Modern views on the determination of the figure of the earth - Physical Geodesy - page 293

where γ Q 0 is the corresponding value on the ellipsoid.
The height anomaly ζ may be considered as the distance between the
geopotential surface W = W P = constant and the corresponding spheropo-
tential surface U = W P = constant at the point P . In Sect. 2.14 (Fig. 2.15),
we have denoted this distance by N P and have found that Bruns' formula
(2-237) also applies to this quantity. Hence, for ζ = N P we have

ζ = T
γ

, (8-26)

where T = W P −

U P is the disturbing potential at ground level, and γ the
normal gravity at the telluroid.
It may be expected that ζ is connected with the ground-level anomalies
∆ g by an expression analogous to Stokes' formula for the geoidal height N .
This is indeed true. However, the telluroid is not a level surface, and to every
point P on the earth's surface corresponds in general a different geopotential
surface W = W P . Therefore, the relation between ∆ g and ζ in the new theory
is considerably more complicated than for the geoid. In Molodensky's original
formulation, the problem involves an integral equation, which may be solved
by an iteration, the first term of which is given by Stokes' formula. We shall
use an equivalent but much simpler approach without integral equation.
Finally, we remark that we may also plot the height anomalies ζ above
the ellipsoid. In this way we get a surface that is identical with the geoid over
the oceans, because there ζ = N , and is very close to the geoid anywhere
else. This surface has been called the quasigeoid by Molodensky. However,
the quasigeoid is not a level surface and has no physical meaning whatever.
It must be considered as a concession to conventional conceptions that call
for a geoidlike surface. From this point of view, the normal height of a point
is its elevation above the quasigeoid, just as the orthometric height is its
elevation above the geoid.

Gravity disturbance
As usual, the gravity disturbance is defined by

δg = g P − γ P . (8-27)

It is a typical new feature introduced into the practice of physial geodesy
by GPS, because GPS determines the ellipsoidal coordinates ϕ, λ, h directly
at the surface point P ,sothatnow δg can be considered observational data
instead of ∆ g .