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

Recent seismic models - Gagnepain-Beyneix et al., PEPI, 2006 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, V P = 7.7 or V P = 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  250 о С  V  0.1 km/s   Т  250 о С

Major goals One 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 problem The 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.

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.

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

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 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.

Temperatures in the lower mantle of the Moon 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.

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( o C) = [1 – exp(  H)]. 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. Upper mantleLower mantle

Radius of a lunar Fe–S core with the constraints on the mass, moment of inertia and seismic velocities – Monte-Carlo method (n models) R max (Fe-core) ~300 km, R max (Fe-FeS-core) ~400 km. (Kuskov, Kronrod, Icarus, 2001; Kuskov et al., PEPI, 2002; Kronrod, Kuskov, Phys. Solid Earth, 2011). R(Fe-10%S) = 340  30 km

Conflict of interests Weber et al., Sci., 2011 Lower mantle Vp = 8.5 km/s Our P-velocities 8.0 < V Р < 8.2 km/s come 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 o C. This means that Vp = 8.5 km/s is the unfeasible value. Weber et al., Sci., 2011 R(Fe-6%S) ~ 330 km R(Fe-10%S) = 340  30 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 km must be as follows 8.0 < V Р < 8.2 km/s, 4.4 < V S < 4.55 km/s.

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.

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