PTYS 411

Geology and Geophysics of the Solar System

TectonicsTectonics

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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

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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

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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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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?

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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°