Folds and Folding. Processes in Structural Geology & Tectonics. Ben van der Pluijm. WW Norton+Authors, unless noted otherwise 3/4/ :15

Transcription

1 Folds and Folding Processes in Structural Geology & Tectonics Ben van der Pluijm WW Norton+Authors, unless noted otherwise 3/4/ :15

2 We Discuss Folds and Folding Fold Description Fold Classification Fold Systems Fault-related Folds Fault-propagation folds Fault-bend folds Detachment folds Elements of Fold Style Superposed Folding Fold Mechanics and Kinematics Bending and Buckling Basic fold math Fold Strain Structure and Society Folds PSG&T 2

3 Elements of Fold Classification fold shape in profile interlimb angle similar/parallel symmetry/vergence fold size amplitude wavelength fold facing upward/downward fold orientation axis/hinge line axial surface fold in 3D cylindrical/non-cylindrical presence of secondary features foliation lineation DePaor, 2002 Folds PSG&T 3

4 Fold Terminology and Measures L w (or W) = Wavelength L a = Arc length a = Amplitude Folds PSG&T 4

5 Fold Facing (a) upward facing antiform or anticline (b) upward facing synform or syncline (c) downward-facing antiform or antiformal syncline (d) downward-facing synform or synformal anticline (e) profile view; (f) map view Folds PSG&T 5

6 Fold Shapes similar fold parallel fold ptygmatic fold Folds PSG&T 6

7 Fold Shape Parallel fold Similar fold t is layer-perpendicular thickness T is axial trace-parallel thickness Folds PSG&T 7

8 Extra: Dip Isogons and Fold Shape Construction of a dip isogon, which connects tangents to upper and lower boundary of folded layer with equal angle (α) relative to a reference frame; dip isogons at 10 intervals are shown for each fold class. Class 1 folds (a c) have convergent dip isogon patterns; dip isogons in Class 2 folds (d) are parallel; Class 3 folds (e) have divergent dip isogon patterns. In this classification, parallel (b) is Class 1B and similar (d) is Class 2. Folds PSG&T 8

9 Fold Systems: Enveloping surface and Fold (a)symmetry The fold enveloping surface a. Symmetric; orthorhombic; ~90 o b. Asymmetric; monoclinic; < 90 o Folds PSG&T 9

10 Fold Vergence Vergence is defined by rotation of axial surface from a symmetrical fold into an asymmetrical fold, without changing orientation of the enveloping surface: (a) Clockwise vergence (b) Counterclockwise vergence Folds PSG&T 10

11 Fold Vergence - Anticlinorium No Xmas tree! Folds PSG&T 11

12 Fold Vergence - Synclinorium Enveloping Surface Axial Surface Folds PSG&T 12

13 Folds in 3D: Cylindrical and Non-cylindrical Folds (a) Cylindrical fold (b) Noncylindrical fold; planar axial surface (c) Noncylindrical fold; curved axial surface Folds PSG&T 13

14 Fold Orientation Folds PSG&T 14

15 Fold Orientation Fold classification based on orientation of hinge line and axial surface Recumbent fold in the Caledonides of northeast Greenland. Folds PSG&T 15

16 Other Fold Geometries: Kink folds and Chevron folds Recumbent chevron folds (Switzerland) Chevron folds (CA) Kink folds (Spain) Folds PSG&T 16

17 Other Fold Geometries: En-echelon Folds 40 32'20.59" N 77 26'36.47" W Hand specimen from N Spain Regional view (central Appalachians) Folds PSG&T 17

18 Other Fold Geometries: Monoclines Monocline near Bighorn Mountains (WY). Folding occurred as Bighorns pushed upward; monocline on western margin of this range. Uplift is part of Laramide deformation in western U.S., which includes the Black Hills (SD), Front Range of the Rockies, and others. C Carrigan Folds PSG&T 18

19 Fault-related Folding fault-bend folds fault-propagation fold Folds PSG&T 19

20 Fault-propagation Folds Fault-propagation fold in Lost River Range, Idaho, showing asymmetric fold dying out updip. Progressive development of a fault-propagation fold. Folds PSG&T 20

