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G2Sd: a new R package for the statistical analysis of unconsolidated sediments

G2Sd : un nouveau package fonctionnant sous R permettant l'analyse statistique des sédiments non-consolidés
Jérôme Fournier, Régis K. Gallon and Raphaël Paris
p. 73-78

Abstracts

Modern depositional environment are mainly investigated in terms of internal sedimentary structures and associated grain-size characteristics. The latter are an intrinsic feature of sediments and hence essential for quantitative descriptions. It is therefore useful to have a tool available which allows direct and rapid calculation of numerous statistical parameters for a large number of samples. The G2Sd package gives full descriptive statistics and a physical description of sediments based on grain-size distributions derived from sieve analyses using a decadic log-transformation of the millimeter scale. Statistics are calculated either by using arithmetic and geometric methods of moments, or the graphic procedure of R.L. Folk and W.C. Ward (1957) to calculate mean grain-size, standard-deviation, skewness, and kurtosis based on the binary log-transformation of the mm scale. Numerical results are thus provided both in metric and phi units. The mode can be determined graphically by the user. Several percentiles and two common indices are calculated: D10, D50, D90, D90/D10, D90-D10, D75/D25, D75-D25, Trask Index (So) and Krumbein Index (Qd). A physical description of texture, sorting, skewness and kurtosis parameters is provided, based on the sediment nomenclature described in R.L. Folk (1966). The weight percentage of particles falling into each predefined size fraction is also included in the results. This package runs within the CRAN R-project.

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Editor's notes

Article soumis le 6 novembre 2013, accepté le 14 février 2014.

Full text

The authors wish to thank Prof. Eric Matzner-Løber from the Department of Statistics of the University of Rennes for encouraging us to create this package and Prof. Brian Ripley (R Core Group) from the Department of Statistics at the University of Oxford and Prof. Kurt Hornik (R Core Group) from the Statistics and Mathematics Unit at the Wirtschaftuniversität Wien for their assistance. We deeply thank Prof. Dr. B.W. Flemming (Senckenberg Institute, Wilhelmshaven) for improving the text of the manuscript.

Introduction

1Basic sedimentological investigations of modern depositional environments mainly focus on internal sedimentary structures and associated grain-size characteristics. Study of the latter requires the measurement of particle sizes and the frequency of their occurrence. As grain-size distributions are an intrinsic feature of sediments, they are an essential element of quantitative descriptions. Grain-size analysis provides information on the statistical distribution of size classes in a sediment sample (Folk, 1966). From such distributions, numerous statistical parameters and indices can be calculated. Fundamental aspects of grain-size analysis are, amongst others, treated in J.A. Udden (1914), C.K. Wentworth (1922), W.C. Krumbein (1934), D.L. Inman (1952), A. Cailleux and J. Tricart (1959), R.B. McCammon (1962), M.W. Davis and P.R. Ehrlich (1970), G.M. Friedman and J.E. Sanders (1978), M. Tucker (1988), D. Hartmann and B.W. Flemming (2007), D. Hartmann (2007), and G.J. Weltje and S. Roberson (2011).

2Particle size distributions evolve in the course of transport and deposition (e.g. A. Rivière, 1932; H.E. Reineck and I.B. Singh, 1980; H.G. Reading, 1996; J.A. Jiménez et al., 2003; J.P. Le Roux, 2005; E.J. Anthony and A. Héquette, 2007; J.P. Le Roux and E.M. Rojas, 2007; P. McLaren et al., 2007). Other important parameters are particle density and shape. Methods yielding grain-size measures include mechanical sieving (dry or wet), optical methods, settling procedures, centrifugation and decantation, X-ray analysis, and electro-optical methods such as, laser diffraction (Laboratoire Central des Ponts et Chaussées, 1988). As the results of these methods are not directly comparable, a decision needs to be made as to which method is the most appropriate for a specific purpose. It is also important to note that the analysis of samples composed of oddly shaped particles (e.g. flat bioclastic particles) will produce different results depending on the method used, for example laser diffraction versus sieving (Friedman, 1979; Bagnold and Barndorff-Nielsen, 1980; Flemming, 2007). The software package presented in this paper is restricted to the results of mechanical sieving using a sieve column of calibrated sieves stacked downward from coarser to finer mesh openings. Sieve stacks are mounted in a shaker which makes the whole sieve column vibrate for a specified time at a set frequency. If the sediment contains particles <0.063 mm, the so-called wet-sieving procedure is used by which water flows through the sieve stack. The sieving procedure sorts a sediment sample into size classes defined by the chosen mesh intervals of the sieve stack. The weight of sediment retained by each sieve is then expressed as a percentage of the total weight of the sample. The weight-percentages form the basis for constructing size frequency distributions of sediment samples.

