A slightly updated version of the talk I gave at the Lunar and Planetary Sciences Conference 2012. This talk was presented to a more general audience (the Earth and Planetary Sciences Department of University of California Santa Cruz).

1. Travis Orloff
Advisors: Erik Asphaug and Mikhail Kreslavsky
6th Year Department Talk
University of California Santa Cruz
4/19/2012

2.  Background
 Hypotheses
 Seasonal CO2 frost traps boulders
 Thermal model of subsurface
 Elastic model of subsurface
 Constant strength frost scenario
 Discussion/Conclusions

3. Boulders outline polygons Boulders cluster in polygon edges
in PSP_008219_2470. in PSP_001341_2485

4. Schiaparelli, 1886

5. Levy et al., 2009

6. Feldman et al., 2004

11. Boulders outline polygons Boulders cluster in polygon edges
in PSP_008219_2470. in PSP_001341_2485

12.  Gravitational Sorting (Mellon et al., 2008)

13.  Surface Creep
 Aeolian Processes (Mellon et al., 2008)
 Sublimation (Levy et al., 2010)
 Something else?
Laity, 2010 Levy et al., 2010

14.  Dry Cryoturbation (Mellon et al., 2008)
Levy et al., 2010

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

16. • 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.

18.  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)

19. 
cm of Variable Name (Units) Value
frost σ Stress (Pa)
Stress (MPa)
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
Boulder Width (cm) h Frost Thickness (m)

20.  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.

21. ~ n t
T ( z, t ) Tya Re T0 n exp (1 i ) z exp 2 i
n 1
~ 1 t
T0 n T0 (t ) exp 2 in dt , n 1,2,...
0
Variable Name (units) Value
T Temperature (K)
z Depth (m)
Temperature (K)
t Time (sols)
Tya Year Average
Temperature
χ Thermal 10-4
Diffusivity (m2 s-1)
τ Martian Year (sols) 668
T0 Day Average
Surface
Temperature (K) Depth (mm)

22.  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).

23. 2.5 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.
4.0 m
-2.70 mm 0.4 mm

24. Frost Thickness (cm)
a b
Solar Longitude (Ls)
Data from Kelly et al., 2007

25. Radial displacement in a polygon at 68°N at two times
Ls = 310° Ls = 375°

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

27.  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)

28.  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.

29. • 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
PSP_001474_2520

30.  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.

31. Δx ~ α ΔT x.

35. Boulders cluster in rubble piles
in TRA_000856_2500