Geoscience Reference
In-Depth Information
localization in large-scale modeling. In most of
modeling studies, the influence of grain-size re-
duction is investigated through the analysis of
competition between grain refinement and grain
growth. In evaluating the grain refinement by
deformation, it is often assumed that the ef-
fective viscosity is sensitive to grain-size (e.g.,
Kameyama
et al
., 1997; Landuyt & Bercovici,
2009). However such a formulation is physi-
cally unsound because grain-size sensitive creep
such as diffusion creep does not cause dynamic
recrystallization. Simultaneous operation of dy-
namic recrystallization and weakening by grain-
size sensitive creep is a key to shear localization.
Co-existence of dynamic recrystallization and
diffusion creep is a natural consequence of
hetero-
geneous microstructure
as depicted in Figure 4.5a.
Geodynamic modeling on shear localizationmust
include this aspect of physics if the variation
in the degree of shear localization among differ-
ent planets were to be investigated through such
modeling.
Also, if the Earth's lithosphere is weak enough
to allow the operation of plate tectonics, one
should ask why plate tectonics does not operate
on other planets such as Venus. Nearly complete
absence of water on Venus and the presence of
some water on Earth (the lithosphere is ''dry'' but
has some water particularly in pyroxenes) might
be an explanation. Alternatively, the higher near-
surface temperatures in Venus than Earth could
be the reason because shear localization is favored
at modest temperatures (Equation (4.16)).
their viscosity must be higher than surround-
ing mantle by a factor of
10
3
.Inamodelof
the strength of the continental lithosphere by
Kohlstedt
et al
. (1995), the deep continental man-
tle is assumed to be ''wet'' (water-saturated). In
these cases, the deep continental roots will be
softer than or have similar viscosity as the sur-
rounding mantle, and the continental roots would
not have survived.
Karato (2010b) revisited a hypothesis originally
proposed by Pollack (1986) that the long-term
stability of the continental roots might be due
to the removal of water by deep partial melting.
A key to evaluate this model is to calculate the
viscosity ratio,
∼
η
dry
(
P
,
T
)
η
wet
(
P
,
T
)
ε
wet
(
P
,
T
)
ε
dry
(
P
,
T
)
ξ
=
=
(4.20)
under
the
deep upper mantle
conditions
(P
1700K) where
η
dry
,
wet
(
P
,
T
)is
the effective viscosity at dry (wet) conditions
(at pressure P and temperature T) (
∼
10GPa, T
∼
ε
dry
,
wet
(
P
,
T
)
is corresponding strain-rate) (wet viscosity is for
the surrounding mantle and dry viscosity for the
continental roots). Such a calculation is now
possible due to the laboratory studies on the
influence of water and pressure on deformation
of olivine as discussed before. Figure 4.18 shows
that indeed, if a large degree of water depletion
occurs as suggested by geochemical observations
(e.g., Carlson
et al
., 2005), then the experimental
results on rheological properties of olivine
explain the stability of the continents.
Continental lithosphere (at least many of them)
have survived for
3Gyrs. At the same time,
many continental lithosphere have rifted. For
rifting to occur, the lithosphere cannot be so
strong (e.g., Huismans
et al
., 2005). How can
we explain both the long-term stability of the
continental lithosphere against convective ero-
sion and the frequent occurrence of rifting? There
are several possibilities. First, the stress mag-
nitude is different between convective erosion
and rifting. Convective erosion is due to con-
vection in the asthenosphere and therefore stress
is low (
∼
(b) How has the continental lithosphere survived
against convectional erosion?
The continental
roots have survived for
3 Gyrs against con-
vective erosion. This is demonstrated by the
age distribution of xenoliths from the continents
showing nearly the same age throughout the sam-
pling depth interval (to
∼
200 km) (e.g., Carlson
et al
., 2005). In order for continental roots to
have survived for
∼
3Gyrs, they must have a high
resistance for plastic deformation. Shapiro
et al
.
(1999) and Lenardic & Moresi (1999) showed that
in order for the deep continental roots to survive,
∼
0.1-1MPa). In contrast, the stress lev-
els associated with rifting is larger,
∼
∼
10-50MPa.
