e. m. parmentier department of geological sciences brown university in collaboration with: linda...
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E. M. ParmentierDepartment of Geological Sciences
Brown University
in collaboration with: Linda Elkins-Tanton; Paul Hess; Yan Liang
Early planetary differentiation processes with implications for long term evolution
(planetary evolution as an “initial value problem”)
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Outline1) Planetary accretion and magma oceans (MOs)
- Moon is the type example – highly fractionated compositions- For the Earth - how many MOs and how deep?- Shallow vs. basal MO
2) Idealized fractional solidification of a MO - unstable stratification and overturn of solidified mantle - how realistic is fractional solidification idealization?
solid state overturn during solidificationbuoyant liquid-solid segregation
3) Is there a hidden reservoir of heat and incompatible elements?
4) Convective heating and mixing of stably stratified fluid layerand the preservation of a hidden reservoir
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Composition of the lunar surface
- Mare basalt volcanism at ~3.9 Gyr to 2.5 Gyr – long after MO solidification- Basalts generated at >400 km depth – olivine-pyroxene multiple saturation- Mantle source composition residual to anorthositic crust crystallization- Global asymmetry in emplacement of basalts and the PKT
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Chambers, Icarus, 2001.
Chambers, EPSL 2004.
Timescales and mixing in terrestrial planetary accretion
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Tonks and Melosh JGR 1993
Magma ocean formation due to a large impact
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Tonks and Melosh JGR 1993
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S. Labrosse, J. W. Hernlund & N. ColticeNature 450, 866-869, 2007.
Basal magma ocean
Develops first 100 Myr and persists during the evolution of the Earth Due to heat generated during core formation Suggest that perovskite fractionation explains trace elements in
continental crust + MORB mantle
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Idealizations:
• convection in liquid maintains adiabatic gradient and homogeneous liquid composition
• crystal fraction >50% forms a stress-supported network and behaves as a porous solid
• solid retains its solidus temperature and composition
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Effect of atmosphere on cooling and solidification of 500 km deep MO
non-convecting grey atmosphere following Abe (1979)
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2gdRT
viscosity initial density gradient layer thickness d
Time for overturn 500 RT
Time scale for solid state overturn
Taking:
= 1018 Pa-s = 2 x 10-4 kg/m3/m
g = 10 m/sec2
d = 500 km
Gives:RT ≈ 0.1 Myr
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MatrixMatrixdensitydensityand flowand flow
Melt retainedMelt retainedagainst buoyantagainst buoyantriserise
PressurePressuredriven meltdriven meltflowflow
The “double diffusion problem” of melt migration in a convecting, compacting, permeable matrix
Buoyancy sources matrix density melt distribution
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Idealizations:
• convection in liquid maintains adiabatic gradient and homogeneous liquid composition
• crystal fraction >50% forms a stress-supported network and behaves as a porous solid
• solid retains its solidus temperature and composition
region of compaction andmelt-solid segregation
Does solidification occur by freezing or squeezing (i.e. compaction)?
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L = compaction length = (Ksolid /liquid)1/2
Buoyant rise of liquid in pore space:
32bK
Permeability: dependence on
Wark and Watson, 2003
f
liquidl Vg
KV
K b2 3
b
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L = compaction length = (Ksolid /liquid)1/2
Buoyant rise of liquid in pore space:
32bK
f
liquidl Vg
KV
Take:
b = grain size = 1 mm
liquid viscosity = 0.1 Pa-s
solid compaction viscosity = 1018 Pa-s
= 300 kg/ m3
Vf = 300 km/ 1 Myr = 10-8 m/ sec
These give: = 3% and L = 300 m
Note that
Relative importance of advection and diffusion;
advection >> diffusion
No diffusional reduction in fractionation
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Boyet and Carlson (2005)
Melt-solid fractionation during the first 100 Myr of Earth evolution
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Hidden reservoir
Complement to continental crust and depleted MORB mantle For a chondritic earth – hidden reservoir would contain
20-30% of incompatible trace elementsproduce about this fraction of global heat flux (U, Th ,K)excess 40Ar (from decay of 40K over earth evolution)low 142Nd – requires formation in first ~100 Myr
How would it form?
Magma ocean is a prime candidatemultiple shallow MOs followed by overturndeep, basal MO
Could it be preserved?
thermal convective mixing
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Farnetani, GRL, 24, 1583, 1997; Alley and Parmentier, PEPI 108, 15, 1998; Davaille, Nature, 402, 756, 1999; Hunt and Kellogg, JGR 106, 6747, 2001; Gonnermann, et al., GRL, 29, 1399, 2002; Samuel and Farnetani, EPSL 207, 39, 2003.
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Convective instability in a continuously stratified fluid layer
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Some numbers:=.25x10-6 /m=10-5/oC give
R=10-1
f = 200 mW/m2
k = 3 W/m-oK
Then z*~500 km after 4 Gyr
How long could stable stratification be preserved?
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Planetary evolution is an “initial value problem”: the structureof the Earth today is not independent of how it formed and evolved in its first hundred Myr.
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horizontally averaged values idealized structure
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Densities of solids and coexisting liquid
Stolper et al. (1981); Walker and Agee (1988)