Geoscience Reference
In-Depth Information
reasonable if considering that the MS state is
a kind of two-phase coexistence. In the model
of Tsuchiya
et al
. (2006b), HS/LS mixing en-
tropy stabilizes the MS state, which is similar
to the two-phase coexistence of solid solution
system. If each phase has no elastic anomaly
in the coexisting region, the MS state should
also have no elastic anomaly either. Furthermore,
the MS state is spread out over a wide pressure
range at high temperatures of the lower mantle
geotherm (Brown & Shankland, 1981). This is also
more compatible with the standard Earth mod-
els (e.g., Dziewonski & Anderson, 1981) with no
anomalous depth dependence in the seismic wave
velocities at the mid lower mantle. In this case,
the elastic wave velocities gradually shift from
the HS values to the LS values with increasing
pressure as shown in Figure 7.3.
Figure 7.3 clearly indicates the effects of iron
of the wave velocities and density of Fp, which
is larger in HS Fp than in LS Fp. The bulk sound
velocity (
V
) is however unchanged across the
spin transition unlike some high-pressure ex-
periments (Lin
et al
., 2005) which reported a
∼
16
Fp
V
P
12
V
Φ
V
S
8
ρ
4
0
50
100
150
P (GPa)
Fig. 7.3
Elastic wave velocities and density calculated
for MgO (gray solid lines), Fp with 12.5 mol% HS (solid
lines) and LS (dashed lines) Fe
2
+
, respectively as a
function of pressure at 300 K, 1000 K, and 2000 K from
top to bottom. A shaded area represents the MS state
region at 2000 K (Tsuchiya
et al
., 2006a). Two models
for the MS state are presented: the simple mixture
(thick solid lines) and the elastic softening (e.g.,
Marquardt
et al
., 2009a) (dotted lines).
15% jump in
V
for Fp with 17% FeO. This
is likely because the increase in bulk modulus
and that in density across the spin transition
(
3% for both for 12.5% FeO) are cancelled out
nearly completely. More recent works report or
suggest no such anomalous increase in
V
(Mar-
quardt
et al
., 2009a; Wentzcovitch
et al
., 2009)
.
LDA
∼+
result, Fp was inferred to be a dominant cause
of seismic anisotropy in the D
layer (Marquardt
et al
., 2009b), but careful mineralogical model-
ing of the seismic velocity structures including
both Pv and Fp and also their rheological prop-
erty is obviously required to analyze the source
of observed anisotropy in more detail (Usui
et al
.,
under review) (Yamazaki & Karato, 2007).
+
U
calculations for Fp with 12.5% FeO
lead to
∂
ln
V
P
∂X
FeO
(%)
∂
ln
V
S
∂X
FeO
(%)
=−
0.6%,
=−
1.0%, and
∂
ln
V
∂X
FeO
(%)
∂
ln
V
P
∂X
FeO
(%)
=−
0.3% for the HS case and
=
∂
ln
V
S
∂X
FeO
(%)
∂
ln
V
∂X
FeO
(%)
−
0.4%,
=−
0.5%, and
=−
0.3%
for the LS case.
It is also pointed out that the spin crossover
in Fp affects its elastic anisotropy (Marquardt
et al
., 2009b). LS Fp was reported to have at least
50% stronger shear anisotropy in the lowermost
mantle compared to MgO, which is originally
quite anisotropic at high pressures (Karki
et al
.,
1999; Tsuchiya & Kawamura, 2001; Wentzcov-
itch
et al
., 2006). LDA
7.4 Elastic Properties of Materials
with Crustal Compositions under Lower
Mantle Conditions
7.4.1 SiO
2
As mid-ocean ridge basalt (MORB) is produced
via partial melt of mantle peridotite at the mid-
ocean ridge, they are rich in iron, aluminum
+
U
calculations also indi-
cate that the spin transition enhances the elastic
anisotropy (Fukui
et al
., 2012). According to this
