Transcript PTYS 554 Evolution of Planetary Surfaces Impact Cratering II PYTS 554 – Impact Cratering II  Impact Cratering I       Impact Cratering II       Size-morphology progression Propagation of shocks Hugoniot Ejecta.

PTYS 554
Evolution of Planetary Surfaces
Impact Cratering II
PYTS 554 – Impact Cratering II

Impact Cratering I






Impact Cratering II






Size-morphology progression
Propagation of shocks
Hugoniot
Ejecta blankets - Maxwell Z-model
Floor rebound, wall collapse
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
2
PYTS 554 – Impact Cratering II

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
3
PYTS 554 – Impact Cratering II
An ideal case…

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
Do £ D £ 2Do

Size-frequency plot generated



In log-log space
Frequency is normalized to some area
Piecewise linear relationship:
N(D, 2D) = kD-b




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
4
PYTS 554 – Impact Cratering II

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)
5
Incremental
Cumulative
Relative
Differential
PYTS 554 – Impact Cratering II

Cumulative plots



Tends to mask deviations from the ideal
Not binned
Incremental plots

The ‘standard’ plot…
(
( D,
N cum (³ D) = cD-b
)
2D) = N
N inc D, 2D = k D-b
N inc
(
\k = c 1- 2
Cumulative
cum
-b
(³ D) - N cum (³ 2D)
)
Incremental
6
PYTS 554 – Impact Cratering II

Incremental plots with √2 diameter bin spacing is favored by Hartmann

Isochrons have become relatively standardized for Mars
Hartmann, 2005
7
PYTS 554 – Impact Cratering II


Cumulative plots
Differential plots
8
N cum (³ D) = cD-b
(
( D,
)
2D) = -éë N
N diff D, 2D = qD-b-1
N diff
(
\q = c 1- 2
-b
)
cum
(
(³ D) - N cum (³ 2D)ùû
é D - 2Dù
ë
û
)
2 -1
Differential
Cumulative
PYTS 554 – Impact Cratering II

R-plots

Size-frequency plot with slope removed - Highlights differences from the ideal
(
)
R(D) = éë N diff D, 2D ùû
R(D) = r D

9
-b+2
é -3 4 -3 ù
êë2 D úû
where r = c 2
3
4
(1- 2 )
(
-b
)
2 -1
æ 1 ö
Area of craters: A D ® 2D = p ç 2 4 D ÷ é N (³ D) - N ³ 2D ù
cum
û
ç 2 ÷ ë cum
 Rarely used
è
ø
(
2
)
(
)
æ 14 ö
-b
2 ÷
A D ® 2D = cp ç
1- 2 D -b+2 = 0.27 R ( D)
ç 2 ÷
è
ø
(
)
2
(
)
Cumulative
Relative (R-Plot)
PYTS 554 – Impact Cratering II

10
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
PYTS 554 – Impact Cratering II

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
11
PYTS 554 – Impact Cratering II
Geometric saturation

Hexagonal packing allows craters to fill 90.5% of
available area (Pf)
N SAT
( Area) =
Pf 4
pD
2
= 1.15D-2
æP 4 ö
or log( N SAT / Area) = - 2log( D) + logç f p ÷
è
ø

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 (N)

12
Log (D)
PYTS 554 – Impact Cratering II

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
1
b-2
eq
D µt
13
PYTS 554 – Impact Cratering II

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
14
PYTS 554 – Impact Cratering II

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
15
PYTS 554 – Impact Cratering II

16
Viscous relaxation of icy topography can make craters undetectable
Pathare and Paige, 2005

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
PYTS 554 – Impact Cratering II
Viscous relaxation on the
icy Galilean satellites

Relaxed craters

Penepalimpset →
Palimpset
Images by Paul Schenk
Lunar and Planetary Institute
17
PYTS 554 – Impact Cratering II

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…
18
PYTS 554 – Impact Cratering II

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
19
PYTS 554 – Impact Cratering II
Linking Crater Counts to Age

Moon is divided into two terrain types




Apollo and Luna missions




Light-toned Terrae (highlands) – plagioclase feldspar
Dark-toned Mare – volcanic basalts
Maria have ~200 times fewer craters
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.
20
PYTS 554 – Impact Cratering II

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
21
PYTS 554 – Impact Cratering II

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
}
weak
Cataclysm referred to as ‘Late Heavy Bombardment’
22
PYTS 554 – Impact Cratering II

23
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
PYTS 554 – Impact Cratering II

Lunar impact rates can be scaled to other planets


24
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)

Hartmann, 2005
Rcrater is the ratio of crater sizes formed by the same projectile
Rcrater = DMars DMoon = ( E Mars E Moon )
0.43
(gMars
gMoon )
 Impact energy ratio come from dynamical studies ~ 0.71
 Ratio of gravities = 2.3
 Rcrater ~ 0.75
Hartmann, 2005
-0.17
Schmitt and Housen, 1987
PYTS 554 – Impact Cratering II

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
25
PYTS 554 – Impact Cratering II

~190 impact events recognized so far



26
Crater sizes from a few meters to a few decameters
Effective diameter of clusters reconstructed from D
Very biased and incomplete sample
eff
æ
ö
3
= çå Di ÷
è i
ø
1
3
Daubar et al.
2012
PYTS 554 – Impact Cratering II

27
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
PYTS 554 – Impact Cratering II

Outer solar system chronology relies entirely on
dynamical models

E.g. Titan shows a global ‘age’ of <1 Gyr
Titan Cratering
Neish and Lorenz, 2011
28
PYTS 554 – Impact Cratering II

Impact Cratering I






Impact Cratering II






Size-morphology progression
Propagation of shocks
Hugoniot
Ejecta blankets - Maxwell Z-model
Floor rebound, wall collapse
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
29