Sedimentary particles with minor differences in overall shape are selectively sorted according to shape during transport. Krumbein in 1942 demonstrated a difference in fall velocity for "disks" and "rollers," and Nagle in 1967 showed that right and left pelecypod valves transported by the same longshore current ended up at different locations along a beach. Selective shape sorting of sand-size particles occurs at various rates and in distinct patterns during different modes of transport, but the subtle shape differences are hard to recognize by conventional techniques. Visual comparison methods for "roundness" and "sphericity" have such low accuracy and reproducibility as to be virtually meaningless. Also, two particles can have equal sphericity and roundness and yet be o different overall shape. The Corey shape factor (widely used by civil engineers) with its various modifications is inadequate for subtle shape variations. In two-dimensional maximum projection, simple symmetrical shapes (i.e., ellipse) are fully defined by two measurements: length of major and minor axes. Less symmetrical shapes (i.e., oval or kidney bean) need more than two measurements. Griffiths in 1967 stated that n measurements are needed for an irregular shape (where n is not known in advance).

Eigenshape analysis is a method of reducing a large number of measurements (i.e., 36 radial lengths at equal angular increments) to the minimum number of linear combinations needed to portray a significant proportion (80 to 90%) of observed shape variation. Reference-rotation is needed for sand grains in order to compare the wide variety of shapes that occur; when comparing only similar objects, reference-rotation may not be necessary. Unlike Fourier shape analysis, which as currently used involves only small-scale irregularities, Eigenshape analysis is a new approach to quantifying larger scale shape characteristics.

Laboratory experiments designed to simulate shape-sorting effects of sediment transport (slow versus fast fall velocity in a sedimentation tube; inner versus outer ring in a gold prospecting pan) separated quartz sand samples composed of grains of the same sieve size into two subsamples. These showed recognizably different assemblages of shape types by Reference-Rotated Eigenshape Analysis. Similar Eigenshape distinctions were observed when the same size fraction of two sands with different Eigenshape "signatures" were mixed in 2:1 ratio and then separated by selective shape sorting as above.

Eigenshape analysis achieved similar results with thin-section input data. Artificial rocks were made with the above sands by "lithifying" with epoxy resin. Thin sections were made perpendicular and parallel to "bedding" and at other orientations. Eigenshape analysis was performed on the grains as seen in section (not "maximum projection"). Results from bedding-parallel sections most closely resemble results from loose-grain mounts.

Inferences about provenance, transport mode, transport distance, mixing from different sources and/or different transport histories, and depositional environments are made from Eigenshape analysis results. The intrinsic R-mode factor analysis approach helps untangle these intermixed effects.

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