Geoscience Reference
In-Depth Information
Table 6.3
Elasticity data set for lower mantle modeling.
K
0
G
0
V
0
(cm
3
/mol)
Phase
K
0
(GPa)
θ
0
(K)
γ
0
q
G
0
(GPa)
η
S0
References
MgSiO
3
perovskite
24.43
253.0
3.9
1100
1.40
1.40
172.9
1.56
2.6
1-3
FeSiO
3
perovskite
25.49
281.0
4.1
841
1.48
1.40
138.0
1.70
2.1
4,5
MgO periclase
11.24
161.0
3.9
773
1.50
1.50
130.9
1.92
2.3
1,6-8
FeO wustite
12.06
152.0
4.9
455
1.28
1.50
47.0
0.70
0.8
1,9-12
References: 1, Smyth & McCormick (1995); 2, Wentzcovitch
et al
. (2004); 3, Fiquet
et al
. (2000); 4, Jeanloz & Thompson (1983); 5, Kiefer
et al
. (2002); 6, Robie & Hemingway (1995); 7, Fiquet
et al
. (1999); 8, Anderson & Isaak (1995); 9, Fei (1995); 10, Jackson
et al
. (1990);
11, Jacobsen
et al
. (2002); 12, Stolen
et al
. (1996).
at elevated temperature is most sensitive to
η
S
0
. The anticipated parameter sensitivity
relationship of
η
S
0
to the shear modulus at high
temperature is described in detail in the litera-
ture (Stixrude & Lithgow-Bertelloni, 2005). The
trade-off between Mg/Fe or Mg/Si ratio and these
parameters were discussed in previous studies on
the lower mantle modeling (Mattern
et al
., 2005;
Matas
et al
., 2007; Deschamps & Trampert, 2004).
0.997)
indicates
an
excellent
agreement
with
PREM
model.
The
values
of
η
S
0
and
Mg-Fe
partitioning
coefficient
between
Pv
and
Fp
(
K
Pv/Fp
Mg
Fe
), adopted in this calculation are fairly
insensitive to the fitting results of
X
Pv
. Thus,
a variation of
η
S
0
by 10%, which covers the
possible uncertainty of this value (Stixrude &
Lithgow-Bertelloni, 2005), and
K
Pv/Fp
Mg
−
Fe
by 10% at
constant bulk iron content changes
X
Pv
less than
∼
−
2% and 0.3%, respectively. The shear velocity
profile calculated from the pyrolitic mantle
model with
X
Pv
of 0.80 (Jackson & Rigden, 1998)
is also shown in Figure 6.12a for comparison. This
profile is
6.4.4 Reconstructed lower mantle model
Calculations of the shear wave velocity profile at
elevated pressure and temperature incorporating
those new shear wave velocity data are made
using the formalism (2nd order) recently pro-
posed by Stixrude & Lithgow-Bertelloni (2005).
The calculated shear wave velocity profiles for Pv
and Fp along with the geotherm for whole mantle
convection model are shown in Figure 6.12a along
with the 1-D global seismic lower mantle model
(PREM) (Dziewonski & Anderson, 1981). The
aggregate shear wave velocities of the two-phase
assemblage were obtained by the Voigt-Reuss-Hill
averaging method (Watt
et al
., 1976). Applying
the fairly low
G
0
for both Pv and Fp (Murakami
et al
., 2007a, 2009), the shear wave velocity pro-
files of both phases become remarkably gentle
ascent with pressure. As shown in Figure 6.12a,
the velocity profile of Pv by itself is remarkably
close to the PREM model, deviating from it by
not more than 1%.
The PREM profile in the lower mantle is then
best fitted within
∼
2% lower than that of PREM model
on average throughout the pressure range of
lower mantle, which is clearly incompatible with
PREM. This regression suggests the invalidity of
the chemically homogeneous mantle model and
hence the whole mantle convection geothermal
model. The layered mantle convection geother-
mal model was then applied and the PREM
profile can be best fitted only by the pv with the
R
-square of 0.993 as shown in Figure 6.12b.
For comparison, using the larger values of
G
0
for both pv (
2.2) reported in
previous studies, the calculated shear wave veloc-
ity profiles show a much steeper slope of velocity
versus depth than that of PREM model. Con-
sequently, calculated best fit velocity-pressure
profiles using the higher
G
0
values form previous
studies clearly show trends that are inconsistent
with PREM, having significantly steeper slopes
and intersecting the PREM model at
=
1.8 and 2.0) and fp (
=
±
70 GPa
(Figure 6.12a). These latter calculated velocity-
depth profiles deviate from PREM by up to 2.1
∼
0.14% on average for
V
S
by a model with
X
Pv
=
0.92 (by volume). The
goodness-of-fit for this regression (R-square
=
