Geoscience Reference
In-Depth Information
line of steepest descent
grad
g
g = 40 mgal
g = 30 mgal
g = 20 mgal
Fig. 2.22. Lines of constant ∆
g
and lines of steepest descent
The direction of grad ∆
g
defines the line of steepest descent (Fig. 2.22).
The values of
g
x
and
g
y
can be obtained from a gravity map. They are the
inclinations of north-south and east-west profiles through
P
. Values for
g
xx
and
g
yy
may be found by fitting a polynomial in
x
and
y
of second degree
to the gravity anomaly function in the neighborhood of
P
.
A remark on accuracy
Deflections of the vertical
ξ, η
, if combined with astronomical observations
of astronomical latitude Φ and astronomical longitude Λ, furnish positions
on the reference ellipsoid, expressed by ellipsoidal coordinates
ϕ
=Φ
− ξ,
(2-438)
λ
=Λ
− η
sec
ϕ,
just as vertical position is obtained by
h
=
H
+
N.
(2-439)
Unfortunately, to get the same precision for horizontal as for vertical po-
sition, is much more dicult, keeping in mind the relation 1
= 30 m on
the earth's surface. So to get an accuracy of 1 m, which is not too dicult
with Stokes' formula, means an accuracy better than 0
.
03
in both Φ and
ξ
(analogously to Λ and
η
), which is almost impossible to achieve practically.
