crater stat
TRANSCRIPT
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Measuring the age of planetary surfaces using crater statistics
Greg Michael
Planetary Sciences and Remote Sensing
Department of Earth Sciences
re e n vers ae er n
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Februarys near miss...
11 m im actor
Flyby at 60,000 km
Would have produced a
crater of ~200 m
diameter
away... one in a
hundred such events
2Planetary surface dating from crater statistics PGM Meeting, USGS Flagstaff, 19 June 2012
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Berlins central park - the Tiergarten
One in a hundred
such near miss
news items will be
followed by one of
these
But probably not in
...impacts (or even
news repor s o
near misses) can be
used as a clock
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Impact craters
Meteor Crater,
Arizona, US
1200m across
~50m iron
impactor
Formed 50ka ago
Tunguska event, 1908
No crater
Impactor likely disrupted by
atmos here
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Planetary impactors
Asteroids, comets,
collisional debris
Size distribution of
asteroids appearsconsistent wit o serve
crater populations
Comet populations lessknown
- Kui er belt Oort cloud
- Capture to inner Solar System,
but short-lived in solar vicinity
Objects moved out of
asteroid belt by planetary
resonances and collisions
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Crater counting
Surface accumulates craters
process
characteristics of process to
obtainpopulationage
relationshi
Single geologic unit with
homo eneous histor
Exclude areas: e.g. steep
defects, secondary crater
clusters
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Crater production function
Differently sized craters form at
different rates
Production function (PF) describes the
sizefrequencydistribution of craterspro uce a e sur ace
i.e. how many craters of diameter D2 can
be expected for each one of size D1.
This is a reverse-cumulative frequency
plot, showing
.
where N(>D) is the number of craters
larger than D.
Directly related to the size-frequency
distribution of impacting objects
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How do we get the production function?
Unfortunately, no single unit shows the full
range o crater iameters in pro uction
because of
saturation
erosion
So, we make a series of crater counts onunits with differing crater densities (i.e. ofdifferent ages)
Then, make a piecewise normalization to
match overlapping size ranges
Finally, we make a polynomial
approximation as our standard curve:
8Planetary surface dating from crater statistics PGM Meeting, USGS Flagstaff, 19 June 2012
...
3
3
2
210 xaxaxaaN
cum
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How do we get the production function?
Some authors (e.g. Neukum, Hartmann) believe the
crater populations are consistent with the PF having
remained constant over the observable history of
planetary surfaces.
Others believe it has chan ed e. . Stroms two-
Small cratersused to dateyoung
population model)
Crater populations do differ on ancient and young
surfaces
surfaces: is this due to different impacting
populations, or differing retention periods for smallerand larger craters?
What are the consequences for crater-dating?
the piecewise-constructed PF should be valid in
either scenarioLarge craters
in the two-population case, the variation is
included implicitly: the small diameter end
represents the late population; the large
diameter end re resents the earl o ulation
used to dateold surfaces
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Chronology function
Chronology function (CF)
describes the changing crater
formation rate with time, for are erence crater size 1 m
The formation rate is constant
exponential
back to 3 Ga, then
exponentially increasing
The rate for other diameters
can be found by multiplying the
1 km by an appropriate
constant
production function
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How do we get the chronology function?
Radiometric dating of
returned lunar samples
Relate samples to their
source units, and measure
These are the calibration
density relationship
with the following empirical
expression:
tkekN tk
cum 31 )1()km1( 2
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ere 1, 2, 3 are cons an s
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Isochron diagram
The production and chronology
unctions toget er permit t e
construction of an isochron
diagram
This shows the expected crater
densities for surfaces of different
The red points are given by the
ages
production function shifted up or
down to intersect the points
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Data preparation
#Model . di amf i l e f or Cr aterst ats
Ar ea = 3036. 61
#di amet er , km Needed:
0. 511
0. 166
0. 0950. 100
Units surface area
Crater diameters (~1900 in this
case)
0. 261
0. 208
0. 208 Divide diameter measurements into
appropriate bins (spaced on a.
0. 1120. 170
0. 100
logarithmic scale)
Make a reverse-cumulative frequency.
0. 219
0. 172
0. 202
plot, i.e.:
plot log N(>D) vs. log D,
where N(>D) is the number of.0. 154
0. 130
0. 098
craters larger than D per km2
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. . .
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Crater counting
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Cumulative PF fitting
Select diameter range where
points are consistent with PF,
i.e. run parallel to it
Shift the PF up or down for
best fit
Read off equivalent crater
Find age from chronologyfunction
(shown without resurfacing correction)
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Partial resurfacing
Partial resurfacing occurs when
portion of the crater population
,
the smallestcraters which are lost
(those below some threshold
diameter, D)
After the event, the population
accumulates again, leaving a kink
in the size-frequency plot
Often better seen in a differentialplot
Note t ical resolution roll-off
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Partial resurfacing
Partial resurfacing occurs when
portion of the crater population
,
the smallestcraters which are lost
(those below some threshold
diameter, D)
After the event, the population
accumulates again, leaving a kink
in the size-frequency plot
Often better seen in a differentialplot
Note t ical resolution roll-off
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Partial resurfacing
In such a case one can obtain
two ages:
the original surface
the artial resurfacin
event
,
than one resurfacing event
,
process can be of extended
duration, so that there is a
continuous range of agespresent
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Resurfacing correction
On a cumulative plot, each point
The younger, partially resurfaced
portion of the plot includes craters
belonging to the older underlying
surface
they would for a unit which was fullyresurfaced at the time of the resurfacing
event
Can correct for this by calculating the
population beyond the resurfaced
the observed PF in the chosen range(Michael & Neukum, 2010)
Iterative calculation
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amount
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Differential fitting
Its ossible to make a fit
directly on a differential
plot
If using Neukum-style
polynomial PF, requires
differential form of
po ynom a (Michael & Neukum,2010)
obtained with cumulative fit
for ideal populations; may
differ sli htl in real data
cause: cumulative data
points are not fully
independent
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Hartmann plot
A Hartmann lot is a s ecial
case of a differential plot
Craters per root-2 bin
Fixed axes
Here, a differential fitting may
It is frequently useful to
cumulative and
differential/Hartmann when
selecting a diameter range forfitting
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Craterstats software
Craterstats is a software tool
for anal sin crater counts
Import, bin and plot crater
Fit a production function
Obtain an age from a
Plot isochrons
Apply resurfacing correction
Export graphics
htt ://hrscview.fu-berlin.de/software.html
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Recalibration to other Solar System bodies
No samples from bodies other than the Moon
Calibration made relative to the Moon, considering:
Asteroidal impactor flux
More/fewer craters per unit time
Impact velocity
Local heliocentric velocity
Body escape velocity
Greater/lesser impact energy for given impactor
Surface gravity
Easier/harder to excavate volume for given
ener of im act
Surface strength
Easier/harder to excavate volume for given
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energy of impact
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Clustering and randomness analysis
Idea is to verify that the spatial
distribution of the craters is random,
as expec e or a sur ace w
homogeneous history
Compare the actual spatial
configuration with a series of
computer-generated random
Clustered, or consistent with beingrandom?
Any type of clustering suggests either
the presence of secondary craters
(which are normally excluded), or anon-uniform counting area
inadequate for drawing conclusions
about either age, or impacting
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