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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

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statistics on venus craters and catastrophes

Statistics on Venus:Craters and Catastrophes (?)

Steven A. Hauck, II

Department of Terrestrial Magnetism

Carnegie Institution of Washington

acknowledgements
Acknowledgements
  • Roger Phillips
    • Washington University
  • Maribeth Price
    • South Dakota School of Mines and Technology
  • Sean Solomon
    • Carnegie Institution of Washington
the big question
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
Outline
  • Why Venus?
  • Why impact craters?
  • Dating with craters.
  • Geology in brief.
  • Monte Carlo models and statistical tests.
  • Implications for Venus.
the basics
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
Motivation
  • Can we learn something about the history of Venus from the distribution of impact craters on the surface?
relevance
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.
slide16

Martian Impact Craters

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

slide17

Terrestrial Impact Craters

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

craters surface ages
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
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
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
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 question1
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
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
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]
venusian plains units

270°

90°

180°

45°N

45°S

PL1

PL2

PL3

PS

Impact Crater

Venusian Plains Units

Plains units after Price [1995]

age of the plains
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
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
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

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

statistical results
Statistical Results

Chi-squared goodness-of-fit

Binomial Probability

results
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
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
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.