DISCUSSION OF RESULTS
Table 3 presents the results for zonal harmonic secular rate solutions which were obtained
froIl) this study. The odd zonal rates are less well behaved than the even zonal rates. When
the J s paramet~r is solved for (shown in Table 3), there is an significant d~gradation in the
uncertainty of J 3 • This is seen when comparing the results of solution with J s adjusted versus
that without. This degradation arises from the large correlation betweep these parameters.
Likewise, odd zonal rate magnitudes increase dramatically when J s is adjusted, and
counteract one another in a classic case of ill-conditioping. Therefore., these parameters are
viewed as inseparable based on this data set. Only J 3 was estimated in the recommended
solution. Since range data (as opposed to Kepler elements or their excitations) are directly
used, and different satellites have different data distribution and weight in the solution, the
aliasing of unsolved for zonal rates uRon the solution is best ascertained numerically. The
sensitivity equation for the "lumped" J 3 is
(3)
Likewise, usin~ a plausible r.ange of t values (up to 0.4 x 1 O-ll/y) , the aliasing effects that
are <0.15 x 10- l/y range for J 4 •
Also shown in Table 3 is a solution where the 18.6 year ocean tide modeling was
perturbed to preserve its equilibrium amplitude but with a 1.0
0
phase offset. Given that solid
Earth and ocean tidal effects are inseparable with regard to their orbit perturbations, this
1.0
0
phase change for the ocean tide was used to assess the bounds of a solid Earth tide's
anelastic response at this tidal frequency. Nevertheless, this simulated anelastic tidal
response causes the even zonal rat.es to .change at a level much smaller than the uncertainty
of the current solution for either J 2 or J 4 •
The data weighting which was used for the Lageos, Starlette and Ajisai SLR data preserve
the relative data weighting which was used in creating JGM-2 with Lageos-2 being given the
same weight as Lageos-1. This data weighting approach was found to produce satisfactory
solution statistics; JGM-2 underwent extensive error calibration to derive these weights.
COMPARISON WITH OTHER INVESTIGATIONS
Table 4 compares the zonal harmonic rates obtained from this investigation with results from
other investigators. In general, the solutions are showing good agreement at their specified
accuracy level, although the uncertainty estimates seem somewhat arbitrary.
Estimates of the observed secular motion of the Earth's spin axis is reviewed in Table 5.
Solutions extending across this century rely on the pole series produced by the International
Latitude Service. The behavior of the secular component of polar motion is variable, and
different averaging intervals and smoothing approaches account for the variation seen in this
table. An estimate of the secular polar motion within the specific period studied was
obtained by fitting a linear trend to a moving 6-year average of the IERS pole series (see
Figure 1a through 1d).
GEOPHYSICAL IMPLICATIONS USING INVERSE SOLUTION
A major challenge arises in the study of temporal gravitational variations when one attempts
to isolate the contribution of an individual geophysical process from the determination of
their aggregate effect from orbit evolution studies. This is an ill-posed, geophysical inversion
type of problem, since it is well known that a particular mass distribution cannot be
156
Table 3 presents the results for zonal harmonic secular rate solutions which were obtained
froIl) this study. The odd zonal rates are less well behaved than the even zonal rates. When
the J s paramet~r is solved for (shown in Table 3), there is an significant d~gradation in the
uncertainty of J 3 • This is seen when comparing the results of solution with J s adjusted versus
that without. This degradation arises from the large correlation betweep these parameters.
Likewise, odd zonal rate magnitudes increase dramatically when J s is adjusted, and
counteract one another in a classic case of ill-conditioping. Therefore., these parameters are
viewed as inseparable based on this data set. Only J 3 was estimated in the recommended
solution. Since range data (as opposed to Kepler elements or their excitations) are directly
used, and different satellites have different data distribution and weight in the solution, the
aliasing of unsolved for zonal rates uRon the solution is best ascertained numerically. The
sensitivity equation for the "lumped" J 3 is
(3)
Likewise, usin~ a plausible r.ange of t values (up to 0.4 x 1 O-ll/y) , the aliasing effects that
are <0.15 x 10- l/y range for J 4 •
Also shown in Table 3 is a solution where the 18.6 year ocean tide modeling was
perturbed to preserve its equilibrium amplitude but with a 1.0
0
phase offset. Given that solid
Earth and ocean tidal effects are inseparable with regard to their orbit perturbations, this
1.0
0
phase change for the ocean tide was used to assess the bounds of a solid Earth tide's
anelastic response at this tidal frequency. Nevertheless, this simulated anelastic tidal
response causes the even zonal rat.es to .change at a level much smaller than the uncertainty
of the current solution for either J 2 or J 4 •
The data weighting which was used for the Lageos, Starlette and Ajisai SLR data preserve
the relative data weighting which was used in creating JGM-2 with Lageos-2 being given the
same weight as Lageos-1. This data weighting approach was found to produce satisfactory
solution statistics; JGM-2 underwent extensive error calibration to derive these weights.
COMPARISON WITH OTHER INVESTIGATIONS
Table 4 compares the zonal harmonic rates obtained from this investigation with results from
other investigators. In general, the solutions are showing good agreement at their specified
accuracy level, although the uncertainty estimates seem somewhat arbitrary.
Estimates of the observed secular motion of the Earth's spin axis is reviewed in Table 5.
Solutions extending across this century rely on the pole series produced by the International
Latitude Service. The behavior of the secular component of polar motion is variable, and
different averaging intervals and smoothing approaches account for the variation seen in this
table. An estimate of the secular polar motion within the specific period studied was
obtained by fitting a linear trend to a moving 6-year average of the IERS pole series (see
Figure 1a through 1d).
GEOPHYSICAL IMPLICATIONS USING INVERSE SOLUTION
A major challenge arises in the study of temporal gravitational variations when one attempts
to isolate the contribution of an individual geophysical process from the determination of
their aggregate effect from orbit evolution studies. This is an ill-posed, geophysical inversion
type of problem, since it is well known that a particular mass distribution cannot be
156