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.