Geoscience Reference
In-Depth Information
•
The solid portions of the Earth are elastic up to a limit. As a consequence, the
mass displacement part of the excitation generates deformations which have to be
treated as loading effects.
•
The changing centrifugal forces accompanying variations of the rotation vector
ω
lead to several indirect effects, which are relative angular momenta and changes
of inertia in basically all subsystems of the planet. Added as increments to
I
and
h
in the rigid Earth solution, these contributions, along with the aforementioned
loading effects, account for significant correction factors modifying the original
matter and motion terms given in Eqs. (
20
) and (
21
).
Δ
h
does not contain contributions frommotions in the crust and themantle due to the def-
inition of the Tisserandmean-mantle frame. In addition, the oceanic response to polar
motion is modeled as equilibrium tidal wave (
pole tide
). According to Wahr (
2005
),
this approximation is sufficient for periods
Complementary to the second issue, incremental relative angular momentum
Δ
1d. The pole tide does not generate
currents so that
h
will be void of any oceanic contributions, too. Owing to the small
atmospheric mass, we can also neglect the relative motion of the atmosphere induced
by perturbed centrifugal forces. Consequently, only Earth's core will contribute
to
Δ
Δ
h
.
Relative Angular Momentum of the Core
Following the fundamental study of Smith and Dahlen (
1981
) on the CWof a dynam-
ically axisymmetric Earth, we now assume a fluid core of ellipsoidal shape. Only
terms of first order in ellipticity are kept at frequencies
. In that case,
the relative motion of the core resulting from a rigid rotation of the mantle reads
⎛
|
σ
|
Ω
⎞
⎛
⎞
⎛
⎞
i
E
Δ
h
1
E
0
m
1
m
2
m
3
⎝
⎠
=
⎝
i
E
E
0
00
E
⎠
⎝
⎠
Δ
h
2
−
(22)
Δ
h
3
σ
A
c
,
2
E
≈−
σ(
E
E
≈
1
−
ε
c
)
A
c
,
=−
Ω
C
c
,
Ω
where
A
c
and
C
c
are the equatorial and polar principal moments of inertia of the
core and
ε
c
denotes the eccentricity of the core-mantle boundary. The third equation
of the given linear system implies that Earth's core is axially decoupled from the
mantle and thus cannot follow changes in the mantle's rotation rate. This assumption
has become the rule in excitation studies with publication of the works of Merriam
(
1980
) or Wahr et al. (
1981
), and is more rigorously addressed by Dickman (
2005
).
Besides, the assumption of dynamical axisymmetry rules out spin-wobble coupling
(Smith and Dahlen
1981
) so that there is no interdependency between the equatorial
and axial components of the core's relative angular momentum response in Eq. (
22
).
