Evolution of the basal magma ocean (BMO) through Earth history ...

Evolution of the basal magma ocean (BMO) 

through Earth history 

Does the present state of the Earth tell us anything on its 

formation 

The MOB (as suggested by Ben Phillips for a new acronym): 

S. Labrosse 1 , N. Coltice 1 and J. Hernlund 2 

M. Ulvrova 1 , N. Machicoane 1 

1 École normale supérieure de Lyon 

Universtité Claude Bernard Lyon-1 

2 UC Berkeley 

Labrosse, Coltice, Hernlund (Lyon) Evolution of the basal magma ocean Braunwald 2009 1 / 28

Introduction 

Our views on the lowermost mantle have largely changed over the last 

∼12 years: 

◮ Discovery of the ULVZ (Garnero & Helmberger ∼1996). 

◮ Recognition of dense thermo-chemical piles (∼1999). 

◮ Discovery of the post-perovskite (Murakami, et al. 2004). 

What are the implications for the evolution of the deep Earth 

ULVZ detection (SPdKS): 

Detected 

Not detected 

Unsampled 

Courtesy of S. Rost (2008) 

High res. detection 

(ScP, PcP, ScS): 

Detected 

Not detected 

(Murakami et al, 2004) 


ULVZ=melt 

Global tomography and ULVZ 

◮ Large V S anomalies in the lower mantle → thermal and chemical 

heterogeneity. 

◮ ULVZs at the edges of dense thermo-chemical piles. 

ULVZ detection (SPdKS): 

Detected 

Not detected 

Unsampled 

shear velocity variation from 1−D 

−1.4% +1.4% 

−1.4 −0.7 0.0 0.7 1.4 

S20RTS 

Ritsema et al. [1999] 

Depth= 2850 km 

Courtesy of S. Rost (2008) 

High res. detection 

(ScP, PcP, ScS): 

Detected 

Not detected 


ULVZ=melt 

Physical properties of the ULVZ 

Evidences for dense partial melt 

(Rost et al, 2005) 

Best fit 

Inversion 

parameters: 

◮ α = δV P 

◮ β = δV S 

◮ D = ULVZ 

thickness 

◮ ρ = ULVZ 

density 

(Rost et al, 2005) 

ULVZ thickness (km) 


ULVZ=melt 

The double crossing model 

Hernlund et al (2005), Nature. 

◮ Double seismic discontinuities explained if 

◮ the core temperature is high enough, 

◮ the temperature gradient is larger than the 

Clapeyron slope. 

◮ Important geophysical implications 

◮ Direct measure of the thermal structure of 

the lower mantle. 

◮ Estimate of heat flux from the core 7–15 TW. 

⇒ Core cooling over the age of the Earth: 

∆T ∼ Q CMB∆t 

MC p 

∼ 1000K . 


ULVZ=melt 

Ideas on melt processes 

L 

Temperature 

S+L 

Time 

S 

(Mg,Fe)SiO 3 CaSiO 3 

Earth Eutectic 

Temperature 

Time 

L 

S+L 

S 

◮ For chemically complex systems, the 

composition of liquid and solid are 

different. 

◮ In particular: Fe partitions 

preferentially in the liquid silicate 

rather than solid. 

◮ Density change on melting: 

∆ρ = ∆ρ φ + ∆ρ χ . 

◮ ∆ρ φ decreases with pressure 

◮ ∆ρχ < 0 

MgSiO 3 FeSiO 3 

Earth 


ULVZ=melt 

Density cross-over in the lower mantle 

Ohtani (1983) : 

(Ohtani, 1983) 

◮ Densities extrapolated 

from upper mantle 

values. 

◮ Melt enrichment in FeO 

⇒ denser than solid. 


ULVZ=melt 

Shock experiments: Density 

MgSiO 3 Mg 2 SiO 4 

(Mosenfelder et al, 2009) 

◮ At high pressure, the volume change upon melting is small 

(MgSiO 3 ) or even negative (Mg 2 SiO 4 ). 

◮ Partitioning of Fe in the melt ⇒ Liquid denser than solid with a 

realistic composition. 


ULVZ=melt 

Shock experiments: Grüneisen parameter 

MgSiO 3 Mg 2 SiO 4 

(Mosenfelder et al, 2009) 

◮ High Grüneisen parameter γ ⇒ Crystallisation of the magma 

ocean from the centre of the mantle. 

