Geology Reference
In-Depth Information
x
r
1
φ
J
x
r
2
i
J
z
Fig. 7.21
Parameters used in defining the magnetic
anomaly of a semi-infinite slab with a sloping edge.
θ
J
where angles are expressed in radians,
J
x
(=
J
cos
i
) and
J
z
(=
J
sin
i
) are the horizontal and vertical components of
the magnetization
J
,
a
is the horizontal angle between
the direction of the profile and magnetic north, and
I
is the inclination of the geomagnetic field. Examples of
this technique have been presented in Fig. 7.15. An
important difference from gravity interpretation is the
increased stringency with which the two-dimensional
approximation should be applied. It can be shown that
two-dimensional magnetic interpretation is much more
sensitive to errors associated with variation along
strike than is the case with gravity interpretation; the
length-width ratio of a magnetic anomaly should be at
least 10 : 1 for a two-dimensional approximation to be
valid, in contrast to gravity interpretation where a 2 : 1
length-width ratio is sufficient to validate two-
dimensional interpretation.
Three-dimensional modelling of magnetic anomalies
is complex. Probably the most convenient methods are
to approximate the causative body by a cluster of right
rectangular prisms or by a series of horizontal slices of
polygonal outline.
Because of the dipolar nature of magnetic anomalies,
trial and error methods of indirect interpretation are dif-
ficult to perform manually since anomaly shape is not
closely related to the geometry of the causative body.
Consequently, the automatic methods of interpretation
described in Section 6.10.3 are widely employed.
The continuation and filtering operations used in
gravity interpretation and described in Section 6.11 are
equally applicable to magnetic fields. A further process-
ing operation that may be applied to magnetic anomalies
is known as
reduction to the pole
, and involves the conver-
sion of the anomalies into their equivalent form at the
north magnetic pole (Baranov & Naudy 1964). This
process usually simplifies the magnetic anomalies as the
ambient field is then vertical and bodies with magnetiza-
tions which are solely induced produce anomalies that
are axisymmetric. The existence of remanent magneti-
zation, however, commonly prevents reduction to the
pole from producing the desired simplification in the
resultant pattern of magnetic anomalies.
7.11 Potential field transformations
The formulae for the gravitational potential caused by a
point mass and the magnetic potential due to an isolated
pole were presented in equations (6.3) and (7.3). A con-
sequence of the similar laws of attraction governing
gravitating and magnetic bodies is that these two equa-
tions have the variable of inverse distance (1/
r
) in
common. Elimination of this term between the two for-
mulae provides a relationship between the gravitational
and magnetic potentials known as
Poisson's equation
.In
reality the relationship is more complex than implied by
equations (6.3) and (7.3) as isolated magnetic poles do
not exist. However, the validity of the relationship be-
tween the two potential fields remains. Since gravity or
magnetic fields can be determined by differentiation of
the relevant potential in the required direction, Poisson's
equation provides a method of transforming magnetic
fields into gravitational fields and
vice versa
for bodies in
which the ratio of intensity of magnetization to density
remains constant. Such transformed fields are known
as
pseudogravitational
and
pseudomagnetic
fields (Garland
1951).
One application of this technique is the transforma-
tion of magnetic anomalies into pseudogravity anom-
alies for the purposes of indirect interpretation, as the
latter are significantly easier to interpret than their mag-
netic counterpart. The method is even more powerful
when the pseudofield is compared with a corresponding
measured field. For example, the comparison of gravity
anomalies with the pseudogravity anomalies derived
from magnetic anomalies over the same area can show
whether the same geological bodies are the cause of the
two types of anomaly. Performing the transformation for
