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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).
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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