Geophysical data acquisition, processing and interpretation - Geophysics for the Mineral Exploration Geoscientist - page 45

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Figure 2.26 Seismic data filtered to pass different frequency bands. Redrawn, with permission, from Juhlin and Palm ( 2003 ).

two filters. Consequently, the central sinusoidal section is
unaffected by the band-pass filter, but is attenuated by both
the high- and low-pass filters. The smooth broad section,
being of longer wavelength/low frequency, is unaffected by
the low-pass filter, but removed (attenuated) by the high-
pass filter. The same is true for the linear gradient, which
has a comparatively long wavelength (low frequency),
although the abrupt changes are smoothed out.
One-dimensional frequency filtering of seismic data is
shown in Fig. 2.26 where the distinct difference in fre-
quency between the signal and noise allows the latter to
be largely removed from the data. The signal, barely
visible in the un ltered data, contains higher frequencies
(90

application is to downhole logs, where the blocked appear-
ance helps identify lithological boundaries (Lanning and
Johnson, 1983 ) .

Smoothing
Smoothing is used to reduce the shorter-wavelength vari-
ations in a dataset. There are various forms of smoothing
filter (Hall, 2007 ), of which the low-pass frequency lter
(see Frequency/wavelength above) is one example. The
simplest smoothing filter involves applying a running aver-
age (mean) window of the data (see Convolution above).
Figure 2.25 shows how smoothing using a running-average
filter alters the rapidly varying parts of the input data, such
as the random variation, the spikes and the abrupt change
or step. Note how the spikes are reduced in amplitude and
broadened over a distance equal to the width of the filter
window. They cannot be completely removed with filters
based on window-averaging. There are also some subtle
changes to the smoothly varying areas, notably a
broadening and reduction in amplitude of the smooth
sinusoidal sections. For a filter to be effective in removing
a higher frequency component from a data series, the com-
ponent being removed must be properly de ned in the
original data series, i.e. the sampling interval needs to satisfy
the conditions of the sampling theorem for the higher
frequency component being removed ( Section 2.6.1 ) .
Another commonly used smoothing filter is the median
filter (Evans, 1982 ; Wessel, 1998 ). Instead of calculating a
mean value from the window, the median value of the
windowed data points is used. The median filter is most
commonly used to remove impulses or spikes (see Section

180 Hz) than the noise. Therefore, the signal can be
preserved and the noise attenuated with a band-pass filter,
even though the noise has much higher amplitude than the
signal. The results of low-pass filtering of magnetic data are
shown in Fig. 4.25d .

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Terracing/blocking
Terracing modi es the data so that its variations have a
more rectilinear form, i.e. more like a stepped function
(Cordell and McCafferty, 1989 ) . Using a topographic ana-
logy, a terrain comprising smooth hills and valleys is con-
verted to one of plains and plateaux with intervening cliffs.
The terracing operation is demonstrated in Fig. 2.25 . The
most obvious result of the filter is that the smoothly vary-
ing sections are converted to a step-like form.
Terracing of gridded data produces a result that is akin
to a geology map, in that homogenous regions are defined
with sharp boundaries between them. The other major