Impact Cratering II

PTYS 554

Evolution of Planetary Surfaces

Impact Cratering IIImpact Cratering II

PYTS 554 – Impact Cratering II 2

Impact Cratering I Size-morphology progression Propagation of shocks Hugoniot Ejecta blankets - Maxwell Z-model Floor rebound, wall collapse

Impact Cratering II The population of impacting bodies Rescaling the lunar cratering rate Crater age dating Surface saturation Equilibrium crater populations

Impact Cratering III Strength vs. gravity regime Scaling of impacts Effects of material strength Impact experiments in the lab How hydrocodes work


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


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…


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)


Cumulative plots Tends to mask deviations from the ideal Not binned

Incremental plots The ‘standard’ plot…

IncrementalCumulative


Incremental plots with √2 diameter bin spacing is favored by Hartmann Isochrons have become relatively standardized for Mars

Hartmann, 2005


Cumulative plots

Differential plots

Cumulative

Differential


R-plots Size-frequency plot with slope removed - Highlights differences from the ideal

Area of craters: Rarely used

Relative (R-Plot)

Cumulative


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

More on this later

Strom et al., 2005


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


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)


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


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


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


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


Viscous relaxation on the icy Galilean satellites

Images by Paul Schenk

Lunar and Planetary Institute

Relaxed craters Penepalimpset →

Palimpset


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…


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


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


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


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


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


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


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


~190 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

Daubar et al.2012


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. 2012


Outer solar system chronology relies entirely on dynamical models

E.g. Titan shows a global ‘age’ of <1 Gyr Titan CrateringNeish and Lorenz, 2011


Impact Cratering I Size-morphology progression Propagation of shocks Hugoniot Ejecta blankets - Maxwell Z-model Floor rebound, wall collapse

Impact Cratering II The population of impacting bodies Rescaling the lunar cratering rate Crater age dating Surface saturation Equilibrium crater populations

Impact Cratering III Strength vs. gravity regime Scaling of impacts Effects of material strength Impact experiments in the lab How hydrocodes work

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Impact Cratering II