Geology Reference
In-Depth Information
Tabl e 8 . 2
Inviscid splitting parameters for four Earth models.
T
0
Earth model
(hours)
g
R
g
A
g
P
Core11
5.8197
0.5218
0.0559
−
0.4628
PREM
5.2384
0.5184
0.0499
−
0.4655
1066A
4.4547
0.5137
0.0421
−
0.4688
Cal8
3.8143
0.5101
0.0358
−
0.4717
for a given
T
0
. Solving the quadratic splitting equation (8.108), the three transla-
tional mode periods are given by
=−
g
R
T
0
T
0
R
T
R
T
s
+
1
+
g
T
s
,
(8.110)
T
A
=−
g
A
T
0
T
0
2
A
T
s
+
1
+
g
T
s
,
(8.111)
=−
g
P
T
0
T
0
T
s
,
P
T
P
T
s
−
1
+
g
(8.112)
with
T
R
representing the period of the retrograde equatorial mode,
T
A
the axial
mode period and
T
P
the period of the prograde equatorial mode counted negative.
For graphing purposes, it is more convenient to count the prograde period as pos-
itive, while counting the splitting parameter g
P
as negative. Starting with an initial
estimate of
T
0
as the mean of
T
R
and
T
P
, the splitting parameters g
R
, g
A
andg
P
are
given by equation (8.109). An improved value of the o
ff
set
T
0
−
T
A
is found using
ff
equation (8.111). By adding the actual value of
T
A
to the o
set, an improved value
of
T
0
is obtained. Repetition of this cycle leads to a rapid convergence for the para-
meters
T
0
, g
r
, g
A
and g
P
for given
T
R
,
T
A
and
T
P
. Results for the inviscid periods
for the four Earth models given in Table 8.1 are shown in Table 8.2. The inviscid
splitting curves are shown dashed in Figure 8.17, using the splitting parameters for
Earth model Cal8. Inviscid periods for the other Earth models fall close to these
curves.
Consideration of pressure and viscous drags on the inner core (Smylie and
McMillan, 2000) leads to a quadratic splitting law of the form
T
T
0
2
T
T
0
2g
ν
T
0
T
s
+
−
1
=
0,
(8.113)
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