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Sheath Folds in Simple Shear: an Analytical and Experimental Study

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Sheath Folds in Simple Shear: an Analytical and Experimental Study Sheath folds in simple shear: An analytical and experimental study Jacqueline E. Reber Thesis submitted for the degree of Philosophiae Doctor Department of Geosciences Faculty of Mathematics and Natural Sciences University of Oslo, Norway August, 2012 © Jacqueline E. Reber, 2012 Series of dissertations submitted to the Faculty of Mathematics and Natural Sciences, University of Oslo No. 1250 ISSN 1501-7710 All rights reserved. No part of this publication may be reproduced or transmitted, in any form or by any means, without permission. Cover: Inger Sandved Anfinsen. Printed in Norway: AIT Oslo AS. Produced in co-operation with Akademika publishing. The thesis is produced by Akademika publishing merely in connection with the thesis defence. Kindly direct all inquiries regarding the thesis to the copyright holder or the unit which grants the doctorate. Principal supervisor: Dr. Daniel W. Schmid Subsidiary supervisors: Dr. Marcin Dabrowski Dr. Olivier Galland A great pleasure in life is doing what people say you cannot do. W. Bagehot (1826-77) Contents Acknowledgments .......................................................................................... 5 Preface ............................................................................................................. 7 1. Introduction .......................................................................................... 9 1.1. What is a sheath fold? .......................................................................................... 10 1.2. Occurrence of sheath folds .................................................................................. 13 1.3. How do sheath folds form? .................................................................................. 13 1.3.1. Pure shear ....................................................................................................... 14 1.3.2. General shear .................................................................................................. 14 1.3.3. Simple shear ................................................................................................... 15 1.3.3.1. Passive amplification ............................................................................................. 15 1.3.3.2. Flow perturbation: rigid inclusion ........................................................................ 17 1.3.3.3. Flow perturbation: weak inclusion ........................................................................ 18 1.4. Application of sheath folds .................................................................................. 19 1.4.1. High strain indicator ....................................................................................... 19 1.4.2. Shear sense indicators ..................................................................................... 20 1.4.3. Shear zone thickness indicator ........................................................................ 21 1.4.3. Bulk strain type indicator ................................................................................ 21 1.4.3.2. Classification ......................................................................................................... 21 1.4.3.3. Application ............................................................................................................. 22 1.4.4. Limitations of the classification and applications ........................................... 23 1.5. Sheath fold formation around a slip surface ........................................................ 23 1.5.1. Introduction to the techniques ......................................................................... 24 1.5.1.1. The analytical model .............................................................................................. 24 1.5.1.2. The experimental model ......................................................................................... 26 1.5.1.3. Method comparison ............................................................................................... 27 1.5.2. Applicability of the models to nature .............................................................. 29 1.6. Introduction to the papers .................................................................................... 31 1.6.1. Paper I ............................................................................................................. 31 1.6.2. Paper II ........................................................................................................... 31 1.6.3. Paper III .......................................................................................................... 32 1.6.4. Additional work .............................................................................................. 33 1.7. References ........................................................................................................... 34 2. Sheath fold formation around slip surfaces .................................... 41 2.1. Abstract ............................................................................................................... 41 2.2. Introduction ......................................................................................................... 41 Contents 2.3. Model .................................................................................................................. 43 2.4. Results ................................................................................................................. 43 2.4.1. Field examples................................................................................................ 46 2.5. Discussion ........................................................................................................... 47 2.6. Conclusion .......................................................................................................... 49 2.7. References ........................................................................................................... 49 3. Experimental study of sheath fold development around a weak inclusion in a mechanically layered matrix ................................................ 53 3.1. Abstract ............................................................................................................... 53 3.2. Introduction ......................................................................................................... 54 3.2.1. Experimental procedure ................................................................................. 56 3.2.1.1. Model material ....................................................................................................... 56 3.2.1.2. Apparatus ............................................................................................................... 57 3.2.1.3. Construction of models .......................................................................................... 58 3.2.1.4. Observation of the deformed model ....................................................................... 59 3.2.1.5. Dimensional analysis ............................................................................................. 61 3.3. Results ................................................................................................................. 63 3.3.1. Experiment T with no inclusion ..................................................................... 64 3.3.2. Experiments with inclusion ............................................................................ 65 3.3.2.1. V-series .................................................................................................................. 66 3.3.2.2. L-series .................................................................................................................. 72 3.4. Discussion ........................................................................................................... 77 3.4.1. Validity of experimental method .................................................................... 77 3.4.2. Experimental results ....................................................................................... 79 3.4.3. Implications .................................................................................................... 80 3.5. Conclusion .......................................................................................................... 82 3.6. Appendix A: Viscosimetry .................................................................................. 83 3.7. Appendix B: 3D modeling .................................................................................. 84 3.8. References ........................................................................................................... 85 4. Analytical modeling of the morphology and internal structure of sheath folds in simple shear ......................................................................... 89 4.1. Abstract ............................................................................................................... 89 4.2. Introduction ......................................................................................................... 90 4.3. Method ................................................................................................................ 92 4.3.1. Analytical model ............................................................................................ 92 4.3.2. Visualization .................................................................................................. 93 4.4. Results
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