correlations have amplitudes of little more than this.
Thus some of the features in figures such as 7 may
well be spurious; the consequence of inadequate
data or an inadequate treatment.
The improvement in accuracy of the field, even
without extending it to a higher order, should there
fore be one of the first goals for future work in this
area. Only then can we be sure about the existence
of those features that we are trying to correlate
with other geophysical data.
The second improvement required is the resolution
of the solution. At present only those features of
areal extent greater than about 1200 km can be
found so that many interesting areas on the globe
pass by unnoticed. A now classical example is the
geoid variation over the Puerto-Rican trench. This
feature is, according to Von-Arx [28], associated
with a variation in geoid height of about 15 meters
over a distance of about 100 km. Yet it does not
appear in the global solution which has an accuracy
of about three meters. The resolution is also re
quired for studying the detail of the anomalies now
observed. Successive solutions in the past for the
earth's gravity field have indicated a breaking up
of the major features as the resolution improved
and this tendency may well continue beyond the
resolution discussed here.
The first type of improvement is fairly readily ob
tained with present methods but using more, better
distributed, and more precise laser range data. There
are now seven satellites with retroreflectors in orbit
around the earth and there are now twelve laser
stations routinely used for tracking these objects.
The international observing campaign now being
coordinated by the Centre National d'Études
Spatiales, will make an important contribution in
this respect. However, as we discussed in the first
part of this paper, the improvement in laser
tracking will not contribute significantly to impro
vements in the resolution: With a good distribution
of 20 cm accurate data we obtain a resolution of
only about 900 km! New methods, which will mea
sure the earth's potential, or its shape will conse
quently be required to give this improvement.
One of the most important of the new methods is
satellite altimetry. The potential of satellite-borne
52
altimetry has been recognized since the early days
of the space age as both a navigation guidance
system for spacecraft and, more important, as a
means of increasing our knowledge of the earth's
shape. The necessary space technology is now suffi
ciently far developed to make such a program fea
sible if we are seeking accuracies of about one or
two meters.
If a radar on board of a satellite transmits a pulse
towards the earth and the reflected signal is received
back at the satellite, the time delay between the
transmitted and received pulses gives a direct mea
sure of the distance between the satellite and the
point from which the signal is reflected. This is
simply the inverse of the more conventional ground
based radar tracking of satellites. If the satellite is
gravity-gradient stabilized so that the radar pulse
reaching the earth contains the point of nearest
approach, the height of the satellite over the ocean
is measured directly. For a satellite in a polar orbit
such observations could be made over 75% of the
total surface of the earth in a very short time indeed.
If we knew, from ground based tracking data, the
satellite orbit, the combination of this orbital data
with the measured heights gives a direct measure
of the height of the ocean surface with respect to
some more or less arbitrary reference. This ocean
surface will to within a meter correspond to the geoid.
If both the reference orbits and the altimetry data
are accurate to a meter or better, all the detail that
is reflected in the geoid with an amplitude of about
a meter and with a spatial resolution of only a few
tens of kilometers can be measured. At the moment
we have not yet reached this level ot refinement in
our orbital computations, but the altimeter data
can also be incorporated, together with the ground
based tracking data, to improve the accuracy of the
reference orbits as well as providing the detailed
information on the geoid.
A major problem with the altimetry data becomes
the question of how to mathematically represent
the earth's surface. If we continue using the spher
ical harmonics we quickly run into difficulties. For
a resolution of 500 km we require an expansion to
degree 36, or about 1400 coefficients and this is
still manageable with large modern computers. For
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