Crater Stat

8/10/2019 Crater Stat

1/24

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


2/24

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


3/24

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



4/24

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



5/24

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



6/24

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



7/24

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



8/24

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:


...

3

3

2

210 xaxaxaaN

cum


9/24

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



10/24

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



11/24

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


ere 1, 2, 3 are cons an s


12/24

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



13/24

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


. . .


14/24

Crater counting



15/24

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)



16/24

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



17/24

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



18/24

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



19/24

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


amount


20/24

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



21/24

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



22/24

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



23/24

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


energy of impact


24/24

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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