Page 19 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology - Chapter 1

Statistics in Geology

All of the techniques of quantitative geology discussed in this book can be regarded
as statistical procedures, or perhaps “quasi-statistical’’ or “proto-statistical” proce-
dures. Some are sufficiently well developed to be used in rigorous tests of statis-
tical hypotheses. Other procedures are ad hoc; results from their application must
be judged on utilitarian rather than theoretical grounds. Unfortunately, there is
no adequate general theory about the nature of geological populations, although
geology can boast of some original contributions to the subject, such as the theory
of regionalized variables. However, like statistical tests, geomathematical tech-
niques are based on the premise that information about a phenomenon can be
deduced from an examination of a small sample collected from a vastly larger set
of potential observations on the phenomenon.
Consider subsurface structure mapping for petroleum exploration. Data are
derived from scattered boreholes that pierce successive stratigraphic horizons. The
elevation of the top of a horizon measured in one of these holes constitutes a single
observation. Obviously, an infinite number of measurements of the top of this
horizon could be made if we drilled unlimited numbers of holes. This cannot be
done; we are restricted to those holes which have actually been drilled, and perhaps
to a few additional test holes whose drilling we can authorize. From these data we
must deduce as best we can the configuration of the top of the horizon between
boreholes. The problem is analogous to statistical analysis; but unlike the classical
statistician, we cannot design the pattern of holes or control the manner in which
the data were obtained. However, we can use quantitative mapping techniques
that are either closely related to statistical procedures or rely on novel statistical
concepts. Even though traditional forms of statistical tests may be beyond our
grasp, the basic underlying concepts are the same.
In contrast, we might consider mine development and production. For years
mining geologists and engineers have carefully designed sampling schemes and
drilling plans and subjected their observations to statistical analyses. A veritable
blizzard of publications has been issued on mine sampling. Several elaborate statis-
tical distributions have been proposed to account for the variation in mine values,
providing a theoretical basis for formal statistical tests. When geologists can con-
trol the means of obtaining samples, they are quick to exploit the opportunity. The
success of mining geologists and engineers in the assessment of mineral deposits
testifies to the power of these methods.
Unfortunately, most geologists must collect their Observations where they can.
Logs of oil wells have been made at too great a cost to ignore merely because the
well locations do not fit into a predesigned sampling plan. Paleontologists must
be content with the fossils they can glean from the outcrop; those buried in the
subsurface are forever beyond their reach. Rock specimens can be collected from
the tops of batholiths in exposures along canyonwalls, but examples from the roots
of these same bodies are hopelessly deep in the Earth. The problem is seldom too
much data in one place. Rather, it is too little data elsewhere. Our observations of
the Earth are too precious to discard lightly. We must attempt to wring from them
what knowledge we can, recognizing the bias and imperfections of that knowledge.
Many publications on the design of statistical experiments and sampling plans
have appeared. Notable among these is the geological text by Griffiths (1967), which

6