Modern views on the determination of the figure of the earth - Physical Geodesy - page 318

Exercise
Collecting all these remarks into a separately readable paper on the various
aspects of free-air reduction would be a nice task for a seminar work. The
present authors offer a prize of Euro 500, the “Molodensky Prize”, to the
first excellent review paper on this topic.

8.10 Determination of the geoid from ground-level

anomalies

We have seen that it is possible to determine the physical surface of the earth
by means of the height anomalies ζ , and the direction of the plumb line on
it by means of the deflection components ξ and η , from free-air anomalies
referred to the ground. If we plot the orthometric height H downward along
the plumb line, starting from the physical surface, then the locus of the
points so obtained will be the geoid (Fig. 8.11).
This geometrical idea may be formulated analytically in the following
way. Conventionally, the height h above the ellipsoid is given by

h = H + N ; (8-106)

according to the modern theory, by

h = H ∗ + ζ. (8-107)

From these two equations we get

ζ = H ∗ − N − H. (8-108)

P

Q ³

earth's
surface

H

telluroid

H *

P 0

geoid

N

ellipsoid

Q 0

Fig. 8.11. Geoid at a depth H below the earth's surface