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On the cluster analysis of grains and crystals in rocks

  • Dougal A. Jerram EMAIL logo and Michael J. Cheadle
Published/Copyright: March 25, 2015
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American Mineralogist
From the journal American Mineralogist Volume 85 Issue 1

Abstract

Cluster analysis has the potential to quantify the size and characteristics of groups or clusters of grains and crystals within a rock texture. We present two techniques: (1) the complete linkage hierarchical cluster analysis (CLHCA) technique that we use to analyze grain-center distributions, and (2) the density linkage cluster analysis (DLCA) technique that we use to analyze grain boundary distributions.

CLHCA applies a cluster algorithm to the distance matrix calculated from grain-center coordinates. This produces a hierarchical cluster distribution that is characteristic of the spatial pattern of the texture. This cluster distribution is normalized to that of a random distribution of points to identify clustered and ordered patterns in the data. The technique successfully identified 3-D cluster sizes from 2-D sections of a modal data set. In the application to real rock textures, the CLHCA of a komatiite cumulate identified a glomerocryst population with cluster sizes in the range of 0.3-2.5 mm, and also a variation of cluster patterns up through the cumulate pile. The CLHCA of a polymodal texture from a pyroxene-scapolite-sphene granulite indicated a clustered distribution for the sphene, which was restricted in growth pattern by the pyroxene and scapolite in the texture.

DLCA computes a single solution of clusters that conforms to the search criteria input into the algorithm. DLCA performed poorly when used to identify distributions of large, randomly packed clusters of small spheres, mainly identifying smaller cluster patterns within each large cluster. Application of DLCA to the komatiite cumulate example indicated cluster lengths of 0.72-0.80 mm similar to the CLHCA results, and an average aspect ratio of 1.52.

Received: 1998-12-14
Accepted: 1999-9-10
Published Online: 2015-3-25
Published in Print: 2000-1-1

© 2015 by Walter de Gruyter Berlin/Boston

Articles in the same Issue

  1. Eclogite-facies relics and inferred ultrahigh-pressure metamorphism in the North Dabie Complex, central-eastern China
  2. Application of INVEQ to the geothermobarometry of metamorphic rocks near a kyanite-sillimanite isograd, Mica Creek, British Columbia
  3. Microstructural characterization of metamorphic magnetite crystals with implications for oxygen isotope distribution
  4. Coexisting monazite and allanite in peraluminous granitoids of the TribečMountains, Western Carpathians
  5. Effect of alkalis, phosphorus, and water on the surface tension of haplogranite melt
  6. Direct observation of immiscibility in pyrope-almandine-grossular garnet
  7. On the cluster analysis of grains and crystals in rocks
  8. Experimental approach to constrain second critical end points in fluid/silicate systems: Near-solidus fluids and melts in the system albite-H2O
  9. Estimation and testing of standard molar thermodynamic properties of tourmaline end-members using data of natural samples
  10. An investigation of matrix effects in the analysis of fluorine in humite-group minerals by EMPA, SIMS, and SREF
  11. New data on the crystal-chemistry of fluoborite by means of SREF, SIMS, and EMP analysis
  12. Effect of aluminum on Ti-coordination in silicate glasses: A XANES study
  13. XAFS study of Cu model compounds and Cu2+ sorption products on amorphous SiO2, γ-Al2O3, and anatase
  14. Oxidation-reduction mechanism of iron in dioctahedral smectites: I. Crystal chemistry of oxidized reference nontronites
  15. Oxidation-reduction mechanism of iron in dioctahedral smectites: II. Crystal chemistry of reduced Garfield nontronite
  16. 15N NMR study of nitrate ion structure and dynamics in hydrotalcite-like compounds
  17. 29Si and 27Al MAS-NMR spectroscopy of b-eucryptite (LiAlSiO4): The enthalpy of Si,Al ordering
  18. The nuclear and magnetic structure of “white rust”—Fe(OH0.86D0.14)2
  19. In-situ study of the R3̅ to R3̅c phase transition in the ilmenite-hematite solid solution using time-of-flight neutron powder diffraction
  20. In situ X-ray diffraction investigation of lawsonite and zoisite at high pressures and temperatures
  21. A shell model for the simulation of rhombohedral carbonate minerals and their point defects
  22. Optical properties of natural and cation-exchanged heulandite group zeolites
  23. The crystal structure of gearksutite, CaAlF4(OH)· H2O
  24. A new anhydrous amphibole from the Eifel region, Germany: Description and crystal structure of obertiite, NaNa2(Mg3Fe3+Ti4+)Si8O22O2
  25. Kinoshitalite, Ba(Mg)3(Al2Si2)O10(OH,F)2, a brittle mica from a manganese deposit in Oman: Paragenesis and crystal chemistry
  26. The crystal structure of parisite-(Ce), Ce2CaF2(CO3)3
  27. High-pressure synthesis of Na2Mg6Si6O18(OH)2—a new hydrous silicate phase isostructural with aenigmatite
https://doi.org/10.2138/am-2000-0107

