Geoscience Reference
In-Depth Information
magnetic derivatives depends on the direction of the
source magnetism and is usually multi-peaked and dipolar
unless the magnetism is vertical. The asymmetric
responses due to non-vertical magnetisation can be over-
come by applying the derivatives to pole-reduced data (see
The
first vertical derivatives of the Las Cruces and
Broken Hill data are dominated by much shorter-
wavelength anomalies than the Bouguer anomaly and
TMI data. Features in areas which are smooth in the TMI
data now contain recognisable anomalies (e.g. 1) and
details of the structure of an intrusive (2) and folded
stratigraphy (3) are easier to resolve. The first vertical
derivative of the Las Cruces gravity data shows a slightly
spotty appearance; this is noise caused by the poor defin-
ition of the short-wavelength component (shallow sources)
of the gravity signal due to the comparatively large distance
between stations. This is nearly always present in ground
gravity data. Note the northeast
3.7.4.2
Analytic signal
Combining the three directional gradients of the gravity or
magnetic field to obtain the total gradient, cf. Gradients
and curvature in
Section 2.7.4.4
, and
Eq. (2.5)
,
removes the
complexities of derivative responses. When applied to
potential
field data, the total gradient at a location (x, y)
is known as the analytic signal (AS) and given by:
s
∂
2
+
2
+
2
f
∂
f
∂
f
AS
ð
x
y
Þ¼
ð
3
:
23
Þ
,
∂
x
y
z
∂
∂
where f is either the gravity or the magnetic field. Where the
survey line spacing is significantly larger than the station
spacing,
the across-line Y-derivative is not accurately
de
ned. It is preferable then to assume that the geology is
two-dimensional and set the Y-derivative to zero.
The analytic signal has the form of a ridge located above
the vertical contact (
Figs. 3.25f
and
3.26c
), and is slightly
displaced laterally when the contact is dipping. The form of
the source prism is clearly visible in the transformed data-
sets; the crest of the ridge delineates the edge of the top
surface. The magnetic data from Broken Hill show distinct
peaks above the relatively narrow sources which de
ne the
northeast
southwest linear feature
traversing the southeast part of the image (1), which is
much less obvious in the original data.
A useful enhancement for gravity data (and also pseu-
dogravity data; see
Section 3.7.2.2
)
, is the total horizontal
gradient which peaks over vertical contacts (
Fig. 3.25e
), or
forms a ridge if the source is narrow. This enhancement
creates a circular ridge at the Las Cruces anomaly
(
Fig. 3.27e
), but since the edges of the source are not
vertical these do not correspond with the edges of the
deposit. The magnetic data from Broken Hill clearly
emphasise source edges (
Fig. 3.28h
)
.
-
-
southwest trending fold (
Fig. 3.28f
). Being based
on derivatives, the gravity data from Las Cruces are quite
noisy (
Fig. 3.27f
). Another example of the analytic signal of
TMI data is shown in
Fig. 4.25b
, in this case the response is
controlled by magnetism-destructive alteration which
greatly reduces the short-wavelength component of the
signal to which the analytic signal responds.
The analytic signal is effective for delineating geological
boundaries and resolving close-spaced bodies. Since the
magnetic analytic signal depends upon the strength and
not the direction of a body
3.7.4.1
Second-order derivatives
Second-order derivatives (see Gradients and curvature in
Section 2.7.4.4
)
can be an effective form of enhancement.
The zero values of the second vertical derivative coincide
with the edges of sources if their edges are vertical, but
more importantly, the response is localised to source edges
increasing their resolution.
Figures 3.25h
and
3.27h
show
the second vertical derivatives of the gravity model and the
Las Cruces gravity data respectively, with the equivalent
responses for the Broken Hill magnetic data shown in
Fig. 3.28e
.
The improved resolution is clearly seen in the
Broken Hill magnetic data, e.g. (4). However, second and
higher order derivatives are very susceptible to noise and
so are only useful on high quality datasets. As shown by the
'
is magnetism, it is particularly
useful for analysing data from equatorial regions, where
the TMI response provides limited spatial resolution, and
when the source carries strong remanent magnetisation
(MacLeod et al.,
1993
).
The gradient measurements are susceptible to noise
which can severely contaminate the computed analytic
signal. This is especially a problem with comparatively
sparsely sampled datasets. Higher-order total gradient sig-
nals calculated from higher-order gradients, such as the
second derivative, have also been proposed, e.g. Hsu et al.
(
1996
). Like the derivatives, the response becomes
narrower as the order increases, offering the advantage of
higher spatial resolution. However, higher-order gradients
amplify noise which leads to a noisier analytic signal.
'
'
appearance of the Las Cruces image, they are rarely
useful for ground gravity data unless the station spacing is
very small.
spotty
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