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then the residue remains in position and is the density anomaly
of its position. Mountain crests are transferred and fill up valleys:
and in effect the movements of matter are almost superficial, and
very much less than those implied in isostatic reductions. The
Model Earth (M.E.), which is the name I have given to the
smoothed Earth, represents the Actual Earth, except as regards
local detail: and is a generalised Earth, more suitable for handling
problems concerning the whole Earth than one complicated by all
local details.
The smoothing obviously affects the gravity anomaly. For the
Model Earth it is easily shown that the anomaly is
AgE g Y ^4 H h) (Orographical correction),
H being the average of h (or of water depth multiplied by 103/267)
and A the Bouguer factor.
Some account of the Model Earth is in various numbers of
Bulletin Géodésique, recording the General Assembly of the U.G.G. 1
at Toronto, 1957, and later; and my contribution to Professor
Cassinis's jubilee volume (Bollettino di Geodesia e Scienze Affini,
Oct. i960), shows how Fa ye and Putnam had similar ideas prior to
1900.
For the M.E. surface and the external field, the gravity anomaly
field can be simulated by a fictitious density layer AgE/277 spread
over the M.E. surface.
One may compare this with the Equivalent layer of Green,
over an equipotential, for which the factor is 1/477. One knows
that the elfect of the immediate vicinity accounts for half of the
Green layer: the other half being provided by the almost entire
surface. Something similar occurs in our case. But over the remote
portions the term A (H h) indicates a quantity, frequently
changing sign, and in which the total H h over the entire surface
vanishes. So the remote portion is ineffectiveand for that reason
the local provision has to be doubled.
This is the case also with the usual Bouguer reduction, which
I have generally heard related to an infinite plate. I think it is much
better to relate it to a thin spherical shell, of which the remote
part is ineffective. Now I feel that I know why the remote part can
be disregarded.
The Bouguer Factor, which I have called "A" is 1/277 in gravi
tational terms: but for expressing effect of topography of thickness
The numerical values of AgE, which lie within 4: 100 mgals,
resemble in some ways the Hayford or Airy anomalies. As just
stated they can be represented by surface layer AgE/277 which is a
measure of the amount of mass anomaly or lack of compensation,
and shows little correspondence with H. In general it suggests that
h the factor is
mgal/metres.
