John C. Griffiths

Size versus Sorting in Some Caribbean Sediments

The relationship between average size (phi median) and sorting (phi percentile deviation) in sediments is explored empirically by means of statistical analysis of data from over twelve hundred individual samples taken from Miocene and Oligocene horizons in southern Trinidad, the Eocene Scotland series from Barbados, and the Pliocene Superficial Gravels of British and Dutch Guiana. The association between size and sorting is estimated by means of the correlation coefficient, and the relationship is reduced to linear equations of the form

Measurement of the Properties of Sediments

PD\phi = bMd\phi + a

Computer Programs for Geology

. Deviations from the trends are measured in terms of the standard error of estimate (Sy). On the basis of the statistics it is shown that, in water-deposited sediments, size varies with sorting over the range oΦ (I.oo mm.) to 6Φ (0.0156 mm.) in median diameter and 0-4.5Φ in phi percentile deviation. Best-sorted sediments (PDΦ < IΦ) possess median diameters around 2.5Φ (0.177 mm.), and sorting becomes poorer with both increasing and decreasing size from the fine-sand range (2-3Φ). Departures from the trend of over 1 Sy unit indicate that in finer-grained sediments (clays and fine silts) flocculation had taken place during grain-size analysis; whereas in coarser-grained sediments (very fine sands and coarse silts) the departures imply events of geological significance which interfered with normal sedimentation.

Petroleum and the Continental Shelf of North West Europe

Petrogenesis of detrital sediments is built into a model in which the measured properties of sediments are ideally related to the factors or causes which lead to variation in the properties. Variation in measured properties of detrital sediments is then analyzed using factor analysis and petrogenesis is interpreted through the model. By incorporating several different objectives and the analytical procedures into a single algorithmic program, the analysis is more efficient and systematic and may largely be automated. A number of examples illustrate that variation in the properties of detrital sediments, measured in thin section, contains much redundant information; the most obvious features which emerge are related to variation in size and size sorting, indicating effects of the process of selective sorting, and variation in proportion of the cementitious constituents which reflect diagenetic processes. It is suggested that new properties should only be added if they supply additional information and contain little redundancy. To specify variation in source area, it will be necessary either to find a new property that is not affected by subsequent processes or to extract factor roots beyond the seventh; the latter alternative will require sample sizes of the order of 100-200 specimens per rock type.

Petroleum and the Continental Shelf of North West Europe. A. W. Woodland

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.