Variational methods and core modes - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 469

10 -7

10 -9

10 -11

0.25 0.26 0.27 0.28

Frequency (cycles per hour)

Figure 8.13 Product spectrum of superconducting gravimeter records at Cantley,
Bad Homburg, Brussels and Strasbourg. The solid curve is a cubic fitted to give a
reference noise level. The two dashed curves indicate the 95% confidence interval.
Vertical lines indicate the locations of the central periods of the three translational
modes. The period of the prograde mode is recovered as 4.0150 hours (left), the
period of the axial mode is recovered as 3.7656 hours (centre) and the period of
the retrograde mode is recovered as 3.5822 hours (right).

5

4

3

2

0.2785 0.2795 0.2805

Frequency (cycles per hour)

Figure 8.14 Retrograde equatorial translational mode resonance. The recovered
central period is 3.5822 ± 0.0012 hours.

The relative locations of the central periods of the three translational mode res-
onances are governed by a splitting law . The equation of motion (7.1), with the
Brunt-Vaisala angular frequency (6.167), is transformed to

2 u 2

− ω + 2 i ω Ω × u =−∇ χ − ω

v s ( s

· u ), (8.90)