Grain-size analyses of sediments and sedimentary rocks have been made for many purposes. During the last 10 to 15 years, grain-size analyses have been made of sands and sandstones as a means of determining their depositional environments. Most of the published work on discrimination of depositional environments has been based on modern sands which contain little fine material. The results of this work generally cannot be applied to sandstones because of the presence of considerable amounts of diagenetic silt- and clay-sized material that often is present in sandstones. In the present study, sandstones were used rather than sands.

A problem that always occurs when using grain-size analyses, regardless of whether they are of sands or sandstones, is that of comparing the size distributions. Canonical analysis is a statistical method of comparing grain-size distributions. The primary aim of canonical analysis is to determine numerical characteristics that best separate size distributions or determine the characteristics they have in common. In using canonical analysis, a typical or model size distribution is selected against which all the size distributions are compared. If physical theory can be applied to the choice of a reference distribution or weight function, then the results may be interpreted more easily in a physical sense. Two sets of numerical values are calculated for each size distribution. The discri inate functions show which variable or variables, size classes in this case, are important for discrimination; and the discriminate moments show how the size distributions are related so they may be sorted and classified. A set of characteristic roots or eigenvalues also are calculated. These eigenvalues, arranged in decreasing numerical order, show the proportion of variation among the distributions. Generally, two to three characteristic roots, each having a set of discriminate functions and moments, account for most of the variation among the size distributions.

Canonical analysis techniques were applied to grain-size distributions of samples from known depositional environments to see if discrimination could be achieved. Outcrop samples from the Gallup Sandstone of the San Juan basin, and Brushy Canyon Formation of the Delaware basin, and core samples from the "J" formation of the Denver basin were used. Even though the samples contained considerable amounts (greater than 20%) of silt- and clay-sized material, consistent grouping of similar types of size distributions were obtained. It was not possible to assign, from the grain-size data alone, groups of sandstone samples to specific depositional environments. The numbers generated by canonical analysis are not unique to a particular environment.

However, by using the canonical analysis techniques with grain-size data combined with a knowledge of sedimentary structures of the same samples, a geologist can obtain more information about transportation mechanisms and depositional environments than could be obtained by the use of either approach separately.

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