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S= SIZE, SORTING
indicate:
- length of transport
-selective sorting
-mode of transport
-flow velocity, competence
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Grade Scales
Grade scales define limits to a range of grain sizes for a given class
(grade) of grain size.
They provide a basis for
a terminology that
describes grain size.
Sedimentologists use the Udden-Wentworth Grade Scale.
Sets most boundaries to
vary by a factor of 2.
e.g., ‘medium sand’ falls
between 0.25 and 0.5 mm.
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Sedimentologists often express grain size in units call Phi Units (φ;
the lower case Greek letter phi).
phi was originally defined as: )(log2 mmd −=φ
To make phi dimensionless it waslater defined as:
phi units assign whole numbers to the boundaries between size classes.
Od mmd )(log 2−=φ
Where d O = 1 mm.
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Detrital Sediments & Sedimentary Rocks
gravelgravel
& &
conglomerateconglomerate
sandsand& &
sandstonesandstone
clay, siltclay, silt
& &
mudstonemudstone
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Displaying Grain Size Data
i) Histograms
Readily shows the relative amount of sediment in each size class.
Each bar width equals
the class interval (0.5 φ
intervals in this case).
Bars extend from the
maximum size to theminimum size for each
size class.
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Note that when grain size is plotted as phi units grain size becomes
smaller towards the right.
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ii) Frequency Curves
A smooth curve that joins the midpoints of each bar on the histogram.
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iii) Cumulative Frequency Curves
A smooth curve that represents the size distribution of the sample.
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Sedimentologists commonly plot cumulative frequency curves on a
probability scale for the cumulative frequency.
On such plots normal, bell shaped distributions plot as a straight line.
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Describing Grain Size Distributions.Folk and Ward (1957) introduced the Graphic Method to estimate the
various statistical parameters describing a grain size distribution usingonly percentiles taken from cumulative frequency curves.
50 Md φ =Median
16 50 84
3 M
φ φ φ + +=Mean
6.64
5951684 φ φ φ φ σ
−+
−=Standard deviation
( ) ( )595
50595
1684
501684
22
22
φ φ φ φ φ
φ φ φ φ φ
−−++
−−+=Sk Skewness
2575
595
(44.2 φ φ
φ φ
−
−=K Kurtosis )
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Standard Deviation (σ; lower case Greek letter sigma)
Also referred to as the sorting coefficient or dispersion coefficient of asediment.
It is a measure of how much variation in grain size is present within a
sample.
68% of the total weight of
sediment in a sample falls within
+/- 1 standard deviation of the
mean.
The units of sorting are phi units.
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Sedimentologists use a specific terminology to describe the sorting
of a sediment:
Very well sorted 0 < σ
< 0.35φ
Well sorted 0.35 < σ
< 0.50φ
Moderately well sorted 0.5 < σ
< 0.71φ
Moderately sorted 0.71 < σ
< 1.00φ
Poorly sorted 1.00 < σ
< 2.00φ
Very poorly sorted 2.00 < σ
< 4.00φ
Extremely poorly sorted σ > 4.00φ
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Sorting - visual estimate
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Skewness (Sk)
A measure of the symmetry of the distribution.
Values range from –1.0 to +1.0.
Sk = 0
Perfectly symmetrical.
Md = M
Sk 0
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Sk > 0
The distribution has more fine particles than a symmetrical distribution
would have.
The distribution is said to be fine tailed .
M is finer than Md
Sk 0
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Sk < 0
The distribution has more coarse particles than a symmetrical
distribution would have.
The distribution is said to be coarse tailed .
M is coarser than Md
T i l Sk 0 3 t l fi k d
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Terminology: Sk > 0.3 strongly fine skewed
0.1 < Sk < 0.3 fine skewed
-0.1 < Sk < 0.1 near symmetrical
-0.3 < Sk < -0.1 coarse skewed
Sk < -0.3 strongly coarse skewed
K t i (K)
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Kurtosis (K)
A measure of the peakedness of the distribution (related to sorting).
K > 1 sharp peaked (Leptokurtic)
K = 1 normal (Mesokurtic)
K < 1 flat peaked (Platykurtic)
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I t t ti
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Sediment transport & sorting
Interpretation
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Interpretation
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Interpretation
Interpretation
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Interpretation
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Interpretation
Interpretation
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Interpretation
Interpretation
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Interpretation
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Interpretation
Interpretation
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Interpretation
I i
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Interpretation
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