Page 91 - Statistics and Data Analysis in Geology

Analysis of Sequences of Data

circumstances such as stratigraphic correlation, equivalent thicknesses may not
represent equivalent temporal intervals and the problem of cross comparison is
much more complex.
As we emphasized in Chapter 1, the computer is a powerful tool for the anal-
ysis of complex problems. However, it is mindless and will accept unreasonable
data and return nonsense answers without a qualm. A bundle of programs for ana-
lyzing sequences of data can readily be obtained from many sources. If you utilize
these as a “black box” without understanding their operation and limitations, you
may be led badly astray. It is our hope in this chapter that the discussions and
examples will indicate the areas of appropriate application for each method, and
that the programs you use are sufficiently straightforward so that their operation
is clear. However, in the final analysis, the researcher must be his own guide. When
confronted with a problem involving data along a sequence, you may ask yourself
the following questions to aid in planning your research
(a) What question(s) do I want to answer?
(b) What is the nature of my observations?
(c) What is the nature of the sequence in which the observations occur?
You may quickly discover that the answer to the first question requires that the
second and third be answered in specific ways. Therefore, you avoid unnecessary
work if these points are carefully thought out before your investigation begins.
Otherwise, the manner in which you gather your data may predetermine the tech-
niques that can be used for interpretation, and may seriously limit the scope of
your investigation.

Interpolation Procedures
Many of the following techniques require data that are equally spaced; the obser-
vations must be taken at regular intervals on a traverse or line, or equally spaced
through time. Of course, this often is not possible when dealing with natural phe-
nomena over which you have little control. Many stratigraphic measurements, for
example, are recorded bed-by-bed rather than foot-by-foot. This also may be true
of analytical data from drill holes, or from samples collected on traverses across
regions which are incompletely exposed. We must, therefore, estimate the variable
under consideration at regularly spaced points from its values at irregular inter-
vals. Estimation of regularly spaced points will also be considered in Chapter 5,
when we discuss contouring of map data. Most contouring programs operate by
creating a regular grid of control points estimated from irregularly spaced observa-
tions. The appearance and fidelity of the finished map is governed to a large extent
by the fineness of the grid system and the algorithm used to estimate values at the
grid intersections. We are now considering a one-dimensional analogy of this same
problem.
The data in Table 4-2 consist of analyses of the magnesium concentration in
stream samples collected along a river. Because of the problems of accessibility,
the samples were collected at irregular intervals up the winding stream channel.
Sample localities were carefully noted on aerial photographs, and later the distances
between samples were measured.
Although there are many methods whereby regularly spaced data might be
estimated from these data, we will consider only two in detail. The first and most
obvious technique consists of simple linear interpolation between data points to

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