalholz frehner@erdw.ethz.ch

2. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 2 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 | Methods| Two-layer folds| Multilayer folds| Conclusions| Outlook | | Motivation

3. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 3 Motivation: The work by Hans Ramberg Ramberg, 1963: Evolution of drag folds Geological Magazine | Methods| Two-layer folds| Multilayer folds| Conclusions| Outlook | | Motivation  Ramberg‘s hypothesis for parasitic folding  Thin layers buckle first  Asymmetry by shearing between the larger folds  Aim  Test hypothesis with numerical methods  Quantify and visualize strain field

4. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 4 Methods: Numerics  Self-developed 2D finite element (FEM) program  Incompressible Newtonian rheology  Mixed v-p-formulation  Half wavelength of large folds  Viscosity contrast: 100 | Two-layer folds| Multilayer folds| Conclusions| Outlook | | Motivation| Methods

5. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 5 Methods: Standard visualization  Resolution  11’250 elements  100’576 nodes | Two-layer folds| Multilayer folds| Conclusions| Outlook | | Motivation| Methods Layer-parallel strainrate 40% shortening

6. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 6 Strain ellipse: A reminder | Two-layer folds| Multilayer folds| Conclusions| Outlook | | Motivation| Methods Haupt, 2002: Continuum Mechanics and Theory of Materials Ramsay and Huber, 1983: Strain Analysis  Incremental deformation gradient tensor G  Finite deformation gradient tensor F  Right Cauchy-Green tensor C  Eigenvalues and eigenvectors are used to calculate principal strain axes

7. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 7 Two-layer folds: Strain distribution Color:Accumulated strainColor: Rotation angle | Methods| Multilayer folds| Conclusions| Outlook | | Motivation| Two-layer folds 40% shortenig

8. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 8 Two-layer folds: Three phases of deformation Fold limb S Transition zone J Fold hinge I | Methods| Multilayer folds| Conclusions| Outlook | | Motivation| Two-layer folds

9. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 9 Two-layer folds: Results of strain analysis  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 | Methods| Multilayer folds| Conclusions| Outlook | | Motivation| Two-layer folds

10. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 10 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 | Methods| Two-layer folds| Conclusions| Outlook | | Motivation| Multilayer folds

11. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 11 Multilayer folds: Results  Layer-parallel compression  No buckling of thick layers  Buckling of thin layers Symmetric fold stacks  Shearing without flattening  Buckling of thick layers: shearing between them  Stacks of multilayer folds become asymmetric  Flattening normal to layers  Increased amplification of thick layers: flattening normal to layers  Amplitudes of thin layers decrease | Methods| Two-layer folds| Conclusions| Outlook | | Motivation| Multilayer folds

12. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 12 Multilayer folds: Similarity to two-layer folding  Deformation of two-layer system is nearly independent of presence of multilayer stack in between 50% shortening: Black: Multilayer system Green: Two-layer system | Methods| Two-layer folds| Conclusions| Outlook | | Motivation| Multilayer folds

13. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 13 Conclusions  Efficient strain analysis with computed strain ellipses  Ramberg‘s hypothesis verified  3 phases of deformation between a two-layer system  Layer parallel compression: Thin layers build vertical symmetric fold-stacks  Shearing without flattening: Asymmetry of thin layers  Flattening normal to layers: Decrease of amplitude of thin layers  Presence of thin multilayers hardly affects deformation of two-layer system | Methods| Two-layer folds| Multilayer folds| Outlook | | Motivation| Conclusions

14. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 14 Accumulated strain Layer n=5, Matrix n=5 | Methods| Two-layer folds| Multilayer folds| Conclusions | Motivation| | Outlook Layer n=1, Matrix n=1 Work in progress: More complex rheology

15. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 15 Work in progress: More complex geometry | Methods| Two-layer folds| Multilayer folds| Conclusions | Motivation| | Outlook  Different thicknesses  Random initial perturbation on all layers

16. EGU Vienna 04/17/2007 M. Frehner & S.M. Schmalholz 16 Thank you Frehner, M. and Schmalholz S.M., 2006: Numerical simulations of parasitic folding in multilayers Journal of Structural Geology