The accuracy of the global solution is of the order
of three meters in geoid height or 9 milligals in
gravity anomalies. These estimates are based on
the formal statistics computed for the solution but
are in excellent agreement with tests made with in
dependent surface gravity data and with astro-
geoid data. Figures 2 and 3 give some typical examp
les and more information is given in [1, 2, 3 and 6].
The interpretation of the earth's gravitational field
In this discussion we will limit ourselves to the im
plications of the long wavelength features in the
earth's gravity field rather than the small features
which are the consequence of near surface density
anomalies and of the topography. By long wave
length we mean gravity anomalies that have an
areal extent of about 1000 km diameter and, as
discussed below, these anomalies will be caused by
density anomalies at some depth below the earth's
surface.
If the earth acted essentially like a fluid over a
suitably long time span, it would take on a spheroi
dal shape which could be calculated from the pre-
cessional constant and its angular velocity [7],
Such a body is said to be in hydrostatic equili
brium and all level surfaces inside the body would
be at the same time surfaces of equal density. For
a body of the earth's mass and the dynamical
ellipticity calculated from the precession constant,
the geometric flattening of an ellipsoid correspond
ing to the hydrostatic figure would be about 1/300.
Figure 4 shows the gravity field as it departs from
such a hydrostatic figure and the anomalies clearly
indicate that the earth differs considerably from a
rotating liquid. This is hardly surprising as we are
quite used to a more or less rigid earth outside of
the oceans. But we emphasize that we are talking
about the shape of the earth over a long time span
so that when materials are subjected to large forces
over a long time span we can expect them to re
adjust in one way or another in response to these
forces. That this happens in the case of the earth, to
at least some extent, is evidenced by the isostatic
compensation of mountain ranges and by areas of
post glacial rebound such as Fenno-Scandinavia.
Two alternative interpretations are possible as to
what supports these departures from hydrostatic
equilibrium. The first is a finite strength interpreta
tion whereby the earth materials are assumed to be
sufficiently rigid to support over very long time
periods the stresses and strains caused by the gravity
anomalies. The second interpretation is that the
earth's strength is low but that the density anoma
lies are dynamically maintained by some form of
thermal convection. Seismology gives us some in
dication as to which of these two interpretations
is most likely and in fact it appears that the two
co-exist. Seismology also indicates that the core of
the earth is sufficiently liquid so as not to depart
significantly from hydrostatic equilibrium so that
we need only consider the earth's mantle and crust
in the following discussion.
The first characteristic of the gravity field is the
difference between the hydrostatic flattening of
about 1/300 and the observed flattening of 1 /29S.255.
The difference may appear small but is real and is
considerably larger than the uncertainties associated
with either flattening estimate. The difference im
plies that the earth's bulge is too large by some
0.5%, and the question is whether this departure is
sufficiently significant, when compared to the other
5° x 5° AVERAGES
COMBINATION SOLUTION
20
S -20
E
80°
60°
LONGITUOE
Fig. 3 Comparisons of gravity profiles based on the global
solution (solid lines) and on data collected by surface
measurements (broken lines).
Indian Ocean. 0
46
ngt 72