For describing variations of fold style, orientation, and location, quantitative scalar variables are preferred to quantitative vectoral or qualitative attributes. T. V. Loudon showed that useful quantitative data are obtained if fold profiles are subdivided into one-wavelength units, and if the inclinations (^Thgr), from the principal axes, or normals to the folded surfaces are measured; the orthogonal principal axes are defined first by factor analysis. The first four statistical moments of these cos ^Thgr values provide scalar descriptors of mean slope, tightness, asymmetry, and shape, respectively. Additional scalars include direction cosines of the principal axes, kurtosis and skewness of the cos ^Thgr values, and the ratio of profile length to wave length.

Vectoral fold attributes plotted on Schmidt equal-area projections necessarily divorce measurements from geographical locations. Scallars facilitate the drawing of contour maps of the areal variability of fold geometry. Surface-trend analyses, widely used in stratigraphic and petrographic research, are used to illustrate regional changes in fold terranes.

Scalar descriptors are useful also in sequential, multivariate regression analyses to search for those geologic factors that controlled the nature and regional variability of folds. Such methods have potential in analyzing subsurface folds for water or petroleum-resource studies. Examples are based on correlations of regional fold patterns with (a) variations of member thickness, lithology, cementation, stratigraphy, etc. and (b) proximity to major tectonic features. Such methods are valuable for prediction and permit quantitative testing of hypotheses, e.g., that fold styles in an area (a) change progressively with metamorphic grade or (b) are dissimilar in sandstone and limestone.

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