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strictly expressed, without knowledge of interior mass distribution
and so fall into the domain of geophysics.
The geodesists Reference System accordingly is meant to be
used as basis for anomalies on, or above, the ground surface. It
should approximate to nature, if possible, so that all anomalies
are small, for ease of handling.
Computations of observations should apply to ground surface,
involving no reduction to geoidal level. This is practically possible.
5 Earth Topography. Gravity provides, at all surface points
of the Earth, the means of levelling instruments used for surveying
measurementsexcellent for local purposes. For the geodesist,
whose field is the entire Earth, the Deflexions of the vertical
cannot be ignored. The deflexions are anomalies, caused by mass
anomalies, which fall into two groups.
First, if one treats the topographic features as of standard density
(2.67 for land and 1.03 for sea) their attractional effects can be
computed.
Second, there are anomalies of density in the Earthespecially
in the crust, including the topographic featuresgenerally unknown
and a frequent object of enquiry.
I will allude to these two groups as "topographic" and "density"
effects.
In gravity survey on a large scalefor the whole Earthover
large areas gravity stations are far apart or non-existent. What is
required is the value of g representative of the locality, rather than
the value at a single point which may well be highly disturbed.
The disturbing effect of topography must in some way be removed.
That of hidden density anomalies is likely to be smaller, as the
density anomaly is smaller than the entire density.
Current practice is to make an isostatic reduction. Now it is
legitimate to make, in imagination, any transfer of topographic
masses which seems useful, provided that all relevant consequential
changes are also computed. So any systematic isostatic reduction
is quite legitimate, irrespective of the truth or reverse of the
underlying hypothesis: but the modified gravity anomaly will
relate to an Earth from which all surface features have been
removed and transferred downwards according to the hypothesis
used—that is an Earth very considerably different from the
Actual Earth which we are trying to investigate.
I have thought that the desired object is better attained by
Smoothing the Topography (in imagination) so that no slopes
exceeding, say, 0.01 remain. This can be done by replacing the
topographic height h of the Actual Earth by a weighted average
of h over a ring of angular diameter 30. More precisely, I average h
multiplied by the standard density of land or water, as the case
may be. There is nothing hypothetical about this. The topography
is actually in existence: and if its density is other than standard,
