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A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions

Geological Society of America Bulletin

By:
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DOI: 10.1130/B25000.1

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Abstract

Size distribution of rigidly embedded spheres in a groundmass is usually determined from measurements of the radii of the two-dimensional (2D) circular cross sections of the spheres in random flat planes of a sample, such as in thin sections or polished slabs. Several methods have been devised to find a simple factor to convert the mean of such 2D size distributions to the actual 3D mean size of the spheres without a consensus. We derive an entirely theoretical solution based on well-established probability laws and not constrained by limitations of absolute size, which indicates that the ratio of the means of measured 2D and estimated 3D grain size distribution should be r/4 (=.785). Actual 2D size distribution of the radii of submicron sized, pure Fe0 globules in lunar agglutinitic glass, determined from backscattered electron images, is tested to fit the gamma size distribution model better than the log-normal model. Numerical analysis of 2D size distributions of Fe0 globules in 9 lunar soils shows that the average mean of 2D/3D ratio is 0.84, which is very close to the theoretical value. These results converge with the ratio 0.8 that Hughes (1978) determined for millimeter-sized chondrules from empirical measurements. We recommend that a factor of 1.273 (reciprocal of 0.785) be used to convert the determined 2D mean size (radius or diameter) of a population of spheres to estimate their actual 3D size. ?? 2005 Geological Society of America.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions
Series title:
Geological Society of America Bulletin
DOI:
10.1130/B25000.1
Volume
117
Issue:
1-2
Year Published:
2005
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Geological Society of America Bulletin
First page:
244
Last page:
249
Number of Pages:
6