Variational methods and core modes - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 468

Tabl e 8 . 1 Translational mode inviscid periods for four Earth models.

Retrograde Axial Prograde

Earth model (hours) (hours) (hours)

Core11 5.1280 5.7412 6.5114

PREM 4.6776 5.1814 5.7991

1066A 4.0491 4.4199 4.8603

Cal8 3.5168 3.7926 4.1118

We focus on the product spectrum of four long records, calculated as described in
Section 2.5.4. The first record is from the superconducting gravimeter installation
at Cantley, Canada (45.5850 ◦ N, 75.8017 ◦ W), running from 16h on 8 November
1989 to 7h on 14 August 1993, for a total record length of 32,992 hours. The second
record is from the installation at Bad Homburg, Germany (50.2285 ◦ N, 8.6113 ◦ E),
running from 0h on 22 March 1986 to 7h on 27 December 1988, for a total record
length of 24,272 hours. The third record is from the installation at Brussels, Bel-
gium (50.7986 ◦ N, 4.3581 ◦ E), running from 0h on 15 November 1986 to 11h on 10
June 1996, for a total record length of 83,892 hours. The fourth record is from the
installation near Strasbourg, France (48.6220 ◦ N, 7.6840 ◦ E), running from 16h on
11 July 1987 to 12h on 24 June 1996, for a total record length of 78,501 hours. Each
record was corrected for glitches and drift before removal of synthetic Earth tides
and barometric e

ff

ects (Smylie et al. , 1993). The spectral analysis was based on
12,000-hour record segments with 75% overlap windowed with a Parzen window
to suppress frequency mixing e

ff ects. The product spectrum for these observations

is shown in Figure 8.13.
A cubic has been fitted to the spectrum and plotted as a solid curve to establish a
background noise level. The 95% confidence interval is indicated by the two dashed
curves. The axial mode (centre) is well above the 95% confidence level, as is the
prograde mode (left), while the retrograde mode is just below the 95% confidence
level.
Detailed linear histogram plots of the three resonances are shown in Figures 8.14,
8.15 and 8.16. The fitted resonance for the retrograde translational mode is shown
in Figure 8.14. The fitted central period is returned as 3.5822 0.0012 hours. The

fitted resonance for the axial translational mode is shown in Figure 8.15. The fitted
central period is returned as 3.7656

±

0.0015 hours. The fitted resonance for the
prograde translational mode is shown in Figure 8.16. It is dominated by the res-
onance of the S 6 solar heating tide centred on exactly a 4-hour period. To accom-
modate the solar heating tide, a double resonance has been fitted, giving a central
period for the prograde mode of 4.0150

±

± 0.0010 hours.