Statistical Analysis of Grain Size for Unconsolidated Sediments

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Description

Calculates mean, median, sorting, skewness, kurtosis, fifth and sixth moments, and creates the verbal classification of the results. Uses the statistical methods of Trask (1930), Otto (1939), Folk & Ward (1957), McCammon(a) (1962), McCammon(b) (1962) and Method of Moments (TANNER, 1995)
Data input can be in logarithmic (phi) or geometric (micrometers) scale. Regardless the input data, the user can choose the output result scale through output argument

Usage

1
gran.stats(data, output = "phi", method = "folk", verbal = FALSE, lang = "en-US")

Arguments

data

a data matrix with grain size samples

output

output result scale. Could be output="phi" for logarithmic scale or output="metric" for geometric scale. The default is "phi"

method

statistical analysis method. Could be method="folk" , method="moment" , method="otto" , method="trask" , method="mcA" and method="mcB". Default is method="folk"

verbal

logical. If TRUE, columns will be added with verbal classification of statistical paramenters. Default is TRUE

lang

language . Could be english ("en-US", "en-GR", "eng", "e"), or portuguese ("pt-BR", "pt-PT", "port", "p"). The default is "en-US"

Details

The particle size matrix used in data entry must contain the first line of grain size classes (logarithmic or geometric scale), each following line should contain the weights of a sample. No header should be used

Example of particle size matrix with classes in logarithmic scale (phi units). Note that the columns names (V2, V3, V4, V5, ...) are automatically created by the R when any headerless dataset is imported.

row names V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13
Samples -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
A 0.0 0.0 0.0 0.02 0.07 0.10 0.18 0.27 0.58 5.08 11.18 1.29
B 0.0 0.0 0.0 0.00 0.00 0.00 0.00 0.05 0.59 12.98 26.60 2.90

Example of particle size matrix with classes in geometric scale (micrometers). Note that the columns names (V2, V3, V4, V5, ...) are automatically created by the R when any headerless dataset is imported.

row names V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13
Samples 2828 2000 1414 1000 707 500 354 250 177 125 88 63
A 0.0 0.0 0.0 0.02 0.07 0.10 0.18 0.27 0.58 5.08 11.18 1.29
B 0.0 0.0 0.0 0.00 0.00 0.00 0.00 0.05 0.59 12.98 26.60 2.90

The grain size scale adopted in this package is those used by Udden (1914) and Wentworth (1922).

phi micrometers Verbal Classification
< -8 >256000 Boulder
-8 to -6 64000 to 256000 Cobble
-6 to -2 4000 to 64000 Pebble
-2 to -1 2000 to 4000 Granules
-1 to 0 1000 to 2000 Very coarse sand
0 to 1 500 to 1000 Coarse sand
1 to 2 250 to 500 Medium sand
2 to 3 125 to 250 Fine sand
3 to 4 63 to 125 Very fine sand
4 to 5 31 to 63 Coarse silt
5 to 6 16 to 31 Medium silt
6 to 7 8 to 16 Fine silt
7 to 8 4 to 8 Very fine silt
> 8 < 4 Clay

If method = "moment" the sorting, skewness and kurtosis is calculated by the method of moments as described by Tanner (1995) and the descriptive terminology is given according to the output scale chosen by the user (geometric or logarithmic), as described bellow.

Sorting (Geometric) Sorting (Logarithmic)
Very well sorted < 1.27 Very well sorted < 0.35
Well sorted 1.27 to 1.41 Well sorted 0.35 to 0.50
Moderately well sorted 1.41 to 1.62 Moderately well sorted 0.50 to 0.70
Moderately sorted 1.62 to 2.00 Moderately sorted 0.70 to 1.00
Poorly sorted 2.00 to 4.00 Poorly sorted 1.00 to 2.00
Very poorly sorted 4.00 to 16.00 Very poorly sorted 2.00 to 4.00
Extremely poorly sorted > 16.00 Extremely poorly sorted > 4.00
Skewness (Geometric) Skewness (Logarithmic)
Very positive < -1.30 Very positive > 1.30
Positive -1.30 to -0.43 Positive 0.43 to 1.30
Approximately symmetrical -0.43 to 0.43 Approximately symmetrical -0.43 to 0.43
Negative 0.43 to 1.30 Negative -0.43 to - 1.30
Very negative > 1.30 Very negative < -1.30
Kurtosis (Geometric) Kurtosis (Logarithmic)
Very platykurtic < 1.70 Very platykurtic < 1.70
Platykurtic 1.70 to 2.55 Platykurtic 1.70 to 2.55
Mesokurtic 2.55 to 3.70 Mesokurtic 2.55 to 3.70
Leptokurtic 3.70 to 7.40 Leptokurtic 3.70 to 7.40
Very leptokurtic > 7.40 Very leptokurtic > 7.40

If method = "folk", "otto", "trask", "mcA" or "mcB" the sorting, skewness and kurtosis is calculated as described by Folk & Ward (1957), Otto (1939), Trask (1930) or McCammon (1962), respectively. The descriptive terminology is given according to the output scale chosen by the user (geometric or logarithmic), as described bellow.

