Page 44 - Petrology of Sedimentary Rocks

Graphic Presentation of Size Data

The data obtained from grain-size analysis may be plotted in many different ways.
For some purposes, one method is best; for other purposes, other methods are best. Get
familiar with all methods, so that you do not become so blindly used to using one
method that you ignore other ways which may be more suitable for a given problem.

All the methods use grain size as the abscissa (horizontal scale) and some measure
of percentage frequency as the ordinate (vertical scale). Grain size analyses may either
be plotted directly in millimeters, using a logarithmic-base paper; or they may be
plotted in phi units (o), in which case arithmeticbase paper is used. The latter is much
more convenient and accurate to read.

I. Histogram. A histogram is essentially a bar graph in which the percentages
for each grade size are plotted as a column. It is very easy to prepare and one can
easily interpret general features of the sediment. However, it is a pictorial method, no
more, and cannot be used for determination of any statistical parameters such as
median, sorting, etc. Furthermore its shape is greatly affected by the sieve interval
chosen; the same sample may look entirely different if it is analyzed on a different set
of screens and another histogram prepared. Nevertheless it proves of value in plotting
distribution of sediments on a map or stratigraphic section, as the heights of the
columns may be more easily compared by eye than if the data were plotted as
cumulative curves. For pictures, yes; otherwise, no.

2. Cumulative Curve, Arithmetic Ordinate. This is the most commonly used
method. As the abscissa, one may use either millimeters (in which case he must use
semi-log paper) or phi units (ordinary “squared” arithmetic paper). The ordinate is an
arithmetic scale running from 0 to 100%; grain size is plotted on the abscissa with
coarser particles to the left (this is customary in all size analysis plots). Cumulative
percentages of the sediment are plotted on this graph; for example, if 32% of the
material is coarser than 24 (caught on the 241 screen) then 32 is plotted as the ordinate
against 2.0 as abscissa. Draw a curve through all the resulting points. YOUR CURVE
MUST PASS THROUGH ALL THE PLOTTED POINTS -- NEVER USE A FRENCH
CURVE TO “SMOOTH” OUT THE GRAPH. The sample analysis normally forms an S-
shaped curve. The advantage of this curve is that all statistical parameters may be
read from it exactly, thus one can compare samples quantitatively as to median,
skewness, etc. The shape of the curve is independent of the sieves used. Its only
disadvantage is that it is difficult for the untrained eye to look at the curve and
interpret it at a glance; it is not “pictorial”. Also if the sieve interval is wide,
sketching the curve between data points is subject to considerable error.

3. Cumulative Curve, Probability Ordinate. Most sediments tend to approach
the “normal probability curve” in their size frequency distribution--in other words,
most of the particles are clustered about a given size, with less and less material on
each side of this size. If the cumulative curve of a sediment following the normal,
symmetrical probability distribution is plotted on probability paper, the result is a
perfectly straight line whose position depends on the average particle size and whose
slope depends on the sorting. This happens because the probability scale is very
condensed in the middle of the scale (30 to 70%) and very much expanded at the ends
(under IO or over YO%), thereby straightening out the S-shaped curve which would result
if arithmetic ordinates were used. Thus it is very valuable for studying the departure of
sediments from the normal probability law. Moreover, since the “tails” are straightened
out and the sample tends to plot as a straight line, it is possible to read the statistical
parameters with much greater accuracy because of the ease of interpolation and

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