21 Thrust Type: Imbricate Fan Relative small displacements. Break-forward ( piggy-back ) thrusting. Successively younger thrusts cut into footwall, and older faults and folds become deformed by younger structures. Folds PSG&T 21

22 Fault-bend Folds Fault-bend fold above McConnell Thrust, Alberta. Paleozoic strata moved 5 km vertically and 40 km horizontally, and lie above Cretaceous foreland basin deposits. (mirror image) Progressive stages during development of fault-bend fold. Dashed lines are traces of axial surfaces. Folds PSG&T 22

23 Thrust Type: Duplex Relatively large displacements. Flat-roofed duplex by progressive breakforward faulting. Roof thrust undergoes a sequence of folding and unfolding. R. Allmendinger Folds PSG&T 23

24 Multiple-ramp Structures ramp anticline and ramp syncline Note that number of hanging-wall ramps must match number of footwall ramps. 3D block diagram with types of fault ramps (hanging wall removed). Tear faults are vertically dipping lateral ramps. Folds PSG&T 24

25 Detachment Folds 47 12'50.95" N 7 27'11.18" E Detachment folds above pre-triassic basement (Jura Mnts, Switzerland). Small-scale folds in anhydrite (Delaware Basin, TX), with detachments in organicrich (dark) calcite layers. Folds PSG&T 25

26 Elements of Fold Classification fold shape in profile interlimb angle similar/parallel symmetry/vergence fold size amplitude wavelength fold facing upward/downward fold orientation axis/hinge line axial surface fold in 3D cylindrical/non-cylindrical presence of secondary features foliation lineation DePaor, 2002 Folds PSG&T 26

27 Elements of Fold Style Fold Style: What is the interlimb angle in profile? Is the fold classified as parallel or similar (or further refinement)? In three-dimensions, is the fold cylindrical or non-cylindrical? Is there an associated axial plane foliation and/or lineation present, and of what type are they (these will be discussed later)? Note: orientation and symmetry are not fold style criteria Folds PSG&T 27

28 Super(im)posed Folding: Fold Interference Patterns Type 1; egg box Type 3; zig-zag Type 2; mushroom Folds PSG&T 28

29 Fold Interference F A F B F A recumbent folds (a) are overprinted by F B upright folds (b), producing the fold interference pattern in (c). ( zig-zag fold ) Folds PSG&T 29

30 Fold Interference F A recumbent folds (a) are overprinted by F B upright folds (b), producing the fold interference pattern in (c). Folds PSG&T 30

31 Basic Fold Interference Patterns F2 shear folds (a 2 is relative shear direction and b 2 is hinge line) are superimposed on pre-existing F1 folds. Folds PSG&T 31

32 Extra: Fold Interference Schema Geometric axes describing orientation of fold generations F1 and F2 (a), and corresponding interference patterns (b). In all patterns, layering initially parallel to front face of cube. F1 resembles case D; F2 is similar to the folding in case D, but with different orientations. Axial surface S1 is shown with dotted lines and axial surface S2 with dashed lines. Folds PSG&T 32

33 Homework: Visible Geology This site allows you to create fold interference patterns and look at them from different angles, and introduce erosional surfaces and topography. You need to create a layered block first. Go to Geologic Beds and add beds until the block is filled. Then go to Folds and create outcrop pattern, and add second fold to calculate outcrop pattern. Fold, Rotate, Erode, Learn Folds PSG&T 34

34 High Strain Zones: Fold Transposition Asymmetric fold develops at perturbation (a d), which then gets refolded (e f). Folds PSG&T 35

35 High Strain Zones: Sheath Folds Grenville Front, Ontario, Canada Folds PSG&T 36

36 Folding: Bending vs Buckling (a) Bending a layer (e.g., monocline). (b) Buckling a layer. Buckling: a) Compression of a foam block; b) with irregularly shaped foam layers separated by thin sheets of rubber; c) with uniform foam layers separated by thin sheets of rubber. Folds PSG&T 38