3Grain-size analyses are widely applied for both industrial/technical applications requiring strict quality controls, a number of legally binding standards have been defined by state-controlled institutions for normation. The French institution for this purpose is the Association Française de Normalisation (AFNOR, 2000), in the United States it is the American Society for Testing and Materials (ASTM), in the United Kingdom it is the British Standards Institution (BSI), in Germany it is the Deutsches Institut für Normung (DIN) and for the world it is the International Standards Organisation (ISO). France and Germany use sieves stacks spaced according to the decadic logarithm of the mm scale as defined by AFNOR and DIN. The base two logarithm of the mm scale, also known as the phi scale, is the internationally most widely applied scale to represent grain-size distributions, especially in the United States, the United Kingdom, Brazil, Australia, South Africa and East Asian countries.

The G2Sd package

4The G2Sd package (Gallon and Fournier, 2013) is a counterpart to Gradistat v.4.0 macro for MS Excel, which has been developed by Blott and Pye (2001) for application of phi-related grain-size data. The G2Sd was developed for the R project for Statistical Computing (R development Core Team, 2011). This package is currently suited for the analysis of data obtained from metrically scaled sieves. The user is required to input the weight of sediment retained on sieves spaced at any metric intervals in a data frame. The data frame consists of at least two columns, the first column listing to the aperture sizes of sieves stacked according the decadic logarithm (e. g. AFNOR sieves; tab. 1). The range of apertures is expressed in microns (31500 to 40 µm; AFNOR, 2000). The last line, which corresponds to the material retained in the pan under the 40 µm sieve, is coded as a “0” in the data frame (see R.K. Gallon and J. Fournier, 2012). The second column (and any others) lists to the weight (in g) or the weight-percentage of the sediment retained by the sieves.

5Statistical parameters are calculated using an arithmetic (based on a normal distribution with metric size values) or geometric (based on a log-normal distribution with metric size values) method of moments, or the phi-transform (log-normal distribution based on phi values: phi(ϕ) = -log2 d, where d is the grain diameter in millimeters) of R.L. Folk and W.C. Ward (1957) : mean, standard-deviation, skewness, kurtosis (see tab. 2). The user can freely choose the statistical procedure best suited for his purpose. The equations used in the package can be found in R.K. Gallon and J. Fournier (2013). They have been adapted from R.L. Folk and W.C. Ward (1957) and W.C. Krumbein and F.J. Pettijohn (1938; see also S. Blott and K. Pye, 2001).

Tab. 1Size scale used in the G2Sd software package, as modified from S. Blott and K. Pye (2001) and adapted from J.A. Udden (1914), C.K. Wentworth (1922) and G.M. Friedman and J.E. Sanders (1978).
Tab. 1Echelle de diamètre des particules utilisée par le package G2Sd, modifiée de S. Blott et K. Pye (2001), adaptée de J.A. Udden (1914), C.K. Wentworth (1922) et G.M. Friedman et J.E. Sanders (1978).

Tab. 1 – Size scale used in the G2Sd software package, as modified from S. Blott and K. Pye (2001) and adapted from J.A. Udden (1914), C.K. Wentworth (1922) and G.M. Friedman and J.E. Sanders (1978). Tab. 1 – Echelle de diamètre des particules utilisée par le package G2Sd, modifiée de S. Blott et K. Pye (2001), adaptée de J.A. Udden (1914), C.K. Wentworth (1922) et G.M. Friedman et J.E. Sanders (1978).

