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

Maiying Kong, Rabi N. Bhattacharya, Christina James, Abhijit Basu

Research output: Contribution to journalArticlepeer-review

79 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)244-249
Number of pages6
JournalBulletin of the Geological Society of America
Issue number1-2
StatePublished - Jan 2005
Externally publishedYes


  • Fe
  • Grain size distribution
  • Maximum likelihood
  • Moment
  • Probability
  • Statistics

ASJC Scopus subject areas

  • Geology


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