Geoscience Reference
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above ground is measured. This case seems rather to belong to the past. If
the case should arise, gravity anomalies ∆
g
can be upward continued just as
δg
as described in Sect. 6.4.
Again, free-air anomalies referred to ground level or, more accurately,
to some level surface, are to be used. If the ground is elevated above sea
level but reasonably flat, it is somewhat better to regard
H
as elevation
above ground rather than above sea level, because the ground may then be
considered locally part of a level surface.
The inverse problem, the downward continuation of gravity anomalies or
rather gravity disturbances, occurs in the reduction of gravity measured on
board an aircraft. There is, of course, a relation to harmonic downward con-
tinuation in the solution of Molodensky's problem as described in Sect. 8.6.
Upward and downward continuation are also tools of geophysical explo-
ration, but here the objective is quite different. Several methods have been
developed in this connection, some of which are also applicable for geodetic
purposes; see, e.g., Dobrin and Savit (1988) or Telfort et al. (1990).
Upward and downward continuation are related as direct and inverse
problems in the theory of inverse problems, see Anger et al. (1993) and also
www.inas.tugraz.at under forschung/InverseProblems/AngerMoritz.html,
where additional references can be found.
