Geoscience Reference
In-Depth Information
geopotential
surface
W=
P
= const.
P
N
P
Q
spheropotential
surface
U=
P
= const.
P
0
geoid
W=
0
N
Q
0
ellipsoid
U=
0
Fig. 2.15. Geopotential and spheropotential surfaces
are often called
geopotential surfaces
; the level surfaces of the normal gravity
field, the surfaces
U
= constant
,
(2-284)
are called
spheropotential surfaces
.
We consider now the point
P
outside the earth (Fig. 2.15) and denote
the geopotential surface passing through it by
W
=
W
P
.
(2-285)
There is also a spheropotential surface
U
=
W
P
(2-286)
of the same constant
W
P
. The normal plumb line through
P
intersects this
spheropotential surface at the point
Q
, which is said to correspond to
P
.
We see that the level surfaces
W
=
W
P
and
U
=
W
P
are related to each
other in exactly the same way as are the geoid
W
=
W
0
and the reference
ellipsoid
U
=
W
0
. If, therefore, the gravity anomaly is defined by
∆
g
P
=
g
P
−
γ
Q
,
(2-287)
as in Sect. 2.12, then all derivations and formulas of that section also apply
for the present situation, the geopotential surface
W
=
W
P
replacing the
geoid
W
=
W
0
, and the spheropotential surface
U
=
W
P
replacing the
ellipsoid
U
=
W
0
. This is also the reason why (2-271) applies at
P
as well
as at the geoid.
Note that
P
in Sect. 2.12 is a point at the geoid, which is denoted by
P
0
in Fig. 2.15.
This situation will be taken up again in Chap. 8, in the context of Molo-
densky's problem.