1. PTYS 554 Evolution of Planetary Surfaces Tectonics I

2. PYTS 554 – Tectonics I 2 l Tectonics I n Vocabulary of stress and strain n Elastic, ductile and viscous deformation n Mohr’s circle and yield stresses n Failure, friction and faults n Brittle to ductile transition n Anderson theory and fault types around the solar system l Tectonics II n Generating tectonic stresses on planets n Slope failure and landslides n Viscoelastic behavior and the Maxwell time n Non-brittle deformation, folds and boudinage etc…

3. PYTS 554 – Tectonics I 3 l Compositional vs. mechanical terms n Crust, mantle, core are compositionally different wEarth has two types of crust n Lithosphere, Asthenosphere, Mesosphere, Outer Core and Inner Core are mechanically different wEarth’s lithosphere is divided into plates…

4. PYTS 554 – Tectonics I 4 l How is the lithosphere defined? n Behaves elastically over geologic time n Warm rocks flow viscously wMost of the mantle flows over geologic time n Cold rocks behave elastically wCrust and upper mantle Melosh, 2011 l Rocks start to flow at half their melting temperature n Thermal conductivity of rock is ~3.3 W/m/K n At what depth is T=T m /2

5. PYTS 554 – Tectonics I 5 l Relative movement of blocks of crustal material Moon & Mercury – Wrinkle Ridges Europa – Extension and strike-slipEnceladus - Extension Mars – Extension and compression Earth – Pretty much everything

6. PYTS 554 – Tectonics I 6 l The same thing that supports topography allows tectonics to occur n Materials have strength n Consider a cylindrical mountain, width w and height h n How long would strength-less topography last? Weight of the mountain Conserve volume w h v F=ma for material in the hemisphere Solution for h: i.e. mountains 10km across would collapse in ~13s

7. PYTS 554 – Tectonics I 7 l Response of materials to stress (σ) – elastic deformation LΔL Linear (normal) strain (ε) = ΔL/LShear Strain (ε) = ΔL/L E is Young’s modulus G is shear modulus (rigidity) Volumetric strain = ΔV/V K is the bulk modulus L

8. PYTS 554 – Tectonics I 8 l Stress is a 2 nd order tensor n Combining this quantity with a vector describing the orientation of a plane gives the traction (a vector) acting on that plane i describes the orientation of a plane of interest j describes the component of the traction on that plane These components are arranged in a 3x3 matrix Are normal stresses, causing normal strain (Pressure is) Are shear stresses, causing shear strain We’re only interested in deformation, not rigid body rotation so:

9. PYTS 554 – Tectonics I 9 l The components of the tensor depend on the coordinate system used… l There is at least one special coordinate system where the components of the stress tensor are only non-zero on the diagonal i.e. there are NO shear stresses on planes perpendicular to these coordinate axes = Shear stresses in one coordinate system can appear as normal stresses in another Where: These are principle stresses that act parallel to the principle axes The tractions on these planes have only one component – the normal component Pressure again:

10. PYTS 554 – Tectonics I 10 l Principle stresses produce strains in those directions n Principle strains – all longitudinal l Stretching a material in one direction usually means it wants to contract in orthogonal directions n Quantified with Poisson’s ratio n This property of real materials means shear stain is always present l Extensional strain of σ 1 /E in one direction implies orthogonal compression of –ν σ 1 /E n Where ν is Poisson’s ratio n Range 0.0-0.5 Where λ is the Lamé parameter G is the shear modulus or LΔL Linear strain (ε) = ΔL/L E is Young’s modulus

11. PYTS 554 – Tectonics I 11 l Groups of two of the previous parameters describe the elastic response of a homogenous isotropic solid n Conversions between parameters are straightforward

12. PYTS 554 – Tectonics I 12 l Typical numbers (Turcotte & Schubert)

13. PYTS 554 – Tectonics I 13 l Materials fail under too much stress n Elastic response up to the yield stress n Brittle or ductile failure after that l Material usually fails because of shear stresses first n Wait! I thought there were no shear stresses when using principle axis… n How big is the shear stress? Brittle failure Ductile (distributed) failure Strain hardening Strain Softening Special case of plastic flow

