Geoscience Reference
In-Depth Information
Fig. 14
Standard transfer
functions
T
p
(
black line
),
T
w
(blue line) and simplified
transfer function
T
0
without
FCN term (red line). Only real
parts are shown
0.015
0.01
0.005
0
T
p
T
w
T
0
−0.005
−0.01
−0.015
−30
−25
−20
−15
Period [h]
of the CW and the NDFW by the corresponding observation-based values as defined
in Eqs. (
32
) and (
81
). Equation (
89
) is modified accordingly, despite the fact that we
evoke inconsistencywith the theory of Sasao andWahr (
1981
). The imaginary parts of
the CW and NDFW eigenfrequencies account for damping and prevent singularities
in the 'broad band' equation of polar motion (Brzezi nski et al.
2002
)
(σ )
=
T
p
(σ ) χ
p
(σ )
+
T
w
(σ ) χ
w
p
ˆ
(σ ).
(90)
T
p
(σ )
T
w
(σ )
Here,
are transfer functions used to accomplish the polar motion
(nutation) contributions induced by pressure and wind excitation
T
p
(σ )
=
σ
cw
and
1
σ
cw
−
σ
a
p
+
(91)
σ
f
−
σ
T
w
(σ )
=
σ
cw
1
σ
cw
−
σ
a
w
+
.
(92)
σ
f
−
σ
Figure
14
displays the real parts of both
T
p
(σ )
and
T
w
(σ )
24h and compares
them with a simplified transfer function that neglects the FCN portions in Eqs. (
91
)
and (
92
). On the one hand, due to the numerical discrepancy recognized between
a
p
and
a
w
, it is evident that the transfer function associated with the matter term
is of stronger weight than its motion counterpart at diurnal retrograde frequencies.
On the other hand, we can assume that an omission of the FCN term outside the
nutation band does not lead to large errors in the excitation estimates. As illustrated
by Brzezi nski (
1994
), the ratio between the pure FCN transfer function and the plain
CW term in Eq. (
91
) amounts to 0.19 and 0.05 at frequencies
at
T
=−
2 and 2 cpd
(cycles per day), respectively. Hence, for applications that do not explicitly focus on
the diurnal retrograde band, it is justified to neglect the effect of the FCN resonance
by setting
a
p
=
σ
=−
a
w
=
0 and only deal with
