1. Midterm next Monday, October 14 Midterm Review

2. What is structural geology? - Study of rock deformation, “the study of the architecture of the Earth’s crust” - “forensic science”

3. What are structures? Two main types: (1) Primary structures: Develop during formation of a rock body; e.g., cross-bedding, ripple marks, mudcracks, pillows (in basalt) (2) Secondary structures: Form in rocks as a result of deformation- the structures this class are focused on!

4. Goals of Structural Analysis Geometry: mapping, measurements Kinematics: movements related to deformation –Translation: change in position –Rotation: change in orientation –Distortion: change in shape –Dilation: change in size Dynamics/Mechanics: relating deformation to stresses

5. Structural measurements Planar structures Strike: compass direction of trace of horizontal line on a plane; bearing (quadrant, E or W of north) or azimuth (degrees clockwise from N) Dip: inclination of plane from horizontal, perpendicular to strike

6. Linear structures Trend: direction of a vertical plane that contains the linear feature in the direction of plunge. Plunge: angle between line and horizontal

7. Oceanic Crust - forms at mid-ocean ridges by partial melting of mantle - basaltic (mafic) in composition - igneous extrusion and intrusion - 5 to 10 km-thick - Oceanic crust is no older than ~200 Ma. Why??

8. Continental Crust - 5 to 10 times thicker than oceanic crust- 40 km avg. - This is a simplified sketch! Continental crust is very heterogeneous - Long and complex deformation history. Majority of continental crust formed during the Precambrian (before ~570 Ma) The oldest known rock is ~4 Ga! Why so much older than oceanic crust??

9. Rheology (behavior during deformation) of the Earth Lithosphere: "lithos" = rock, implying strength. It exhibits a component of elastic strength over geological time scales. Includes crust + uppermost mantle! Varies in thickness. Moves as a plate- exceptions are orogens. Asthenosphere: Weak. It is solid, but behaves like a viscous fluid (convective flow) over geological time scales.

10. How do we know that plates move? - Earthquakes localized along plate boundaries

11. Transform faults: more evidence for plate motion Not observed! Observed!

12. Continents also break- to form new oceans

13. Ocean-Continent convergent margins

14. An example of continent-continent collision: The Indo-Asian Collision

15. Transform plate boundaries An example: San Andreas

16. Pangea supercontinent and Tethys Ocean http://www.scotese.com/earth.htm

17. Joint: A natural fracture that forms by tensile loading- walls of fracture move apart slightly as joint develops

18. Plumose structure: A subtle roughness on surface of some joints; resembles imprint of a feather. Due to inhomogeneity of rock.

19. Joints/Fractures: Kinematics ribs are arrest lines- opening is not instantaneous, but rhythmic, like splitting wood

20. Cooling joints: form by thermal contraction

21. Exfoliation joints: Form by unloading of bedrock through erosion. They form parallel to topography

22. Tectonic joints: Form by tectonic stresses as opposed to stresses induced by topography.

23. Strike-slip faults: Accommodate horizontal slip between adjacent blocks left lateral vs. right lateral: sense-of-slip relative to a chosen block left lateral (sinistral) right lateral (dextral)

24. Hanging wall: The block toward which the fault dips. Footwall: The block on the underside of the fault.

25. http://earth.leeds.ac.uk/learnstructure/index.htm

26. Slip vs. Separation Slip: actual relative displacement Separation: apparent relative displacement

27. The key to describing slip along a fault lies in measuring (1) Direction of displacement (2) Sense of displacement (3) Magnitude of displacement

28. Main types of folds Anticline: fold that is convex in the direction of the youngest beds Syncline: Fold that is convex in the direction of the oldest beds *requires that you know facing direction (direction of youngest beds); know stratigraphy! Antiform: convex up Synform: convex down *simply describes geometry anticline syncline synformal anticline antiformal syncline

29. Geometric analysis inflection point: point of opposing convexity median surface: imaginary surface connecting inflection points fold width, fold height symmetrical vs. asymmetrical concept of vergence

30. hinge zone – hinge line: zone of max. curvature fold axis: imaginary line, which when moved parallel to itself can define the form of a fold Geometric analysis cont.