37 Trick in a Box: Experiments with Analogues (a) Foam-only box shows thickening of marker line, but no folding. (b) Boxes with rubber bands show folds with arc lengths varying as a function of thickness of each band. (c) When using more than one rubber band, behavior depends on combination of bands and their thicknesses, with thicker bands dominant. Folds PSG&T 39

38 Wavelength-Thickness Relationship 39 42'52.80" N 78 17'07.94" W Log log plot of wavelength (W) versus layer thickness (t) in folded sandstone layers (US Appalachians). Sideling Hill, MD Folds PSG&T 40

39 Fold Math: Single Layer Biot-Ramberg equation Linear (Newtonian) viscosity, the wavelength-thickness (W-t) relationship for a single layer with viscosity L in matrix with viscosity M : W = 2 t( L /6 M ) 1/3 or, viscosity ratio is proportional to the cube of the L/t ratio: L / M = 6/8 3 (W/t) 3 Folds PSG&T 41

40 Thickness, Wavelength and Viscosity W s = 2 t( L /6 M ) 1/3 L / M = 6/8 3 (W/t) 3 Appalachian folds: calculated viscosity ratio, sandstone / shale (layer/matrix), is ~500. Box Experiments: calculated viscosity ratio rubber / foam is ~1000. Folds PSG&T 42

41 More Fold Math: Multi-Layer Biot-Ramberg equation Linear (Newtonian) viscosity, the wavelength-thickness (W-t) relationship for a single layer with viscosity L in matrix with viscosity M : W = 2 t( L /6 M ) 1/3 or, viscosity ratio is proportional to the cube of the L/t ratio: L / M = 6/8 3 (W/t) 3 Interacting Multilayers For N interacting multilayers: W multi = 2 t(n L /6 M ) 1/3 Note: W single /W multi =N 2/3 so N multilayers N.t single layer Folds PSG&T 43

42 Effect of Viscosity Contrast (η L )/(η M ) Finite-element modeling of single-layer buckling for various viscosity contrasts between layer (η L ) and matrix (η M ), and shortening strains (%). Smaller contrast, greater layer thickening (modified Biot-Ramberg equation). viscosity contrast Short tick marks are orientation of long axis of strain ellipse in profile plane. Folds PSG&T 44

43 Extra: Fold Math and Strain Biot-Ramberg equation Linear (Newtonian) viscosity, the wavelength-thickness (W-t) relationship for a single layer with viscosity L in matrix with viscosity M : W s = 2 t( L /6 M ) 1/3 or, viscosity ratio is proportional to the cube of the W/t ratio: L / M = 6/8 3 (W/t) 3 Strain-modified Biot-Ramberg equation Incorporating the role of strain, with R=X/Z: W s = 2 t [( L (R-1))/(6 M.2R 2 )] 1/3 Folds PSG&T 45

44 Flexural Folding and Strain Strain pattern of flexural folding in fold profile plane (plane perpendicular to hinge line). Formation of parallel folds. Folds PSG&T 46

45 Neutral-surface Folding and Strain Strain pattern of neutral-surface folding in fold profile plane. Formation of parallel folds. What about similar folds? Folds PSG&T 47

46 Superimposed Homogeneous Strain and Similar Folds Effect of superimposed homogeneous strain on: (a) flexural fold; (b) neutral-surface fold. Constant volume, plane strain with X/Z = 1.6 (20% shortening), and X/Z = 6.3 (60% shortening). In both cases a parallel fold evolves into a similar fold. Folds PSG&T 48

47 Natural Example of Fold Strain L (a) Strain pattern in natural fold of limestone-pebble conglomerate; (c) vs. strain predicted in flexural folding; (d) and neutral-surface folding. W (b) With further modification, initial compaction and material transport away from inner arc region, a strain pattern like that observed in natural sample is re produced. e = (W-L)/L = (= 35% shortening) Folds PSG&T 49

48 Representative Folding Scenario with Incremental and Finite Strains Deformation history: (a) deposition (b) 20% compaction (volume loss) (c) layer-parallel shortening (layer thickening) (d) buckling (flexural flow) creating parallel fold (e) homogeneous shortening creating similar fold Strain at each step shown (~70% total shortening) Folds PSG&T 50