Christopher W. Hamiltonhamilton@dal.ca

Hawai‘i Institute of Geophysics and Planetology, University of Hawai‘i

 Explosive Lava–Water Interactions

on Earth and Mars

Ph.D. Co-Advisor: Thor Thordarson

Co-Authors: Lionel Wilson Ciarán Beggan

Ph.D. Advisor: Sarah Fagents

Acknowledgements National Aeronautics and Space Administration Icelandic Centre for Research National Science FoundationGeological Society of AmericaHawai‘i Geographic Information Coordinating Council University of Hawai‘i Graduate Student Organization

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

3. Thermodynamic modeling

1. Geological mapping and geomorphology

2. Statistical nearest neighbor (NN) analysis

Explosive Lava–Water Interactions

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Explosive Lava–Water InteractionsEarth:

Hamilton CW, T Thordarson, and SA Fagents (2010a) Explosive lava-water interactions I: architecture and emplacement chronology of volcanic rootless cone groups in the 1783- 1784 Laki lava flow. Bulletin of Volcanology, 10.1007/s00445-009-0330-6.

Hamilton CW, SA Fagents, and T Thordarson (2010b) Explosive lava-water interaction II: Self-organization processes among volcanic rootless eruption sites in the 1783-1784 Laki lava flow, Iceland. Bulletin of Volcanology, 10.1007/s00445-009-0331-5.  

Mars:Hamilton CW, SA Fagents, and L Wilson (2010c) Explosive lava-water interactions in Elysium

Planitia, Mars: constraints on the formation of the Tartarus Colles cone groups. Journal of Geophysical Research, (in press).

Hamilton CW, SA Fagents, and T Thordarson (2010d) Lava-ground ice interactions in Elysium Planitia, Mars: geomorphological and geospatial analysis of the western Tartarus Colles cone groups. Journal of Geophysical Research, (in review).

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

 

Introduction

Lake Mývatn, Iceland

Volcano–H2O Interactions

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Volcanic Rootless Cones (VRCs)

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Skaftá River, Iceland

Volcanic Rootless Cones (VRCs)

VRC group in the Laki lava flow, Iceland

Introduction Methods Results Discussion Conclusions

Volcanic Rootless Cones (VRCs)

Introduction Earth Mars Discussion Conclusions

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

100 m

VRC group in the Laki lava flow, Iceland

Volcanic Rootless Cones (VRCs)

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conceptual Model

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Neural Networks

VRC cross-section within Rauðhólar, Iceland

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Volcanic Rootless Cones (VRCs)

Neural Networks

VRC cross-section within Rauðhólar, Iceland

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Volcanic Rootless Cones (VRCs)

Neural Networks

VRC cross-section within Rauðhólar, Iceland

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Volcanic Rootless Cones (VRCs)

Neural Networks

VRC cross-section within Rauðhólar, Iceland

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Volcanic Rootless Cones (VRCs)

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Volcanic Rootless Cones (VRCs)

1 km

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

VRC analogs among the western Tartarus Colles cone groups, Mars

Volcanic Rootless Cones (VRCs)

1 km

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Volcanic Rootless Cones (VRCs)

VRC analogs among the eastern Tartarus Colles cone groups, Mars

Mars Exploration Rover Spirit images of volcanic rocks in Gusev Crater, Mars

Volcano–H2O Interactions on Mars

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Mars Exploration Rover Spirit images of volcanic rocks in Gusev Crater, Mars

Volcano–H2O Interactions on Mars

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Mars Exploration Rover Spirit images of volcanic rocks in Gusev Crater, Mars

Volcano–H2O Interactions on Mars

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Volcanic Rootless Cones (VRCs)

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Mars Exploration Program Goals:1. Determine if life ever arose on Mars

2. Climate processes and history

3. Evolution of the surface and interior

4. Prepare for human exploration

Fossil hydrothermal systems

Obliquity-driven ground ice stability

Volcanic and magmatic processes

Identification of water resources

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

 

Earth

Terrestrial Analog: Laki, Iceland

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

N

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

N

Terrestrial Analog: Laki, Iceland

1070ºC

150 m

564

570

568

566

E

leva

tio

n (

m)

Rootless Cone Archetypes Brittle Crust

Viscous Layer

Molten Core Saturated

Unsaturated

Lava Flow Sediments

800ºC

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

150 m

564

570

568

566

E

leva

tio

n (

m)

Rootless Cone Archetypes

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

150 m

564

570

568

566

E

leva

tio

n (

m)