∂T ad 

∂P 

= γT ad 

K S 


ULVZ=melt 

Arguments for a hot start in Earth history 

◮ Gravitational energy from Earth formation 

◮ Large impacts 

◮ Core segregation 

⇒ Enough energy to raise the average temperature by a few 1000 

K. A large amount of melting! 

◮ Runaway process: Iron 

melting → segregation → 

more melting (Ricard et al, in 

press, see movie of 

temperature). 

◮ Partitioning of energy between 

the core and the mantle still 

uncertain. 


ULVZ=melt 

Melting the mantle from below 

r 

a f 

a i 

b 

T m 

q = Ck ∆T 

h 

( ) αρg∆Th 

3 1/3 

≃ 100 

Solid 

Melt 

Core 

T 

κµ 

∆T 

4/3 

Wm−2 

µ 1/3 

If the core starts superheated (T > mantle 

solidus) 

◮ heat transported by convection in the 

melt layer. 

◮ melting front moves upward until all 

the initial superheat is consumed by 

heating and melting the lower mantle. 

1000 K superheat →∼ 700 km mantle 

melting. 

T 

T 


ULVZ=melt 

Importance of melting in the lowermost mantle 

◮ Dense melt present now at the bottom of the mantle (ULVZ). 

◮ The core has been cooling down as is evidenced by the 

maintenance of the geodynamo. 

⇒ There should have been more melt in the past. 

◮ This is also compatible with Earth forming scenarios. 


Basal magma ocean (BMO) 

Our cartoon view (Labrosse, Hernlund and Coltice, Nature 2007) 

B Crystallisation of the magma ocean starting at mid-depth. 

A=MgSiO 3 

or MgO 

B=FeSiO3 

or FeO 

C Crystals formed at the base of the mantle 

entrained by convection in the solid mantle. 

D Crystals too dense to be entrained and FeO 

rich magma lakes under chemical piles. 



Time necessary for the crystallisation of the basal 

magma ocean 

A=MgSiO3 

or MgO 

B=FeSiO3 

or FeO 

τ = MC∆T 

Q 

∼ 6Gyr 

M = 2 10 24 kg, C ∼ 1000JK −1 kg −1 

∆T ∼ 1000K, Q ∼ 10TW. 

Time scale controlled by 

◮ the heat flux taken up by convection in the solid mantle, 

◮ the variation of the liquidus with chemical composition, 

◮ the heat capacity of the core. 



Conservation equations 

Energy: 

4πa 2 k T L − T M 

δ 

= ( M m C pm + M C C pC 

) dT L 

dt 

+ H(t) − 4πa 2 ρ∆ST L 

da 

dt 

Mass fraction (ξ L ) of FeO: 

da 

dt 

= a3 − b 3 

3a 2 ∆ξ 

dξ L dT L 

dT L dt 

Approximate analytic solution: 

} 

a − b = (a 0 − b)e −t/τc 

T L = T L0 − ∆ξ(T A − T B ) t τ c = M CC pc (T A − T B )∆ξ 

τ c 

Q − H 


Long term evolution 


Numerical solution of conservation equations: 


Dynamo implications 

Earth budget in Uranium 

Box [U] Q (U+Th+K) 

BSE (if CI) 20 ppb 20 TW 

Continents (Rudnick & Gao, 2003) 1.3 ppm 7 TW 

MORB source 8.3–11 ppb 7–9 TW 

between 20 and 30% of the budget must be stored at depth! 

◮ Classical solution: the whole lower mantle or thermochemical 

piles. 

◮ Our solution: the melt at the base of the mantle. 



Long term evolution: the preferred model 

10 6 

5000 

Thickness, m 

10 5 

10 4 

Thickness 

Temperature 

4500 

Temperature, K 

10 3 

-4 -3 -2 -1 0 

4000 

Time, Gyr 

Important implication: delayed onset of the dynamo! 

Tarduno et al (2006) : the earliest well established record is 3.2 Ga old. 


