ptys 411 geology and geophysics of the solar system tectonics
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PTYS 411
Geology and Geophysics of the Solar System
TectonicsTectonics
PYTS 411– Tectonics 2
Relative movement of blocks of crustal material
Moon & Mercury –
Wrinkle Ridges
Europa – Extension and strike-slip Enceladus - Extension
Mars –
Extension and compressionEarth –
Pretty much everything
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Compositional vs. mechanical terms Crust, mantle, core are compositionally different
Earth has two types of crust
Lithosphere, Asthenosphere, Mesosphere, Outer Core and Inner Core are mechanically different
Earth’s lithosphere is divided into plates…
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How is the lithosphere defined? Behaves elastically over geologic time
Warm rocks flow viscously Most of the mantle flows over geologic time
Cold rocks behave elastically Crust and upper mantle
Melosh, 2011
Rocks start to flow at half their melting temperature
Thermal conductivity of rock is ~3.3 W/m/K At what depth is T=Tm/2
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Response of materials to stress (σ) – elastic deformation
LΔL ΔL
Linear strain (ε) = ΔL/L Shear 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
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Stresses act in three orthogonal directions Principle stresses – all longitudinal Pressure is
And produces strains in those directions Principle strains – all longitudinal
Stretching a material in one direction usually means it wants to contract in orthogonal directions
Quantified with Poisson’s ratio This property of real materials means shear stain is always
present
Extensional strain of σ1/E in one direction implies orthogonal compression of –ν σ1/E
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
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Groups of two of the previous parameters describe the elastic response of a solid
Conversions between parameters is straightforward Personal preference to use E and v
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Earth – plate tectonics… Plate margins are very active Stresses also drive tectonics far from
plate margins
What drives planetary tectonics
Basin and range extension, USA Himalayas, Tibet
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What about the other planets? – shape changes…
Moon Recedes from the Earth and synchronously locked Tidal bulge shrinks
Mercury Spindown into Cassini state
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Europa Thickening ice shell provides extension Cooling ice shell
compression near surface Extension at depth
Nimmo, 2004
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Core freezes into a solid inner core over time Slowed by sulfur Causes planetary contraction
Core still liquid? Cooling models say probably not
Unless there’s a lot of (unexpected) sulfur Earth-based radar observations of longitudinal librations – core is still partly molten
Size changes
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Extensive set of lobate scarps exist. No preferred azimuth Global distribution Sinuous or arcuate in plan Interpreted as thrust faults
Shortened craters give estimates of fault movement Fault angle is still a guess (usually ~30 deg) Shrinkage inferred is 1-2km
Discovery Rupes
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Io – global compression Burial by volcanic debris compresses the whole crust Burial rates 1cm/year
~135 mountains found, 104 definitely tectonic Average height 6km, max height 17km Steep sided with asymmetric shape
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Ridged plains – 70 % Venusian surface Emplaced over a few 10’s Myr Deformed with wrinkle ridges (compressional faults)
1-2 km wide, 100-200 km long
Extensive graben areas also record extension
Global extension and compression
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Emplacement of plains material followed by widespread compression
Solomon et al. (and some other papers) describe a climate-volcanism-tectonism feedback mechanism
Resurfacing releases a lot of CO2 causing planet to warm up Heating of surfaces causes thermal expansion resulting in
compressive forces. Explains pervasive wrinkle ridge formation on volcanic plains
Climate-Driven Tectonics?
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Shape Changes From Tides
Eccentric orbits + tides = heating Satellite rotation cannot be synchronous
Bulge position moves around surface – causes deformation and heating
Satellite distance varies Size of bulge varies – causes deformation and heating
Repeated squeezing can cause a lot of energy dissipation
2 orbits
Eccentricity get damped down by tidal dissipation Europa?
Still getting tidally pumped because e≠0 Io is in a 2:1 resonance with Europa Europa is in a 2:1 resonance with Ganymede Europa eccentricity gets pumped by both moons
Moon e
Io 0.004
Europa 0.010
Ganymede 0.002
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Double ridges – Europa’s most common landform V-shaped groove in center 0.5-2km wide 1000’s km long Surface texture preserved on slopes
Alternating extension and compression Pumps material to the surface One pump per orbit Expelled material forms ridges Time-limited by non-synchronous rotation
Cross-section!