Rootless Cone Archetypes

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

150 m

564

570

568

566

E

leva

tio

n (

m)

Rootless Cone Archetypes

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

150 m

564

570

568

566

E

leva

tio

n (

m)

Rootless Cone Archetypes

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

150 m

564

570

568

566

E

leva

tio

n (

m)

Rootless Cone Archetypes

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

150 m

564

570

568

566

E

leva

tio

n (

m)

Geospatial Analysis

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

150 m

564

570

568

566

E

leva

tio

n (

m)

Geospatial Analysis

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150 m

564

570

568

566

E

leva

tio

n (

m)

Geospatial Analysis

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Hekla 1104 pumice layer

150 m

564

570

568

566

E

leva

tio

n (

m)

Geospatial Analysis

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Kipuka Mantled Terrain

Lava Rootless Cone Crater Crater Floor

1000 m

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

○

e

a

R

RR

Ra: mean actual distance between Nearest Neighbor (NN) pairs

Re: mean expected distance between NNs

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

if R < 1 then clustered if R ≈ 1 then random if R > 1 then repelled

R: 1.00

|c|: 0.05

R: 1.91

|c|: 6.64

R: 0.47

|c|: 7.13

Clustered Poisson (Random) Evenly Spacedx

R < 1 R = 1 R > 1

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

Figure adapted from Bruno et al. (2006)

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

Population size (N)

Repelled

Clustered

Discharge from extraction wellMaximum radius of influenceDistance from extraction wellAquifer thicknessWater saturated depth at rWater table draw down at r

QRrHhS

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

Discharge from extraction wellMaximum radius of influenceDistance from extraction wellAquifer thicknessWater saturated depth at rWater table draw down at r

QRrHhS

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

Discharge from extraction wellMaximum radius of influenceDistance from extraction wellAquifer thicknessWater saturated depth at rWater table draw down at r

QRrHhS

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Geospatial Analysis

3. Sample-size-dependent organization

1. Lava pathways effect VRC morphology

2. VRC groups are diachronous constructs

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Summary

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

 

Mars

Tartarus Colles Cone Groups, Mars

MOLA Digital Terrain Model of Elysium Planitia, Mars

1000 km

9 km

-9 km

0 km

E

leva

tio

n

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

9 km

-9 km

0 km

E

leva

tio

n

1000 km

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Tartarus Colles Cone Groups, Mars

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Tartarus Colles Cone Groups, Mars Cerberus Fossae 3 unit

Late AmazonianCerberus Fossae 2 unitLate to Middle Amazonian

Elysium Rise unitEarly Amazonian to Early Hesperian

Crater unitLate Amazonian to Early Hesperian

Arcadia Planitia unitLate to Early Hesperian

Nepenthes Mensae unitEarly Hesperian to Early Noachian

Noachian Hesperian Amazonian

3.5 1.8 0 Billions of years before present

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Tartarus Colles Cone Groups, Mars

Elysium Rise unitEarly Amazonian to Early Hesperian

Nepenthes Mensae unitEarly Hesperian to Early Noachian

VRC-hosting Tartarus Colles lava

Shield-like Tartarus Colles lava

Elevation (m)

Noachian Hesperian Amazonian

3.5 1.8 0 Billions of years before present

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Tartarus Colles Cone Groups, Mars

Elysium Rise unitEarly Amazonian to Early Hesperian

Nepenthes Mensae unitEarly Hesperian to Early Noachian

VRC-hosting Tartarus Colles lava

Shield-like Tartarus Colles lava

VRCs

Elevation (m)

Noachian Hesperian Amazonian

3.5 1.8 0 Billions of years before present

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Tartarus Colles Cone Groups, Mars

Elysium Rise unitEarly Amazonian to Early Hesperian

Nepenthes Mensae unitEarly Hesperian to Early Noachian

VRC-hosting Tartarus Colles lava

Shield-like Tartarus Colles lava

VRCs

Elevation (m)

Noachian Hesperian Amazonian

3.5 1.8 0 Billions of years before present

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Tartarus Colles Cone Groups, Mars

Elysium Rise unitEarly Amazonian to Early Hesperian

Nepenthes Mensae unitEarly Hesperian to Early Noachian

VRC-hosting Tartarus Colles lava

Shield-like Tartarus Colles lava

VRCs

Elevation (m)

Pitted terrain

Noachian Hesperian Amazonian

3.5 1.8 0 Billions of years before present

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Tartarus Colles Cone Groups, Mars

Elysium Rise unitEarly Amazonian to Early Hesperian

VRC-hosting Tartarus Colles lavaLate to Middle Amazonian (75–250 Ma)