AFNOR and phi lines are not strictly equivalent in this table. A precise conversion can be obtained using the formula: x(phi) = -log2[x(mm)].
Les correspondances entre les lignes AFNOR et phi ne sont pas strictement équivalentes dans cette table. La conversion correcte peut être obtenue en utilisant la formule : x(phi) = -log2[x(mm)].

Tab. 2Item 1: descriptive statistics in the G2Sd package (Gallon and Fournier, 2013).
Tab. 2Item 1 : statistiques descriptives fournies par le package G2Sd (Gallon et Fournier, 2013).

mean.arith

1829.18

sd.arith

1471.63

skewness.arith

1.62

kurtosis.arith

5.73

mean.geom

1315.43

sd.geom

2.35

skewness.geom

-0.54

kurtosis.geom

3.36

sediment

Very Coarse Sand, Poorly Sorted, Fine Skewed, Leptokurtic

mean.fw.mm

1.26

sd.fw.mm

2.35

skewness.fw.mm

-0.11

kurtosis.fw.mm

1.27

mean.fw.phi

-0.46

sd.fw.phi

1.23

skewness.fw.phi

0.11

kurtosis.fw.phi

1.27

6The determination of the modal grain size, i.e. the size class with the greatest frequency percentage, is optional (tab. 3). Because all samples are successively illustrated with a graph, the user can choose the graphic mode(s) (maximum of 4 modes) by clicking on the graph. If 4 modes are chosen, the following graph appears automatically (Gallon and Fournier, 2013; fig. 1). If 1, 2 or 3 modes are chosen, the user has to use the R function stop locator in the graphic window. This option was selected for several reasons. The user has to visually inspect every grain-size distribution. A strictly mathematical calculation of the mode can be problematical in a number of circumstances. For instance, when a sample of medium sand from a beach contains several large broken shell fragments. Such shell fragments can strongly distort a size distribution towards a coarser mean diameter because of their disproportionate large mass. It is then possible that the program selects the shell fragments as the first mode of this distribution. The user thus has the possibility to ignore this mode, which can be considered to represent an artefact.

Fig. 1Example of the graphic window of the G2Sd software package for the determination of the modal size class(es).
Fig. 1Illustration de la fenêtre graphique du package G2Sd pour la détermination du mode.

Fig. 1 – Example of the graphic window of the G2Sd software package for the determination of the modal size class(es). Fig. 1 – Illustration de la fenêtre graphique du package G2Sd pour la détermination du mode.

7The program also calculates a range of percentiles: D10, D50, D90, D90/D10, D90-D10, D75/D25, D75-D25. Among the numerous indices which can be found in the literature, we suggest the usage of (in this program version) the Trask Index (So) and the Krumbein Index (Qd). In addition, a physical description of the textural parameters, sorting, skewness and kurtosis parameters, based on the sediment nomenclature described in R.L. Folk (1966) is provided (see tab. 2 and tab. 4). Finally, the program also lists the weight-percentages of particles in each predefined size fraction (see tab. 5).

8There are four functions: granstat which provides all results organized in two ways: either in a complete matrix (by default) or by separate items; granplot which provides a histogram with a cumulative percentage curve commonly used by sedimentologists, grandistrib which provides a barplot of the different fractions composing the sediment; and granmap which provides a georeferenced map of the sediment distribution in an isotropic environment if the samples are spatially connected.

9It is possible to calculate several hundred samples at the same time. There are however some limitations to the use of this package. If the weight of sediment retained on the sieve with the largest mesh openings (uppermost sieve in the stack) exceeds 5 percent of the total sample mass, then the R.L. Folk and W.C. Ward statistics cannot be computed. Furthermore, the package is best adapted to the analysis of sediments in the range from 40 µm to 31.5 mm, but not beyond.

Tab. 3Item 2: modal size class(es) in the G2Sd package (Gallon and Fournier, 2013).
Tab. 3Item 2 : mode de la distribution fournie par le package G2Sd (Gallon et Fournier, 2013).