31. axial surface: surface that passes through successive hinge lines axial trace: line of intersection of axial surface and ground surface Geometric analysis cont.

33. parallel/concentric folds: layer thickness does not change (lower T) similar folds: layer thickness changes; thickening in hinge and thinning along limbs (higher T)

34. Fold mechanisms for "free folds", where fold shapes depend on layer properties (1) Flexural-slip folding- accommodates buckling by layer-parallel slip -direction of relative slip is perpendicular to hinge -individual displacement small, but sum is enough to accommodate bending of rock -marked by strong stiff layers with contacts of low cohesive strength -occurs in uppermost levels of crust

35. minor structures related to flexural- slip folding

36. minor structures related to flexural-flow folding occur at higher temperature

37. plunging folds and map patterns, cont.

38. Introduction to geologic maps Geologic maps show traces of contacts between different rock units, commonly superimposed on topography First step: Every time you see a contact, ask yourself the following questions: (1) Is it a depositional contact? (2) Is it an intrusive contact? (3) Is it a fault contact? So far, we have talked quite a bit about faults, but not the other types of contacts. To fill you in...

39. ophiolitic melange Permian limestone Which way does the fault dip? Second step: Study how the trace of the contact interacts with topography- It will tell you about orientation!

40. Stereographic projection plotting 3D structural data on a hemisphere (usually the lower), which is projected onto a horizontal plane

41. Rake = The acute angle between the horizontal (strike line) and a line in the plane, MEASURED IN THE PLANE

42. Determining the true thickness of a bed For a dipping bed, the map-view thickness is an "apparent" as opposed to "true" thickness! 1. Draw a structural profile (X- section) perpendicular to strike 2. Plot the true dip of the beds and project them to depth 3. Use trigonometry to calculate the true thickness

43. Determining strike and dip from geologic maps (revisited) 75 m

44. What is strain? Strain is dilation (change in size) and/or distortion (change in shape). The Goal of strain analysis is to explain how every line in a body changes in length and angle during deformation. How is this attempted?

45. Some important quantities for describing strain Extension (e): (Lf-Lo)/Lo, where Lf is the final length of a line and Lo is the initial length of a line Stretch (S): Lf/Lo, where 0 = severe shortening, 1 = no shortening, and infinity = severe stretching Quadratic elongation (  (1+e) 2 = (Lf/Lo) 2 = S 2

46. So far- we have only talked about changes in lengths of lines- what about angles? Angular shear ( , psi): degree to which 2 initially perpendicular lines are deflected from 90 degrees Shear strain ( , gamma): = tan (  )

47. What does 'finite' mean? It is total strain, the final result of deformation that we see as geologists Instantaneous or infinitesimal strain describes a tiny increment of deformation As will become apparent when studying how fabrics form in rocks, the orientation of finite strain may be very different than that of instantaneous strain Finite vs. Instantaneous strain

48. Strain ellipse and ellipsoid for homogeneous deformation: Shows how circular reference object is deformed 2-D 3-D Vs=4/3  r 3 Ve=4/3  abc

49. 2 end-member types of plane strain Simple shear: Rock is sheared like a deck of cards. A square becomes a parallelogram. **The finite stretching axes rotate during deformation. Distortion by simple shear is the most important process in shaping shear-zone structures!

50. Pure shear: Rock is shortened in one direction and extended in the perpendicular direction. A square becomes a rectangle. **The finite stretching axes do not rotate.

51. Strain Rate strain rate = extension (e) divided by time (t) = e/t The rate at which a rock is strained has important implications for the manner in which it deforms. "Lab" Strain Rates During 1 hour experiment, an initially 2.297 cm-long sample is shortened to 2.28 cm. What is the average strain rate during this experiment?