(log Ni)

Nearest Neighbor (NN) Results

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Repelled

Clustered

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Nearest Neighbor (NN) Results

Repelled

Clustered

Nearest Neighbor (NN) Results

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Repelled

Clustered

(log Ni)

Nearest Neighbor (NN) Results

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Repelled

Clustered

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Nearest Neighbor (NN) Results

Lava Thickness

N

10 km

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Nearest Neighbor (NN) Results

Lava Thickness

N

10 km

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Nearest Neighbor (NN) Results

Lava Thickness

N

10 km

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Nearest Neighbor (NN) Results

3 km

Lava Thickness

N

10 km

3 km

3 km

Lava Thickness

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

N

10 km

Nearest Neighbor (NN) Results

Thermodynamic Model

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Thermodynamic Model

Differences in isotherm depths on Mars and the Earth

Mars (TA = 210 K) Earth (TA = 270 K)

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Thermodynamic Model

Hydrothermal system longevity (substrate temperature >273 K)

Mars (TA = 210 K) Earth (TA = 270 K)

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Thermodynamic Model

X Y

X Y

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X

Y

Thermodynamic Model

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X Y

X Y X Y

X

Y

Thermodynamic Model

273 K at TL = 1273 K

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

X Y

X Y X Y

X

Y

Thermodynamic Model

273 K at TL = 1273 K

Maximum 273 K

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

X Y

X Y X Y

X

Y

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

 

Discussion

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Summary

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Summary

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Summary

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Summary

Summary

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

SummaryMinimum H2O volume = (VRC domain area) × (Isotherm depth at TL = 1273 K) × (Substrate porosity)

Minimum H2O volume = (2014 km2) x (21 to 42 m for 30 to 60 m-thick lava) × (0.1 to 0.3) Minimum H2O volume = ~3.7 to 22.5 km3

SummaryMinimum H2O volume = (VRC domain area) × (Isotherm depth at TL = 1273 K) × (Substrate porosity)

Minimum H2O volume = (2014 km2) x (21 to 42 m for 30 to 60 m-thick lava) × (0.1 to 0.3) Minimum H2O volume = ~3.7 to 22.5 km3

Paleo-climate = intermediate obliquity (~35°) 75–250 Ma ago, with excursions to ~25–32°

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

SummaryMinimum H2O volume = (VRC domain area) × (Isotherm depth at TL = 1273 K) × (Substrate porosity)

Minimum H2O volume = (2014 km2) x (21 to 42 m for 30 to 60 m-thick lava) × (0.1 to 0.3) Minimum H2O volume = ~3.7 to 22.5 km3

Paleo-climate = intermediate obliquity (~35°) 75–250 Ma ago, with excursions to ~25–32°

Hydrothermal system longevity = up to ~1300 years for 75 m-thick lava and TA = 210 K

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

 

Conclusions

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Conclusions

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Lo

cal

Glo

bal

1. How do volcanic rootless constructs (VRCs) form?

VRCs form due to explosive lava–water interactions that indicate at random in favorable environments

VRC groups are diachronous structures with VRCmorphologies recording stages of lava emplacement

Thermokarst can form in association with VRCs ifextended ground ice melting causes lava foundering

Conclusions

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

Lo

cal

Glo

bal

1. How do volcanic rootless constructs (VRCs) form?

2. Can rootless cones be identified using geospatial analysis?

VRCs form due to explosive lava–water interactions that indicate at random in favorable environments

VRC groups are diachronous structures with VRCmorphologies recording stages of lava emplacement

Thermokarst can form in association with VRCs ifextended ground ice melting causes lava foundering Rootless eruption sites exhibit scale-dependent variations in nearest neighbor statistics, but cannotbe distinguished using one geospatial parameter

VRCs form due to explosive lava–water interactions that indicate at random in favorable environments

VRC groups are diachronous structures with VRCmorphologies recording stages of lava emplacement

Thermokarst can form in association with VRCs ifextended ground ice melting causes lava foundering Rootless eruption sites exhibit scale-dependent variations in nearest neighbor statistics, but cannotbe distinguished using one geospatial parameter

During VRC formation, the western Tartaus Colles region contained >4–22 km3 H2O, and could have had active hydrothermal systems for up to ~1300 years

This major volcanic event occurred on Mars ~125 Maago, under intermediate (~35°) obliquity conditionssupporting a mid-latitude ice table at <21–42 m depth

Conclusions1. How do volcanic

rootless constructs (VRCs) form?