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Materials fail under too much stress Elastic response up to the yield stress Plastic deformation after that Brittle or ductile failure after that
Brittle failure Ductile (distributed) failure
Strain hardening
Strain Softening
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Crack are long and thin Approximated as ellipses a >> b Effective stress concentrators
Larger cracks are easier to grow
a
b
σ
σ
What sets this yield strength? Mineral crystals are strong, but rocks are packed with microfractures
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Consider differential stress as what is driving material to fail Tresca criterion:
Von Mises Criterion:
Increase confining pressure Increases yield stress Promotes ductile failure Increase temperature
Decrease yield stress Promotes ductile failure
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Low confining pressure Weaker rock with brittle faulting
High confining pressure (+ high temperatures) Stronger rock with ductile deformation
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Failure envelopes When shear stress exceeds a critical value then failure occurs Critical shear stress increases with increasing pressure Rocks have finite strength even with no confining pressure
Coulomb failure envelope Yo is rock cohesion (20-50 MPa)
fF is the coefficient of internal friction (~0.6)
Melosh, 2011
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Brittle to ductile transition Confining pressure increases
with Depth (rocks get stronger)
Temperature increases with depth and promotes rock flow
Upper 100m – Griffith cracks
P~0.1-1 Kbars, z < 8-15km, shear fractures
P~10 kbar, z < 30-40km distributed deformation (ductile)
This transition sets the depth of faults
Melosh, 2011
PYTS 411– Tectonics 26
What about supporting planetary topography?
Lithostatic case Stress differences are zero
Confined sedimentary basin Vertical compression causes horizontal stresses Stress differences increases with depth
Surface loads, maximum Maximum stress differences are deeper than the
base of the mountain Maximum stresses differences are about
½ to ⅓ of the maximum load
Melosh, 2011
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If topography is limited by the strength of the rocks then:
Or
Or:
Bigger planets mean smaller mountains Works well for some planets
Max h on the Earth ~8km Max h on Venus ~8km Max h on Mars ~24km
Not so well for the Moon and Mercury
Melosh, 2011
PYTS 411– Tectonics 28
Large objects have small irregularities – limited by rock strength
Small objects have large irregularities – limited by friction
Melosh, 2011
Vesta is right at the elbow in this curve
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Most asteroids are probably rubble piles i.e. the rock is already broken up How much shear stress do you need to slide broken rocks past each other? Limited by friction
Experiments show: Amonton’s or Byerlee’s law – the harder you press the fault together the stronger it is Coefficient of friction fs= tan(Φ), about 0.6 for many geologic materials
Within an asteroid: Pressure ( ) presses the rocks together and irregularities in the shape produce the
shear stress. 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 radiusMelosh, 2011
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Large objects have small irregularities – limited by rock strength
Small objects have large irregularities – limited by friction
Melosh, 2011
Vesta is right at the elbow in this curve
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Anderson theory of faulting All faults explained with shear stresses No shear stresses on a free surface means
that one principle stress axis is perpendicular to it.
Three principle stresses σ1 > σ2 > σ3
σ1 bisects the acute angle
σ2 parallel to both shear plains
σ3 bisects the obtuse angle
So there are only three possibilities One of these principle stresses is the one that
is perpendicular to the free surface.
Note all the forces here are compressive…. Only their strengths differ
σ2
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Before we talk about faults….
Fault geometry Dip measures the steepness of the fault plane Strike measures its orientation
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Largest principle (σ1) stress perpendicular to surface
Typical dips at ~60°
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Crust gets pulled apart
Final landscape occupies more area than initial
Can occur in settings of Uplift (e.g. volcanic dome) Edge of subsidence basins (e.g. collapsing
ice sheet)
Extensional Tectonics
Shallowly dipping
Steeply dipping
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Horst and Graben Graben are down-dropped blocks of crust Parallel sides Fault planes typically dip at 60 degrees Horst are the parallel blocks remaining
between grabens Width of graben gives depth of fracturing On Mars fault planes intersect at depths of
0.5-5km
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In reality graben fields are complex… Different episodes can produce different orientations Old graben can be reactivated
Lakshmi -VenusCeraunius Fossae - Mars
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Smallest (σ3) principle stress perpendicular to surface
Typical dips of 30°
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Compressional Tectonics
Crust gets pushed together
Final landscape occupies less area than initial
Can occur in settings of Center of subsidence basins (e.g. lunar maria)
Overthrust – dip < 20 & large displacements
Blindthrust – fault has not yet broken the surface
Shallowly dipping
Steeply dipping
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Intermediate (σ2) principle stress perpendicular to surface
Typically vertical
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Strike Slip faults Shear forces cause build up of strain Displacement resisted by friction Fault eventually breaks
Right-lateral (Dextral)
Left-lateral (Sinistral)
Shear Tectonics
Vertical Strike-slip faults = wrench faults
Oblique normal and thrust faults have a strike-slip component
Europa
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Extras
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Basically because the coefficients of static and dynamic friction are different
Stick-slip faults store energy to release as Earthquakes
Shear-strain increases with time as:
Stress on the fault is: G is the shear modulus σfd (dynamic friction) left over from previous break
Fault can handle stresses up to σfs before it breaks (Static friction)
Breaks after time:
Fault locks when stress falls to σfd (dynamic friction) If σfd < σfs then you get stick-slip behavior
Why do faults stick and slip?
PYTS 411– Tectonics 43
How much of a stress difference? Depends on orientation relative to the principle stresses In two dimensions… Normal and shear stresses form
a Mohr circle
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Coulomb failure criterion is a straight line Intercept is cohesive strength Slope = angle of internal friction
In geologic settings Angle of internal friction ~30°
Angle of intersection gives fault orientation
So θ is ~60°