On Sorting, Sorting Coefficients, and the Lognormality of the Grain-Size Distribution of Sandstones

Abstract

The coefficient of sorting in sedimentary petrography is commonly considered to be the statistical measure introduced by Trask. Several investigators have objected to the use of the Trask coefficient on theoretical grounds. Others have continued to uphold its usefulness. Two new sorting coefficients have been introduced within recent years (Inman's and Folk and Ward's sorting measures), based on the geometry of the normal curve. On theoretical grounds these measures should more adequately describe the sorting characteristics of sediments than does the coefficient of Trask. However, some practical considerations argue against the use of these new sorting parameters for many types of sediments. Empirical correlations have been made in this study between the three sorting measures (Trask's, Inman's, and Folk and Ward's) and the standard deviation. The standard deviation is a moment measure which represents the most suiTable statistic for describing the sorting characteristics of sedimentary rocks. The empirical correlations permit an appraisal of the advantages and disadvantages of each sorting parameter which has not been possible in the past. Correlation diagrams show that both the Trask coefficient and the Inman sorting measure approximate the standard deviation and that a high correlation exists between the standard deviation and the sorting measure of Folk and Ward. The Inman measure is more satisfactory for describing the sorting of moderate to poorly sorted sandstones. The Trask coefficient is more satisfactory for describing very well to well-sorted sandstones. The Folk and Ward sorting measure appears to be satisfactory for the entire range of sorting characteristics. A new genetic classification of sorting based on the standard deviation and on environmental significance is recommended. The standard deviation ranges for sands from different environments are tabulated. Three figures in this paper demonstrate how the standard deviation of the sediment distribution compares with the sorting coefficients of Trask, Inman, and Folk and Ward. Trask sorting values corresponding to the class intervals of the recommended standard deviation classification serve as a new sorting classification for studies where grain size is expressed in millimeters. A new genetic classification of sorting based on the standard deviation and on environmental significance is recommended. The standard deviation ranges for sands from different environments are tabulated. Three figures in this paper demonstrate how the standard deviation of the sediment distribution compares with the sorting coefficients of Trask, Inman, and Folk and Ward. Trask sorting values corresponding to the class intervals of the recommended standard deviation classification serve as a new sorting classification for studies where grain size is expressed in millimeters. To determine the extent of deviation from lognormality of the grain-size distribution of sandstones, a more sensitive method than the straight-line probability plot has been employed. A normal curve can be defined as a frequency distribution which has a skewness (third moment) of 0 and a kurtosis (fourth moment) of 3. A study of 612 ancient and modern sand samples indicates that the grain-size distribution of most sands and sandstones does not follow a lognormal function. Omitting the sign for skewness, the mean for skewness for the samples studied is 0.76 and the mean for kurtosis is 5.31. These data indicate that the grain-size distribution curve of the average sand is skewed and considerably more peaked than that of the normal curve. There is a tendency for deviation from lognormality as the sands are being deposited. River and dune sands are for the most part positively skewed, whereas beach sands are generally negatively skewed. Deviation from lognormality of the grain-size distribution of sands is an environment-sensitive parameter. The standard deviation (sorting index) of a sand is another significant environment-sensitive textural attribute. plot of deviation from lognormality as expressed by the skewness (third moment) against the sorting index (standard deviation) for medium-to fine-and very fine-grained sands serves to distinguish beach sands from river sands.