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## Statistics on Venus: Craters and Catastrophes (?)

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### 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

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

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

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.

Craters > 4km from Barlow database over Mars shaded relief from MOLA

Space Imagery Center: http://www.lpl.arizona.edu/SIC/

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

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

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]

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].

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.

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.

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 Venusp value

Mth Nearest Neighbor

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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