1. PTYS 411 Geology and Geophysics of the Solar System Tectonics

2. PYTS 411– Tectonics 2 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

3. PYTS 411– Tectonics 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 411– Tectonics 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 411– Tectonics 5 l Response of materials to stress (σ) – elastic deformation LΔL Linear strain (ε) = ΔL/LShear Strain (ε) = ΔL/L E is Young’s modulus G is shear modulus Volumetric strain = ΔV/V K is the bulk modulus L Warning Shear is sometimes defined as half this quantity

6. PYTS 411– Tectonics 6 l Stresses act in three orthogonal directions n Principle stresses – all longitudinal n Pressure is l And produces 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 Where λ is the Lamé parameter G is the shear modulus or LΔL Linear strain (ε) = ΔL/L E is Young’s modulus

7. PYTS 411– Tectonics 7 l Groups of two of the previous parameters describe the elastic response of a solid n Conversions between parameters is straightforward n Personal preference to use E and v

8. PYTS 411– Tectonics 8 l Earth – plate tectonics… n Plate margins are very active n Stresses also drive tectonics far from plate margins What drives planetary tectonics l Basin and range extension, USA l Himalayas, Tibet

9. PYTS 411– Tectonics 9 l What about the other planets? – shape changes… l Moon n Recedes from the Earth and synchronously locked n Tidal bulge shrinks l Mercury n Spindown into Cassini state

10. PYTS 411– Tectonics 10 l Europa n Thickening ice shell provides extension n Cooling ice shell wcompression near surface wExtension at depth Nimmo, 2004

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13. PYTS 411– Tectonics 13 l Core freezes into a solid inner core over time n Slowed by sulfur n Causes planetary contraction l Core still liquid? n Cooling models say probably not wUnless there’s a lot of (unexpected) sulfur n Earth-based radar observations of longitudinal librations – core is still partly molten Size changes

14. PYTS 411– Tectonics 14 l Extensive set of lobate scarps exist. n No preferred azimuth n Global distribution n Sinuous or arcuate in plan n Interpreted as thrust faults l Shortened craters give estimates of fault movement n Fault angle is still a guess (usually ~30 deg) n Shrinkage inferred is 1-2km Discovery Rupes

15. PYTS 411– Tectonics 15 l Io – global compression n Burial by volcanic debris compresses the whole crust n Burial rates 1cm/year l ~135 mountains found, 104 definitely tectonic n Average height 6km, max height 17km n Steep sided with asymmetric shape

16. PYTS 411– Tectonics 16 l Ridged plains – 70 % Venusian surface n Emplaced over a few 10’s Myr n Deformed with wrinkle ridges (compressional faults) w1-2 km wide, 100-200 km long l Extensive graben areas also record extension Global extension and compression

17. PYTS 411– Tectonics 17 l Emplacement of plains material followed by widespread compression l Solomon et al. (and some other papers) describe a climate-volcanism-tectonism feedback mechanism n Resurfacing releases a lot of CO 2 causing planet to warm up n Heating of surfaces causes thermal expansion resulting in compressive forces. n Explains pervasive wrinkle ridge formation on volcanic plains Climate-Driven Tectonics?

18. PYTS 411– Tectonics 18 Shape Changes From Tides l Eccentric orbits + tides = heating n Satellite rotation cannot be synchronous wBulge position moves around surface – causes deformation and heating n Satellite distance varies wSize of bulge varies – causes deformation and heating n Repeated squeezing can cause a lot of energy dissipation 2 orbits l Eccentricity get damped down by tidal dissipation l Europa? n Still getting tidally pumped because e≠0 n Io is in a 2:1 resonance with Europa n Europa is in a 2:1 resonance with Ganymede n Europa eccentricity gets pumped by both moons Moone Io0.004 Europa0.010 Ganymede0.002

19. PYTS 411– Tectonics 19 l Double ridges – Europa’s most common landform n V-shaped groove in center n 0.5-2km wide n 1000’s km long n Surface texture preserved on slopes l Alternating extension and compression n Pumps material to the surface n One pump per orbit n Expelled material forms ridges n Time-limited by non-synchronous rotation Cross- section!

