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

Research Article| January 01, 2005 A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions Maiying Kong; Maiying Kong 1Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA Search for other works by this author on: GSW Google Scholar Rabi N. Bhattacharya; Rabi N. Bhattacharya 1Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA Search for other works by this author on: GSW Google Scholar Christina James; Christina James 2Indiana Geological Survey, Indiana University, Bloomington, Indiana 47405, USA Search for other works by this author on: GSW Google Scholar Abhijit Basu Abhijit Basu 3Department of Geological Sciences, Indiana University, Bloomington, Indiana 47405, USA Search for other works by this author on: GSW Google Scholar Author and Article Information Maiying Kong 1Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA Rabi N. Bhattacharya 1Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA Christina James 2Indiana Geological Survey, Indiana University, Bloomington, Indiana 47405, USA Abhijit Basu 3Department of Geological Sciences, Indiana University, Bloomington, Indiana 47405, USA Publisher: Geological Society of America Received: 12 Feb 2003 Revision Received: 11 Apr 2004 Accepted: 30 Apr 2004 First Online: 02 Mar 2017 Online ISSN: 1943-2674 Print ISSN: 0016-7606 Geological Society of America GSA Bulletin (2005) 117 (1-2): 244–249. https://doi.org/10.1130/B25000.1 Article history Received: 12 Feb 2003 Revision Received: 11 Apr 2004 Accepted: 30 Apr 2004 First Online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Get Permissions Search Site Citation Maiying Kong, Rabi N. Bhattacharya, Christina James, Abhijit Basu; A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions. GSA Bulletin 2005;; 117 (1-2): 244–249. doi: https://doi.org/10.1130/B25000.1 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search 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 π/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. You do not have access to this content, please speak to your institutional administrator if you feel you should have access.