Geoscience Reference
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Fig. 9.14 Top part . Cubic interpolation splines with knots at data points fitted to irregularly
spaced data. (a) Use of same 12 data points as in Fig. 9.13 gives good result; (b) Deletion of three
points in the valleys still gives a fair interpolation spline although local minima at both sides of the
peak are not supported by original data set of 49 measurements; (c) deletion of two more points in
the valleys results in poor cubic interpolation spline. Bottom part : Indirect method of cubic spline-
fitting. (d) The six intervals along the x-axis between data points were made equal before
calculation of cubic interpolation spline; (e) non-decreasing cubic spline with small positive
value of smoothing factor (SF
0.0038) was fitted to interval as function of “levels”; (f) curves
of (d) and (e) were combined with one another and re-expressed as cubic spline function
which does not show the unrealistic fluctuations of the cubic interpolation spline of Fig. 9.14c
(Source: Agterberg 1990 , Fig. 3.10)
¼
9.2.3 Tojeira Sections Correlation Example
A great variety of methods are available for eliminating noise from geoscience data.
Several of these methods including (1) curve-fitting and 2-D or 3-D trend analysis
using polynomial or Fourier series, (2) geostatistical kriging, (3) signal-extraction
(from statistical theory of engineering), (4) inverse distance weighting, and (5) sim-
ple moving averaging, are applied in various case histories in this topic. Smoothing
splines used later in this chapter for estimation of the ages of stage boundaries in the
geologic time scale and in long-distance correlation between biostratigraphic sec-
tions in wells drilled in sedimentary basins. The following example is a case history
study of using smoothing splines between two land-based sections using microfos-
sil abundance data.
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