Statistics on Venus: Craters and Catastrophes (?)

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

2. Acknowledgements • Roger Phillips • 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 = 225 days • 1 Venus day = 243 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: http://www.lpl.arizona.edu/SIC/

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: • 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 • 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 PS PL1 100 km 200 km

27. 270° 0° 90° 180° 45°N 0° 0° 45°S PL1 PL2 PL3 PS Impact Crater Venusian Plains Units 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 • 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. 1.0 0.9 Nominal 0.8 MB 1 0.7 MB 2 SAP 0.6 DAP DAP 2 0.5 TAP 0.4 CSR CSR vs. Random 0.3 0.2 0.1 0.0 1 2 3 4 Two-sided p values of Testing the Hypothesis that Plains Resurfacing Models Represent Venus p value Mth Nearest Neighbor

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

36. 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.

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