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In searching for subtle depositional traps, it would be useful to have a reliable method for determining the depositional environment of sand bodies from internal evidence. Attempts using various grain-size parameters have met with limited success. Recent advances in grain-shape analysis have not lived up to initial hopes. The potential of Fourier analysis is reduced when harmonic amplitudes are used without considering phase angles. Two types of errors can occur: (1) dissimilar shapes can produce similar sets of amplitudes, and (2) similar (but not identical) shapes can produce dissimilar sets of amplitudes. Phase angles can be compared between grains only when the grains are rotated to comparable positions; this can be accomplished by cross-correlation with an empirical asymmetric reference shape. Data reduction is desirable, but paired variables cannot be easily handled by standard multivariate techniques.
After rotation to standard position, raw shape data (sets of radial lengths) are adequate shape descriptors. These can be reduced by factor analysis that can be compared between grains and between large sets of grains more meaningfully than can Fourier descriptors (which provide a poor basis for comparisons between grains).
Results from the two approaches are compared in a preliminary re-study of the river-beach-dune discrimination problem. Gross grain shapes are classified into natural categories by multivariate analysis of rotated radials.
Distinguishable associations of shape categories are quantitatively related to specific environments. Shape sorting, in combination with size sorting (different responses to transport processes), may extend the discriminating power.
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