Mathematics – Logic
Scientific paper
Nov 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988e%26psl..90..457s&link_type=abstract
Earth and Planetary Science Letters, Volume 90, Issue 4, p. 457-466.
Mathematics
Logic
28
Scientific paper
Shape statistics have been compiled from 85 profiles of well-surveyed Pacific seamounts in the height range 140-3800 m. A flat-topped cone was fit to each seamount's cross-sectional profile maintaining the slopes of the sides as closely as possible. On each profile a basal width db, a summit width dt, and a maximum height h, were measured. The height-to-basal-radius ratio is ξh is estimated by the ratio 2h/db and flatness f by the ratio dt/db. Slope angle φ = arctan(ɛ) is estimated from ɛ = 2h/(db - dt). Summit height and basal radius are found to be highly correlated (r = 0.93). The 85-point sample mean of the height-to-basal-radius ratio is ξh = 0.21 +/- 0.08 implying that a seamount's summit height is typically one fifth its basal radius. Despite the high correlation, individual points show some scatter, and there may be groupings into different morphological types. For example, all but one of the seamounts with summit heights above 1000 m have values of ξh that are larger than the sample mean. The 85-point sample mean of flatness is f = 0.31 +/- 0.18. Data points show a large scatter with values of f varying between 0 (a pointy cone) and 0.69 (a flat-topped cone). A histogram representation of flatness, however, indicates that certain values of f may be more common than others: the histogram shows a bimodal distribution with maxima occurring at values of f in the ranges 0.10-0.20 and 0.35-0.50. Moreover, there is some evidence that the mean flatness decreases with summit height so that the preferred shape of a large-sized seamount may be a pointy cone. Slope angle has an 85-point sample mean of φ = 18 +/- 6° individual values of φ vary between 5° and 36°. In addition to having a lower than average mean flatness seamounts with heights above 2600 m also have a lower than average mean slope angle (15°). To determine which variables account for most of the observed variation in the seamount shapes, a multivariate principal component analysis was performed on the data using five shape variables (summit height, basal radius, summit radius, flatness, and slope). The analysis indicates that most of the variation is described by two variables: flatness and summit height.
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