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)
V P, km s
7 ,4
7 ,6
7 ,8
V S, km s
-1
8 ,0
4 ,2
8 ,2
-1
4 ,4
200
200
K h a n e t a l. (2 0 0 0 )
400
600
L o g n o n n e (2 0 0 5 )
H , km
H, km
400
600
800
800
1000
1000
L o g n o n n e (2 0 0 5 )
seismic velocities have an anticorrelated behavior at depths of
the lower mantle
4 ,6
Recent seismic models - Gagnepain-Beyneix et al., PEPI, 2006
V P, km s
7 ,4
7 ,6
7 ,8
-1
V S, km s
8 ,0
8 ,2
4 ,3
200
G a g n e p a in -B e y n e ix e t a l., 2 0 0 6
400
H , km
H, km
4 ,5
200
400
600
4 ,4
-1
600
800
800
1000
1000
seismic velocities have an anticorrelated
behavior at depths below 240 and 500 km
4 ,6
• 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?
V P, km s
7 ,4
7 ,6
7 ,8
-1
8 ,0
8 ,2
200
K h a n e t a l. (2 0 0 0 )
H, km
400
600
800
1000
L o g n o n n e (2 0 0 5 )
•
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
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.
Thermodynamic approach - Temperature dependence of seismic
velocities comes both from anharmonic and anelastic properties
Method of minimization of the total Gibbs free energy in the
Na2O-TiO2-CaO-FeO-MgO-Al2O3-SiO2 system with nonideal 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.
Forward/inverse problem
Bulk
composition
Temperature
distribution
Phase diagram
and theoretical
velocity profiles
Thermodynamics,
equations of state
MANTLE
STRUCTURE
Seismic
velocities
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
0.25
0 .2 5
0.2
0 .2
0.15
0 .1 5
0.1
0 .1
0.05
0 .0 5
0
0
Ringwood (1979)
FeO, wt.%
14
Lognonne et al. (2003)
Jones and Delano
(1989)
12
Khan et al. (2007)
Taylor (1982)
Galimov (2004)
O'Neill (1991)
Morgan et al.
(1978)
Kuskov and Kronrod (1998a)
10
Warren (2005)
McDonough and Sun (1995)
8
Earth
Geochemical models
Geophysical models
6
4
6
8
10
12
Al2O3 + CaO, wt.%
•
14
16
4.8
5.6
6.4
7.2
Al2O3
8
8.8
9.6
8 .8
9 .6
1 0 .4
1 1 .2
12
1 2 .8
FeO
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.
V P, km s
7 ,6
7 ,8
Ringwood (1979)
14
8 ,0
8 ,2
FeO, wt.%
7 ,4
-1
200
2
Lognonne et al. (2003)
Jones and Delano
(1989)
12
Khan et al. (2007)
Taylor (1982)
Galimov (2004)
O'Neill (1991)
Morgan et al.
(1978)
Kuskov and Kronrod (1998a)
10
Warren (2005)
McDonough and Sun (1995)
8
Earth
400
Geochemical models
Geophysical models
H , km
6
4
6
8
10
12
14
16
Al2O3 + CaO, wt.%
600
800
•
1000
4
S e ism ic m o d e ls:
1 - G a g n e p a in -B e y n e ix e t a l. (2 0 0 6 ),
2 - K h a n e t a l. (2 0 0 0 ),
3 – K u sk o v e t a l. (2 0 0 2 ),
4 - L o g n o n n é e t a l. (2 0 0 5 )
3
1
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 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; GagnepainBeyneix et al., 2006] for the pyroxenite and pyrolite compositions
TP, oC
TP, oC
500
600
700
800
600
900
100
100
200
200
H, km
H, km
400
300
400
500
Pyroxenite
Gagnepain-Beyneix
et al. (2006)
Lognonne (2005)
800
1000
1200
1400
300
400
500
Pyrolite
Gagnepain-Beyneix et al. (2006)
Lognonne (2005)
•
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
o
T S, C
900
1100
1300
1500
•
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.
(B )
p x -G
ar
ar
p x -G
te
te
e n it e
P yr o li
P yr o li
900
P yr o x
H, km
O l- C
O l- C
800
1000
G a g n e p a in -B e yn e ix e t a l. (2 0 0 6 )
K u s k o v e t a l. (2 0 0 2 )
S o lid u s
o
T P, C
1200
1300
1400
1500
1600
1700
(A )
•
Ol
-G
ar
e
lit
e
ro
lit
lit
ar
Py
ro
-G
ro
ar
Py
px
Py
-G
-C
px
px
-C
-C
Ol
900
Ol
H, km
800
e
1000
L o g n o n n e (2 0 0 5 )
K u s k o v e t a l. (2 0 0 2 )
S o lid u s
G a g n e p a in -B e yn e ix e t a l. (2 0 0 6 )
Temperature profiles in the upper and lower mantle of the Moon
o
T, C
500
700
900
o
T, C
1100
1300
1100
1300
1500
700
H, km
us
H, km
800
lid
H eat flo w estim ates
dus
So
200
S o li
TS
900
400
1000
TS
TP
TS
TP
TS
Upper mantle
Lower mantle
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(-0.00082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.
A
F e -F e S
400
300
200
Fe
100
0
3 .2 0
R(Fe-10%S) =
34030 km
0.25
500
R e la t iv e f r e c u e n c y
R a d iu s o f lu n a r c o re , k m
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)
3 .2 4
3 .2 8
3 .3 2
3 .3 6
U p p e r m a n tle d e n s ity , g c m
-3
0.2
0.15
0.1
0.05
0
260
320
380
440
R a d ii o f th e F e -F e S c o r e , k m
• 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).
Conflict of interests
Weber et al.,
Sci., 2011
R(Fe-6%S) ~
330 km
R e la t iv e f r e c u e n c y
0.25
R(Fe-10%S) =
34030 km
0.2
0.15
Weber et al., Sci., 2011
Lower mantle Vp = 8.5 km/s
Our P-velocities
8.0 < VР < 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 600-700oC. This means
that Vp = 8.5 km/s is the
unfeasible value.
0.1
0.05
0
260
320
380
440
R a d ii o f th e F e -F e S c o r e , k m
Thermal and compositional constraints on
velocities
V P , km s
7,6
-1
7,8
8,0
200
H, km
400
600
800
1000
p yro lite
p yro xen ite
O l-C p x-G ar
G ag n ep ain -B eyn eix et al. (2006)
L o g n o n n e (2005)
8,2
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 5001000 km must be as follows
8.0 < VР < 8.2 km/s,
4.4 < VS < 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.
Thank you for your attention!