Articles in the same Issue

  1. Eclogite-facies relics and inferred ultrahigh-pressure metamorphism in the North Dabie Complex, central-eastern China
  2. Application of INVEQ to the geothermobarometry of metamorphic rocks near a kyanite-sillimanite isograd, Mica Creek, British Columbia
  3. Microstructural characterization of metamorphic magnetite crystals with implications for oxygen isotope distribution
  4. Coexisting monazite and allanite in peraluminous granitoids of the TribečMountains, Western Carpathians
  5. Effect of alkalis, phosphorus, and water on the surface tension of haplogranite melt
  6. Direct observation of immiscibility in pyrope-almandine-grossular garnet
  7. On the cluster analysis of grains and crystals in rocks
  8. Experimental approach to constrain second critical end points in fluid/silicate systems: Near-solidus fluids and melts in the system albite-H2O
  9. Estimation and testing of standard molar thermodynamic properties of tourmaline end-members using data of natural samples
  10. An investigation of matrix effects in the analysis of fluorine in humite-group minerals by EMPA, SIMS, and SREF
  11. New data on the crystal-chemistry of fluoborite by means of SREF, SIMS, and EMP analysis
  12. Effect of aluminum on Ti-coordination in silicate glasses: A XANES study
  13. XAFS study of Cu model compounds and Cu2+ sorption products on amorphous SiO2, γ-Al2O3, and anatase
  14. Oxidation-reduction mechanism of iron in dioctahedral smectites: I. Crystal chemistry of oxidized reference nontronites
  15. Oxidation-reduction mechanism of iron in dioctahedral smectites: II. Crystal chemistry of reduced Garfield nontronite
  16. 15N NMR study of nitrate ion structure and dynamics in hydrotalcite-like compounds
  17. 29Si and 27Al MAS-NMR spectroscopy of b-eucryptite (LiAlSiO4): The enthalpy of Si,Al ordering
  18. The nuclear and magnetic structure of “white rust”—Fe(OH0.86D0.14)2
  19. In-situ study of the R3̅ to R3̅c phase transition in the ilmenite-hematite solid solution using time-of-flight neutron powder diffraction
  20. In situ X-ray diffraction investigation of lawsonite and zoisite at high pressures and temperatures
  21. A shell model for the simulation of rhombohedral carbonate minerals and their point defects
  22. Optical properties of natural and cation-exchanged heulandite group zeolites
  23. The crystal structure of gearksutite, CaAlF4(OH)· H2O
  24. A new anhydrous amphibole from the Eifel region, Germany: Description and crystal structure of obertiite, NaNa2(Mg3Fe3+Ti4+)Si8O22O2
  25. Kinoshitalite, Ba(Mg)3(Al2Si2)O10(OH,F)2, a brittle mica from a manganese deposit in Oman: Paragenesis and crystal chemistry
  26. The crystal structure of parisite-(Ce), Ce2CaF2(CO3)3
  27. High-pressure synthesis of Na2Mg6Si6O18(OH)2—a new hydrous silicate phase isostructural with aenigmatite
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