Journal : Acta Geologica Polonica
Article : Digital Concentration-Distribution Models – tools for a describing heterogeneity of the hybridized magmatic mass as reflected in elemental concentration of growing crystal

Authors :
Fedorowski, J.
Institute of Geology, Adam Mickiewicz University, Maków Polnych 16, PL-61-606 Poznań, Poland, jerzy@amu.edu.pl,
Lehmann, J.
Faculty of Geosciences, University of Bremen, Klagenfurter Strasse, 28357 Bremen, Germany, jens.lehmann@uni-bremen.de,
Nagm, E.
Geology Department, Faculty of Science, Al-Azhar University, Assiut, Egypt, emad.nagm@yahoo.com,
Machalski, M.
Institute of Paleobiology, Polish Academy of Sciences, ul. Twarda 51/55, PL-00-818 Warszawa, mach@twarda.pan.pl,
Mollen, F.
Elasmobranch Research, Meistraat 16, B-2590 Berlaar, Belgium, frederik.mollen@telenet.be,
Śmigielski, M.
Institute of Geology, University of Warsaw, Al. Żwirki i Wigury 93, PL-02-089 Warszawa, Poland, m.smigielski@uw.edu.pl,
Abstract : Raster digital models (digital concentration-distribution models – DC-DMs) as interpolations of geochemical data are proposed as a new tool to depict the crystal growth mechanism in a magmatic environment. The Natural Neighbour method is proposed for interpolation of Electron Microprobe Analysis (EMPA) data; the Natural Neighbour method and Kriging method are proposed for interpolating data collected by the LA-ICP-MS method. The crystal growth texture was analysed with the application of DC-DM derivatives: 3D surface models, shaded relief images, aspect and slope maps. The magmatic mass properties were depicted with the application of solid models. Correlation between the distributions of two elements on a single crystal transect was made by operations on the obtained raster DC-DMs. The methodology presented is a universal one but it seems to be significant for the depiction of magma mixing processes and the heterogeneity of the magmatic mass.

Keywords : cyfrowe stężenia dystrybucji modeli, mieszanie magmy, model cyfrowy, raster, wzrost kryształów, Crystal growth, DC-DM, EMPA, LA-ICP-MS, Magma mixing, Raster digital model,
Publishing house : Faculty of Geology of the University of Warsaw
Publication date : 2012
Number : Vol. 62, no. 1
Page : 129 – 141

