The uses and limitations of beta-diagrams and pi-diagrams in the geometrical analysis of folds

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Abstract
The two standard procedures for determining the directions of fold-axes from measurements of the orientation of planar surfaces in the fold are examined to determine the validity of the conclusions that are generally based on them. With some types of folds, an analysis of the data using a β -diagram gives results that are particularly difficult to interpret with precision. Great errors in the position of the significant β -intersections may be expected under certain circumstances, and geologically meaningless β -points may also be abundant. Where the folding is inhomogeneous, β -diagrams generally produce a particularly high proportion of spurious β -points, often greatly outnumbering the significant β -points. Under these circumstances β -diagrams are unreliable and may give a false impression of the structural geometry. The most satisfactory method of analysing field data is by using π-diagrams. Although there may be difficulties in their interpretation when used with certain types of fold, modifications of the method can be employed to determine accurately the axes of both very open and near-isoclinal folds. If π-diagrams are prepared from data collected in regions of inhomogeneous folding the inhomogeneities are often immediately apparent, making it possible to subdivide the region into smaller areas of greater homogeneity. No mass of spurious points will be produced in such circumstances as would be found in a β -diagram prepared from the same data.

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