Nb Mode

2 Modes

2

1250

3

200

4

<NA>

5

<NA>

Tab. 4Item 3: percentiles and indices in the G2Sd package (Gallon and Fournier, 2013).
Tab. 4Item 3 : percentiles and index in G2Sd package (Gallon et Fournier, 2013).

D10(mm)

380.36

D50(mm)

1407.07

D90(mm)

3961.07

D90/D10

10.41

D90-D10

3580.71

D75/D25

2.65

D75-D25

1410.89

Trask (So)

1.63

krumbein (Qd)

0.7

Tab. 5Item 4: description of texture and weight-percentage of sediment retained in individual grain-size classes in the G2Sd package (Gallon and Fournier, 2013).
Tab. 5Item 4 : description de la texture et pourcentage des sédiments retenus dans chaque classes de taille fournies par le package G2Sd (Gallon et Fournier, 2013).

Texture

Sandy Gravel

boulder

0

gravel

31.2

sand

68.59

mud

0.2

boulder

0

vcgravel

0

cgravel

0

mgravel

0

fgravel

9.78

vfgravel

21.41

vcsand

36.57

csand

19.91

msand

6.32

fsand

5.5

vfsand

0.27

vcsilt

0.2

silt

0

Example

10In spite of the size limitations, the G2Sd package allows the analysis of a very wide range of sediments e.g. well-sorted sands from dunes (Regnauld et al., 1995), heterogeneous shell banks (Bonnot-Courtois et al., 2004), sediment from biogenic structures (Noernberg et al., 2010), nannoliths (Paris et al., 2010a), marine gravels (Paris et al., 2010b) and fine sediment. The results are organized into four items presented in tables 2 to 5.

11An example of the graphic provided by the G2Sd package is presented for a variety of sediments in figure 2.

Fig. 2Examples of G2Sd Graphics.
Fig. 2Exemples de graphiques fournis par G2Sd.

Fig. 2 – Examples of G2Sd Graphics. Fig. 2 – Exemples de graphiques fournis par G2Sd.

From left to right and from top to bottom: Gravelly sand, moderately sorted, from a Lanice conchilega tube (Callaway et al., 2010); slightly gravelly muddy sand, very poorly sorted, from a Sabellaria alveolata tube (Desroy et al., 2011); sand, well sorted, from a dune on Grande-Ile, Chausey archipelago; slightly gravelly sand, moderately sorted, from a subtidal channel, Chausey archipelago; sandy gravel, poorly sorted, from an intertidal shell bank, Chausey archipelago; muddy sand, very poorly sorted, from a muddy sand flat, Chausey archipelago (Godet et al., 2009).
De gauche à droite et de haut en bas : Sable graveleux modérément trié d'un tube élaboré par Lanice conchilega (Callaway et al., 2010); sable vaseux légèrement graveleux, très mal trié d'un tube construit par Sabellaria alveolata (Desroy et al., 2011); sable bien trié d'une dune de Grande-Ile, archipel de Chausey; sable légèrement graveleux, modérément trié d'un chenal subtidal, archipel de Chausey; gravier sableux, mal trié d'un banc coquillier intertidal, archipel de Chausey; sable vaseux, très mal trié d'une vasière intertidale, archipel de Chausey (Godet et al., 2009).

Conclusion

12The G2Sd software package is a useful tool for the analysis of a large variety of sediment. The package in particular addresses physical geographers, geomorphologists, geologists and sedimentologists, but also biologists, especially benthologists. For that reason, the output data frame provided in the results is compatible with contingency species data frames for ecological studies. Of course, the user is responsible for the interpretation of the results in the context of the aims of his research. The choice between the method of moments and the R.L. Folk and W.C. Ward statistics depends on the nature of the sediment and hence the shape of the distribution (Blott and Pye, 2001). It should be noted, however, that the R.L. Folk and W.C. Ward statistics are not sufficiently accurate to act as a substitute for geometric moment measures if these are available.

Access

13The package is freely available in the R project. The compressed file, pdf tutorial and code source of the G2Sd package can be downloaded from the CRAN R-project web site (URL: http://cran.r-project.org/​web/​packages/​G2Sd/​index.html).

