Geoscience Reference
In-Depth Information
the method is not objective. By including a geological
interpretation a bias is introduced; if the interpretation is
erroneous there is less chance of adequately removing the
regional variation.
The most common analytical approach involves
tting a
polynomial function to the data using the method of least-
order, but the smoothness of the regional response means
that the curved surface is not complex and, therefore,
should be adequately defined by a low-order function.
Different types of polynomial and fitting methods have
also been proposed; see examples in Beltrão et al.(
1991
).
The method is equally applicable to 1D or 2D datasets.
Fitting a smooth surface to the entire dataset using least-
squares cannot achieve its goal unless the short-wavelength
variations are randomly distributed about the regional, i.e.
the short-wavelength features have a zero mean, which will
The curve approximating the regional is de
ected by the
local response. At best this produces an incorrect base level
for the residual, or worse, this de
ection will be broader
than the local anomaly, resulting in a residual whose amp-
litude is too small and which is
flanked by side-lobes of
tions to the problem have been suggested. These range
from only using data points perceived to be
a)
Nickel sulphides
+ mafic-ultramafic contact
+ base of greenstones
Nickel sulphides +
mafic-ultramafic contact
Nickel sulphides only
b)
Nickel sulphides
Mafic-ultramafic contact
Base of greenstones
c)
Nickel
sulphides
Mafics
Ultramafics
Figure 2.38
A model showing how the various components of the
geology contribute to the overall geophysical response; represented
with gravity data. A hypothetical massive nickel sulphide body
occurs at a mac
-
ultramac contact in a greenstone belt; see
geological section (c). (a) The different gravity responses of
the mineralisation with various component responses of the
surrounding geology included. (b) The three component gravity
responses producing the resultant measured response.
when
fitting the curve, through to an iterative approach where
residuals are analysed and used as a basis to modify subse-
quent fittings of the curve and so on. Another problem is
deciding the order of the polynomial. If it is too high there
is loss of detail in the residual, and if too low the regional
component severely distorts the residual. In
Fig. 2.39
the
straight
'
regional
'
line (linear) is correct, but
the second-order
shorter-wavelength variations. A smooth mathematical
function is used to describe the regional variation, a curve
for 1D data and a surface for 2D data, and the computed
curve/surface is subtracted from the observed data. Often
the regional variation over a small area can be adequately
represented by a straight line (1D) or a sloping plane (2D).
In its simplest form, the interpolation can be done by
manually estimating the form of the regional; the process is
given the rather grand name of graphical. The basic idea is
to extrapolate the field from areas of the data perceived to
be free of shorter-wavelength responses into the area con-
taining the local response of interest. The great advantage
of the graphical approach is that the effects of the known
geological features can be factored in, for example the
polynomial produces a regional
that
is too complex
(i.e. curved).
2.9.2.2
Wavelength filtering methods
Wavelength-based regional removal involves applying a
filter to the data to remove the long-wavelength variations
in order to reveal the shorter-wavelength residual response
(see Frequency/wavelength in
Section 2.7.4.4
)
. Fourier
transforms (see
Appendix 2
)
can be computed to identify
the spatial frequencies of the various responses in data.
Both the local and regional responses usually extend over a
range of frequencies/wavelengths and there is often over-
lap, so it is impossible to separate the two responses com-
pletely. The wavelength
filter in
Fig. 2.39
produces a
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