Geology Reference
In-Depth Information
Tabl e 4 . 3
Parameters fitted to successive prograde free core
nutation (PFCN) resonances at 400-day steps along the time axis.
a
2
mas
2
/cpd
f
0
10
−
3
cpd
Time in days
Q
Period (days)
1600
53.325
4.5749
2.69687
370.800
2000
31.711
3.1478
2.10148
475.855
2400
36.673
3.8327
2.14004
467.202
2800
33.130
3.5322
2.22373
473.097
3200
37.052
4.2476
2.14632
465.914
3600
17.125
3.8659
2.62315
381.221
4000
13.095
3.8692
2.58883
386.275
4400
10.443
3.5525
2.53401
394.631
4800
7.7695
2.6363
2.36099
423.551
5200
3.6543
1.9723
2.27559
439.446
5600
3.7166
2.1370
1.79344
557.588
6000
3.9700
2.0140
1.80939
552.672
a
2
f
0
4
Q
.
A
2
=−
π
(4.115)
The estimate of the RFCN amplitude,
A
, is found to be 186.5907 microarcseconds
(μas).
4.4.3 Ring down of the free core nutations
Examination of the individual spectral density estimates of the four segments of
nutation residuals, entering the average spectral density plotted in Figure 4.15,
shows that the nutation resonances rapidly diminish with time.
In order to investigate this time dependence in more detail, we have divided the
record of nutation residuals into 2000-day segments with 75% overlap, advancing
along the time axis in 400-day steps. The discrete Fourier transform (DFT) for
each of the resulting 17 segments is found by singular value decomposition (SVD).
Spectral density estimates were then made based on four successive segments with
75% overlap. This leads to 14 spectral density estimates centred at 1600 days into
the record and advancing along the time axis in 400-day steps. Resonance curves
of the form (4.111) were then fitted to both the prograde free core nutation (PFCN)
and the retrograde free core nutation (RFCN) features to recover values of
a
2
,
Q
and
f
0
. The results for the PFCN are given in Table 4.3, and those for the RFCN
are given in Table 4.4.
The rapid decrease with time of both the PFCN and RFCN modes shown in
Tables 4.3 and 4.4 suggests that they may be in free decay. In free decay, the amp-
litudes of the free core nutations, with squares given by expressions (4.114) and
(4.115), follow the exponential decay schemes
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