Lo

cal

Glo

bal

2. Can rootless cones be identified using geospatial analysis?

3. What information do rootless cones provide about the geological evolution of Mars?

Introduction Methods Results Discussion ConclusionsIntroduction Earth Mars Discussion Conclusions

 

DGPS Mapping

Introduction Methods Results Discussion Conclusions

Terrestrial Analogue: Laki, Iceland

Introduction Methods Results Discussion Conclusions

N

Terrestrial Analogue: Laki, Iceland

Introduction Methods Results Discussion Conclusions

Kipuka Mantled Terrain

Lava Rootless Cone Crater Crater Floor

1000 m

Facies Mapping

Introduction Methods Results Discussion Conclusions

Introduction Methods Results Discussion Conclusions

Facies Mapping

Differential GPS tracks define facies boundaries

15 m

Introduction Methods Results Discussion Conclusions

Facies Mapping

DGPS boundaries were digitized in ArcGIS

15 m

Introduction Methods Results Discussion Conclusions

Facies Mapping

15 m

DGPS boundaries were digitized in ArcGIS

2216 rootless eruptions sites defined using Differential GPS

86 stratigraphic sections used to constrain kipuka locations and emplacement chronology

On Wednesday, August 20, 2008this geological map was usedto prevent renewed quarrying of the Laki rootless cones

Introduction Methods Results Discussion Conclusions

Facies Mapping

0.5 m

1.0 m

Katla 1918

Laki (S2)

Emplacement ChronologyLaki S1a Layer (Fissures 1)June 8, 1783

Laki S1b Layer (Fissures 2)June 10-11, 1783

Laki S2 Layer (Fissure 3)June 14, 1783

Introduction Methods Results Discussion Conclusions

0.5 m

Katla 1918

Laki (S2)

Emplacement Chronology

1.0 m

Laki S1a Layer (Fissures 1)June 8, 1783

Laki S1b Layer (Fissures 2)June 10-11, 1783

Laki S2 Layer (Fissure 3)June 14, 1783

Introduction Methods Results Discussion Conclusions

0.5 m

Katla 1918

Laki (S1 + S2)

Katla 1755

Katla 1625

Emplacement Chronology

1.0 m

Laki S1a Layer (Fissures 1)June 8, 1783

Laki S1b Layer (Fissures 2)June 10-11, 1783

Laki S2 Layer (Fissure 3)June 14, 1783

Introduction Methods Results Discussion Conclusions

Emplacement Chronology

Introduction Methods Results Discussion Conclusions

 

Nearest Neighbor (NN) Analysis

Introduction Methods Results Discussion Conclusions

○

e

a

R

RR

Ra: mean actual distance between Nearest Neighbor (NN) pairs

Re: mean expected distance between NNs

c: test statistic for measuring the significance of R

σ : standard error of the mean expected NN distance

eR

ea RRc

Re

Introduction Methods Results Discussion Conclusions

Geospatial Analysis

Introduction Methods Results Discussion Conclusions

Geospatial Analysis

Population size (N)

Introduction Methods Results Discussion Conclusions

Geospatial Analysis

Population size (N)

 

Thermodynamic Modeling

Introduction Methods Results Discussion Conclusions

Thermodynamic Model

t

dx

t

dxerf

t

xerfTTTT BLB 2222

2

1

T = temperature at time t in secondsTL = temperature of the lava (initially equal to TM)TB = temperature at the base of the flow (initially equal to TM)TM = temperature of basaltic magma (1450 or 1617 K)d = depth beneath the top of the flow in metersk = thermal diffusivity (7 × 10-7 m2 s-1)

Other boundary conditions and considerations: 1. Upper flow surface of the lava is kept at ambient temperature (TA) 2. Substrate temperature is initially set to TA

3. k adjusted to account for the heat absorbed in melting and vaporizing H2O

Analytical model:

Introduction Methods Results Discussion Conclusions

Thermodynamic Model

Introduction Methods Results Discussion Conclusions

Effects of ambient temperature (TA) on isotherm depth

Mars (TA = 210 K) Earth (TA = 270 K)

Thermodynamic Model

Introduction Methods Results Discussion Conclusions

 

Obliquity-Driven Climate Change

Introduction Methods Results Discussion Conclusions

Obliquity-Driven Climate Change

Introduction Methods Results Discussion Conclusions

Probabilistic obliquity scenarios for Mars during the past 250 Ma (Laskar et al., 2004)

Obliquity (Axial Tilt)

Plane of the ecliptic

If ice then obliquity >25°If desiccation then obliquity <32°