The Quantitative Mapping of Directional Minor Structures

Abstract

Lineations of any kind can have their orientation pattern represented quantitatively on maps by contour-type lines which may be called isogons. The orientation pattern is more accurately and clearly defined by isogonic maps than by any other method, and these maps also lend themselves to trend-surface analysis. Methods are presented for constructing isogonic maps, selecting the most accurate and useful type of angle for representing on the map, and determining the size and position of the statistically significant interval between adjacent isogons. The use of these techniques is illustrated by an example from the Scottish Highlands. Statistical techniques of analyzing two- and three-dimensional distributions of directional minor structures are discussed. It is shown how an arbitrary sense of direction may always be assigned so that the absence of a unique sense of direction as determined by internal features is not such a serious problem as would appear. Rather than the various methods of vector statistics proposed to date, methods involving the Schmidt net are favored because they are non-parametric, more useful in determining geologically representative attitudes, and also highly economical. The reliability of the map depends upon the distribution of the measurements over the area. Careful siting of the control stations is of greater importance than the total density, but the total density of control stations is more important than the number of measurements per station. Varying density of the control stations is favored rather than a regular grid. The subarea method has been widely used in the analysis of directional minor structures. A more precise method of determining the position and size of the subareas using isogonic maps is described.