Analysis of Two-Dimensional Shapes by Principal Component Score Descriptors: Geological Interpretations from Sand Grains, Pebbles, Benthic Foraminifera, and Bivalve Mollusks

James M. Parks

Computerized quantitative shape analysis provides useful geological information not readily obtained in other ways. Principal Components Analysis (PCA) of properly rotated images reduces digitized outlines to a few shape descriptors. R-mode PC loadings, displayed graphically, exhibit the distinctive components of shape (elongation, triangularity, rectangularity, etc) in different orientations. Q-mode estimated PC scores are the shape descriptors for individual objects. Six shape descriptors are adequate to characterize typical geological outline shapes, such as silhouettes of sand grains, pebbles, and fossils. The original outlines are reconstructed using these shape descriptors as proportions for recombining the PC loadings.

Proportions and rates of sand mixing from two sources are revealed by shape analysis of populations of sand grains from the Kansas and Missouri rivers sampled above and below their confluence. Unmixing (differential sorting during transport) is revealed by gradual shape changes in sands sampled along 330 mi of the Rio Grande (Del Rio, Texas, to the Gulf of Mexico). Pebbles from the Jackson Hole, Wyoming, area are readily identified as to fluvial or glacial origin by quantified shape.

Outline shapes of benthic foraminifera from Maryland Miocene assemblages are classified by cluster and discriminant analyses of PC scores into 20 or more morphological types. Relative proportions of each morpho-type in stratigraphic samples are statistically correlated with independent paleoenvironmental indicators.

Intra- and inter-specific changes in shapes of several genera of middle Miocene bivalves from Maryland show three distinct patterns through time: minor irregular changes (= stasis?); abrupt jumps (= punctuated equilibria?); and gradual trends (= gradualism?).

AAPG Search and Discovery Article #91038©1987 AAPG Annual Convention, Los Angeles, California, June 7-10, 1987.