Geoscience Reference
In-Depth Information
2.7.1.3
Microlevelling
Small residual errors can be dealt with through a process
known as microlevelling. These algorithms operate on the
gridded data (see
Section 2.7.2
)
; a method based on
directional
a)
Cell
size
Grid nodes
Cell
size
filtering (see Trend in
Section 2.7.4.4
)is
residual errors remaining after the levelling process and
new errors introduced by the gridding process. The com-
puted corrections can be applied to the levelled line data to
produce
Data points
b)
line data.
The key aspect of microlevelling is that it is a cosmetic
process designed to make the data look good, i.e. to make it
look as it is expected to look! If not applied carefully,
these methods can remove signi
cant amounts of signal,
especially higher-frequency components, and may even
introduce unreal features. An example of microlevelled
magnetic data is shown in
Fig. 3.24d
.
'
microlevelled
'
Non-contributing
point
Weight/distance
Contributing
point
c)
Non-contributing
point
Contributing
point
Surface/function
2.7.2
Interpolation of data
Figure 2.14
Gridding a 2D dataset. (a) Data points in the vicinity of
the grid nodes are used to determine an interpolated value at each
node. (b) Node-to-station distance-based weighting. (c) A smooth
2D function is
Most data processing and data display methods require the
data points to be regularly distributed, i.e. to be equally
spaced. As noted in
Section 2.6.3.3
,
data are rarely acquired
in this way, so there is a need to interpolate the data into an
evenly spaced network. For example, a 1D unevenly spaced
dataset can be interpolated into an evenly spaced series of
measurements in terms of time or distance. The interpol-
ated data points are often called nodes. Similarly, an
uneven 2D distribution of data points, acquired either
randomly or along a series of approximately parallel survey
lines, is usually interpolated into a regular grid network.
Logically, the process is known as gridding (
Fig. 2.14a
)
and
the distance between the nodes is the cell size or grid
interval.
Gridding is a very common operation in geophysical
data processing, and there are various ways in which it
can be done. Normally, it is assumed that spatial variations
in geophysical parameters will be continuous. Somewhat
counter-intuitively, interpolation schemes whose results
honour the data points exactly do not usually produce
the best results. This is because the data contain both signal
and noise, so allowing the gridding algorithm to
t the data
to within some prescribed limit helps to reduce the influ-
ence of the noise component.
Interpolation is based on an analysis of a window of data
points in the vicinity of the node. The window is centred at
the node, and when gridding a 2D dataset its shape must
fitted to the data and the interpolated value computed
from that. In (b) and (c) the grey area represents the region that
in
uences the interpolated value.
be defined. Normally it is circular, but if the data exhibit a
well-developed trend direction the window may be elong-
ated parallel to that direction, since this will ensure the
trend is preserved in the interpolated data. The size of the
window needs to be large enough to enclose a representa-
tive sample of measurements, although if it is too large
potentially important short-wavelength variations will be
lost in the
of the data within it.
There are two main ways of establishing the value of the
parameter at a node: either statistically or using a simple
mathematical function. Both methods can be applied to
1D and 2D datasets; the process as applied to gridding is
shown in
Figs. 2.14b
and
c
.
A key concept in gridding is the
concept of minimum curvature. The human vision system
perceives smoothness if the
first and second derivatives of
the parameter being visualised are continuous. Put simply,
if the curvature (the gradient of the gradient) of a line or
surface varies gradually, it is perceived as smooth. The
spatial variation of the parameter being gridded can be
thought of as defining a
'
averaging
'
'
topographic
'
surface. To make
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