Geoscience Reference
In-Depth Information
80
-
1
-
1
ln(5
-
1
)
to the microstructural processes observed in
laboratory. The mechanical constitutive rela-
tionships obtained from the contiguity model
include contiguity as an ''internal state variable.''
By solving these constitutive relationships,
together with the other governing equations
of the two-phase dynamics, the large-scale
distribution of melt can be simulated together
with an evolution of contiguity. The contiguity
model facilitates such ''multiscale'' dynamics,
relating laboratory studies to mantle dynamics,
and this is particularly important in the case of
viscous deformation, because viscosity is very
sensitive to the contiguity change (Section 3.4.4).
Using the viscosity tensor given by Equation
(3.19), Takei and Holtzman (2009c) demonstrated
the occurrence of such multiscale interactions.
They showed that the development of shear
induced contact anisotropy, as reported from
experimental studies (Figure 3.2a-c), would
cause a strong anisotropy in the viscosity of
the matrix. In an isotropic system, the shear
stress in the solid matrix does not directly
affect melt pressure. However, with viscous
anisotropy, a direct coupling between shear stress
and melt pressure occurs, which significantly
enhances shear-induced melt migration (Takei &
Holtzman, 2009c). With this mechanism, the for-
mation of low-angle melt-rich bands, consistent
with experimental observations (Figure 3.2d), can
be explained without taking into account the
power law viscosity considered by Katz
et al
.
(2006). Viscous anisotropy also causes melts to
migrate up stress gradients, providing a possible
mechanism for melt-lubrication of plate motions
(Takei & Holtzman, 2009c).
0.6%. Therefore, the total
reduction due to the poroelastic and anelastic
effect is 2.4% or 1.5%. This preliminary result
suggests that the possibility of seismological
detection of small amounts of melt is not utterly
hopeless.
π
∼−
3.7.3 The importance of seismic anisotropy
By analyzing the SV to P and P to SV conver-
sions at the lithosphere-asthenosphere boundary
(LAB), Kawakatsu
et al
. (2009) found that the
contrast in shear wave velocity at the LAB is
7%. If this contrast is explained by the poroe-
lastic effect of the texturally equilibrated melt
(
2.2) in the asthenosphere, the melt
fraction is estimated to be
ln
V
S
/φ
=−
0.032, which is
unrealistically high in an oceanic mantle with an
age of
φ
=
25 million years (e.g., Hirschman, 2009).
By using the viscous contiguity model with equi-
libriummelt geometry, the viscosity contrast cor-
responding to the velocity contrast of 7% is 10
1
.
Kawakatsu
et al
. (2009) showed that if the melt
phase is mostly segregated into thin layers that
occupy 1%of the total space, and are disposed hor-
izontally in the manner of a ''millefeuille cake,''
their observations can be explained by
>
φ
=
0.0025
(in other words,
28). For the mille-
feuille model, the viscosity contrast at the LAB is
estimated to be 10
4
, which is much higher than in
the homogeneous model. Therefore, our insights
into the Earth are significantly affected by the
introduction of heterogeneity and/or anisotropy,
which cause a large deviation from the standard
properties. Because the millefeuille model is char-
acterized by a strong anisotropy, further studies
of seismic anisotropy become important in at-
tempting to verify its reality (e.g., Holtzman &
Kendall, 2010). In addition, the lattice preferred
orientation (LPO) of minerals, not discussed in
this chapter, must also play a part in seismic
anisotropy (e.g., Jung
et al
., 2006).
ln
V
S
/φ
=−
3.8 Concluding Remarks
The present state of knowledge on themechanical
properties of partially molten rock has been sum-
marized in this chapter. Despite intensive and ex-
tensive study using both theory and experiments,
there is still room for debate about the fundamen-
tals of equilibrium melt geometry and the the-
oretical formulation of melt-enhanced diffusion
3.7.4 Multiscale dynamics of shear induced
melt segregation
A challenging problem is to relate the large-scale
distribution of melt determined by seismology
