Page 89 - Statistics and Data Analysis in Geology

Analysis of Sequences of Data

Table 4-1. Techniques discussed in this chapter classified by the nature of the
variable and its spacing along a line. Locations are explicit if X is specified for
every Y; locations are implicit if X is implied by the order of observations.
Explicit Location Implicit Location
Nature of Variables in Time or Space in Time or Space
Interval or Ratio Data Interpolation Zonation
Regression Seriation
Splines Autocorrelation
Cross-correlation
Semivariograms
Periodograms
Spectral Density
Nominal or Ordinal Data Series of Events Markov Chains
Runs Tests

this category does not consider the spacing at all, and only the sequence of the
observations is important.
The techniques also may be classified on the type of observations they require.
Some necessitate interval or ratio Observations; the variate must be measured on
a scale and expressed in real numbers. Other methods accept nominal or ordinal
data, and observations need only to be categorized in some fashion. In the methods
discussed in this chapter, the classes are not ranked; that is, state A is not “greater”
or “larger” in some sense than states B or C. Nominal data may be represented by
integers, alphabetic characters, or symbols.
In the remainder of this chapter, we are going to examine the mathematical
techniques required to analyze data in sequences. The methods described here
do not exhaust the possibilities by any means. Rather, these are a collection of
operations that have proved valuable in quantitative problem-solving in the Earth
sciences, or that seem especially promising. Other methods may be more appropri-
ate or powerful in specific situations or for certain data sets. However, a familiarity
with the techniques discussed here will provide an introduction to a diverse field of
analytical tools. Unfortunately, many of these methods were developed in scientific
specialties alien to most geologists, and the description of an application in radar
engineering, stock market analysis, speech therapy, or cell biology may be difficult
to relate to a geologic problem. Some of the methods involve nonparametric statis-
tics, and these are not widely considered in introductory statistics courses. Because
of the general unfamiliarity of most Earth scientists with developments in the nu-
merical analysis of data sequences, we have thought it best to present a potpourri
of techniques and approaches. As you can see from Table 4.1, these cover a variety
of sequences of different types, and are designed to answer different kinds of ques-
tions. None of the techniques can be considered exhaustively in this short space,
but from the examples and applications presented, one or another may suggest
themselves to the geologist with a problem to solve. The list of Selected Readings
can then provide a discussion of a specific subject in more detail.
These methods provide answers to the following broad categories of questions:
Are the observations random, or do they contain evidence of a trend or pattern? If a
trend exists, what is its form? Can cycles or repetitions be detected and measured?

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