NATURE|Vol 436|4 August 2005 

Vol 436|4 August 2005|doi:10.1038/nature03929 

ARTICLES 

legend). Among the three mixing Several authors have suggested that the 40 Ar/ 36 Ar ratio may be 

/ 4 He for the ancient atmosphere used as an antiquity parameter for the surface exposure of lunar 

ce there are two prominent He soil 26 . However, Ozima et al. 27 questioned the validity of this method, 

System, namely pre-D-burning He since the assumed process (degassing from lunar interior and reimplanting 

in soil) requires an unrealistically large Ar degassing rate 

post-D-burning He ( 

Terrestrial 3 He= 4 He ¼ 

rved in Jupiter’s atmosphere nitrogen and noble gases in 

22 and from the lunar interior. Relevant information regarding surface 

ent 23 in primitive meteorites. The exposure age of lunar soils may be obtained by the use of cosmic 

t SW (it differs lunar from the soils primordial ray and surface neutron irradiation effects, but this only tells the time 

by nuclear ‘burning’ of D in the pres 

also observed in some meteorites 24 . exposure time of ilmenite grains directly exposed to the SW. Several 

during which samples were within a few metres of the surface, not the 

M. Ozima 1 , K. Seki 2 , N. Terada 2 †, Y. N. Miura 3 , F. A. Podosek 4 & H. Shinagawa 2 † 

ixing diagrams, The nitrogen we note in lunarthat soilsif is correlated the samples to the surface fromandApollo therefore 14clearly and implanted from Apollo from outside. 17 have Thebeen straightforward studied for the 

mixing of interpretation the SW and is thathe nitrogen Earth is implanted relevant by the cosmic solar wind, ray butand this explanation surface has neutron difficultiesirradiation accounting for both data 26,28 . 

the abundance of nitrogen and a variation of the order of 30 per cent in the 15 N/ 14 N ratio. Here we propose that most of 

He can fairly 

the nitrogen 

well 

and 

besome assigned 

of the other 

as 

volatile 

Although 

elementsitinis lunar 

difficult 

soils maytoactually relatehave thecome irradiation 

from the Earth’s 

age 

atmosphere 

of lunar soil to 

rather than the solar wind. We infer that thethisurface hypothesis implantation is quantitativelyage reasonable of anifindividual the escape of ilmenite atmosphericgrain gases, in the 

e betweenand SWimplantation and terrestrial into lunar comtentatively 

soil grains, soil, occurred theat conclusion a time when the byEarth Bernatowicz had essentially et al. no 28 geomagnetic may be worth field. Thus, noting: they 

evidence preserved in lunar soils might be useful in constraining when the geomagnetic field first appeared. This 

hypothesis 

used the 

could 

solar 

be tested 

isotopic 

by examination 

stated 

of lunar 

“thefarside extreme 

soils, which 

case 

should 

that the 

lack the 

irradiation 

terrestrial component. 

age coincided with the 

10 2 4 and 40 Ar/ 36 Ar ¼ 10 2 4 ) and formation age (of minerals in soils) was most easily in accord with the 

ratio for the Since primitive the Apollo missions, Earth. itHow- 

e 40 Ar/ 36 Arveryfor strongly 

has been recognized datathat hand”. the MoonHence, is the fundamental it may be issue possible of when itthat first appeared the substantial remains enigmatic. fractions 

thedepleted ancient 

in volatile 

Earth 

elements, including 

of ilmenite 

N, H, C and 

grains 

the The 

used 

oldest 

in 

palaeomagnetic 

this study had 

information 

a surface 

available 

implantation 

is based age 

noble gases 1,2 . The inventory of these elements in lunar materials is palaeointensity measurements on the Komati formation (age 

of the extremely not intrinsically rapidlunar evolution but rather reflects in anclose extralunar to 3.8–3.9 origin. TheGyr 3.5ago, Gyr) 10 , which showed is generally a much smaller assigned virtual geomagnetic to the formation 

dipole 

extralunar source is generally understood to be the Sun, via direct moment than the present value. (But also note that this conclusion is 

osphere owing to the addition of age 29,30 of major impact basins from where the Apollo samples were 

implantation of solar wind (SW) ions in the surface of the Moon. not unchallenged 11 .) 

example, the This interpretation present atmospheric 

suffices well for the other collected. volatile elements, It isbuthen If tempting the origin of the toGMF speculate were concomitant that the with the GMF formation wasofnull a or 

encounters difficulty with N—that is, there is too much N compared liquid core, the age of the appearance of the GMF would probably be 

ix orders of 

to the 

magnitude 

canonical solar 

larger 

abundance 

than 

4 (of, for 

very 

example, 

weak 

Ar), and 

before 

the 

about 

essentially3.9 the same 

Gyrasago. 

that of the Earth, earlier than the formation of 

)). We examined isotopic composition mixing( curves 15 N/ 14 N) of for surface-correlated and presumably 

extralunar N is strongly variable, by as much as 30%. The appearance of the GMF, we could thus not expect preservation of any 

any significant fraction of the present regolith. For such an early 

¼ 50 andoverabundance 150; here of Nsubscript has been attributed E to underabundance Test of the of noble hypothesis record in lunar soils. On the other hand, if the appearance of the 

gases such as Ar (refs 1, 2), and the isotopic variation to the variation GMF were significantly delayed, is possible that there was a 

Observed data so far available in the literature appear to be consistent


The delayed onset of the dynamo 

Budget in incompatible elements: 

◮ Radiogenic heating important in the basal magma ocean. 