20. PYTS 411– Tectonics 20 l Materials fail under too much stress n Elastic response up to the yield stress n Plastic deformation after that n Brittle or ductile failure after that Brittle failure Ductile (distributed) failure Strain hardening Strain Softening

21. PYTS 411– Tectonics 21 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

22. PYTS 411– Tectonics 22 l Consider differential stress as what is driving material to fail n Tresca criterion: n Von Mises Criterion: l Increase confining pressure n Increases yield stress n Promotes ductile failure l Increase temperature n Decrease yield stress n Promotes ductile failure

23. PYTS 411– Tectonics 23 l Low confining pressure n Weaker rock with brittle faulting l High confining pressure (+ high temperatures) n Stronger rock with ductile deformation

24. PYTS 411– Tectonics 24 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

25. PYTS 411– Tectonics 25 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

26. PYTS 411– Tectonics 26 l What about supporting planetary topography? n Lithostatic case n Stress differences are zero n Confined sedimentary basin n Vertical compression causes horizontal stresses n Stress differences increases with depth n Surface loads, maximum n Maximum stress differences are deeper than the base of the mountain n Maximum stresses differences are about ½ to ⅓ of the maximum load Melosh, 2011

27. PYTS 411– Tectonics 27 l If topography is limited by the strength of the rocks then: n Or n Or: n Bigger planets mean smaller mountains n Works well for some planets wMax h on the Earth ~8km wMax h on Venus ~8km wMax h on Mars ~24km n Not so well for the Moon and Mercury Melosh, 2011

28. PYTS 411– Tectonics 28 l Large objects have small irregularities – limited by rock strength l Small objects have large irregularities – limited by friction Melosh, 2011 Vesta is right at the elbow in this curve

29. PYTS 411– Tectonics 29 l Most asteroids are probably rubble piles n i.e. the rock is already broken up n How much shear stress do you need to slide broken rocks past each other? n Limited by friction l Experiments show: n Amonton’s or Byerlee’s law – the harder you press the fault together the stronger it is n Coefficient of friction f s = tan(Φ), about 0.6 for many geologic materials l Within an asteroid: n Pressure ( ) presses the rocks together and irregularities in the shape produce the shear stress. n If shear stress overcomes then that shape cannot be supported Yield Stress Shear Stress Equating these i.e. topography is just a constant fraction of the asteroids radius Melosh, 2011

30. PYTS 411– Tectonics 30 l Large objects have small irregularities – limited by rock strength l Small objects have large irregularities – limited by friction Melosh, 2011 Vesta is right at the elbow in this curve

31. PYTS 411– Tectonics 31 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 wσ 2 parallel to both shear plains wσ 3 bisects the obtuse angle 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

32. PYTS 411– Tectonics 32 l Before we talk about faults…. l Fault geometry n Dip measures the steepness of the fault plane n Strike measures its orientation

33. PYTS 411– Tectonics 33 l Largest principle (σ 1 ) stress perpendicular to surface n Typical dips at ~60°

34. PYTS 411– Tectonics 34 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

35. PYTS 411– Tectonics 35 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

36. PYTS 411– Tectonics 36 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

37. PYTS 411– Tectonics 37 l Smallest (σ 3 ) principle stress perpendicular to surface n Typical dips of 30°

38. PYTS 411– Tectonics 38 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

39. PYTS 411– Tectonics 39 l Intermediate (σ 2 ) principle stress perpendicular to surface n Typically vertical

40. PYTS 411– Tectonics 40 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

41. PYTS 411– Tectonics 41 l Extras

42. PYTS 411– Tectonics 42 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?

43. PYTS 411– Tectonics 43 l How much of a stress difference? n Depends on orientation relative to the principle stresses n In two dimensions… n Normal and shear stresses form a Mohr circle

44. PYTS 411– Tectonics 44 l Coulomb failure criterion is a straight line n Intercept is cohesive strength n Slope = angle of internal friction l In geologic settings n Angle of internal friction ~30° l Angle of intersection gives fault orientation l So θ is ~60°