Constraining the composition and thermal state of the Moon from inversion of

seismic velocities

Oleg Kuskov,

Victor Kronrod, Ecaterina Kronrod

Vernadsky Institute of Geochemistry

IKI, Moscow, 2011

Reinterpretation of seismic studies

• Recently, reinterpretation of earlier Apollo seismic studies has occurred [Khan et al., 2000, 2007; Lognonné, 2003, 2005; Gagnepain-Beyneix et al., 2006; Weber et al., 2011].

• New data have shown a fair agreement in P and S velocity profiles with those from earlier studies [Goins, Nakamura] at depths of the upper mantle but found a significant difference in the lower mantle.

Recent seismic models - Lognonné et al. (2003), Lognonné (2005)

seismic velocities have an anticorrelated behavior at depths of the lower mantle

VP, km s-1

7,4 7,6 7,8 8,0 8,2

H,

km

200

400

600

800

1000

Lognonne (2005)

Khan et al. (2000)

VS, km s-1

4,2 4,4 4,6

H,

km

200

400

600

800

1000

Lognonne (2005)

Recent seismic models - Gagnepain-Beyneix et al.,

PEPI, 2006 VS, km s-1

4,3 4,4 4,5 4,6

H,

km

200

400

600

800

1000

Gagnepain-Beyneix et al., 2006

VP, km s-1

7,4 7,6 7,8 8,0 8,2

H, k

m

200

400

600

800

1000

seismic velocities have an anticorrelated behavior at depths below 240 and 500 km

• In spite of the limited amount of information and appreciable divergence of seismic data, studies of lunar internal structure open possibilities for derivations of mantle composition and/or temperature from P- and S-wave velocity profiles.

• Temperature is not modeled directly. Seismic studies are probably the best tool to infer (indirectly) the thermal state of the Moon.

Key question – what thermal and petrological models would satisfy the seismic models?

• Because we never know what is the “best” value in the lunar mantle, for example, VP = 7.7 or VP = 8.0 km/s the conversion of velocity for temperature yields a strong independent tool, which can discriminate between the seismic profiles.

Note that a velocity contrast of 0.1 km/s (~1%) leads to a temperature contrast of about 250оС

V 0.1 km/s Т 250оС

VP, km s-1

7,4 7,6 7,8 8,0 8,2

H, k

m

200

400

600

800

1000

Lognonne (2005)

Khan et al. (2000)

Major goalsOne of the most difficult factors to determine is the

present temperature of the lunar interior. We invert the lunar seismic models, together with petrological models, for the thermal state of the Moon.

• The first goal is to assess temperatures in the upper and lower mantle of the Moon from both P- and S wave velocities. To place constraints on the temperature distribution in the lunar mantle, we have calculated a family of selenotherms from seismic velocities, making various assumptions regarding the chemical composition of the zoned mantle.

• The second goal is to estimate the reliability of the proposed petrological models of the lunar interior based on the derived temperature profiles.

Method of minimization of the total Gibbs free energy in the Na2O-TiO2-CaO-FeO-MgO-Al2O3-SiO2 system with non-ideal solid solutions

Mie-Grüneisen EOS for solids

Self-consistent database with thermodynamic properties of minerals (H, S, Cp, , Ks, , etc.)

These thermodynamic properties are used to calculate phase diagrams and seismic velocities and density of the lunar mantle.

Calculated temperatures include both anelastic and anharmonic effects in the seismic velocities as well as the effects of phase transitions.

Thermodynamic approach - Temperature dependence of seismic velocities comes both from anharmonic and

anelastic properties

Forward/inverse problemThe focus in the forward

modeling is to convert potentially possible bulk composition models into stable mineral assemblages, and to calculate the seismic velocities and densities.

• serious obstacle - there is no data on mantle’s temperature.

Inverse code computes the temperature distribution in the mantle from seismic and compositional constraints.

Solution of the inverse problem yields a temperature profile consistent with the seismic velocities and equilibrium phase composition at given P–T parameters and constraints imposed onto the bulk system composition.

equations of state

Bulk com position

Therm odynam ics,

Phase diagramand theoretical velocity profiles

Seism ic velocities

M ANTLE STR UCTUR E

Tem peraturedistribution

Bulk composition models of the Moon

• There is a rich variety of bulk composition models proposed for the Moon: from models enriched in Ca and Al to Earth-like compositions in which Ca and Al content is lower (e.g., Wieczorek et al., 2006). The FeO content of 10-12% in the bulk Moon is intermediate between that of Mars with 18% and the terrestrial mantle with 8% FeO.

