Travis Orloff

Advisors: Erik Asphaug and Mikhail Kreslavsky

6th Year Department Talk

University of California Santa Cruz

4/19/2012

Background

Hypotheses

Seasonal CO2 frost traps boulders

Thermal model of subsurface

Elastic model of subsurface

Constant strength frost scenario

Discussion/Conclusions

Boulders outline polygonsin PSP_008219_2470.

Boulders cluster in polygon edgesin PSP_001341_2485

Schiaparelli, 1886

Levy et al., 2009

Feldman et al., 2004

Boulders outline polygonsin PSP_008219_2470.

Boulders cluster in polygon edgesin PSP_001341_2485

Gravitational Sorting (Mellon et al., 2008)

Surface Creep

Aeolian Processes (Mellon et al., 2008)

Sublimation (Levy et al., 2010)

Something else?

Laity, 2010 Levy et al., 2010

Dry Cryoturbation (Mellon et al., 2008)

Levy et al., 2010

Ice Lensing / Frost Heave (Zent et al., 2010, Balme et al., 2011)

• Thermal contraction and expansion of ice in polygons also moves boulders.

• The seasonal CO2 frost formed during Martian winter prevents boulder movement inward during the contraction phase.

• Boulders move outward during the expansion phase.

• This leads to progressive movement of boulders towards polygon edges.

Dust plumes in spring show slab capable of trapping vapor. (Kiefer et al., 2006)

Vapor generated at soil/frost interface due to heat flux from below. This vapor travels through frost and may refreeze sintering frost into a slab.

Grain size of frost increases over time in spectral observations. (Langevin, 2007)

Opacity of frost changes over time. (Kiefer, 2007)

CO2 frost strength ~0.1 - 1 MPa (Clark and Mullin, 1975)

cm of

frost

Variable Name (Units) Value

σ Stress (Pa)

F Force (N)

A Area (m2)

f Frictional Coefficient 0.5

m Mass (kg)

g Gravity (m s-2) 3.7

d Boulder Diameter (m)

ρ Boulder Denisty (kg m-3) 3000

h Frost Thickness (m)

Str

ess (

MP

a)

Boulder Width (cm)

Simulate T(z, t) (James, 1952)

Solve the linear diffusive heat conduction equation in a semi-infinite solid with periodic plane source.

Surface temperatures from Mars Climate Database (Forget et al., 1999) and interpret between points with cubic spline.

1

0 2exp)1(exp~

Re),(n

nya

ti

nziTTtzT

,...2,1,2exp)(1~

0

00 ndtt

intTT n

Variable Name (units) Value

T Temperature (K)

z Depth (m)

t Time (sols)

Tya Year Average Temperature

χ Thermal Diffusivity (m2 s-1)

10-4

τ Martian Year (sols) 668

T0 Day Average Surface Temperature (K)

Tem

pera

ture

(K

)

Depth (mm)

Created in ADINA

2.5 m radius x 4.0 m depth rotationally symmetric cylinder

Temperatures taken from thermal model

Young’s modulus (7.8 1010 Pa), coefficient of thermal expansion = 4.5 10-5 °K-1, and Poisson ratio of 0.33 representative of pure water ice

Free surface on upper and right boundaries.

Zero displacement on bottom boundary.

ADINA computes stress, strain, and displacement using finite element procedures (Bathe, 1996).

-2.70 mm 0.4 mm

2.5 m

4.0 m

Radial Displacement in a polygon at 68°N at Ls = 310° compared to a polygon whose temperature is entirely at the year averaged daily surface temperature.

a b

Data from Kelly et al., 2007

Solar Longitude (Ls)

Fro

st T

hic

kness (

cm

)

Ls = 310° Ls = 375°

Radial displacement in a polygon at 68°N at two times

Difference in radial displacement between the two times discussed in the previous slide.

Detailed (but still order of magnitude) thermal and elastic modeling suggest ~0.1 mm of contraction while boulders are locked in place

Mechanism is more effective at higher latitudes due to thicker and longer lasting frost cover.

Mechanism is more effective at higher obliquity due to thicker frost at a given latitude and larger temperature change

Timescale (~104 – 105 yrs) of clustering consistent with cratering statistics (Orloff et al., 2011)

There is a size threshold for clustering of boulders depending on frost thickness and strength.

Size threshold for clustered boulders changes with latitude.

Boulders should move today although we cannot yet observe changes at this scale.

PSP_001474_2520

• Boulders cluster at polygon margins meaning they must move.

• Seasonal thermal contraction and expansion of ground ice combined with the seasonal appearance of CO2 frost drive boulders towards polygon margins.

• We predict boulder movement rates of ~0.1 mm per year and clustering timescales of ~104-105 years.

30 m

Large variability in both dynamic viscosity and Young’s modulus of soil ice mixture making up patterned ground terrains.

For viscosity = 1014 Pa s and Young’s modulus = 106 Pa, Maxwell Time = 108 s, longer than the ~106 – 107 s of our scenario.

Δx ~ α ΔT x.

Boulders cluster in rubble piles in TRA_000856_2500