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strength of the oceanic lithosphere becomes less
than the model shown in Figure 4.17. Indeed,
the magnitude of deviatoric stress in the litho-
sphere inferred from recrystallized grain-size sel-
dom exceeds
orthopyroxene (
20-30%) also exist. Orthopy-
roxene (with some orientations) is much weaker
than olivine particularly at low temperatures
(Ohuchi
et al
., 2011). However, with the assump-
tion of homogeneous deformation, the presence
of a small fraction of a weak phase does not affect
the strength so much (e.g., Handy, 1994).
Situation is different if deformation is localized.
Indeed, geological observations of deformation
of the lithosphere strongly suggest that most of
the lithosphere deformation occurs in the narrow
shear zones (e.g., Handy, 1989; Drury
et al
., 1991).
And theory suggests that plastic deformation at
relatively low temperatures is often localized as
discussed before.
Several mechanisms of shear localization have
been discussed, but the best documented mecha-
nism is shear localization associated with grain-
size reduction (e.g., Handy, 1989; Jin
et al
., 1998).
However, there are two issues in this model of
shear localization. First, dynamic recrystalliza-
tion occurs only after certain finite strain, so if
a material is too strong then initiation of shear
instability will be difficult. Second, even if fine
olivine grains are formed, grain-growth will ter-
minate the instability quickly if grain-growth is
fast. Karato (2008) showed that for pure olivine
grain-growth kinetics is too fast to realize shear
localization. The effect of secondary phases to
slow down the grain-growth kinetics may be
needed as suggested by Warren and Hirth (2006).
It is possible that the secondary mineral, orthopy-
roxene, solves these problems simultaneously.
Orthopyroxne with certain orientations are much
softer than olivine under lithospheric conditions
(Ohuchi
et al
., 2011). Therefore these orhtopy-
roxene grains will be deformed and recrystallized.
The recrystallized grains of orthopyroxene are
much smaller than those of olivine (e.g., Ske-
mer & Karato, 2008) and hence mobile, and
they might penetrate into regions of recrystal-
lized olivine grain to stabilize small grain-size
and hence promote shear localization (e.g., Farla
et al
., 2011). Further experimental studies are
needed to clarify these processes.
The remaining issue is to develop a theoreti-
cal framework to include the influence of shear
∼
100MPa (e.g., Nicolas, 1978; Av e
Lallemant
et al
., 1980).
One obvious mechanism to reduce the strength
is to invoke mechanisms to cause smaller fric-
tional resistance (
σ
∼
=
μP
eff
,
μ
: friction coefficient,
P
eff
=
P
pore
(
P
pore
: pore pressure)). This could
be either by the smaller effective pressure or by
the smaller friction coefficient. However, the re-
duction in the strength by this mechanism is
likely limited for two reasons. First, in the model
by Kohlstedt
et al
. (1995), the pore pressure is
considered to be the hydrostatic pressure (i.e.,
P
P
−
=
ρ
water
gz
,
ρ
water
: density of water), so the ef-
fective pressure cannot be reduced unless some
mechanisms to increase the pore pressure higher
than the hydrostatic pressure are invoked. Sec-
ond, the friction coefficients could be lower than
the values assumed by Kohlstedt
et al
. (1995) if
some layered silicates are present on the fault
plane, but for serpentine (a typical layered sili-
cate), the friction coefficient is not much different
from the standard value corresponding to the By-
erlee's law at low temperatures where the friction
law is applicable (Chernak & Hirth, 2010).
Consequently, the reduction in the strength
in the ductile (plastic) regime is essential in
order to explain the weak strength of the litho-
sphere. One obvious way to reduce the strength
is to include a high-stress deformation mecha-
nism such as the Peierls mechanisms as first
suggested by Goetze and Evans (1979), but its
effect is only modest. Grain-size sensitive mech-
anismof plastic deformation is another option but
the majority of the lithosphere has coarse grain-
size (e.g., Av e Lallemant
et al
., 1980) and deforms
by dislocation creep judging from the presence
of seismic anisotropy. Therefore this mechanism
cannot reduce the strength of the major portion
of the lithosphere homogeneously.
How about the contributions from minerals
other than olivine? The lithosphere is made of
∼
40-60% of olivine, but other phases such as
