Geology Reference
In-Depth Information
(a)
125
124
123
122
(b)
70
1200
+
Observed
anomaly
+
+
I II
Computed
anomaly
+
+
+
800
+
+
Darnley
Bay
0
+
+
400
+
+
+
+
+
+
+
0
km
40
+
0
+
+
+
+
+
+
+
+ +
A
B
+
A
B
0
1000
20
69
500
Model I
(
= 0.30 Mg m
-3
)
Δρ
40
0
0
0
km
25
Model II
(
20
= 0.50 Mg m
-3
)
Δρ
Fig. 6.20
(a) The circular gravity anomaly at Darnley Bay, NWT, Canada. Contour interval 250 gu. (b) Two possible interpretations of the
anomaly in terms of a model constructed from a suite of coaxial vertical cylinders. (After Stacey 1971.)
x
(0, 0)
+
φ
1
-
r
1
(
x
1
,
z
1
)
z
φ
2
+
r
2
Δρ
-
θ
+
(
x
2
,
z
2
)
Fig. 6.21
Parameters used in defining the gravity anomaly of a
semi-infinite slab with a sloping edge.
Fig. 6.22
The computation of gravity anomalies of two-
dimensional bodies of irregular cross-section.The body (dashed
line) is approximated by a polygon and the effects of semi-infinite
slabs with sloping edges defined by the sides of the polygon are
progressively added and subtracted until the anomaly of the
polygon is obtained.
D
g
=
2
G
D
r
[
-
{
x
sin
q
+
z
cos
q
}
1
1
¥
{
sin
q
log
(
rr
)
+
cos
q f
(
-
f
)
}
e
21
2
1
Figure 6.23 illustrates a two-dimensional interpreta-
tion, in terms of a model of irregular geometry repre-
sented by a polygonal outline, of the Bodmin Moor
granite of southwest England. The shape of the upper-
most part of the model is controlled by the surface out-
crop of granite, while the density contrasts employed are
based on density measurements on rock samples. The
interpretation shows unambiguously that the contacts of
the granite slope outwards. Ambiguity is evident, how-
ever, in the interpretation of the gravity gradient over the
northern flank of the granite. The model presented
in Fig. 6.23 interprets the cause of this gradient as a
+
z
f
-
z
f
]
(6.22)
22
11
where
Dr
is the density contrast of the slab, angles are ex-
pressed in radians and other parameters are defined as in
Fig. 6.21 (Talwani
et al.
1959).To calculate the anomaly
of a two-dimensional body of irregular cross-section, the
body is approximated by a polygon as shown in Fig. 6.22.
The anomaly of the polygon is then found by pro-
ceeding around it summing the anomalies of the slabs
bounded by edges where the depth increases and
subtracting those where the depth decreases.
