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

Steven A. Hauck, II

Department of Terrestrial MagnetismCarnegie Institution of Washington

AcknowledgementsAcknowledgements

• Roger Phillips– Washington University

• Maribeth Price– South Dakota School of Mines and Technology

• Sean Solomon– Carnegie Institution of Washington

The big questionThe 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?

OutlineOutline

• Why Venus?

• Why impact craters?

• Dating with craters.

• Geology in brief.

• Monte Carlo models and statistical tests.

• Implications for Venus.

The BasicsThe 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

MagellanMagellan SAR Mosaic of Venus SAR Mosaic of Venus

• Why study impact craters?

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MotivationMotivation

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

RelevanceRelevance

• 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

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

Martian Impact Craters

Terrestrial Impact Craters

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

Craters Craters Surface Ages 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 units5) Relative differences give relative ages

Convert to absolute age if an estimate of mean surface age is available

Absolute AgesAbsolute 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 AgesCrater 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 BackgroundMore 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 questionThe 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 ModelsEarly Models

• Based on the notion that Venus’ impact craters are randomly distributed, two end-member models were proposed :– The equilibrium resurfacing model (ERMERM)

[Phillips et al., 1992] – The catastrophic resurfacing model (CRMCRM)

[Phillips et al., 1992; Schaber et al., 1992; Bullock et al., 1993; Strom et al., 1994]

Large-scale GeologyLarge-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 PSSAR Images of Type PL1 and PS

100 km100 km

PL1PL1

200 km200 km

PSPS

Venusian Plains UnitsVenusian Plains Units

Plains units after Price [1995]

0°0°

45°S

45°N

270° 0° 90° 180°

PL1PL2PL3PS

Impact Crater

Age of the PlainsAge of the Plains

Unit Area Craters Relative Age Estimated Age (Ma)

PL1 11.86 19 0.79 ± 0.36 T 589 270PL2 84.43 149 0.87 ± 0.14 T 649 106PL3 93.05 217 1.14 ± 0.16 T 857 116PS 99.82 267 1.31 ± 0.16 T 983 120PL1+PL2 96.29 168 0.86 ± 0.13 T 641 ± 99PL3+PS 192.87 484 1.23 ± 0.11 T 923 ± 84SAP 289.16 652 1.11 ± 0.09 T 829 ± 65

• A unit of area is 106 km2. Errors listed are 2. Note that both PL2 and PL1+PL2 have relative ages that do not overlap within 2 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].

ModelingModeling

• > 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 ModelsResurfacing Models

Nominal Each unit has the observed age MB1 PL3 - 2, PS + 2 MB2 PL2 - 2, PS + 1.5 SAP Single age for all plains units DAP Combine young and old units as

PL1+PL2 and PL3+PS DAP2 DAP young + 2, DAP old - 2 TAP Divide units as PL1, PL2, and PL3+PS

ModelModel

QQ and PP PlotsQQ and PP Plots

QQ Plot of Venus Resurfacing Model with Units of Distinct Crater Production Ages

0

4

8

12

0 4 8 12Expected Distance [Deg]

Obs

erve

d [D

eg]

PP Plot of Venus Resurfacing Model with Units of Distinct Crater Production Ages

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Expected Distance [Deg/Deg]O

bse

rved

Dis

tan

ce [

Deg

/Deg

]

TestsTests

• 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 Two-sided pp values of Testing the values of Testing the Hypothesis that Plains Resurfacing Models Hypothesis that Plains Resurfacing Models

Represent VenusRepresent Venus

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.01 2 3 4

NominalMB 1MB 2SAPDAPDAP 2TAPCSRCSR vs. Random

Mth Nearest Neighbor

p va

lue

Statistical ResultsStatistical Results

Unit P

PL1 1.7 x 10-1

PL2 3.0 x 10-2

PL3 1.3 x 10-2

PS 4.5 x 10-7

PL1+PL2 1.4 x 10-2

PL3+PS 6.5 x 10-10

SAP 4.2 x 10-6

Model P

SAP 2.0 x 10-4

DAP 4.9 x 10-1

TAP 5.2 x 10-1

CRM 4.0 x 10-6

Binomial Probability Chi-squared goodness-of-fit

ResultsResults

• 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.

ConclusionsConclusions

• CSR cannot be used as a constraint on resurfacing or geodynamic models because it is a non-uniquenon-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 IIConclusions 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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