Transcript M. Parmentier

Early planetary differentiation processes
with implications for long term evolution
(planetary evolution as an
“initial value problem”)
E. M. Parmentier
Department of Geological Sciences
Brown University
in collaboration with: Linda Elkins-Tanton; Paul Hess; Yan Liang
Outline
1) 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 solidification
buoyant liquid-solid segregation
3) Is there a hidden reservoir of heat and incompatible elements?
4) Convective heating and mixing of stably stratified fluid layer
and the preservation of a hidden reservoir
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
Timescales and mixing in terrestrial planetary accretion
Chambers, EPSL 2004.
Chambers, Icarus, 2001.
Magma ocean formation due to a large impact
Tonks and Melosh JGR 1993
Tonks and Melosh JGR 1993
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
S. Labrosse, J. W. Hernlund & N. Coltice
Nature 450, 866-869, 2007.
Idealizations:
• convection in liquid
maintains adiabatic
gradient and
homogeneous liquid
composition
•
crystal fraction
>50% forms a stresssupported network
and behaves as a
porous solid
• solid retains its
solidus temperature
and composition
Effect of atmosphere on cooling and solidification of 500 km deep MO
non-convecting grey atmosphere
following Abe (1979)
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
 RT
viscosity 


gd 2 initial density gradient 
layer thickness d
Time for overturn  500 RT
The “double diffusion problem” of melt migration
in a convecting, compacting, permeable matrix
Buoyancy sources
matrix density
melt distribution
Matrix
density
and flow
Melt retained
against buoyant
rise
Pressure
driven melt
flow
Does solidification occur by
freezing or squeezing (i.e. compaction)?
Idealizations:
• convection in liquid
maintains adiabatic
gradient and
homogeneous liquid
composition
•
crystal fraction
>50% forms a stresssupported network
and behaves as a
porous solid
• solid retains its
solidus temperature
and composition
region of compaction and
melt-solid segregation
Permeability: dependence on 
b
23
K

b

K  b2  3
Buoyant rise of liquid in pore space:

K

V


g

V
l
f


liq
u id
L = compaction length
= (Ksolid /liquid)1/2
Wark and Watson, 2003
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 

23
K

b

Relative importance of advection and diffusion;
Buoyant rise of liquid in pore space:

K

V


g

V
l
f


liq
u id
L = compaction length
= (Ksolid /liquid)1/2
advection >> diffusion
No diffusional reduction in fractionation
Melt-solid fractionation during the first 100 Myr of Earth evolution
Boyet and Carlson (2005)
Hidden reservoir
Complement to continental crust and depleted MORB mantle
For a chondritic earth – hidden reservoir would contain
20-30% of incompatible trace elements
produce 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 candidate
multiple shallow MOs followed by overturn
deep, basal MO
Could it be preserved?
thermal convective mixing
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.
Convective instability in a continuously stratified fluid layer
How long could stable stratification be preserved?
Some numbers:
=.25x10-6 /m
a=10-5/oC
f = 200 mW/m2
k = 3 W/m-oK
give R=10-1
Then z*~500 km after 4 Gyr
Planetary evolution is an “initial value problem”: the structure
of the Earth today is not independent of how it formed and
evolved in its first hundred Myr.
horizontally averaged values
idealized structure
Densities of solids and coexisting liquid
Stolper et al. (1981); Walker and Agee (1988)