1. Statistics on Venus: Craters and Catastrophes (?)
Steven A. Hauck, II
Department of Terrestrial Magnetism
Carnegie Institution of Washington

2. Acknowledgements Roger Phillips Maribeth Price Sean Solomon
Washington University
Maribeth Price
South Dakota School of Mines and Technology
Sean Solomon
Carnegie Institution of Washington

3. 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?

4. Outline Why Venus? Why impact craters? Dating with craters.
Geology in brief.
Monte Carlo models and statistical tests.
Implications for Venus.

5. The Basics 2nd planet from Sun Mean radius = 6052 km ( = 6371 km)
Mean density = 5243 kg/m3 ( = 5515 kg/m3)
1 Venus year = days
1 Venus day = days (retrograde)
Surface pressure = 91 atmospheres
Surface temperature = 740 K

8. Magellan SAR Mosaic of Venus

10. Why study impact craters?

12. 50 km

13. Motivation
Can we learn something about the history of Venus from the distribution of impact craters on the surface?

14. 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.

15. Venusian Impact Craters

16. Martian Impact Craters
Craters > 4km from Barlow database over Mars shaded relief from MOLA

17. Terrestrial Impact Craters
Space Imagery Center:

18. Craters  Surface Ages
Assume the rate of impact crater formation is approximately constant (only to first-order)
The rate has an impact size-dependence
Assume that cratering process is spatially and temporally random
Divide the surface into units based upon geologic criteria (e.g., morphology, superposition relationships)
Calculate area density of points (craters) within units
Relative differences give relative ages
Convert to absolute age if an estimate of mean surface age is available

19. 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

20. Crater Ages Production Age: Retention 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.

21. More Background ~1000 impact craters on the surface*
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 *

22. Venusian Impact Craters

23. 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?

24. *
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] *

25. 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]

26. SAR Images of Type PL1 and PS
100 km
200 km

27. Venusian Plains Units 0° 45°S 45°N 270° 90° 180° PL1 PL2 PL3 PS
Impact Crater
Plains units after Price [1995]

28. Age of the Plains
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].

29. Modeling > 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.

30. Resurfacing Models

31. Model

32. *
QQ and PP Plots *

33. Tests Distance based Density 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.

34. Two-sided p values of Testing the Hypothesis that Plains Resurfacing Models Represent Venus
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 1 2 3 4
Nominal
MB 1
MB 2
SAP
DAP
DAP 2
TAP
CSR
CSR vs. Random
p value
Mth Nearest Neighbor

35. Statistical Results
Binomial Probability
Chi-squared goodness-of-fit

36. Results Mth Nearest Neighbor Analysis Binomial probability
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.

37. 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.

38. 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.

39. 50 km