Geoscience Reference
In-Depth Information
earth's
surface
quasigeoid
³
ellipsoid
Fig. 8.12. Quasigeoid
To get a quantitative estimate of the difference
N
−
ζ
, we again use the
fact that
g
−
γ
∆
g
B
981 gal
=
.
=10
−
3
∆
g
B
,
(8-115)
γ
where ∆
g
B
is the Bouguer anomaly in gal, so that
=
(
ζ
−
N
)
[
m
]
−
∆
g
B
[
gal
]
·
H
[
km
]
.
(8-116)
Since ∆
g
B
N
are
usually positive there. In other words, the height anomaly
ζ
is in general
greater than the corresponding geoidal undulation
N
on land. We have
ζ
=
N
on the oceans. If ∆
g
B
=
−
100 mgal =
−
0
.
1 gal and
H
=1km,then
is usually negative on the continents, the differences
ζ
−
ζ
−
N
=0
.
1m
.
(8-117)
Furthermore, the Bouguer anomaly depends on the
mean
elevation of the
terrain, decreasing approximately by 0.1 gal per 1 km average elevation. As-
suming as a rough estimate, which may be verified by inspecting maps of
Bouguer anomalies,
∆
g
B
[
gal
]
=
−
0
.
1
H
av
[
km
]
,
(8-118)
we obtain
.
=+0
.
1
H
av
(
ζ
−
N
)
[
m
]
[
km
]
H
[
km
]
,
(8-119)
where
H
is the height of the station and
H
av
is an average height of the
area considered. We see that the difference
ζ
N
increases faster than the
elevation, almost as the square of the elevation. As a matter of fact, this
formula is suited only to give an idea of the order of magnitude (see also
Sect. 11.3).
Since
ζ
−
H
∗
, the approximate formulas given above may also
be used to estimate the differences between the orthometric height
H
and
the normal height
H
∗
.
A theoretically important point is that the quasigeoid can be determined
without hypothetical assumptions concerning the density, but not so the
−
N
=
H
−