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Annex

Version française abrégée

Les sédiments meubles sont principalement étudiés à travers leur analyse granulométrique. La distribution granulométrique constitue d’ailleurs une caractéristique intrinsèque essentielle pour toute description quantitative des sédiments. Pour cette raison, l’utilisation d’un outil permettant le calcul rapide d’un grand nombre de statistiques pour un grand nombre d’échantillons peut s’avérer utile. Le package G2Sd fournit un jeu complet des statistiques les plus souvent utilisées et une description du sédiment à partir de données acquises via une colonne de tamis AFNOR. Ce package fonctionne à partir du projet R développé par le CRAN et qui est de plus en plus utilisé de par le monde pour plusieurs raisons : sa gratuité, son inter-opérabilité (il fonctionne avec des plateformes différentes, UNIX, Windows ou encore MacOS), ses mises à jour régulières. G2Sd peut être considéré comme une évolution de la macro Gradistat pour Excel initialement développée par S. Blott and K. Pye (2001) qui permettait d’analyser préférentiellement des sédiments préalablement tamisés à partir de colonnes de tamis phi ou à l’aide d’un granulomètre laser. Ce package a été conçu pour produire des statistiques pour des sédiments d’un diamètre pouvant aller jusqu’à 31 500 µm. Le fichier d’entrée est de construction simple puisque la première colonne est composée des tailles d’ouverture des tamis en microns (de 40 à 31 500 µm ; les sédiments d’une taille inférieure à 40 µm sont pris en considération dans le calcul, l’ouverture du tamis sera alors codée en « 0 »).

Les statistiques sont calculées avec les méthodes des moments arithmétiques et géométriques et la méthode logarithmique de R.L. Folk and W.C. Ward (1957) : moyenne, écart-type, skewness (coefficient de dissymétrie), kurtosis (coefficient d’aplatissement). Les résultats numériques sont fournis en système métrique et en unités phi pour permettre aux utilisateurs de les publier dans des pays qui utilisent le système basé sur le logarithme de base 2 (Etats-Unis, Grande-Bretagne…). Le mode peut être déterminé graphiquement par l’utilisateur, option qui s’avère utile dans le cas d’un sédiment homogène qui contiendrait un gros fragment de coquille de bivalve par exemple. Il est dans ce cas possible de ne pas tenir compte de ce fragment coquillier dont on peut estimer qu’il n’appartient pas au sédiment. Le choix est laissé à l’utilisateur. Plusieurs centiles et deux indices encore communément utilisés sont calculés : D10, D50, D90, D90/D10, D90-D10, D75/D25, D75-D25, l’indice de Trask (So) et l’indice de Krumbein (Qd). Une description physique des paramètres de texture, de tri, de skewness et de kurtosis est proposée à partir de la nomenclature décrite par R. L. Folk (1966). Le pourcentage des différentes fractions des refus de tamis est aussi inclus dans les résultats.

G2Sd propose quatre fonctions. La fonction « granstat » fournit les statistiques de deux manières : une matrice complète ou par rubriques. La fonction « granplot » propose un histogramme avec une courbe de pourcentage cumulé. La fonction « grandistrib » fournit un diagramme en barre avec les différentes fractions qui composent les différents échantillons sédimentaires. Enfin, la fonction "granmap" permet de produire une carte géoréférencée simple de la distribution des sédiments pour peu que l’on fournisse un tableau avec les coordonnées des stations. G2Sd permet de calculer plusieurs centaines d’échantillons en même temps. Ce package est donc adapté pour la production de statistiques pour des sédiments fins à grossiers, jusqu’aux graviers mais pas au-delà. Cet outil peut être utilisé par des géographes, des géomorphologues, des géologues et des sédimentologues mais aussi par des biologistes, des benthologues notamment.

