Geology Reference
In-Depth Information
Fig. 14.6
Terrain correction for the calculation of com-
plete Bouguer anomalies. The mountain to the
left
of the
observation point is located externally to the Bouguer slab
and exerts a negative (
upward
) attraction on
P
. Therefore,
the corresponding correction must have positive sign.
Similarly, the contribution of the
dashed region
to the
right
of
P
, which was included in the simple Bouguer
correction with negative sign, should be removed through
a correction having positive sign
z
0
D
—(
x
0
,
y
0
) for each location with projected
geographic coordinates (
x
0
,
y
0
)(Fig.
14.6
). If
P
(
x
,
y
,
z
) is an observation point, the vertical
component of the gravity field at
P
generated
by mass elements
dm
D
¡
dx
0
dy
0
dz
0
at positions
(
x
0
,
y
0
,
z
0
)
lies behave differently with respect to the re-
gional isostatic equilibrium. In fact,
g
FA
Š
0
when a region is in isostatic equilibrium, whereas
g
SB
Š
0 in case of uncompensated structure.
between
the
Bouguer
slab
and
the
14.6
Isostasy and Dynamic
Topography
topographic surface is given by:
—
.
x
0
;y
0
/
C
Z
C
Z
Z
The major part of the Earth's surface topography
can be explained by
isostatic compensation
of
density variations within the lithosphere. In Chap.
be expressed as a law of invariance for the hydro-
static pressure at some compensation depth
z
c
in
the uppermost asthenosphere:
dx
0
dy
0
•g
T
.x;y;h/
D
G¡
1
1
h
.h
z
0
/d
z
0
h
.x
x
0
/
2
C
.h
z
0
/
2
i
3=2
(14.64)
C
.y
y
0
/
2
Z
z
c
This quantity is termed
terrain correction
.The
corresponding complete Bouguer anomaly is ob-
tained by adding (
14.64
) to the simple anomaly:
P.x;y;
z
c
/
D
g
¡.x;y;
z
/d
z
D
const
H
max
(14.66)
g
CB
.§;¥;h/
D
g
SB
.§;¥;h/
C
•g
T
.§;¥;h/
(14.65)
where
H
max
is the maximum altitude. This equa-
tion implies that lateral variations of crustal or
lithospheric thickness must be compensated by
variations of topography, as illustrated in the
example of Fig.
14.7
.
The mechanism of isostatic compensation
can explain the
5
8 km elevation of the
Tibetan Plateau and the Hymalayan range, which
result essentially from the crustal thickening that
followed the collision of India with Eurasia.
In the case of crustal scale studies, the ter-
rain correction is usually negligible, thereby it
is ignored. In general, Bouguer anomalies are
negative in continental regions and positive over
oceanic basins. This is also a consequence of
the presence of low-density crustal roots below
mountain regions. Free-air and Bouguer anoma-
