Page 51 - Petrology of Sedimentary Rocks

The following verbal limits are suggested: KG under 0.67, very platykurtic; 0.67-
0.90, platykurtic; 0.90-I. I I, mesokurtic; I. I I- I SO, leptokurtic; KG over I .50-3.00, very
leptokurt ic; KG over 3.00, extremely leptokurtic. The absolute mathematical limits of
the measure are from 0.41 to virtually infinity; few analyzed samples fall beyond the
range from 0.60 to 5.0, however.

The distribution of KG values in natural sediments is itself strongly skewed, since
most sediments are around .85 to 1.4, yet some values as high as 3 or 4 are not
uncommon. Thus for all graphic and statistical analysis (computation of mean or
standard deviation of kurtosis, running of t tests, etc.) the kurtosis distribution must be
normalized by using the transformation KG/(1 + KG). Using transformed kurtosis
(written KG) a normal curve has a value of .50, and most sediments fall between
.40-.65.

Characterization of Frequency Distribution

For characterization of the size frequency distributions of sediments, the limits
suggested above should be followed. For size terms use the grain-size triangle
(page 28). Here are some examples:

Fine sand, well-sorted, fine-skewed mesokurtic.

Sandy pebble gravel, moderately sorted, strongly fine skewed Ieptokurtic.

Granular medium sand, very poorly sorted, coarse-skewed very platykurtic.

Very fine sandy mud, very poorly sorted, near-symmetrical platykurtic.

These various statistical measures may be plotted against each other to see
how, for example, skewness values may be related to mean size (although geometrically
independent, in any given set of samples the two values may show some correlation).
They may be plotted on recent sediment maps and contoured to show the regional
variation of the measures, and provide a clue to identification of ancient environments.

Frequency distributions of other sets of data may be statistically analyzed in
exactly the same way as grain size. The measures of mean size, standard deviation,
skewness and kurtosis used here may be used for any type of data at all, in any field of
science. The verbal limits for skewness and kurtosis suggested here may also be used
for data in any other field, but the verbal limits on size and standard deviation are of
course inapplicable.

The Method of Moments

The second method of obtaining statistical parameters is called the method of
moments. It is a computational (not graphical) method of obtaining values, in which
every grain in the sediment affects the measure. Thus it probably gives a truer picture

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