Page 87 - Statistics and Data Analysis in Geology

In this chapter we will consider ways of examining data that are characterized
by their position along a single line. That is, they form a sequence, and the posi-
tion at which a data point occurs within the sequence is important. Data sets of
this type are common in geology, and include measured successions of lithologies,
geochemical or mineralogical assays along traverses or drill holes, electric logs of
oil wells, and chart recordings from instruments. Also in this general category are
measurements separated by the flow of time, such as a sequence of water quality
determinations at a river station, or the production history of a flowing gas well.
Techniques for examining data having a single positional characteristic tradition-
ally are considered part of the field of time-series analysis, although we will take the
broader view that time and space relationships can be considered interchangeably.

Geologic Measurements in Sequences

Before proceeding to some geological examples and appropriate methods of ex-
amination, we must consider the nature of different types of sequences apt to be
encountered by geologists. At one extreme, we may have a record which is quite
precise, both in the variable which is measured and in the scale along which suc-
cessive observations are located. Examples might include an electrical resistivity
log from a borehole, or the production history of a commercial well. In the for-
mer, the variable is a measured attribute expressed in ohms (R) and the scale is
measured in feet. In the latter example, the variable again is a measured attribute,
barrels (bbl) of oil, and the scale is measured in days, months, or years. There are
two important characteristics in either record. First, the variable being measured
is expressed in units of an interval or ratio scale; 1000 bbl of oil is twice as large
a quantity as 500 bbl, and a measurement of 10 R is ten times the resistance of
1 SZ. Second, the scales along which the data points are located also are expressed