Geology Reference
In-Depth Information
Fig. 6.2.
Chart for visually estimating of sorting
(based on Pettijohn et al. 1973). The chart was developed for sandstones and
differs from the charts in Fig. 6.3 by the overrepresentation of larger grains. After Tucker (1981).
Average grain size
is the easiest parameter to deter-
mine but is sometimes a rather inaccurate value. The
average grain size depends on the grain sizes of the
material available and the amount of energy in the trans-
port medium. Average grain sizes are measured by
mode, median size or mean size distribution. The
mode
or modal diameter (Mo) describes the most frequently
occurring particle size in a population of grains. The
modal size diameter corresponds to the diameter rep-
resented by the steepest point (inflection point) on the
cumulative curve or the highest point on the frequency
curve. The
median size
(Md) is expressed by the mid-
point of the grain size distribution and corresponds to
the 50% percentile diameter on the cumulative curve.
The
mean size
(Mz) is determined by the arithmetic
average of all the particle sizes in a sample.
Beach sands, for example, tend to have negative skew-
ness, since fine particles have been removed by the per-
sistent wave action. River sands are often positively
skewed, since not much silt and clay is removed by the
currents.
The degree of the peakedness or sharpness of grain-
size curves is expressed by
kurtosis
values, which are
commonly calculated along with the other grain-size
parameters.
Commonly used formulas for calculating grain-size
parameters by graphic methods are shown in Tab. 6.1.
Grain-size statistical parameters can also be calculated
without reference to graphic plots by the mathematical
method of moments
. The parameters obtained by this
method are analogous to those of graphical statistics,
but because moment measures employ the entire fre-
quency distribution rather than a few selected percen-
tiles, the parameters are considered to be more repre-
sentative for the sample than the graphically derived
values. For overviews on the various grain-size para-
meters see Folk (1966) and Syvitski (1991).
Sorting
is a measure of the grain sizes present in a
grain population and describes the magnitude of the
spread or scatter of these sizes around the mean size.
Sorting of water-laid sediments is produced by currents,
waves and splashing. Sorting can be described with the
help of visual comparison charts (Figs. 6.2 and 6.3) or,
more precisely, by parameters which document the
number and the percentage of grain-size fractions within
a grain mixture. The φ
sorting standard deviation
and
skewness (Sk) values are determined graphically or by
calculation (Tab. 6.1). φ
skewness
describes the devia-
tion from a normal or lognormal grain size distribution
and the degree of asymmetry. Skewness reflects sort-
ing in the tails of a grain-size population. Positively
skewed populations have a tail of excess fine particles,
negatively skewed populations a tail of excess coarse
particles. Terms for sorting that correspond to various
values of standard deviations and skewness have been
proposed by Folk and Ward (1957) and Friedman
(1962); Fig. 6.5. Skewness is given an environment sen-
sitive significance by many authors (e.g. Friedman
1967; Folk and Robles 1964; Valia and Cameron 1977).
Table 6.1.
Formulas for calculating statistical parameters
for grain sizes by graphic methods
(Folk and Ward 1957).
The Greek letter φ (phi) for grain sizes indicates that the per-
centiles were measured using the phi and not the mm-scale.
φ
16
+ φ
50
+ φ
84
3
Inclusive graphic standard deviation
Graphic mean M
z
=
φ
84
- φ
16
φ
95
- φ
5
σ
i
=
+
4
6.6
Inclusive graphic skewness
(φ
84
+ φ
16
-
2
φ
50
)
(φ
95
+ φ
5
-
2
φ
50
)
SK
i
= +
2
(φ
84
- φ
16
)
2
(φ
95
- φ
5
)
(φ
95
- φ
5
)
K
G
=
Graphic kurtosis
2.44
(φ
75
- φ
25
)
