Variational methods and core modes - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 478

Tabl e 8 . 3 Comparison of the observed translational mode periods
with those of the Cal8 Earth model.

Retrograde Axial Prograde

Periods (hours) (hours) (hours)

Observed periods 3.5822 3.7656 4.0150

Cal8 viscous periods 3.5840 3.7731 4.0168

Cal8 inviscid periods 3.5168 3.7926 4.1118

14.00

13.50

13.00

T 0 (hr)

Cal8
1066A
PREM
CORE11

3.82470

12.50

4.45471
5.23836
5.81973

12.00

0 300 600

Radius (km)

900 1200 1500

Figure 8.20 Density profiles of the inner core for Earth models Cal8, 1066A,
PREM and Core11. The range of 0.6gcm − 3 causes a nearly 2-hour di

ff erence in

the unsplit period, T 0 , giving a resolution of 200 min/(g cm − 3 ).

In Figure 8.20, we show the density profiles of the inner core for Earth models Cal8,
1066A, PREM and Core11, together with their unsplit periods, T 0 . The axial mode
period su

ff

ers little rotational or viscous splitting. Its observed period provides a
strict constraint on inner core density. The calculated axial mode period for Cal8 is
only 27 s longer than the observed period. An overall density decrease in the inner
core of only 2.25 mg cm 3 would bring them into coincidence, giving a very strong

confirmation of Cal8. In Table 8.4 we show a comparison between the unsplit peri-
ods, T 0 , for the four Earth models and the observed value.

/

8.7 A viscosity profile for the outer core
In addition to the viscosity estimates at the bottom of the fluid outer core, from
the reduction in the rotational splitting of the two equatorial translational modes,
the ring downs of the free core nutations, found from their spectral analysis (Sec-
tion 4.4.2), lead to viscosity estimates near the top of the fluid outer core. A detailed