Page 143 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology - Chapter 5

treated as though they occurred along a single, straight sampling line. This and
other methods for investigating the density of patterns of lines are reviewed by
Getis and Boots (1978). A computer program for computing nearest-neighbor dis-
tances, orientation, and other statistical measures of patterns of lines is given by
Clark and Wilson (1994).

Analysis of Directional Data

Directional data are an important category of geologic information. Bedding planes,
fault surfaces, and joints are all characterized by their attitudes, expressed as
strikes and dips. Glacial striations, sole marks, fossil shells, and water-laid peb-
bles may have preferred orientations. Aerial and satellite photographs may show
oriented linear patterns. These features can be measured and treated quantitatively
like measurements of other geologic properties, but it is necessary to use special
statistics that reflect the circular (or spherical) nature of directional data.
Following the practice of geographers, we can distinguish between directional
and oriented features. Suppose a car is traveling north along a highway; the car’s
motion has direction, while the highway itself has only a north-south orientation.
Strikes of outcrops and the traces of faults are examples of geologic observations
that are oriented, while drumlins and certain fossils such as high-spired gastropods
have clear directional characteristics.
We may also distinguish observations that are distributed on a circle, such
as paleocurrent measurements, and those that are distributed spherically, such as
measurements of metamorphic fabric. The former data are conventionally shown
as rose diagrams, a form of circular histogram, while the latter are plotted as
points on a projection of a hemisphere. Although geologists have plotted direc-
tional measurements in these forms for many years, they have not used formal
statistical techniques extensively to test the veracity of the conclusions they have
drawn from their diagrams. This is doubly unfortunate; not only are these statis-
tical tests useful, but the development of many of the procedures was originally
inspired by problems in the Earth sciences.
Figure 5-13 is a map of glacial striations measured in a small area of south-
ern Finland; the measurements are listed in Table 5-4 and contained in file FIN-
LAND.TXT. The directions indicated by the striations can be expressed by plotting
them as unit vectors or on a circle of unit radius as in Figure 5-14 a. If the circle is
subdivided into segments and the number of vectors within each segment counted,
the results can be expressed as the rose diagram, or circular histogram, shown as
Figure 5-14 b.
Nemec (1988) pointed out that many of the rose diagrams published by ge-
ologists violate the basic principal on which histograms are based and, as a con-
sequence, the diagrams are visually misleading. Recall that areas of columns in a
histogram are proportional to the number (or percentage) of observations occurring
in the corresponding intervals. For a rose diagram to correctly represent a circular
distribution, it must be constructed so that the areas of the wedges (or “petals”) of
the diagram are proportional to class frequencies. Unfortunately, most rose dia-
grams are drawn so that the radii of the wedges are proportional to frequency. The
resulting distortion may suggest the presence of a strong directional trend where
none exists (Fig. 5-15).

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