8 . 8 9 . 6 1 0 . 4 1 1 . 2 1 2 1 2 . 8

F eO

0

0.05

0.1

0.15

0.2

0.25

4 . 8 5 . 6 6 . 4 7 . 2 8 8 . 8 9 . 6

Al2O3

0

0.05

0.1

0.15

0.2

0.25

Al2O3 + CaO, wt.%

4 6 8 10 12 14 16

FeO

, w

t.%

6

8

10

12

14

McDonough and Sun (1995)

Geochemical models

Geophysical models

Earth

Ringwood (1979)

Jones and Delano (1989)

O'Neill (1991)

Khan et al. (2007)

Lognonne et al. (2003)

Taylor (1982)

Galimov (2004)

Morgan et al. (1978)

Warren (2005)

Kuskov and Kronrod (1998a)

• A comparison of these Figures shows that neither geochemical nor geophysical bulk composition models are able to satisfy seismic constraints in the upper and lower mantle simultaneously because such models fail to explain the topology of the seismic structure of chemically stratified lunar mantle

VP, km s-1

7,4 7,6 7,8 8,0 8,2

H,

km

200

400

600

800

10001

2

34

Seismic models: 1 - Gagnepain-Beyneix et al. (2006), 2 - Khan et al. (2000), 3 – Kuskov et al. (2002), 4 - Lognonné et al. (2005)

Al2O3 + CaO, wt.%

4 6 8 10 12 14 16

FeO

, w

t.%

6

8

10

12

14

McDonough and Sun (1995)

Geochemical models

Geophysical models

Earth

Ringwood (1979)

Jones and Delano (1989)

O'Neill (1991)

Khan et al. (2007)

Lognonne et al. (2003)

Taylor (1982)

Galimov (2004)

Morgan et al. (1978)

Warren (2005)

Kuskov and Kronrod (1998a)

Inversion of seismic data for temperature

We inverted for temperature the P- and S- velocity models together with three petrologic models (Kuskov and Kronrod, 1998, 2009):

• an olivine-bearing pyroxenite composition depleted in Ca and Al at depths of 50-1000 km,

• a Ca–Al-rich assemblage for the lower mantle,

• a pyrolite composition for the entire mantle.

Temperature profiles for the upper lunar mantle derived from recent seismic models [Lognonné, 2003, 2005;

Gagnepain-Beyneix et al., 2006] for the pyroxenite and pyrolite compositions

• Upper mantle temperature estimates for pyrolite are much higher than those for pyroxenite.

(1) Ca–Al-depleted olivine-bearing pyroxenite composition (~2% CaO, Al2O3) leads to reasonable temperatures in accord with seismic evidence for a rigid upper mantle .

(2) pyrolite composition (4-5% CaO, Al2O3) gives too high temperatures approaching the solidus – the pyrolitic model is unacceptable in the upper mantle.

(3) It is likely that the upper mantle is depleted in Ca and Al.

TP, oC

400 500 600 700 800 900

H, k

m

100

200

300

400

500

Gagnepain-Beyneix et al. (2006)Lognonne (2005)

Pyroxenite

TP, oC

600 800 1000 1200 1400

H, k

m

100

200

300

400

500Gagnepain-Beyneix et al. (2006)Lognonne (2005)

Pyrolite

Temperatures in the lower mantle of the Moon

TS, oC

900 1100 1300 1500

H, k

m

800

900

1000Gagnepain-Beyneix et al. (2006)

Kuskov et al. (2002)

Solidus

Ol-C

px-G

ar

Pyro

lite

(B)

Pyro

lite

Ol-C

px-G

ar

Pyro

xenite

• As it is seen, the pyroxenite model depleted in Ca and Al and fitting well for the thermal regime of the upper mantle, leads to unreasonably low temperatures in the lower mantle.

• In contrast, petrological assemblages enriched in Ca and Al provide a good match to the lower mantle temperature.

• Both petrological assemblages – pyrolite and Ol-Cpx-Gar - provide a good match to the lower mantle composition of the Moon.

