The Analysis of Aggregates of Orientation Data in the Earth Sciences

Investigations involving orientations permeate virtually all branches of the earth sciences. Statistical methodology depends upon the requirements of the subject matter and the availability of suitable methods. Some developments in other sciences apply to earth-science problems. In all orientation studies in which the spread of data occupies an appreciable part of the period, periodicity presents special problems. We require clarification of statements of precision of measurement; the order of measuring error may not be constant for all observations of one type. Most angle-sampling problems are believed to be similar to those of non-periodic variables. Application of variance analysis to the design of many investigations must await determination of variance properties which are as yet unknown. Sample-size criteria are now best derived by sequential sampling. Statistical models and measures of departure from the models must be carefully defined. Operational definitions provide considerable insight into the meaning of analytical techniques. Single-variate (two-dimensional) and bivariate (three-dimensional) techniques are outlined; periodic analogues of linear normal theory are introduced, with tables and figures. None of the treatments discussed accounts for spatial distributions of the entities whose orientations are the subject of study.