14. PYTS 554 – Tectonics I 14 l How much shear stress is there? n Depends on orientation relative to the principle stresses n In two dimensions… n Normal and shear stresses form a Mohr circle Maximum shear stress: On a plane orientated at 45° to the principle axis Depends on difference in max/min principle stresses Unaffected (mostly) by the intermediate principle stress

15. PYTS 554 – Tectonics I 15 l Consider differential stress n Failure when: l Increase confining pressure n Increases yield stress n Promotes ductile failure l Increase temperature n Decrease yield stress n Promotes ductile failure (Tresca criterion) (Von Mises criterion)

16. PYTS 554 – Tectonics I 16 l Low confining pressure n Weaker rock with brittle faulting l High confining pressure (+ high temperatures) n Stronger rock with ductile deformation

17. PYTS 554 – Tectonics I 17 l Crack are long and thin n Approximated as ellipses n a >> b n Effective stress concentrators n Larger cracks are easier to grow a b σ σ l What sets this yield strength? l Mineral crystals are strong, but rocks are packed with microfractures

18. PYTS 554 – Tectonics I 18 l Failure envelopes n When shear stress exceeds a critical value then failure occurs n Critical shear stress increases with increasing pressure n Rocks have finite strength even with no confining pressure n Coulomb failure envelope wY o is rock cohesion (20-50 MPa) wf F is the coefficient of internal friction (~0.6) Melosh, 2011 What about fractured rock? Cohesion = 0 Tensile strength =0 Byerlee’s Law:

19. PYTS 554 – Tectonics I 19 l Basically because the coefficients of static and dynamic friction are different l Stick-slip faults store energy to release as Earthquakes n Shear-strain increases with time as: n Stress on the fault is: wG is the shear modulus wσ fd (dynamic friction) left over from previous break wFault can handle stresses up to σ fs before it breaks (Static friction) n Breaks after time: n Fault locks when stress falls to σ fd (dynamic friction) n If σ fd < σ fs then you get stick-slip behavior Why do faults stick and slip?

20. PYTS 554 – Tectonics I 20 l Brittle to ductile transition n Confining pressure increases with Depth (rocks get stronger) n Temperature increases with depth and promotes rock flow n Upper 100m – Griffith cracks n P~0.1-1 Kbars, z < 8-15km, shear fractures n P~10 kbar, z < 30-40km distributed deformation (ductile) n This transition sets the depth of faults Melosh, 2011 Golembek

21. PYTS 554 – Tectonics I 21 l Back to Mohr circles… l Coulomb failure criterion is a straight line n Intercept is cohesive strength n Slope = angle of internal friction n Tan(slope) = f s l In geologic settings n Coefficient of internal friction ~0.6 n Angle of internal friction ~30° l Angle of intersection gives fault orientation l So θ is ~60° l θ is the angle between the fault plane and the minimum principle stress,

22. PYTS 554 – Tectonics I 22 l Anderson theory of faulting n All faults explained with shear stresses n No shear stresses on a free surface means that one principle stress axis is perpendicular to it. n Three principle stresses wσ 1 > σ 2 > σ 3 wσ 1 bisects the acute angle (2 x 30°) wσ 2 parallel to both shear plains wσ 3 bisects the obtuse angle (2 x 60°) n So there are only three possibilities n One of these principle stresses is the one that is perpendicular to the free surface. n Note all the forces here are compressive…. Only their strengths differ σ2σ2

23. PYTS 554 – Tectonics I 23 l Before we talk about faults…. l Fault geometry n Dip measures the steepness of the fault plane n Strike measures its orientation

24. PYTS 554 – Tectonics I 24 l Largest principle (σ 1 ) stress perpendicular to surface n Typical dips at ~60°

25. PYTS 554 – Tectonics I 25 l Crust gets pulled apart l Final landscape occupies more area than initial l Can occur in settings of n Uplift (e.g. volcanic dome) n Edge of subsidence basins (e.g. collapsing ice sheet) Extensional Tectonics Shallowly dipping Steeply dipping

