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”)

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

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

Chambers, Icarus, 2001.

Chambers, EPSL 2004.

Timescales and mixing in terrestrial planetary accretion

Tonks and Melosh JGR 1993

Magma ocean formation due to a large impact

Tonks and Melosh JGR 1993

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

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

Effect of atmosphere on cooling and solidification of 500 km deep MO

non-convecting grey atmosphere following Abe (1979)

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

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

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)?

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

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

Boyet and Carlson (2005)

Melt-solid fractionation during the first 100 Myr of Earth evolution

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

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

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?

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.

horizontally averaged values idealized structure

Densities of solids and coexisting liquid

Stolper et al. (1981); Walker and Agee (1988)