EART 160: Planetary Science

Last Time

• HW 2 due Today– How are people doing?

• Planetary Surfaces– Volcanism– Magma– Volcanic Features on Planets

Today

• HW 2 due Today (for reals)

• Planetary Surfaces– Tectonics– Stress and Strain– Faults and Folds

Tectonics• Global tectonic patterns give us information

about a planet’s thermal evolution• Abundance and style of tectonic features

tell us how much, and in what manner, the planet is being deformed – How active is it?

• Some tectonic patterns arise because of local loading (e.g. by volcanoes)

Modes of Deformation

• Extension

• Compression

• Shear

Extensional Tectonics

37km diameter

Pappalardo & Collins 2005Diam. appx 40km

Craters on Ganymede

Valles Marineris, Mars (~8km deep)

Crater on Venus

Extension• Extension accommodated by normal faulting

L0

L

0

0

sinsin

LL

Stretching factor:

• Fault blocks rotate as extension proceeds

• Typical normal faults start with dips of 60o and lock up when dips=30o, giving stretching factor = 1.7

• Stretching factor also controls amount of subsidence that happens during extension

A Martian Rift Valley

Hauber and Kronberg, JGR Planets, 2001

•Looks similar to terrestrial continental rifts.•Not been heavily studied, but may provide useful insights into crustal properties.

Graben Systems

across)

15km

Steep scarp

Relay ramp?

Flatfloor

Canyonlands graben, Utah, 2km across

Graben, Ganymede

Bands (Europa)

Sullivan et al., Nature (1998)

20km

What drives the extension?

Compression

• Accomodated by reverse (or thrust) faulting• Typical reverse faults start with dips of 30o

L0

L

Rarely Seen on Icy Satellites

Prockter and Pappalardo, Science 2000

The only exampleof unambiguously documented compressional features on Europa to date

Lots of Extension, No compression. How can this be?

Wrinkle Ridges and Lobate Scarps• Probably thrust faults at depth (see

cartoon)• Found on Mars, Moon, Mercury,

Venus• Possibly related to global

contraction due to cooling?• Spacing may be controlled by

crustal structure

Tate et al. LPSC 33, 2003

50km

Krieger crater, Moon

25 km

Mars, MOC wide-angle

Io compressional tectonics• Burial leads to large compressive stresses due to change in

radius• Stresses easily large enough to

initiate faulting• Additional compressive stresses may

arise from reheating the base of the crust

R

After McKinnon et al.,Geology 2001

Low-angle thrust faulting is probably responsible for many of the mountain ranges seen on Io

Schenk and Bulmer, Science 1998

550 km10km

stereo

• Horizontal Movement

Strike-slip Motion

Right-LateralLeft-Lateral

• Relatively rare (only seen on Earth & Europa)• Associated with plate tectonic-like behaviour

Europa, oblique strike-slip (image width 170km)

Plate Tectonics• Dominant style of

tectonics on Earth• Unknown elsewhere• Early Plate Tectonics

on Mars?– (Sleep 1994, Nimmo &

Stevenson, 2000)

Image Credit: USGS

Stress

• Stresses are forces per unit area that are transmitted through a material.– Stresses transmitted perpendicular to a

surface are normal stresses– Stresses transmitted parallel to a surface are

shear stresses zz xz

Strain

• Stress in an elastic solid results in strain, or deformation of the solid– Normal strain is the change in length

compared to the original length– Shear strain is the change in

angle due to deformation.

x

x‘

wx

xx = x’/x xz = -½ (1 – 2)

Stress and Strain in Solids

• Stress and Strain are Tensors (think of it as a vector of vectors)

Maximum direction of principal stress controls style of fault.

xxxx

yy

yyzz

zz

zzzyzx

yzyyyx

xzxyxx

Rheology

• Rheology is the study of the deformation and flow of matter under the influence of an applied stress

• If the deformation (or strain, ) follows the stress, , the material is elastic– Returns to original state when stress is

released

• If the strain rate, d/dt follows the stress, , the material is viscous

Elastic Viscous

E

y

Plastic behavior

E is the Young’s Modulus, or elasticity

Analagous to the spring constant in Hooke’s Law

is the viscosity

Rarely a straight line plot in reality

0Failure Strength

YieldStrength

Brittle Behavior

Deformation• You can think of Young’s modulus (units: Pa) as

the stress required to cause a strain of 100%• Typical values for geological materials are

– E = 100 GPa (rocks) and 10 GPa (ice)– = 1021 Pa s (rocks) 1014 Pa s (ice)

• HIGHLY Temperature, Pressure, Stress-dependent

• Elastic deformation is reversible; but if strains get too large, material undergoes fracture (irreversible)

• Material may be both elastic AND viscous, depending on the time-scale.

