Transcript Powerpoint
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 Valles Marineris, Mars (~8km deep) Craters on Ganymede 37km diameter Crater on Venus Pappalardo & Collins 2005 Diam. appx 40km Extension • Extension accommodated by normal faulting 0 Stretching factor: L0 L L0 sin 0 sin L • 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 •Looks similar to terrestrial continental rifts. •Not been heavily studied, but may provide useful insights into crustal properties. Hauber and Kronberg, JGR Planets, 2001 Graben Systems 15km Steep scarp Relay ramp? across) Canyonlands graben, Utah, 2km across Flat floor Graben, Ganymede Bands (Europa) 20km What drives the extension? Sullivan et al., Nature (1998) Compression • Accomodated by reverse (or thrust) faulting • Typical reverse faults start with dips of 30o L0 0 L Rarely Seen on Icy Satellites Lots of Extension, No compression. How can this be? The only example of unambiguously documented compressional features on Europa to date Prockter and Pappalardo, Science 2000 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 25 km Krieger crater, Moon 50km Mars, MOC wide-angle Tate et al. LPSC 33, 2003 Io compressional tectonics • Burial leads to large compressive stresses due to change in radius • Stresses easily large enough to DR initiate faulting After McKinnon et al., • Additional compressive stresses may arise from reheating the base of the crust Geology 2001 stereo 550 km 10km Schenk and Bulmer, Science 1998 Low-angle thrust faulting is probably responsible for many of the mountain ranges seen on Io Strike-slip Motion • Horizontal Movement Right-Lateral Left-Lateral Europa, oblique strike-slip (image width 170km) • Relatively rare (only seen on Earth & Europa) • Associated with plate tectonic-like behaviour Plate Tectonics • Dominant style of tectonics on Earth • Unknown elsewhere • Early Plate Tectonics on Mars? – (Sleep 1994, Nimmo & Stevenson, 2000) 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 szz s 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. wx f1 dx‘ dx exx = 1 - dx’/dx f2 exz = -½ (f1 – f2) Stress and Strain in Solids s xx s xy s s yx s yy s zx s zy • Stress and Strain are Tensors (think of it as a vector of vectors) szz syy sxx sxx Maximum direction of principal stress controls style of fault. s xz s yz s zz syy szz Rheology • Rheology is the study of the deformation and flow of matter under the influence of an applied stress • If the deformation (or strain, e) follows the stress, s, the material is elastic – Returns to original state when stress is released • If the strain rate, de/dt follows the stress, s, the material is viscous Elastic s s0 sy s Ee Failure Strength Brittle Behavior Yield Strength Plastic behavior Viscous s s e e e E is the Young’s Modulus, or elasticity is the viscosity Analagous to the spring constant in Hooke’s Law Rarely a straight line plot in reality Deformation • You can think of Young’s modulus (units: Pa) as the stress s 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. 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? ice water 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 e DT Where is the thermal expansivity (3x10-5 K-1), DT is the temperature change and the strain is the fractional change in radius Solid core Tectonic Stresses & Byerlee’s law • Byerlee’s law says that faults don’t move unless the shear stress fault exceeds the normal stress times the friction coefficient f • For almost all geological materials, f=0.6 (unless the fault is lubricated somehow) • In general, the normal stress is simply the overburden pressure: Shear stress Normal stress Also applies to atmospheres! P = rgh • 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 Stress on a Fault P = rgz z stec sn sn = Normal Stress t = Shear Stress P = Pressure (Lithostatic Stress) t 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 load Crust Elastic plate Mantle • 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 Flexural Parameter • Consider a load acting on an elastic plate: rw load rm Te • 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 3g ( r ETe3 m - r w )(1- 2 ) 1 4 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 10 km • 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, Dr=900 kg m-3 (there is no overlying ocean), g=1.3 ms-2 Distance, 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 Depth •E.g. for ice the base of the elastic layer 270 K 110 K 190 K is at about 190 K • The measured elastic layer thickness is 1.4 km 1.4 km (from previous slide) elastic • So the thermal gradient is 60 K/km • This tells us that the (conductive) ice viscous shell thickness is 2.7 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) Body Te 30 dT/dz (K/km) 15 Earth (cont.) Venus (450oC) 30 Mars (recent) Europa 100 5 2 40 Moon 15 (ancient) Ganymed 2 dT/dz (K/km) 15 30 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)