Sorting (Geometric) Sorting (Logarithmic)
Very well sorted < 1.27 Very well sorted < 0.35
Well sorted 1.27 to 1.41 Well sorted 0.35 to 0.50
Moderately well sorted 1.41 to 1.62 Moderately well sorted 0.50 to 0.70
Moderately sorted 1.62 to 2.00 Moderately sorted 0.70 to 1.00
Poorly sorted 2.00 to 4.00 Poorly sorted 1.00 to 2.00
Very poorly sorted 4.00 to 16.00 Very poorly sorted 2.00 to 4.00
Extremely poorly sorted > 16.00 Extremely poorly sorted > 4.00
Skewness (Geometric) Skewness (Logarithmic)
Very positive -0.3 to -1.0 Very positive 0.3 to 1.0
Positive -0.1 to -0.3 Positive 0.1 to 0.3
Approximately symmetrical -0.1 to 0.1 Approximately symmetrical 0.1 to -0.1
Negative 0.1 to 0.3 Negative -0.1 to -0.3
Very negative 0.3 to 1.0 Very negative -0.3 to -1.0
Kurtosis (Geometric) Kurtosis (Logarithmic)
Very platykurtic < 0.67 Very platykurtic < 0.67
Platykurtic 0.67 to 0.90 Platykurtic 0.67 to 0.90
Mesokurtic 0.90 to 1.11 Mesokurtic 0.90 to 1.11
Leptokurtic 1.11 to 1.50 Leptokurtic 1.11 to 1.50
Very leptokurtic 1.50 to 3.00 Very leptokurtic 1.50 to 3.00
Extremely leptokurtic > 3.00 Extremely leptokurtic > 3.00

gran.stats automatically detects which scale of grain size is being used and converts the results according to the output argument
For further details on the structure of the input table see data examples camargo2001, sed.phi and sed.metric included in this package

Value

An array of variable number of dimensions, depending on the chosen arguments, with the statistical parameters for each sample. The values of this matrix should be used in rysgran.plot function, available in this package

Author(s)

Eliandro R. Gilbert (eliandrogilbert@gmail.com)
Mauricio G. Camargo (camargo.ufpr@gmail.com)

References

- Folk, R. L. and Ward W. C. (1957) Brazos river bar: A study in the significance of grain size parameters. Journal of Sed. Petrol., 27: 3–27.

- McCammon, R. B. (1962) Efficiencies of percentile measurements for describing the mean size and sorting of sedimentary particles. Journal of Geology, 70: 453–465.

- Otto, G. H. (1939) A modified logarithmic probability paper for the interpretation of mechanical analysis of sediments. Journal os Sed. Petrol., 9: 62–76.

- Tanner, W.F. (1995) Environmental clastic granulometry. Florida Geological Survey, Special Publication 40. 142 pp.

- Trask, P. D. (1930) Mechanical analysis of sediments by centrifuge. Economic Geology, 25: 581–599.

- Udden J. A. (1914) Mechanical composition of clastic sediments. Bulletin of the Geological Society of America, 25: 655–744.

- Wentworth, C. K. (1922) A scale of grade and class terms for clastic sediments. Journal of Geology, 30: 377–392.

See Also

rysgran.plot , rysgran.ternary , rysgran.hist , class.percent

Examples

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library (rysgran)
data (camargo2001)
data (sed.metric)

#Folk & Ward

gran.stats(camargo2001, output="phi", method = "folk" , verbal = FALSE)


#Folk & Ward with verbal classification

gran.stats (camargo2001, output="phi", method = "folk" , verbal = TRUE)


#Folk & Ward with geometric data and verbal classification

gran.stats (sed.metric, output="phi", method = "folk" , verbal = TRUE)


#Method of Moments with geometric data and verbal classification

gran.stats (sed.metric, output="phi", method = "moment" , verbal = TRUE)