Page 121 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology - Chapter 5

peel prints, photomicrographs, and electron micrographs. In fact, any sort of two-
dimensional spatial representation is included.
Among the topics we will consider that have obvious applications to fields as
diverse as geophysics and microscopy is the probability of encountering an object
with a systematic search across an area. We will look at the statistics of directional
data in both two and three dimensions. Many natural phenomena are expressed
as complicated patterns of lines and areas that can best be described as fractals,
which we will touch upon. We will also look at ways of describing and comparing
more conventional shapes of individual objects, ranging in size from islands to oil
fields to microfossils.
Map relationships are almost always expressed in terms of points located on
the map. We are concerned with distances between points, the density of points,
and the values assigned to points. Most maps are estimates of continuous func-
tions based on observations made at discrete points. An obvious example is the
topographic map; although the contour lines are an expression of a continuous
and unbroken surface, the lines are calculated from measurements taken at trian-
gulation and survey control points. An even more obvious example is a structural
contour map. We do not know that the structural surface is continuous, because
we can observe it only at the locations where drill holes penetrate the surface.
Nevertheless, we believe that it is continuous and we estimate its form from the
measurements made at the wells, recognizing that our reconstruction is inaccurate
and lacking in detail because we have no data between wells.
When mapping the surface geology of a desert region, we can stand at one
locality where strike and dip have been measured and extend formation bound-
aries on our map with great assurance because we can see the contacts across the
countryside. In regions of heavy vegetation or deep weathering, however, we must
make do with scattered outcrops and poor exposures; the quality of the finished
map reflects to a great extent the density of control points. Geologists should be
intensely interested in the effects which control-point distributions have on maps,
but few studies of this influence have been published. In fact, almost all studies of
point distributions have been made by geographers. In this chapter, we will exam-
ine some of these procedures and consider their application to maps and also to
such problems as the distribution of mineral grains in thin sections.
Geologists exercise their artistic talents as well as their geologic skills when
they create contour maps. In some instances, the addition of geologic interpre-
tation to the raw data contained in the observation points is a valuable enhance-
ment of the map. Sometimes, however, geologic judgment becomes biased, and the
subtle effects of personal opinion detract rather than add to the utility of a map.
Computer contouring is totally consistent and provides a counterbalance to overly
interpretative traditional mapping. Of course, subjective judgment is necessary in
choosing an algorithm to perform mapping, but methods are available that allow
a choice to be made between competing algorithms, based upon specified criteria.
The principal motive behind the development of automatic contouring is economic,
an attempt to utilize the petroleum industry’s vast investment in stratigraphic data
banks. Aside from this, one of the prime benefits of computerized mapping tech-
niques may come from the attention they focus on the contouring process and the
problems they reveal about map reliability. Contour mapping is the subject of one
section in this chapter.
Trend-surface analysis is a popular numerical technique in geology. However,
although it is widely applied, it is frequently misused. Therefore, we will discuss

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