Geology Reference
In-Depth Information
2.5
2.0
1.5
1.0
0.5
-0.006
-0.004
-0.002
0.0
Frequency in cycles per day
0.002
0.004
0.006
Figure 4.15 Average spectral density of the nutation residuals.
records from the Goddard Space Flight Center and the United States Naval Obser-
vatory, both in excess of 23 years in length (Palmer and Smylie, 2005).
Resonances of the form
a 2
f 0 )/ f 0 2 ,
(4.111)
4 Q 2 ( f
1
+
used previously in the study of polar motion (4.15), derived from the equation of
motion for polar wobble (4.73), are fitted to the PFCN and the RFCN resonances.
For the PFCN, a peak power of a 2
23.36 milliarcseconds squared (mas 2 )was
=
10 3 cycles per day,
equivalent to a period of 388.178 days. The fitted resonance curve is shown plotted
over the local power spectrum in Figure 4.16. In order to obtain an estimate of the
amplitude of the PFCN, we integrate the fitted resonance curve (4.111) between its
half-power points to get the square of the amplitude as
found with Q
=
5.8912 and central frequency f 0
=
2.57614
×
a 2 f 0 (1 + 1/2 Q )
f 0 (1 1/2 Q )
df
A 2
=
f 0 )/ f 0 2 .
(4.112)
4 Q 2 ( f
1
+
On changing the integration variable to
2 Q f
f 0
f 0 ,
f =
(4.113)
we find that
1
a 2 f 0
2 Q
df
a 2 f 0
4 Q .
A 2
=
+ f 2 = π
(4.114)
1
1
 
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