◮ Initial mass important rapidly decaying. 

⇒ Latent and radiogenic heat important in the early BMO can 

prevent efficient (super-isentropic) core cooling. 

Can we avoid the delayed onset by 

increasing the early CMB heat 

flow 



The delayed onset of the dynamo 

Budget in incompatible elements: 

◮ Radiogenic heating important in the basal magma ocean. 

◮ Initial mass important rapidly decaying. 

⇒ Latent and radiogenic heat important in the early BMO can 

prevent efficient (super-isentropic) core cooling. 

30 

Can we avoid the delayed onset by 

increasing the early CMB heat 

flow 

No! An initially higher temperature 

gives a more important latent heat. 

Power, TW 

25 

20 

15 

10 

5 

0 

−4 −3 −2 −1 0 

Time, Gyr 


Convection in the BMO 

Thermal convection and crystallisation 

PhD work of Martina Ulvrova 

◮ Convection in the melt 

◮ Diffusion in the solid 

◮ Interface motion following 

Stefan’s condition 

q = Ck ∆T 

h 

( αρg∆Th 

3 

κµ 

) 1/3 

◮ Small convection ⇒ buffering 

the thermal coupling between 

the core and the mantle 



Composiotional convection 

Internship of Nathanael Machicoane 

Temperature 

L 

S+L 

S 

377ºC 

-15.9ºC 

H 2 O 

Eutectic 

Initial C 

NH 4 Cl= 

solid 

formed 

◮ Freezing from below a dense 

solid. 

◮ Releasing a lighter fluid. 



Composiotional convection 

Internship of Nathanael Machicoane 


Summary 

Conclusions: Basal magma ocean and dynamo 

Arguments in favor of the basal magma ocean: 

◮ ULVZs ⇒ Presence of dense silicate melts. 

◮ Evolution of the core: ∼ 1000 K cooling in 4.5 Ga ⇒ 

Melt more important in the past. 

◮ Conditions of Earth formation. 

Early evolution of the BMO 

◮ Large radiogenic and latent heat ⇒ Delayed onset 

of the dynamo. 

◮ Possible re-equilibration between the core and the 

mantle via the magma ocean at CMB pressure! 


Summary 

The end! 


Conditions for a convective dynamo 

Q CMB 

Minimum necessary conditions for the geodynamo: 

ither an inner core crystallising fast enough. 

⇒ Compositional convection driven by the release of light 

elements upon inner core growth. 

or a heat flow larger than that conducted along core’s 

isentrope. 

⇒ Thermal convection. 

⇒The present heat flow can be lower than the isentropic one (Q i ), 

provided it was larger before the inner core started to crystallise. 



Q CMB 






isentrope. 


Q CM 





Q CMB 






isentrope. 


In addition: 

◮ Thermal convection is necessary early in the history to 

reach the freezing point at the center. 

Q CM 




The cheapest dynamo 

Take 

10 

Q(age) = Q 0 + B × age 

Energy budget for the core 

with 

◮ Q 0 < Q i 

◮ Q(IC age) = Q i . 

Contribution to the Ohmic dissipation 

Power, TW 

5 

Isentropic heat flow 

CMB heat flow 

Secular cooling 

Φ, TW 

1.0 

0.5 

Secular cooling 

Diffusion along isentrope 

Compositionnal 

Compositionnal E Latent heat 

0.0 

0 

4000 3000 2000 1000 

0 

4000 

Age, Ma 

Note that the inner core is about 2.2 Gyr old! 

Total ohmic diss. 

3000 2000 

Age, Ma 

Latent heat 

ICB heat flow 

1000 

0 


Phase transitions and the thermal structure of D” 

Hernlund et al (2005), Nature. 

Core temperature uniform: 

◮ Cool core: ubiquitous single 

discontinuity. 

◮ Hot core: discontinuity is either 

absent (warm mantle) or double 

(cold mantle).

Evolution of the basal magma ocean (BMO) through Earth history ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?