Geoscience Reference
In-Depth Information
influence of pressure and water on rheological
properties needs to be well-characterized by high-
pressure experimentation. In addition, most min-
erals undergo a series of phase transformations.
The influence of phase transformation must also
be evaluated. These are important issues (some
of these factors can change the effective viscosity
by several orders of magnitude), but due mainly
to the technical difficulties, there is not much
consensus as to the influence of these factors.
In the following, I will review some of the
important observations and their interpretations
related to these issues, which is the frontier in the
study of rheological properties of Earth materials.
depth, km
410
660
Paterson
Griggs
D-DIA
RDA
2500
2000
1500
1000
500
15
0
5
10
20
25
30
4.4.2 Effect of pressure
pressure, GPa
Pressure can have a large effect on rheological
properties. This is seen from Equation (4.9): a
positive activation volume reduces strain-rate
exponentially with pressure. The importance of
activation volume is shown in Figure 4.10. The
values of activation volume for typical oxides
or minerals range from
Fig. 4.7
The pressure-temperature range of operation
of various deformation apparatus.
data that indicate the operation of highly
nonlinear, relatively temperature insensitive
deformation mechanism such as the Peierls
mechanism (Figure 4.8d) at low temperatures and
high stresses.
The results summarized in Figure 4.8 are
obtained at low pressures (P
<
0
.
3GPa) at which
high-resolution mechanical measurements are
possible. Therefore as far as the dependence of
plastic deformation on temperature, stress and
grain-size (and oxygen fugacity) are concerned,
these are well-established solid data sets. How-
ever, the applicability of these data to the Earth's
interior is limited to the depth of
20 cm
3
/mol, and
this range of
V
∗
makes a large difference in the
estimated depth variation in viscosity.
However, the precise determination of pressure
effects on rheological properties is challenging. To
appreciate this, take a look at Figure 4.9 which
shows that there were nearly 10 orders of magni-
tude difference in the viscosity in the deep upper
mantle calculated from the results of different ex-
perimental studies (Figure 4.9). Challenges here
include (i) the precise measurements of pressure
effects and (ii) the correction for other effects such
as water content and grain-size. As can be seen
from Equation (4.9), the influence of pressure on
viscosity (or creep strength) is exponential, so
the pressure effect is small at low pressures but
increases exponential with pressure. Therefore
although a low-pressure apparatus such as the
Paterson apparatus has high resolution in stress
(and strain-rate) measurements, pressure effect
can be estimated better from high-pressure mea-
surements even though these methods have lower
resolution in stress measurements. For instance,
if the activation volume is 10 cm
3
/mol, then if
∼
3to
∼
15 km. But
most plastic deformation in the Earth occurs
below 20 km. In the past, these low-pressure
results were often extrapolated to high pressures
using poorly constrained parameters such as the
activation volume (e.g., Karato & Wu, 1993;
Hirth & Kohlstedt, 1996, 2003). A recent review
by Karato (2010b) showed that the uncertainties
in activation volume were so large (see Figure 4.9
below) that conclusions in these previous papers
have a rather weak basis.
To make further advance in our understand-
ing of dynamics of the Earth's deep interior, the
∼