TP, oC

1200 1300 1400 1500 1600 1700

H, k

m

800

900

1000

Lognonne (2005)

Kuskov et al. (2002)

Solidus

Gagnepain-Beyneix et al. (2006)

Ol-C

px-Gar

Ol-C

px-Gar

Pyrolite

Pyrolite

Ol-C

px-Gar

Pyrolite

(A)

Temperature profiles in the upper and lower mantle of the Moon

Temperature distribution in the entire mantle derived from P- and S-velocity models for the depleted and fertile compositions. Crosses: T(oC) = 351 + 1718[1 – exp(-0.00082H)].

As shown in this Figure our temperature models are much colder than temperatures found by Keihm and Langseth (1977) from heat flow and thorium abundance measurements. We get the upper mantle heat flow value of 3.6 mW/m2, which is not consistent with heat fluxes in the range of 7-13 mW/m2 at depth of 300 km found by Keihm and Langseth (1977).

We assume that that these heat-flow estimates are too high by a factor of two to three.

T, oC500 700 900 1100 1300

H, k

m

200

400

TSTPTS

Heat flow estimates

T, oC1100 1300 1500

H, k

m

700

800

900

1000

So

lidu

s

TS

TS

TP

Upper mantle Lower mantle

Radius of a lunar Fe–S core with the constraints on the mass, moment of inertia and seismic velocities –

Monte-Carlo method (n 106-7 models)

• Rmax(Fe-core) ~300 km, Rmax(Fe-FeS-core) ~400 km. (Kuskov, Kronrod, Icarus, 2001; Kuskov et al., PEPI,

2002; Kronrod, Kuskov, Phys. Solid Earth, 2011).

2 6 0 3 2 0 3 8 0 4 4 0

R a d ii o f th e F e-F eS co re, k m

0

0.05

0.1

0.15

0.2

0.25

Rel

ativ

e fr

ecu

ency

Fe-FeS

Fe

3.20 3.24 3.28 3.32 3.36

Upper m antle density, g cm

0

100

200

300

400

500

Rad

ius

of

lun

ar c

ore

, km

-3

AR(Fe-10%S) = 34030 km

Conflict of interests

Weber et al., Sci., 2011

Lower mantle Vp = 8.5 km/s

Our P-velocities 8.0 < VР < 8.2 km/scome into conflict with

Weber et al.Our calculations show that Vp

= 8.5 km/s may be reached at a depth of 1000 km for temperatures as low as 600-700oC. This means that Vp = 8.5 km/s is the unfeasible value.

Weber et al., Sci., 2011

R(Fe-6%S) ~ 330 km

2 6 0 3 2 0 3 8 0 4 4 0

R a d ii o f th e F e-F eS co re, k m

0

0.05

0.1

0.15

0.2

0.25

Rel

ativ

e fr

ecu

ency

R(Fe-10%S) = 34030 km

Thermal and compositional constraints on velocities

General increase in seismic velocities from the upper to lower mantle is consistent with a change in bulk composition from a dominantly pyroxenite upper mantle depleted in Al and Ca (~2 wt% CaO and Al2O3) to a fertile lower mantle enriched in Al and Ca (~4-6 wt% CaO and Al2O3). A pyrolitic model cannot be regarded as a geochemical-geophysical basis for the entire mantle of the Moon.

For adequate lower mantle temperatures the allowed velocity values in the depth range 500-1000 km must be as follows

8.0 < VР < 8.2 km/s, 4.4 < VS < 4.55 km/s.

VP, km s-1

7,6 7,8 8,0 8,2

H, k

m

200

400

600

800

1000

pyrolitepyroxeniteOl-Cpx-GarGagnepain-Beyneix et al. (2006) Lognonne (2005)

Conclusions(1) Our temperature model inferred

from the seismic velocities is much colder than temperatures found by Keihm and Langseth (1977) from heat flow and thorium abundance measurements. We get the upper mantle heat flow value of 3.6 mW/m2, which is by a factor of two to three less that that found by Keihm and Langseth (1977).

(2) Our results indicate that upper and lower mantle compositions are strikingly different. Upper mantle consist of pyroxenite depleted in Al and Ca (~2 wt% CaO and Al2O3), while lower mantle has a fertile composition enriched in Al and Ca (~4-6 wt% CaO and Al2O3).

(3) The derived temperature profiles provide a means to put bounds on the range of reasonable petrological models and seismic velocities.

Thank you for your attention!