Transcript HauckSteven.presentation

Statistics on Venus:
Craters and Catastrophes (?)
Steven A. Hauck, II
Department of Terrestrial Magnetism
Carnegie Institution of Washington
Acknowledgements
• Roger Phillips
– Washington University
• Maribeth Price
– South Dakota School of Mines and Technology
• Sean Solomon
– Carnegie Institution of Washington
The big question
• What does it mean for the
evolution of a planet if the
spatial distribution of impact
craters on its surface cannot be
distinguished from a completely
spatially random distribution?
Outline
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Why Venus?
Why impact craters?
Dating with craters.
Geology in brief.
Monte Carlo models and statistical tests.
Implications for Venus.
The Basics
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2nd planet from Sun
Mean radius = 6052 km ( = 6371 km)
Mean density = 5243 kg/m3 ( = 5515 kg/m3)
1 Venus year = 225 days
1 Venus day = 243 days (retrograde)
Surface pressure = 91 atmospheres
Surface temperature = 740 K
Magellan SAR Mosaic of Venus
• Why study impact craters?
50 km
Motivation
• Can we learn something about
the history of Venus from the
distribution of impact craters on
the surface?
Relevance
• Surface history places a
constraint on the evolution of the
whole planet.
–Ultimately provides a contrast to
the Earth which is comparable in
size and presumably composition.
Venusian Impact Craters
Martian Impact Craters
Craters > 4km from Barlow database over Mars shaded relief from MOLA
Terrestrial Impact Craters
Space Imagery Center: http://www.lpl.arizona.edu/SIC/
Craters  Surface Ages
1) Assume the rate of impact crater formation is
approximately constant (only to first-order)

The rate has an impact size-dependence
2) Assume that cratering process is spatially and
temporally random
3) Divide the surface into units based upon geologic
criteria (e.g., morphology, superposition
relationships)
4) Calculate area density of points (craters) within units
5) Relative differences give relative ages
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Convert to absolute age if an estimate of mean surface
age is available
Absolute Ages
• Calibration points:
– Earth and moon
• Other bodies?
– Assumption that Mars, Venus, and Mercury
have some multiple of the lunar impactor
population
– Comparison of present day minor planets with
(asteroids) known oribital elements with
planetary orbits
• Uncertainty abounds…
• Venus has the additional problem of its thick
atmosphere
Crater Ages
• Production Age:
– Number of craters superposed on a geologic
unit reflect the time since the unit was
emplaced.
• Retention Age:
– Number of craters within a geologic unit reflect
a competition between crater emplacement and
removal.
More Background
• ~1000 impact craters on the surface
• Early analysis showed that the spatial distribution
of impact craters cannot be distinguished from
one that is completely spatially random [CSR]
• Most craters appear pristine.
• Dense atmosphere has a profound filtering effect
• Surface mean crater production age ~750 Myr
Refs: Phillips et al., 1992; Schaber et al., 1992;
Herrick and Phillips, 1994; McKinnon et al., 1997
Venusian Impact Craters
The big question
• What does it mean for the
evolution of a planet if the
spatial distribution of impact
craters on its surface cannot be
distinguished from a completely
spatially random distribution?
Early Models
• Based on the notion that Venus’ impact
craters are randomly distributed, two
end-member models were proposed :
– The equilibrium resurfacing model (ERM)
[Phillips et al., 1992]
– The catastrophic resurfacing model (CRM)
[Phillips et al., 1992; Schaber et al., 1992; Bullock et al.,
1993; Strom et al., 1994]
Large-scale Geology
• Distinct morphologic units can be defined at
the 1:8,000,000 scale (C1-MIDR). [Price and
Suppe, 1994, 1995; Tanaka et al., 1997]
• The volcanic plains are the areally most
extensive unit covering ~65% of the planetary
surface.
– Plains can be divided into sub-units based upon
dominant flow morphology and radar brightness.
