Measurement of the Properties of Sediments

The definition of a rock as an aggregate of minerals is equivalent to defining a population as an assemblage of elements. In order to achieve a unique definition of a population, whether the population is a small rock sample or the entire universe, a single crystal or an atom, it is necessary to specify five fundamental properties, namely, the kinds and proportions of elements composing the population (m), their sizes (s), their shapes (sh), and their arrangement or their orientation (o), and packing (p). This may be symbolically expressed as P = (m, s, sh, o, p) When attempts are made to devise measurement procedures aimed at operationally specifying these properties, the nature of the interrelationships among the properties becomes important. In cases where the properties are dependent or independent, many measurement procedures suffice to achieve the objective. When the properties are interdependent, it becomes necessary to isolate them either by physically reducing the objects measured to a single kind and performing direct measurement upon them or by making a set of simultaneous measurements of different properties upon the set of objects, and, using suitable experimental designs, the effects of the various properties may be isolated mathematically from the interfering interactions among them. As an example the implications of grain-size measurement performed by different procedures may be elucidated by manipulating the defining equation. It is deduced that, if the objective is to interpret the geological history of the rock from its variations in grain size, then direct measurement upon grains of a single kind is required. Discrepancies between different size measures obtained from different techniques applied to the same rock specimens are shown to depend upon the confounding effects of interactions. Ultimately, it seems evident that, since most geological populations possess interdependent interacting properties, the solutions to problems of geological interest will require multivariate statistical analysis.