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strong evidence that a majority of the lower man-
tle except for the D'' layer deforms by diffusion
creep (see the later section on the lower mantle).
If so the viscosity depends on the grain-size that
is not well constrained. Secondly, currently there
is no experimental data on the water effects on
rheological properties on lower mantle minerals.
In addition there are no observational constraints
on the water distribution in the lower mantle
(Karato, 2011b). The inferred large viscosity in-
crease at around 660 km from the geodynamic
studies (e.g., Hager, 1984; Nakada & Lambeck,
1989) could be due to the variation in water con-
tent, grain-size and/or diffusion coefficients.
Consequently, the usefulness of these results is
questionable. Better-defined results have been
obtained for wadsleyite and ringwoodite under
constant strain-rate (to
2100K)
using RDA operated at the synchrotron facility
(Nishihara
et al
., 2008; Kawazoe
et al
., 2010;
Hustoft
et al
., 2013). Also semi-quantitative
results were obtained on ringwoodite by Karato
et al
. (1998).
These results showed that, in the dislocation
creep regime, transition zoneminerals are slightly
stronger than olivine (at a similar water content),
but grain-size sensitive mechanisms become
important when grain-size is less than
∼
23GPa and
∼
∼
1
μ
m
10
−
4
-10
−
5
s
−
1
,
at
laboratory
conditions
(
∼
=
=
T
15-22GPa). When extrap-
olated, these results suggest that diffusion creep
would become important at geological strain-
rates for the grain-size less than
1500-2000 K, P
(b) Why do cold slabs deform in the transition
zone?
According to the high-resolution seismic
tomography, subducted slabs are highly deformed
in the western Pacific (e.g., Fukao
et al
., 1992,
2009), but not much in the eastern Pacific
(Karason & van der Hilst, 2000; Grand
et al
.,
1997). This is a puzzling observation because
slabs in the western Pacific are colder than those
in the eastern Pacific. Not only this apparent
paradoxical correlation, but also the deformation
of a slab in the deep mantle itself is a puzzle in the
first place because a cold slab in the deep mantle
(high pressure) should have a high viscosity.
These observations suggest that there must be
some mechanisms by which a cold slab becomes
weaker than a warm slab in the transition zone.
In order to address these questions, one needs to
understand the rheological properties of minerals
under the transition zone conditions.
Direct measurements of rheological proper-
ties of transition zone minerals (wadsleyite,
ringwoodite and majorite) have been made
only recently. Early measurements used stress
relaxation tests (Chen
et al
., 1998; Xu
et al
.,
2003; Karato
et al
., 1998) and powder samples
were used in some of them (Chen
et al
., 1998;
Xu
et al
., 2003). In stress relaxation tests,
there is no guarantee if the results correspond
to steady-state flow law. Furthermore, when
powder samples are used, crushing and resultant
creation of high density of dislocations affect the
mechanical properties and stress measurements.
1mm that is
consistent with the estimate from the diffusion
coefficients (Shimojuku
et al
., 2009) (Figure 4.20).
Because the grain-size in the shallow lithosphere
is several mm (Av e Lallemant
et al
., 1980), and
the subducted lithosphere are at high pressures,
low temperatures and dry (e.g., Kubo
et al
., 2009),
these results imply that the subducted slabs will
have much higher viscosity than the surrounding
mantle (at least by several orders of magnitude)
and hence will not deform if grain-size remains
the same.
Due to the poor constraints on the influence
of water on deformation and diffusion of wads-
leyire, a robust estimate of the strength difference
between olivine and wadsleyite (or ringwood-
ite) cannot be made at this time. However, a
conservative estimate of a viscosity of the cold
slab is possible based on the similarity in the
creep strength in the power-law creep regime
between olivine and wadsleyite. Because the pres-
sure is high (
∼
20GPa) and temperature is low in
the central portions of a cold slab (T
∼
∼
1000 K),
10
30
Pa s if the
rheological properties of dry wadsleyite (or ring-
woodite) in the power-law creep regime is used.
Consequently, without any weakening effects, a
cold slab will not deform appreciably. In con-
trast to this expectation, subducted cold slabs in
the viscosity there will exceed
∼