[Price, 1995; Tanaka et al., 1997]
SAR Images of Type PL1 and PS
PS
PL1
100 km
200 km
Venusian Plains Units
270°
0°
90° 180°
45°N
0°
0°
PL1
PL2
PL3
PS
Impact Crater
45°S
Plains units after Price [1995]
Age of the Plains
Unit
PL1
PL2
PL3
PS
PL1+PL2
PL3+PS
SAP
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Area
11.86
84.43
93.05
99.82
96.29
192.87
289.16
Craters
Relative Age
19
149
217
267
168
484
652
0.79 ± 0.36 T
0.87 ± 0.14 T
1.14 ± 0.16 T
1.31 ± 0.16 T
0.86 ± 0.13 T
1.23 ± 0.11 T
1.11 ± 0.09 T
Estimated Age (Ma)
589  270
649  106
857  116
983  120
641 ± 99
923 ± 84
829 ± 65
A unit of area is 106 km2. Errors listed are 2s. Note that both PL2 and PL1+PL2 have
relative ages that do not overlap within 2s of the single-age plains (SAP) model,
suggesting that the younger plains have distinct ages that are statistically significant.
The mean surface production age, used to calculate the last column, is estimated as T =
750 Ma [McKinnon et al., 1997].
Modeling
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> 200 Monte Carlo simulations
Density of craters within a unit prescribed
Modeling done with ArcView GIS
Results post-processed to measure distances
to all neighbors
• Mean distances to nearest neighbors
compared to Venus observations using Mth
nearest neighbor analysis.
Resurfacing Models
Nominal
MB1
MB2
SAP
DAP
DAP2
TAP
Each unit has the observed age
PL3 - 2s, PS + 2s
PL2 - 2s, PS + 1.5s
Single age for all plains units
Combine young and old units as
PL1+PL2 and PL3+PS
DAP young + 2s, DAP old - 2s
Divide units as PL1, PL2, and PL3+PS
Model
QQ and PP Plots
PP Plot of Venus Resurfacing Model with
Units of Distinct Crater Production Ages
Observed Distance [Deg/Deg]
QQ Plot of Venus Resurfacing Model with
Units of Distinct Crater Production Ages
Observed [Deg]
12
8
4
1
0.8
0.6
0.4
0.2
0
0
0
0
4
8
Expected Distance [Deg]
12
0.2
0.4
0.6
0.8
Expected Distance [Deg/Deg]
1
Tests
• Distance based
– Nearest Neighbor Analysis (and Mth Nearest Neighbor )
• compare mean distance from each crater to the 1st, 2nd, …, Mth
nearest neighbor to the expected distance.
• Density based
– Binomial probability
• probability of finding the number of craters that are observed
in each unit if the hypothesis that distribution of craters in the
plains is controlled only by a single random process is true.
– Chi-squared goodness-of-fit test
• compare the observed number of craters in each plains unit to
the number expected by a particular model.
Two-sided p values of Testing the
Hypothesis that Plains Resurfacing Models
Represent Venus
1.0
0.9
Nominal
MB 1
MB 2
SAP
DAP
DAP 2
TAP
CSR
CSR vs. Random
0.8
p value
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1
2
Mth
3
Nearest Neighbor
4
Statistical Results
Binomial Probability
Unit
P
Chi-squared goodness-of-fit
Model
PL1
1.7 x 10
-1
PL2
3.0 x 10
-2
PL3
1.3 x 10
PS
P
2.0 x 10
-4
DAP
4.9 x 10
-1
-2
TAP
5.2 x 10
-1
4.5 x 10
-7
CRM
4.0 x 10
-6
PL1+PL2
1.4 x 10
-2
PL3+PS
6.5 x 10
-10
SAP
4.2 x 10
-6
SAP
Results
• Mth Nearest Neighbor Analysis
– None of the models presented (including a CSR
population) can be distinguished from Venus’ crater
distribution.
• Binomial probability
– The hypothesis that variations in the crater distribution are
due to a single random process for the planet can be
rejected for all units except PL1.
• Chi-squared goodness-of-fit test
– It is extremely unlikely that a SAP or CRM could result in
the observed number of craters in each plains unit.
– Dual- or tri-age plains models cannot be rejected.
Conclusions
• CSR cannot be used as a constraint on resurfacing
or geodynamic models because it is a non-unique
interpretation of the crater distribution.
• None of the resurfacing models can be rejected as
being representative of Venus based upon Mth
nearest neighbor analysis.
• Chi-squared test on crater populations within the
plains units suggests that both the single-age
plains and single-age planet (CSR) models can be
rejected as being representative of Venus.
Conclusions II
• Binomial probability tests on plains crater
populations suggest that the sub-unit ages are
significant.
• The spread in plains ages on the order of one-half
the mean production age of the surface is significant
and suggests that Venus has been geologically active
more recently than believed in the past.
• Hypotheses such as CRM and episodic resurfacing
[Turcotte, 1993;1995] are unnecessary to explain the
crater distribution of Venus.
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