many experimental fits. We continue our work to improve the smoothing, editing, and
weighting choices with the goal of reducing the quoted uncertainties in the future.
In order to solve for individual zonal rates from these constraint (~quations one must
make the dubious assumption that the effect of degrees higher than 4 (for two constraints)
are negligible, and then use the two equations to solve for i2 and i 4 . Applying this
approach to the Starlette and Lageos-l results in eq. (12) leads to
i2 = (-2.56± 0.34) x 1O-llyr- 1
(13)
which is a result we hesitate to include for fear someone will try to use the values in further
analysis. Instead we suggest that in constraining geophysical models such as post-glacial
rebound and current ice-sheet buildup one should directly use eq. (12), thus avoiding the
error incurred by assuming the higher degree terms are negligible. Nou~ that because of the
small Starlette sensitivity to degree 4, the observation equation uncertainties quoted (0.3)
produce a large uncertainty in i4 (1.3) and a high correlation to i2 (-0.78).
18.6-Year Variations
The 18.6-year signals in the Starlette and Lageos-l Im(\f Q) yield analogous constraint
equations for the 18.6-year period variation of the even-degree zonal harmonics. The most
likely source for such a signal is a departure of the external potential degree 2 solid Earth
Love number from the elastic Earth values used in the nominal model (Lam beck and
Nakiboglu, 1983; Merriam, 1985). Assuming that the ocean tides at this long period are
accurately computed with a self-consistent equilibrium model (Ray and Cartwright, 1994)
and that the atmospheric variations at this period are negligible allows interpretation of
these constraint equations in terms of the effect of anelasticity on the Love number.
Using the theory ofWahr and Bergen (1986) for the effect of anelasticity on the degree 2
order zero external potential Love number allows our results to be used to constrain the
lower mantle shear modulus relative to its elastic value. The elastic Earth Love number
used in the nominal model is k = 0.299 (Wahr, 1981) and the self-consistent equilibrium
ocean tides are equivalent to an increase in the effective Love number of 0.043. Assuming
these models are correct, our result yields estimates for the Love number dispersion due to
anelasticity of
ok(L) = (0.035 ± 0.006) + i( -{).OO5 ± 0.012)
ok(S) = (0.032 ±0.01O) + i(+O.OO3± 0.015)
(14)
which, using the Wahr and Bergen result for Model B, ok = -{).19R:, lead to constraints
on the lower mantle shear modulus perturbation of
R:(L) = (-Q.184±0.032)+ i(+O.026 ±0.063)
R:(S) = (-{).168± 0.052)+ i(-{).016 ± 0.079)
(15)
Using the real part of the Lageos-l result and modeling the frequency dependence of
Earth's Q as being proportional to m a leads to a value of a of 0.14 with a possible range
from 0.12 to 0.15 as illustrated in Fig. 2. The imaginary or out-of-phase part of the Love
number perturbation observed using Lageos-l is of the sense required for dissipation, but
the error bar is large and doesn't rule out values of a less than 0.18. The Starlette result
has the opposite sense of that required by tidal dissipation, but the large error bar
38
weighting choices with the goal of reducing the quoted uncertainties in the future.
In order to solve for individual zonal rates from these constraint (~quations one must
make the dubious assumption that the effect of degrees higher than 4 (for two constraints)
are negligible, and then use the two equations to solve for i2 and i 4 . Applying this
approach to the Starlette and Lageos-l results in eq. (12) leads to
i2 = (-2.56± 0.34) x 1O-llyr- 1
(13)
which is a result we hesitate to include for fear someone will try to use the values in further
analysis. Instead we suggest that in constraining geophysical models such as post-glacial
rebound and current ice-sheet buildup one should directly use eq. (12), thus avoiding the
error incurred by assuming the higher degree terms are negligible. Nou~ that because of the
small Starlette sensitivity to degree 4, the observation equation uncertainties quoted (0.3)
produce a large uncertainty in i4 (1.3) and a high correlation to i2 (-0.78).
18.6-Year Variations
The 18.6-year signals in the Starlette and Lageos-l Im(\f Q) yield analogous constraint
equations for the 18.6-year period variation of the even-degree zonal harmonics. The most
likely source for such a signal is a departure of the external potential degree 2 solid Earth
Love number from the elastic Earth values used in the nominal model (Lam beck and
Nakiboglu, 1983; Merriam, 1985). Assuming that the ocean tides at this long period are
accurately computed with a self-consistent equilibrium model (Ray and Cartwright, 1994)
and that the atmospheric variations at this period are negligible allows interpretation of
these constraint equations in terms of the effect of anelasticity on the Love number.
Using the theory ofWahr and Bergen (1986) for the effect of anelasticity on the degree 2
order zero external potential Love number allows our results to be used to constrain the
lower mantle shear modulus relative to its elastic value. The elastic Earth Love number
used in the nominal model is k = 0.299 (Wahr, 1981) and the self-consistent equilibrium
ocean tides are equivalent to an increase in the effective Love number of 0.043. Assuming
these models are correct, our result yields estimates for the Love number dispersion due to
anelasticity of
ok(L) = (0.035 ± 0.006) + i( -{).OO5 ± 0.012)
ok(S) = (0.032 ±0.01O) + i(+O.OO3± 0.015)
(14)
which, using the Wahr and Bergen result for Model B, ok = -{).19R:, lead to constraints
on the lower mantle shear modulus perturbation of
R:(L) = (-Q.184±0.032)+ i(+O.026 ±0.063)
R:(S) = (-{).168± 0.052)+ i(-{).016 ± 0.079)
(15)
Using the real part of the Lageos-l result and modeling the frequency dependence of
Earth's Q as being proportional to m a leads to a value of a of 0.14 with a possible range
from 0.12 to 0.15 as illustrated in Fig. 2. The imaginary or out-of-phase part of the Love
number perturbation observed using Lageos-l is of the sense required for dissipation, but
the error bar is large and doesn't rule out values of a less than 0.18. The Starlette result
has the opposite sense of that required by tidal dissipation, but the large error bar
38