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List of illustrations

Title Tab. 1 – Size scale used in the G2Sd software package, as modified from S. Blott and K. Pye (2001) and adapted from J.A. Udden (1914), C.K. Wentworth (1922) and G.M. Friedman and J.E. Sanders (1978). Tab. 1Echelle de diamètre des particules utilisée par le package G2Sd, modifiée de S. Blott et K. Pye (2001), adaptée de J.A. Udden (1914), C.K. Wentworth (1922) et G.M. Friedman et J.E. Sanders (1978).
Caption AFNOR and phi lines are not strictly equivalent in this table. A precise conversion can be obtained using the formula: x(phi) = -log2[x(mm)].Les correspondances entre les lignes AFNOR et phi ne sont pas strictement équivalentes dans cette table. La conversion correcte peut être obtenue en utilisant la formule : x(phi) = -log2[x(mm)].
URL http://journals.openedition.org/geomorphologie/docannexe/image/10513/img-1.png
File image/png, 23k
Title Fig. 1 – Example of the graphic window of the G2Sd software package for the determination of the modal size class(es). Fig. 1Illustration de la fenêtre graphique du package G2Sd pour la détermination du mode.
URL http://journals.openedition.org/geomorphologie/docannexe/image/10513/img-2.png
File image/png, 28k
Title Fig. 2 – Examples of G2Sd Graphics. Fig. 2Exemples de graphiques fournis par G2Sd.
Caption From left to right and from top to bottom: Gravelly sand, moderately sorted, from a Lanice conchilega tube (Callaway et al., 2010); slightly gravelly muddy sand, very poorly sorted, from a Sabellaria alveolata tube (Desroy et al., 2011); sand, well sorted, from a dune on Grande-Ile, Chausey archipelago; slightly gravelly sand, moderately sorted, from a subtidal channel, Chausey archipelago; sandy gravel, poorly sorted, from an intertidal shell bank, Chausey archipelago; muddy sand, very poorly sorted, from a muddy sand flat, Chausey archipelago (Godet et al., 2009). De gauche à droite et de haut en bas : Sable graveleux modérément trié d'un tube élaboré par Lanice conchilega (Callaway et al., 2010); sable vaseux légèrement graveleux, très mal trié d'un tube construit par Sabellaria alveolata (Desroy et al., 2011); sable bien trié d'une dune de Grande-Ile, archipel de Chausey; sable légèrement graveleux, modérément trié d'un chenal subtidal, archipel de Chausey; gravier sableux, mal trié d'un banc coquillier intertidal, archipel de Chausey; sable vaseux, très mal trié d'une vasière intertidale, archipel de Chausey (Godet et al., 2009).
URL http://journals.openedition.org/geomorphologie/docannexe/image/10513/img-3.png
File image/png, 186k
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References

Bibliographical reference

Jérôme Fournier, Régis K. Gallon and Raphaël Paris, G2Sd: a new R package for the statistical analysis of unconsolidated sedimentsGéomorphologie : relief, processus, environnement, vol. 20 - n° 1 | 2014, 73-78.

Electronic reference

Jérôme Fournier, Régis K. Gallon and Raphaël Paris, G2Sd: a new R package for the statistical analysis of unconsolidated sedimentsGéomorphologie : relief, processus, environnement [Online], vol. 20 - n° 1 | 2014, Online since 01 January 2016, connection on 29 March 2024. URL: http://journals.openedition.org/geomorphologie/10513; DOI: https://doi.org/10.4000/geomorphologie.10513

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About the authors

Jérôme Fournier

CNRS, UMR 7208 BOREA – Muséum National d'Histoire Naturelle – 43 rue Cuvier, CP 26, 75231 Paris Cedex 05, France (fournier@mnhn.fr). Muséum National d'Histoire Naturelle – Station Marine de Dinard – 38 rue du Port Blanc, 35800 Dinard, France.

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Régis K. Gallon

Muséum National d'Histoire Naturelle – Station Marine de Dinard – 38 rue du Port Blanc, 35800 Dinard, France (gallon@mnhn.fr).

Raphaël Paris

Clermont Université – Université Blaise Pascal – BP 10448, F-63000 Clermont-Ferrand, France. CNRS, UMR 6524 Magmas et Volcans – F-63038 Clermont-Ferrand, France (r.paris@opgc.univ-bpclermont.fr).

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