Geology Reference
In-Depth Information
10
11
10
9
10
7
10
5
10
3
1216
1670
2124
2578
3032
3486
Radius (km)
Figure 8.21 Viscosity profile for Earth's outer core.
Since the activation volume increases strongly with pressure (Brazhkin, 1998) as
represented by our parameter
D
in equation (8.127), we allow for a linear variation
with depth through
b
−
r
D
=
D
b
+
a
D
a
,
(8.129)
b
−
where
a
is the radius of the inner core while
D
b
and
D
a
are constants. The integ-
ration in (8.128) is carried out by Simpson's rule over 100 steps with spline inter-
polation across the whole outer core. It is found that the constant,
D
b
, controls
the curvature of the viscosity profile near the core-mantle boundary, while the
curvature otherwise departs only slightly from log-linear. Some numerical exper-
imentation shows that the profile is closely log-linear, even near the core-mantle
boundary,
10
−
4
m
−
2
s
2
K. Moreover,
for a value
D
b
=
4.5
×
for
D
a
=
2.976
×
10
−
3
m
−
2
s
2
K, the viscosity at the bottom of the outer core, η
a
10
11
Pa s,
is closely matched. The resulting viscosity profile is shown in Figure 8.21.
=
1.247
×
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