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in conductivity is attributed to the regional
variation in the amount and/or the connectivity
of subducted oceanic crust.
The inferred large contrast in the electrical
conductivity between the upper mantle and the
transition zone implies a large contrast in the
chemical composition (either the hydrogen con-
tent or the eclogite content or both). In either case,
if indeed there is a layering in chemical composi-
tion, there must be some large-scale material seg-
regation in the middle mantle (at around 410 km).
This is due to the fact that without large-scale
material segregation, it is impossible to change
the chemical composition of a large region (
>
100
km) of the mantle because of the slow diffusion.
A plausible model is partial melting at
depth relative to the solid-state buffers used in
the lab studies (Frost & McCammon, 2008). This
leads to the deferent depth dependence of con-
ductivity for ''dry'' (Fe-based) conductivity and
''wet'' (hydrogen-based) conductivity because the
dependence of electrical conductivity on oxygen
fugacity is opposite between Fe-based conduction
and hydrogen-based conduction (see Figure 5.15).
Khan and Shankland (2012) did not make correc-
tions for the oxygen fugacity when they applied
the lab data to Earth's mantle. The large differ-
ence in the inferred water content between Karato
(2011) and Khan and Shankland (2012) is likely
due to the incorrect treatment of the influence of
oxygen fugacity by Khan and Shankland (2012).
Also important is the treatment of hydrogen parti-
tioning. As emphasized by Dai and Karato (2009a),
the partitioning coefficient is not a constant but
depends on the physical (temperature and pres-
sure) and chemical conditions (water fugacity).
This is particularly true for hydrogen partitioning
between olivine and orthopyroxene (Figure 5.17).
The analysis by Khan and Shankland (2012) does
not include this detail, which results in a large
difference in the inferred total water content.
Similarly, Jones
et al
. (2012) ''tested'' var-
ious lab-based conductivity versus water
content relationships against geophysical (
MT
(magnetotelluric)) and geological (xenolith)
observations on the continental upper mantle.
They chose some xenolith data on temperature
(pressure - i.e., depth) and water content (from
Peslier
et al
., 2010) and compared these values
with
MT
-based conductivity at the same depth.
Then they used various lab-based model to see
if they could reproduce the inferred
T
∼
410 km
(e.g., Bercovici &Karato, 2003; Karato
et al
., 2006)
for which some support has been provided by
seismological observations (Tauzin
et al
., 2010).
Recently Khan and Shankland (2012) used a
sophisticated statistical treatment to infer the
water content in the upper mantle and the tran-
sition zone from geophysically inferred electrical
conductivity profiles. They obtained much lower
water contents than those by Karato (2011) and
Yoshino
et al
. (2006). For example, the water con-
tent of the upper mantle that they inferred is
far less than the well-constrained value by the
geochemical studies (
0.01wt %). Their ''dry''
models predict much higher conductivity than
Karato (2011), and as a result, most of the ob-
served conductivity in the upper mantle and the
transition can be explained by the ''dry'' model
in their analysis. The reason for this difference
is unclear. One possibility is the difference in
the treatment of the influence of oxygen fugac-
ity. Although the influence of oxygen fugacity
is not as large as that of water, oxygen fugac-
ity can change the conductivity by a factor of
∼
∼
C
W
relationship (at a given depth). They found that
Yoshino
et al
. (2006) and Poe
et al
. (2010) results
are largely inconsistent with these observations.
The results from Dai and Karato (2009a) and
Wang
et al
. (2006) are not far from these
''observations'' but they do not reproduce these
observations exactly. Based on these observa-
tions, they concluded that ''none of the models
of proton conduction in olivine proposed by three
laboratories are consistent with the field obser-
vations.'' However, we should emphasize that
−
5 in the deep upper mantle and transition zone
(Karato, 2011). In the lab measurements, oxygen
fugacity is controlled by some solid-state buffers
(Ni-NiO etc.). The oxygen fugacity correspond-
ing to these buffers increases exponentially with
pressure (e.g., Karato, 2008a). In contrast, in the
upper mantle, the oxygen fugacity is likely con-
trolled by a different buffer and decreases with
