Geophysical data acquisition, processing and interpretation - Geophysics for the Mineral Exploration Geoscientist - page 46

2.7.1.1 ) from a window of three consecutive data points in
1D, or a square window of nine neighbouring points in 2D.
The high-amplitude spikes become the

where P n is the window of n data points and p and r are
coef cients chosen by the user. When p ¼ 2 and r ¼ 0.5

'
when the windowed data are sorted according to their
values (to find the median) and, therefore, are never the
lter

' end-members ( 1/p), the central data value is the root-mean-square

(RMS) value of the window. In lower-amplitude regions
the central amplitude is increased, and vice versa;

¼

'
regions (all values the same) are unaffected. Care must be
taken when selecting the window size; if it is too small the
filtered output tends to alternate between

' at

'

s output. Unlike the mean filter, the median filter can
completely remove an isolated single-point spike; but
removal of wider

' ' -

and closely spaced spikes may
require several passes of the median filter (Hall, 2007 ),
which can lead to unwanted distortion of the signal. Spike
removal is a common pre-processing requirement, and
they can be removed with little effect on the other types
of variations in the input data, as demonstrated in
Fig. 2.25 .

spikes 1 and +1 creat-

ing data with a step-like form, and when it is too large it
may span several anomalous features, reducing its effect-
iveness. For data comprising a range of wavelengths the
best window size for scaling particular features is deter-
mined by trial and error. The effectiveness of this AGC
filter is reduced by long-wavelength variations in the data,
so high-pass frequency filtering prior to applying the AGC

filter is often desirable.
The equalising of amplitudes using wavelength-
dependent AGC is seen in the sinusoidal variations and
the smoothly varying gradient in Fig. 2.25 . Note how the
random variation and the spikes are largely unaffected by
the filter.

Amplitude scaling
When a data series exhibit a large amplitude range (as
commonly occurs with ratios, gradient data and also elec-
trical property data) or when low-amplitude signals are of
interest, it is sometimes helpful to rescale the data. The
basic idea is to amplify small-amplitude features and
attenuate large amplitudes based on the amplitude of the
values and/or the wavelength of a window of the data. To
some extent the problem can be addressed during its
display (see Section 2.8 ) , the simplest and often highly
effective way of amplitude scaling being to work with the
logarithm of the amplitude of the parameter P (Morris
et al., 2001 ) , which attenuates larger amplitudes more than
the lower ones. The square root of the value

Trend
Directional filters respond to the orientation of elongate
features and directional trends in the data and therefore are
only applicable to 2D data.
A common application for directional filtering is the
suppression of coherent noise from seismic data. Another
application is the removal of linear spatial features:
examples include responses from dykes that may conceal
features in the country rock, and the corrugations caused
by variable survey height in airborne geophysical datasets
(Minty, 1991 ) . Figure 2.27 illustrates directional filtering of
aeromagnetic data. The original dataset contains numerous
approximately parallel dykes. The linear anomalies associ-
ated with the west-northwest trending dykes are greatly
attenuated in the

p Þ

is a
highly effective scaling for magnetic derivatives (Mudge,
1991 ) and ratios; values less than 1 are amplified and those
larger are attenuated. Conversely, squaring the value (P 2 )
amplifies large values more than smaller values and is often
applied to low-count radiometric data (see Section 4.5.3 ) .
Amplitude scaling using automatic gain control (AGC)
is routinely applied to seismic data, and increasingly to
other kinds of geophysical data, especially magnetic data.
An AGC based on both amplitude and wavelength is
described by Rajagopalan and Milligan ( 1995 ) . This
involves averaging a window of data points and replacing
the centre value of the window (P central ) with the rescaled
value (P AGC ). Varying the window length changes the
wavelength dependency of the AGC. A commonly used
AGC filter is given by:

ð

filtered data.
Directional filters can also be used outside the spatial
domain. For example, seismic re ection data are not dis-
played as a conventional map with dimensional axes, e.g.
easting and northing, but as a group of time-series (traces)
plotted side by side in accordance with their relative
recording positions along a survey traverse (see Section
6.4.3.2 ) . Different types of seismic waves with different
frequencies and velocities cause responses with different
trends to appear across the data plotted in this form. Trend
filtering based on time frequency (f) in one direction and
spatial frequency (k) in the other (see Appendix 2 ) can be

" ! # r

X

n

1
n

P n

P AGC ¼ P central = ð 2 : 6 Þ

i ¼ 1