Page 116 - Statistics and Data Analysis in Geology

Statistics and Data Analysis in Geology - Chapter 4

Both of these values lie within the critical region, and we would reject the hypothesis
that they contain the number of runs expected in random sequences.
Geologic applications of this test may not be obvious, because we ordinarily
must consider more than two states in a succession. Stratigraphic sections or tra-
verses across thin sections, for example, usually include at least three states and
these cannot be ranked in a meaningful way. We will consider ways that certain se-
quences can be reduced to dichotomous states, but first we will examine a geologic
application of the runs test to a traverse through a two-state system.
Simple pegmatites originate by crystallization of the last, volatile-laden sub-
stances squeezed off from solidifying granitic magma. Their textures result from
simultaneous crystallization of quartz and feldspar at the eutectic point. If the
solidifying pegmatite is undisturbed, we might suppose that quartz and feldspar
begin to appear at random locations within the cooling body. This situation may
persist, with grains crystallizing at random, until the entire mass is solid. However,
the presence of one crystal, perhaps feldspar, might stimulate the local crystalliza-
tion of additional crystals of feldspar, eventually producing a patchwork texture.
Alternatively, growth of a crystal of one state might locally deplete the magma of
that constituent, retarding crystallization and resulting in a highly alternating mo-
saic of quartz and feldspar. A large slab of polished pegmatite used as a window
ledge in the washroom of a geology building provides a way for students to investi-
gate these alternative possibilities. The polished surface allows easy discrimination
of adjacent grains, so a line drawn on the ledge produces a sequence through the
quartz and feldspar grains in the pegmatite. The line on the polished slab may
be regarded as a random sample of possible successions through the pegmatite
body from which the slab was quarried. The quartz-feldspar sequence along the
line is listed in Table 4-6. Our problem is to determine if the alternations between
quartz and feldspar form a random pattern; if there is a systematic tendency for
one state to succeed itself; or whether there is a tendency for one state to imme-
diately succeed the other. Perform a runs test on this data and evaluate the three
possibilities.

Table 4-6. Sequence of 100 feldspar (F) and quartz (Q) grains encountered
along traverse through pegmatite.

(Start) F QQF QQFF QF QFFFFFFFQQFQFFF
QFF FFQFFF QQF QFQQQFFFFFQFF

FFF QQQQFFQQQFFFFFF QF QFFFF
FQF QF QFF QFFFFF QFFF QQF QF F Q (End)

We will now consider a related statistical procedure for examining what are called
runs up and runs down. We are concerned, not with two distinct states, but whether
an observation exceeds or is smaller than the preceding observation. Figure 4-13
shows a typical sequence that can be analyzed by means of a runs test.
The segment abc is a run up, because each observation is larger than the pre-
ceding one; similarly, the segment ghi is a run down. Segment cdef is a run down
even though the difference between d and e is zero. This is because the interval
de lies between segments cd and ef, both of which run downward; therefore, the

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