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excitation are stripped off their respective secular trends. Moreover, as an appropri-
ate initial condition, the offset of
χ(
)
before convolution is chosen to be identical
with that of the geodetic excitation function determined in the foregoing example.
As apparent from both components in Fig.
12
, the analysis indeed recovers the beat-
like signature of geodetic polar motion, since the annual signal component is well
represented in the equatorial AAM. The largest discrepancies between observed and
modeled pole curves persist at years of minimum amplitude. Moreover, throughout
the second half of the analyzed time span, the atmospheric excitation features a con-
siderable phase lag with respect to the geodetic series, whereas before 1995 the AAM
data cannot fully account for the magnitude of the CW. Note, however, that within
the integration approach, any resemblance between the observed and geophysically
modeled pole curves does not allow drawing conclusions about the actual excitation
of the CW, see Chao (
1985
) for a deeper discussion.
t
3.2 Polar Motion and Nutation: Extended Model
As a preparation for the argumentation and terminology used in the following, the
reader is advised to recall the general parametrization of Earth rotation presented in
Sect.
1
. It is prerequisite to understand the frequency-based distinction between nuta-
tion and polar motion, and, in particular, the dualismof nutation and terrestrial pertur-
bations of the CIP with nearly diurnal retrograde frequency
σ
t
∈
(
−
.
,
−
.
)
cpsd.
The extension of the equatorial excitation equation for high frequencies, which has
been already indicated more generally in Sect.
2.4
(last paragraph), must be seen in
the context of this discrimination. In detail, this section will echo the derivations of
Brzezi nski (
1994
), which specifically focus on the creation of an adequate model
for studying geophysically-induced nutational variations. The extended formulation
has also a marginal impact on modeling CIP variations outside the nearly diurnal
frequency band, but basically represents only a partial solution of the requested thor-
ough scheme for excitation studies at terrestrial frequencies of a few days or smaller,
see the end of this section for further discussions.
The special significance of geophysical effects on Earth rotation in the nutation
band [discussed e.g. by Dehant et al. (
1999
) in the frame of a non-rigid Earth nutation
theory] is essentially down to the strong inertial coupling between the mantle and
the liquid core in the vicinity of the diurnal retrograde frequency
1
5
0
5
(Brzezi nski
et al.
2002
). This coupling at the core-mantle-boundary (CMB) manifests itself in the
rotational eigenmode of the FCN. According to Zürn (
1997
), the flattened shape of
the CMB gives rise to restoring forces if the rotation axis of the core and the CMB's
axis of symmetry do not coincide. Earth's reaction to the internal torque associated
with those restoring forces is a diurnal retrograde oscillation of the rotation axis
with respect to the body-fixed reference system. This oscillation is usually called
Nearly Diurnal Free Wobble
(NDFW), and its related space-referred motion is better
known as FCN. Precession-nutation corrections that are estimated with respect to an
−
Ω
