Geology Reference
In-Depth Information
-
-
-
-
+
-
+
-
-
A
+
δ
J
-
δ A'
+
l
+
-
Fig. 7.19 The representation of the
magnetic effects of an irregularly-shaped
body in terms of a number of elements
parallel to the magnetization direction.
Inset shows in detail the end of one such
element.
+
θ
-
+
+
+
+
0
0
km
20
-300
Magnetic North
0
-
-
-
-
-
-
-
-
-
-
+
Fig. 7.20 The total field magnetic
anomaly of a faulted sill.
J = 1A m -1
+
5
B
+
+
+
+
+
+
+
+
+
+
formed analytically for bodies of regular shape, while
irregularly-shaped bodies may be split into regular
shapes and the integration performed numerically.
In two-dimensional modelling, an approach similar
to gravity interpretation can be adopted (see Section
6.10.4) in which the cross-sectional form of the body is
approximated by a polygonal outline. The anomaly of
the polygon is then computed by adding or subtracting
the anomalies of semi-infinite slabs with sloping edges
corresponding to the sides of the polygon (Fig. 7.21). In
the magnetic case, the horizontal D H , vertical D Z and
total field D B anomalies (nT) of the slab shown in
Fig. 7.21 are given by (Talwani et al . 1965)
pole strength per unit area = J cos q
(7.17)
A consequence of the distribution of an equal number
of positive and negative poles over the surface of a mag-
netic body is that an infinite horizontal layer produces no
magnetic anomaly since the effects of the poles on the
upper and lower surfaces are self-cancelling. Conse-
quently, magnetic anomalies are not produced by
continuous sills or lava flows.Where, however, the hori-
zontal structure is truncated, the vertical edge will
produce a magnetic anomaly (Fig. 7.20).
The magnetic anomaly of a body of regular shape is
calculated by determining the pole distribution over the
surface of the body using equation (7.17). Each small el-
ement of the surface is then considered and its vertical
and horizontal component anomalies are calculated
at each observation point using equations (7.10) and
(7.11).The effects of all such elements are summed (inte-
grated) to produce the vertical and horizontal anomalies
for the whole body and the total field anomaly is calcu-
lated using equation (7.9). The integration can be per-
D Z
=
200
sin
J
sin
log
r
r
) +
cos
q
[
{
q
(
f
q
}
x
e
21
+
J
cos
log
r
r
) -
sin
(7.18a)
{
q
(
f
q
} ]
z
e
21
D H
=
200
sin
J
sin
-
cos
log
r
r
q
[
{
f
q
q
(
)
}
x
e
21
+
J
cos
+
sin
log
r
r
sin
(7.18b)
{
fq
q
(
)
} ]
a
z
e
21
D B = D Z sin I + D H cos I
(7.18c)
 
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