Goldreich and Toomre [17] have argued however,
that the difference in flattening is no more signi
ficant than some of the other departures from
hydrostatic equilibrium as indicated in figure 4.
They argue therefore that a separate interpretation
of the bulge discrepancy is both unwarranted and
misleading, [nstead, they argue that the earth is a
viscous body rotating about an axis selected so as
to maximize the resultant polar moment of inertia.
If during the geologic past these unknown features
were differently distributed as indicated by, for
example, continental drift, the pole of rotation
would lie in a different position. With this inter
pretation we do not need to invoke a time constant
of about 10 million years obtained from the earth's
deceleration. We can use instead a time constant
estimated from the polar motion and if the pole has
really moved at a rate of 10 km per million years
(or faster [18]) we obtain a measure of the viscosity
of about 1024cgs. This value is representative of the
mantle as a whole, is in better agreement with the
value obtained by the observed rates of uplift for
the upper mantle and also reinstates the possibility
of thermal convection in the lower mantle.
However, the information on polar wandering in
turn is based on a number of hypothesis whose
validity is not clear. The first hypothesis is that the
earth's magnetic field has always been that of a
dipole, and a second hypothesis is that this dipole
field has been coupled to the earth's rotation axis
throughout the geologic past. Neither hypothesis
is completely supported by the palaeomagnetic
data [14].
The two radically different conclusions drawn
from the earth's bulge are indicative of the problems
that exist when interpreting these results without
adequate information on the other necessary para
meters of the earth. The gravity field is probably
better known globally than any other geophysical
quantity pertaining to the solid earth and yet we
reach the two widely divergent interpretations for
just one part of the field!
If we accept Munk and MacDonald's hypothesis
of the fossil bulge we have to explain the other
gravity anomalies with respect to the 1/298.25
ellipsoid. In the case of the Goldreich and Toomre
explanation it is the anomalies with respect to the
1/300 ellipsoid that need explaining. In either case,
when we look at figures 1 and 4 we are struck by
the lack of correlation between the gravity field and
the distribution of the continents. This leads us to
the important conclusion that the density anomalies
giving the gravity field are not associated with the
continents but have their origin somewhere in the
mantle.
This suggests that if the earth is reasonable viscous
the displacements of density anomalies that cause
the polar wandering are not necessarily associated
with the distribution of the continents and that we
would not expect to find a close relation between
the motion of the continents and of the pole.
Density models of the earth as deduced from seis
mology indicate that between the core and mantle
there is a density jump of about 5 grams/cm3. It
has been suggested by Hide and Horai [20] that
there is a transition zone of perhaps 5 km thickness
in which density anomalies occur and which would
contribute to the gravity field observed at the earth's
surface. Some straightforward calculations [21]
show that only the observed harmonics up to degree
4 or 5 can be placed in this interface if the thick
ness and density jump are to be in agreement with
the above values. Such anomalies are also useful
for explaining certain features of the earth's rota
tion (the decade wobble) and of the earth's mag
netic field. Hide and Malin [22] have in fact found
a correlation between the low order geomagnetic
field and gravity field if the former is rotated through
160° in longitude. Figure 5 gives the residual gravity
field after all tesseral terms up to fourth degree are
removed.
Seismology has also indicated that between the
core-mantle boundary to a depth of about 1000 km
below the surface, the mantle is laterally quite homo
geneous. At least, no significant variations have yet
been found and the question as to whether there
exist large scale convection cells throughout this
layer is still uncertain. Thus we will not consider
this region to be a particularly fruitful one for
seeking an explanation of the gravity anomalies
given in figure 5. We look instead to the very upper
most regions of the mantle. Here the seismic
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