• We’ll talk more about this next week – Planetary Interiors.

water

ice

Mechanisms: Extension• For icy satellites, one possible

explanation for the ubiquitous extension is that they possess floating ice shells which thickened with time (see below)

• Why should the shell thicken?

Mechanisms: Compression• Silicate planets frequently exhibit

compression (wrinkle ridges etc.)• This is probably because the planets

have cooled and contracted over time• Why do planets start out hot?• Further contraction occurs when a liquid

core freezes and solidifies• Contractional strain given by

Hot mantle

Liquid core

Cool mantle

Solid core

T Where is the thermal expansivity (3x10-5 K-1), T is the temperature change and the strain is the fractional change in radius

Tectonic Stresses & Byerlee’s law

• Byerlee’s law says that faults don’t move unless the shear stress exceeds the normal stress times the friction coefficient f

• For almost all geological materials, f=0.6 (unless the fault is lubricated somehow)

fault

Shear stress Normalstress

• In general, the normal stress is simply the overburden pressure:

• The shear stresses are provided by tectonic effects• E.g. to cause a fault 10 km deep on Earth to move requires tectonic stresses of 180 MPa

(a lot!)• Typical tectonic stresses on Earth are usually 10-100 MPa

P = ghAlso applies to atmospheres!

P = gz

n

z

Stress on a Fault

n = Normal Stress = Shear StressP = Pressure (Lithostatic Stress)

tec

Elastic Flexure• The near-surface, cold parts of a planet (the

lithosphere) behaves elastically• This lithosphere can support loads (e.g. volcanoes)• We can use observations of how the lithosphere

deforms under these loads to assess how thick it is• The thickness of the lithosphere tells us about how

rapidly temperature increases with depth i.e. it helps us to deduce the thermal structure of the planet

• The deformation of the elastic lithosphere under loads is called flexure

• EART162: Planetary Surfaces

Flexural Stresses

• In general, a load will be supported by a combination of elastic stresses and buoyancy forces (due to the different density of crust and mantle)

• The elastic stresses will be both compressional and extensional (see diagram)

• Note that in this example the elastic portion includes both crust and mantle

Elastic plateCrust

Mantle

load

Flexural Parameter• Consider a load acting

on an elastic plate: Te

m

load

3

2

1

4

3 ( )(1 )e

m w

ET

g

w

• The plate has a particular elastic thickness Te

• If the load is narrow, then the width of deformation is controlled by the properties of the plate• The width of deformation is called the flexural parameter and is given by

E is Young’s modulus, g is gravity and n is Poisson’s ratio (~0.3)

• If the applied load is much wider than , then the load cannot be supported elastically and must be supported by buoyancy (isostasy)

• If the applied load is much narrower than , then the width of deformation is given by

• If we can measure a flexural wavelength, that allows us to infer and thus Te directly.

• Inferring Te (elastic thickness) is useful because Te is controlled by a planet’s temperature structure

Example• This is an example of a profile

across a rift on Ganymede• An eyeball estimate of would

be about 10 km• For ice, we take E=10 GPa,

=900 kg m-3 (there is no overlying ocean), g=1.3 ms-2

Distance, km

10 km

• If =10 km then Te=1.5 km

• A numerical solution gives Te=1.4 km – pretty good!

• So we can determine Te remotely

• This is useful because Te is ultimately controlled by the temperature structure of the subsurface

Te and temperature structure• Cold materials behave elastically• Warm materials flow in a viscous fashion• This means there is a characteristic temperature

(roughly 70% of the melting temperature) which defines the base of the elastic layer

110 K270 K

elastic

viscous

190 K•E.g. for ice the base of the elastic layer is at about 190 K• The measured elastic layer thickness is 1.4 km (from previous slide)• So the thermal gradient is 60 K/km• This tells us that the (conductive) ice shell thickness is 2.7 km (!)

Depth

1.4 km

Temperature

Te in the solar system• Remote sensing observations give us Te

• Te depends on the composition of the material (e.g. ice, rock) and the temperature structure

• If we can measure Te, we can determine the temperature structure (or heat flux)

• Typical (approx.) values for solar system objects:Body Te (km) dT/dz

(K/km)Body Te dT/dz

(K/km)

Earth (cont.)

30 15 Venus (450oC)

30 15

Mars (recent)

100 5 Moon (ancient)

15 30

Europa 2 40 Ganymede

2 40

Next Time

• Paper Discussion– Mars Crust and Mantle (Zuber et al., 2001)– Io Volcanism (Spencer et al., 2007)

• Planetary Surfaces: Gradation– Fluvial (Water)– Aeolian (Wind)– Glacial (Ice)– Mass Wasting (Gravity)– Sputtering (Charged Particles)