26. PYTS 554 – Tectonics I 26 l Horst and Graben n Graben are down-dropped blocks of crust n Parallel sides n Fault planes typically dip at 60 degrees n Horst are the parallel blocks remaining between grabens n Width of graben gives depth of fracturing n On Mars fault planes intersect at depths of 0.5-5km

27. PYTS 554 – Tectonics I 27

28. PYTS 554 – Tectonics I 28 l In reality graben fields are complex… n Different episodes can produce different orientations n Old graben can be reactivated Lakshmi -Venus Ceraunius Fossae - Mars

29. PYTS 554 – Tectonics I 29 l Smallest (σ 3 ) principle stress perpendicular to surface n Typical dips of 30°

30. PYTS 554 – Tectonics I 30 Compressional Tectonics l Crust gets pushed together l Final landscape occupies less area than initial l Can occur in settings of n Center of subsidence basins (e.g. lunar maria) l Overthrust – dip < 20 & large displacements l Blindthrust – fault has not yet broken the surface Shallowly dipping Steeply dipping

31. PYTS 554 – Tectonics I 31 Montesi and Zuber, 2003.

32. PYTS 554 – Tectonics I 32 l Intermediate (σ 2 ) principle stress perpendicular to surface n Fault planes typically vertical

33. PYTS 554 – Tectonics I 33 l Strike Slip faults n Shear forces cause build up of strain n Displacement resisted by friction n Fault eventually breaks Right-lateral (Dextral) Left-lateral (Sinistral) Shear Tectonics l Vertical Strike-slip faults = wrench faults l Oblique normal and thrust faults have a strike-slip component Europa

34. PYTS 554 – Tectonics I 34 l Tectonics I n Vocabulary of stress and strain n Elastic, ductile and viscous deformation n Mohr’s circle and yield stresses n Failure, friction and faults n Brittle to ductile transition n Anderson theory and fault types around the solar system l Tectonics II n Generating tectonic stresses on planets n Slope failure and landslides n Viscoelastic behavior and the Maxwell time n Non-brittle deformation, folds and boudinage etc…

35. PYTS 554 – Tectonics I 35 l Random extras

36. PYTS 554 – Tectonics I 36 l How to faults break? l Shear zone starts with formation of Riedel shears (R and R’) n Orientation controlled by angle of internal friction l Formation of P-shears n Mirror image of R shears n Links of R-shears to complete the shear zone Revere St., San Francisco (Hayward Fault)

37. PYTS 554 – Tectonics I 37 l Wrinkle ridges n Surface expression of blind thrust faults (or eroded thrust faults) n Associated with topographic steps n Upper sediments can be folded without breaking n Fault spacing used to constrain the brittle to ductile transition on Mars Montesi and Zuber, 2003.

38. PYTS 554 – Tectonics I 38 l Rocks flow as well as flex n Stress is related to strain rate n Viscous deformation is irreversible n Motion of lattice defects, requires activation energies n Viscous flow is highly temperature dependant Where η is the dynamic viscosity w h v Solution for h: Back to our mountain example Works in reverse too… In the case of post-glacial rebound τ ~ 5000 years w ~ 300km Implies η ~ 10 21 Pa s – pretty good

39. PYTS 554 – Tectonics I 39 l How to quantify τ fs n Sliding block experiments n Increase slope until slide occurs n Normal stress is: n Shear stress is: n Sliding starts when: l Experiments show: n Amonton’s law – the harder you press the fault together the stronger it is n So f s =tan(Φ) n f s is about 0.85 for many geologic materials l In general: n Coulomb behavior – linear increase in strength with confining pressure n C o is the cohesion n Φ is the angle of internal friction n In loose granular stuff Φ is the angle of repose (~35 degrees) and C o is 0.

40. PYTS 554 – Tectonics I 40 l Effect of pore pressure n Reduces normal stress… n And cohesion term… n Material fails under lower stresses n Pore pressure – interconnected full pores n Density of water < rock n Max pore pressure is ~40% of overburden l Landslides on the Earth are commonly triggered by changes in pore pressure