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kind of overrun which creates non-existent maxima,
minima or in ections: for example a high-amplitude posi-
tive anomaly surrounded by a negative
a)
Locations of
data points
. There are
various ways of reducing these artefacts. Unlike the cubic
spline, the Akima spline uses polynomials based on the
slopes of the data points local to the new interpolated
point, so it copes well with abrupt variations in the data.
An alternative strategy is to introduce tension into the
spline (Smith and Wessel, 1990 ) . This involves relaxing
the minimum curvature property, but has the advantage
of reducing overruns etc. The greater the tension, the less
overrun that occurs, but the less smooth is the overall
interpolation.
When the data are in the form of sub-parallel lines,
gridding is possible based on successive perpendicular 1D
interpolation, usually with splines. Firstly, interpolation is
done along the (approximately) parallel survey lines to
produce an equally spaced along-line distribution of
samples. The new samples are then used in a second inter-
polation perpendicular to the interpolated lines, to com-
pute new samples between adjacent lines. This is known as
bi-directional gridding ( Fig. 2.16 ). The physical analogy
would be bending a sheet of flexible material so it approxi-
mates the form of the variation in the data with a smooth
surface. Two-dimensional spline gridding is often used
when the data points are irregularly distributed along a
series of approximately parallel survey lines. It is not suit-
able for randomly distributed data, or line-based data
where the lines have random directions.
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Field
data
b)
Interpolated
data points (nodes)
1st 1D spline
Interpolated
data points (nodes)
2n d 1D spli ne
c)
Final grid
Figure 2.16 Bi-directional gridding of a dataset, comprising a series
of approximately parallel survey lines, using splines.
Comparing the final grid with the distribution of data
points is an effective way of determining whether features
of interest are properly represented, distorted or signifi-
cantly aliased. The distribution of the points will strongly
influence the gridded data, with most gridding-induced
artefacts occurring in areas where there are fewer data
points to control the gridding process. Ideally the gridding
algorithm should automatically not interpolate beyond
some speci ed distance, assigning
2.7.2.3 Interpolation parameters and artefacts
Setting the appropriate spacing between the interpolated
values, i.e. the grid cell size, when interpolating data is
fundamental in producing a grid that depicts the survey
data with a high degree of accuracy ( Fig. 2.14a ) . If the
chosen cell size is too small, instability may occur in the
algorithm resulting in artefacts (see below). On the other
hand, a very large cell size will result in the loss of useful
short-wavelength information and introduce spurious long
wavelengths because of spatial aliasing (see Section 2.6.1 ).
In practice, the uneven distribution of samples inevitably
leads to variable degrees of spatial aliasing within the inter-
polated dataset.
When the data are random or form a regular grid
network, the cell size is usually set at about half the nom-
inal distance between the data points. Calculating min-
imum or average spacing from the data is rarely useful
since the results may be affected by clusters, cf. Fig. 2.10c .
values to nodes
that the data do not adequately constrain. If this is not the
case then features that occur in gaps in the data, or near its
edges, should be viewed with suspicion. Furthermore, fea-
tures centred on a single data point, referred to as single-
point anomalies, must be considered highly unreliable. For
these reasons it is good practice to have a map of survey
station/point locations available when analysing the data
(cf. Fig. 3.18 ). This is also useful for recognising changes
in survey specifications, as inevitably occurs when datasets
have been merged to form a single compilation (see
Section 2.7.3 ) . This can cause changes in the wavelengths
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