Bibliography
: 1. Chiles, J.P. and Delfiner, P. 1999. Geostatistics: Modeling spatial uncertainty, 350 p. Wiley & Sons; New York.
2. Cooper, G.R.J. 2003. Feature detection using sun shading. Computers & Geosciences, 29, 941–948.
3. Cressie, N.A.C. 1990. The origins of Kriging. Mathematical Geology, 22, 239–252.
4. Draper, N.R. and Smith, H. 1998. Applied regression analysis. Third Edition. John Wiley & Sons, Inc.; New York.
5. Domonik, A., Słaby, E. and Śmigielski, M. 2010. The Hurst Exponent as The Tool for Description of Magma Field Heterogeneity Reflected in The Geochemistry of Growing Crystals. Acta Geologica Polonica, 60, 437–443.
6. Fleming, M. D. and Hoffer, R. M. 1979. Machine processing of Landsat MSS data and LARS Technical Report 062879.
7. Laboratory for Applications of Remote Sensing, Purdue University; West Lafayette, USA.
8. Fourcade, S. and Allegre, C.J. 1981. Trace element behavior in granite genesis: a case study. The calc-alkaline plutonic association from Querigut complex (Pyrenees, France). Contributions to Mineralogy and Petrology, 76, 177–195.
9. Gagnevin, D., Daly, J.S., Poli, G. and Morgan, D. 2005a. Microchemical and Sr isotopic investigation of zoned K-feldspar megacrysts: insights into the petrogenesis of a granitic system and disequilibrium crystal growth. Journal of Petrology, 46, 1689–1724.
10. Gagnevin, D., Daly, J.S., Waight, T., Morgan, D. and Poli, G. 2005b. Pb isotopic zoning of K-feldspar megacrysts determined by laser ablation multiple-collector ICP-MS: insights into granite petrogenesis. Geochimica and Cosmochimica Acta, 69, 1899–1915.
11. Ginibre, C., Wörner, G. and Kronz, A. 2002. Minor- and trace-element zoning in plagioclase: implications for magma chamber processes at Parinacota volcano, northern Chile. Contribution to Mineralogy and Petrology, 143, 300–315.
12. Ginibre, C., Wörner, G. and Kronz, A. 2004. Structure and Dynamics of the Laacher See magma chamber (Eifel, Germany) from major and trace element zoning in sanidine: a cathodoluminescence and electron microprobe study. Journal of Petrology, 45, 2197–2223.
13. Ginibre, C., Wörner, G. and Kronz, A. 2007. Crystal zoning as an archive for magma evolution. Elements, 3, 261–266.
14. Green, P.J. and Silverman, B. W. 1994. Nonparametric Regression and Generalized Linear Models. Chapman and Hall; London.
15. Hoskin, P.W.O. 2000. Patterns of chaos: Fractal statistics and the oscillatory chemistry of zircon. Geochimica et Cosmochimica Acta, 64, 1905–23.
16. Hurst, H.E. 1951. Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770–808.
17. Jones, K.H. 1998. A Comparison of algorithms used to compute hill slope as a property of the DEM. Computers & Geosciences, 24, 315–323.
18. Konon, A. and Śmigielski, M. 2006. DEM-based structural mapping; examples from the Holy Cross Mountains and the Outer Carpathians, Poland. Acta Geologica Polonica, 56, 1–16.
19. Pelton, C. 1987. A computer program for hill-shading digital topographic data sets. Computers & Geosciences, 13, 545–548.
20. Peters, E.E. 1997. Teoria chaosu a rynki kapitałowe. Nowe spojrzenie na cykle, ceny i ryzyko. WIG-Press; Warszawa.
21. Sibson, R. 1981. A Brief Description of Natural Neighbour Interpolation. In: V. Barnett (Ed.), Interpreting Multivariate Data. John Wiley and Sons, New York, p. 21–36.
22. Słaby, E. and Götze, J. 2004. Feldspar crystallization under magma-mixing conditions shown by cathodoluminescence and geochemical modelling – a case study from the Karkonosze pluton (SW Poland). Mineralogical Magazine,64, 541–557.
23. Słaby, E., Galbarczyk-Gąsiorowska, L., Seltmann, R. and Műller, A. 2007a. Alkali feldspar megacryst growth: geochemical modelling. Mineralogy and Petrology, 68, 1–29.
24. Słaby, E., Götze, J., Wörner, G., Simon, K., Wrzalik, R., Śmigielski, M. 2008. K-feldspar phenocrysts in microgranular magmatic enclaves: A cathodoluminescence and geochemical study of crystal growth as a marker of magma mingling dynamics. lithos, 105, 85–97.
25. Słaby, E. and Martin, H. 2008. Mafic and felsic magma interactions in granites: the Hercynian Karkonosze pluton (Sudetes, Bohemian Massif). Journal of Petrology, 49, 353–391.
26. Słaby, E., Seltmann, R., Kober, B., Műller, A., Galbarczyk-Gąsiorowska, L. and Jeffries, T. 2007b. LREE distribution patterns in zoned alkali feldspar megacrysts – implication for parental melt composition. Mineralogical Magazine, 71, 193–217.
27. Słaby, E., Śmigielski, M., Śmigielski, T., Domonik, A., Simon, K. and Kronz, A. 2011. Chaotic three-dimensional distribution of Ba, Rb, Sr in feldspar megacrysts grown in an open magmatic system. Contribution to Mineralogy and Petrology, 162, 889–1113.
28. Słaby, E., Martin, H., Hamada, M., Śmigielski, M., Domonik, A., Götze, J., Hoefs, J., Hałas, J., Simon, K., Devidal, J.-L., Moyen, J.-F. and Jayananda, M. 2012. Evidence in Archaean Alkali Feldspar Megacrysts for High-Temperature Interaction with Mantle Fluids. Journal of Petrology, 53, 67–98.
29. Voronoi, G. 1907. Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Journal für die Reine und Angewandte Mathematik, 133, 97–178.
30. West, B.J. 1990. Fractal physiology and chaos in medicine. World Scientific; Singapore.
31. Yang Z.Y. and Lo S. C. 1997. An Index for Describing the Anisotropy of Joint Surfaces. International Journal of Rock Mechanics and Mining Sciences, 34, 1031–1044.
32. Yoeli, P. 1965. Analytical hill shading. Surveying and Mapping, 25, 573–579.
33. Zhou, Q. and Liu, X. 2004. Analysis of errors of derived slope and aspect related to DEM data properties. Computers & Geosciences, 30, 369–378.
DOI :
Qute : Fedorowski, J. ,Lehmann, J. ,Nagm, E. ,Machalski, M. ,Mollen, F. ,Śmigielski, M. ,Śmigielski, M. , Digital Concentration-Distribution Models – tools for a describing heterogeneity of the hybridized magmatic mass as reflected in elemental concentration of growing crystal. Acta Geologica Polonica Vol. 62, no. 1/2012
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