52. Force vs. Stress Force: That which changes, or tends to change, body motion Newton's first law of motion: F=ma mass in kg; acceleration in m/s 2 1 Newton (1N) = 1kg m/s 2 Forces are vector quantities; they have magnitude and direction.

53. Stress may be thought of as a description of force concentration Stress on a plane (traction),  = F/A 1N/m 2 = 1 Pa what about units of stress? 100 MPa = 1 kbar

54. lithostatic stress vertical force =  Vg =  L 3 g vertical stress =  L 3 g/L 2 =  gL  gL = (2700 kg/m 3 )(10m/s 2 )(1500m) = 40500000 Pa = 40.5 MPa =.405 kbar

55. A complete definition of Stress = a description of tractions at a given point on all possible surfaces going through the point  1: axis of greatest principal stress  3: axis of least principal stress 11 11 33 33  1 and  3 always perpendicular and always perpendicular to planes of no shear stress

56. Geometric approach: Mohr Stress Diagram a plot of  s vs.  n first step: plot  1 and  3 recalling that they are in directions of no shear stress; draw Mohr circle

57. second step: Draw a line representing the plane at 2 , measured from  3.

58. mean stress: (  1 +  3 )/2 center of circle causes dilation differential stress: (  1 -  3 ) diameter of circle causes distortion

59. 11 11 33 33 instantaneous strain ellipse

60. Common types of deformation experiments

61. Compressive strength tests: The Approach   

62.  c = critical shear stress required for failure  0 = cohesive strength tan  = coefficient of internal friction (  )  N = normal stress Coulomb's Law of Failure  c =  0 + tan  (  n )

63. Tensile strength tests with no confining pressure Approach: Similar to compressive strength tests Results: (1) Rocks are much weaker in tension than in compression (2) Fracture oriented parallel to  1 (  = 0)

64. Failure envelopes for different rocks: note that slope of envelope is similar for most rocks  c =  0 + tan  (  n )  c = critical shear stress required for failure  0 = cohesive strength tan  = coefficient of internal friction  N = normal stress

65. Byerlee's Law Question: How much shear stress is needed to cause movement along a preexisting fracture surface, subjected to a certain normal stress? Answer: Similar to Coulomb law without cohesion Frictional sliding envelope:  c = tan  (  N ), where tan  is the coefficient of sliding friction

66. Preexisting fractures of suitable orientation may fail before a new fracture is formed

67. Increasing pore fluid pressure favors failure by counteracting confining pressure! Effective stress =  n – fluid pressure What about fluid pressure?

68. What happens at higher confining pressures? Von Mises failure envelope - Failure occurs at 45 degrees from  1

69. Anderson's Theory of Faulting The Earth's surface is a free surface (contact between rock and atmosphere), and cannot be subject to shear stress. As the principal stress directions are directions of zero shear stress, they must be parallel (2 of them) and perpendicular (1 of them) to the Earth's surface. Combined with an angle of failure of 30 degrees from  1, this gives:

71. An isotropic, homogeneous elastic material follows Hooke's Law Hooke's Law:  = Ee E (Young's Modulus): measure of material "stiffness"; determined by experiment

72. Elastic limit: no longer a linear relationship between stress and strain- rock behaves in a different manner Yield strength: The differential stress at which the rock is no longer behaving in an elastic fashion

73. What happens at higher confining pressure and higher differential stress? Plastic behavior produces an irreversible change in shape as a result of rearranging chemical bonds in the crystal lattice- without failure! Ductile rocks are rocks that undergo a lot of plastic deformation E.g., Soda can rings!

75. Viscous (fluid) behavior Rocks can flow like fluids!

76. For an ideal Newtonian fluid: differential stress = viscosity X strain rate viscosity: measure of resistance to flow

77. The brittle-ductile transition