Page 47 - Petrology of Sedimentary Rocks

Measures of Average Size

It is desirable to have a measure which will say, “sample A is so much coarser
than sample 6.” This is not nearly as easy as it looks, though, because there are many
different measures of average size. Using one measure, sample A might be “coarser”;
using another measure, sample B might be coarser. There is no consensus yet as to
which is best. Until then, become familiar with all of them.

Mode (MO) is the most frequently-occurring particle diameter. It is the diameter
corresponding to the steepest point (point of inflection) on the cumulative curve (only if
the curve has an arithmetic frequency scale). It corresponds to the highest point on the
frequency curve. Several formulae have been developed for determination of the mode,
but none of them are satisfactory. The only way the mode can be determined is by
successive trials. Using the graph of the sample plotted on probability paper, one
selects a point where the mode ought to be, and measures the percentage of the sample
that occurs within the diameter range from Y4$ coarser than that point to Y4$ finer than
that point (i.e., within Y2@ interval centered on the presumed modal point). Then he
moves over a small distance (say 0.1 or 0.2$) to a new presumed mode and measures the
percentage occurring in the Y2$ interval centered on that new point. This is done
repeatedly until the highest value is obtained which then corresponds to the modal
diameter. It is often difficult to fix the mode more accurately than 0.1 or 0.2$.
Sediments not uncommonly have two or more modes, located by finding other points of
inflection on the cumulative curve or other peaks on the frequency curve. Advantages:
the mode is quite valuable in sediment genesis and transport studies, especially when
two or more sources are contributing. The modal diameter often stays fairly constant
in an area while the other, more “synthetic” measures tend to vary more erratically. It
deserves more common use. The disadvantages are its lack of common usage, and in
the fact that it is difficult to determine. Also, it is independent of the grain size of the
rest of the sediment, therefore is not a good measure of overall average size.

Median (Md). Half of the particles by weight are coarser than the median, and
half are finer. It is the diameter corresponding to the 50% mark on the cumulative
curve and may be expressed either in @ or mm. (Md+ or Md,,). The advantage is that
it is by far the most commonly used measure and the easiest to determine. The
disadvantage is that it is not affected by the extremes of the curve, therefore does not
reflect the overall size of sediments (especially skewed ones) well. For bimodal
sediments it is almost worthless. Its use is not recommended.

Graphic Mean (MZ) (Folk). The best graphic measure for determining overall size
is the Graphic Mean, given by the formula MZ = ($ I6 + @SO + 4 84)/3. It corresponds
very closely to the mean as computed by the method of moments, yet is much easier to
find. It is much superior to the median because it is based on three points and gives a
better overall picture. This will be the standard measure of size used. lnman has used
(+I6 + $84)/2 as a measure of mean size but this is not satisfactory in skewed curves.

Measures of Uniformity

Several measures are available for measuring the uniformity or sorting of
sediments. As a general rule, the more of the curve that enters into the sorting
coefficient, the better the measure.

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