ptys 411 geology and geophysics of the solar system dating planetary surfaces
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PTYS 411
Geology and Geophysics of the Solar System
Dating Planetary SurfacesDating Planetary Surfaces
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Older surfaces have more craters
Small craters are more frequent than large craters
Relate crater counts to a surface age, if: Impact rate is constant Landscape is far from equilibrium
i.e. new craters don’t erase old craters No other resurfacing processes Target area all has one age You have enough craters
Need fairly old or large areas
Techniques developed for lunar maria Telescopic work established relative ages Apollo sample provided absolute calibration
Mercury – Young and Old
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Crater population is counted Need some sensible criteria
e.g. geologic unit, lava flow etc… Tabulate craters in diameter bins Bin size limits are some ratio e.g. 2½
Size-frequency plot generated In log-log space Frequency is normalized to some area
Piecewise linear relationship:
Slope (64km<D, b ~ 2.2 Slope (2km<D<64km), b ~ 1.8 Slope (250m<D<2km), b ~ 3.8 Primary vs. Secondary Branch
Vertical position related to age
These lines are isochrones
Actual data = production function - removal
An ideal case…
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Incremental
Cumulative
DifferentialRelative
There are at least 4 ways to represent crater count data
Bin spacing should be geometric, √2 is most common
Plots from craterstats (Michael & Neukum, EPSL, 2010) Definitions from the “CRATER ANALYSIS TECHNIQUES
WORKING GROUP” (Icarus, 37, 1979)
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Cumulative plots Tends to mask deviations from the ideal Not binned
Incremental plots The ‘standard’ plot…
IncrementalCumulative
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Incremental plots with √2 diameter bin spacing is favored by Hartmann Isochrons have become relatively standardized for Mars
Hartmann, 2005
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Cumulative plots
Differential plots
Cumulative
Differential
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R-plots Size-frequency plot with slope removed - Highlights differences from the ideal
Area of craters: Rarely used
Relative (R-Plot)
Cumulative
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R-plots reveal different populations of cratering bodies
Young surfaces are flat close to a -2 slope in log(N) vs. log(D)
Older surfaces show a different impacting population
Strom et al., 2005
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When a surface is saturated no more age information is added Number of craters stops increasing The whole premise of crater dating is that c (or k) increases linearly with time
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Geometric saturation Hexagonal packing allows craters to fill 90.5% of available area
(Pf)
A mix of crater diameters allows Ns = 1.54 D-2
Crater arrays separated by a factor of two in diameter
For equal sized craters
Log (D)
Lo
g (
N)
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Equilibrium saturation: No surface ever reaches the geometrically saturated limit. Saturation sets in long beforehand
(typically a few % of the geometric value) Mimas reaches 13% of geometric saturation – an extreme case
Craters below a certain diameter exhibit saturation This diameter is higher for older terrain – 250m for lunar
Maria This saturation diameter increases with time
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Summary of a classic crater size-frequency distribution
Typical size-frequency curve Steep-branch for sizes <1-2 km Saturation equilibrium for sizes
<250m
Sample of Mare Orientale
Multiple slope breaks
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In general, it’s hardly ever as neat and tidy as the lunar mare.
Craters can get removed as fast as they arrive – an equilibrium population
production x lifetime = population production & population known
Can find the crater lifetime… Usually crater lifetime is a power-law of diameter: a Dx
If x=0, then the crater lifetime is the surface age i.e. all craters are preserved If x=1, then crater lifetime is proportional to depth… e.g. constant infill rate
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Viscous relaxation of icy topography can make craters undetectable
Maxwell time Stress causes elastic deformation and creep Time after which creep strain equals elastic strain tM = εel / (Δεcreep/t) = η/μ μ is the shear modulus (rigidity), η is the viscosity
On Earth tM for rock >109 years tM for ice ~ 100s sec Ganymede ice is intermediate
Pathare and Paige, 2005
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Viscous relaxation on the icy Galilean satellites
Images by Paul Schenk
Lunar and Planetary Institute
Relaxed craters Penepalimpset →
Palimpset
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Secondary craters confuse the picture Steep-branch of lunar production function caused
controversy Are these true secondaries or collisional fragments
generated in space
Asteroid Gaspra Also has steep-branch Definitely lacks true secondaries Case closed? Not really…
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Analysis of Zunil by McEwen et al. Modeling suggests this one crater can account
for all craters a few 10’s of meters in size They suggest most small craters on Mars should
be secondaries
Secondary distribution Lumpy in space and time Can’t use these craters for dating a surface
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Moon is divided into two terrain types Light-toned Terrae (highlands) – plagioclase feldspar Dark-toned Mare – volcanic basalts Maria have ~200 times fewer craters
Apollo and Luna missions Sampled both terrains Mare ages 3.1-3.8 Ga Terrae ages all 3.8-4.0 Ga
Lunar meteorites Confirm above ages are representative of most of the moon.
Linking Crater Counts to Age
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Crater counts had already established relative ages Samples of the impact melt with geologic context
allowed absolute dates to be connected to crater counts
Lunar cataclysm? Highland crust solidified at ~4.45Ga Impact melt from large basins cluster in age
Imbrium 3.85Ga Nectaris 3.9-3.92 Ga
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Before and after the late heavy bombardment Cataclysm or tail-end of accretion?
Lunar mass favors cataclysm Impact melt >4Ga is very scarce Pb isotope record reset at ~3.8Ga
Cataclysm referred to as ‘Late Heavy Bombardment’
} weak
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Origin of the late heavy bombardment projectiles Convert crater size distribution to projectile size distribution
Using Pi scaling laws
Display both as R-plots to highlight structure LHB – matches main-belt asteroids Post LHB craters – match the near-Earth asteroid population
LHB caused by surge of asteroidal material entering the inner solar system Migration of Jupiter can move orbital-resonances through the asteroid belt
Strom et al., 2005
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Lunar impact rates can be scaled to other planets Must assume the same projectile population
i.e. this doesn‘t work for the outer solar system where a different projectile population dominates
Two-step process – e.g. Mars Rbolide is the ratio of projectile fluxes
Comes from dynamical studies ~2.6 (very uncertain)
Rcrater is the ratio of crater sizes formed by the same projectile
Impact energy ratio come from dynamical studies ~ 0.71 Ratio of gravities = 2.3 Rcrater ~ 0.75
Schmitt and Housen, 1987
Hartmann, 2005
Hartmann, 2005
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The problem is that we can’t date martian materials in the lab…
But we can start to test these impact rates on Mars….
June 4th 2008 August 10th 2008
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~300 impact events recognized so far Crater sizes from a few meters to a few decameters Effective diameter of clusters reconstructed from
Very biased and incomplete sample
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Crater flux close to what we expect, but we’re not seeing all impacts… Efficiency of atmospheric screening also not well known
Daubar et al., 2013
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Outer solar system chronology relies entirely on dynamical models
E.g. Titan shows a global ‘age’ of <1 Gyr
Titan CrateringNeish and Lorenz, 2011