Geoscience Reference
In-Depth Information
earth's
surface
B
A
geoid
A
0
B
0
Fig. 4.5. Orthometric and dynamic correction
From (4-17), we have
∆
H
dyn
=∆
n
AB
+DC
AB
.
(4-36)
AB
Consider now the differences between the orthometric and dynamic heights,
H
A
−
H
dyn
H
dyn
. Imagine a fictitious leveling line leading from
point
A
0
at the geoid to the surface point
A
along the plumb line. Then the
measured height difference would be
H
A
itself: ∆
n
A
0
A
=
H
A
,sothat
and
H
B
−
A
B
DC
A
0
A
=∆
H
dyn
A
0
A
−
∆
n
A
0
A
=
H
dyn
A
−
H
A
(4-37)
and
H
dyn
H
A
−
=
−
DC
A
0
A
,
A
(4-38)
H
dyn
H
B
−
=
−
DC
B
0
B
.
B
Substituting (4-36) and (4-38) into (4-35), we finally have
∆
H
AB
=∆
n
AB
+DC
AB
+DC
A
0
A
−
DC
B
0
B
(4-39)
or
∆
H
AB
=∆
n
AB
+OC
AB
,
(4-40)
where
(4-41)
is the orthometric correction. This is a remarkable relation between the or-
thometric and dynamic corrections (Ledersteger 1955). We may write this
OC
AB
=DC
AB
+DC
A
0
A
−
DC
B
0
B
OC
AB
=DC
AB
+DC
A
0
A
+DC
BB
0
,
(4-42)
where we have reversed the sequence of the subscripts of the last term and,
consequently, the sign. With DC
B
0
A
0
=0(why?),wemaywrite
OC
AB
=DC
AB
+DC
BB
0
+DC
B
0
A
0
+DC
A
0
A
.
(4-43)
