# Statistical Analysis of Grain Size for Unconsolidated Sediments

### 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 |

`method` |
statistical analysis method. Could be |

`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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
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)
``` |