AFC-Modeler: a Microsoft® Excel© workbook program for modelling assimilation combined with fractional crystallization (AFC) process in magmatic systems by using equations of DePaolo (1981)

AFC-Modeler is a user-friendly, interactive Microsoft Excel workbook program which is specifically designed to model up to ten theoretical AFC curves (corresponding to ten different r values; r being the ratio of mass assimilation rate to fractional crystallization rate) for a set of variables that can be interactively and precisely modified by the user (i.e. D, initial element concentration and isotope ratio in magma and element concentration and isotope ratio in wallrock). Being able to model ten curves for ten different 'r' values is an important feature of the program, because results of many studies indicate that the r values for a magmatic suite usually vary widely instead of following a single curve. Particular care has been taken in the design of the program in order to turn rather complex modelling into a simple and error-free procedure by utilizing a specifically designed graphical user interface, consisting of combo boxes placed around a scatter chart which continuously displays up-to-date results of a petrological model. It enables the user of the program to plot elements, ratios of elements and radiogenic (i.e. Sr, Nd and Pb) and stable (d18O) isotopic ratios against each other. Up to eight data series can be entered into the program and stored on eight separate spreadsheets and then plotted along with the modelled theoretical curves. This enables the user to compare the modelled curves and the trends shown by his/her magma series and hence enables him/her to make interpretations and estimations about the degree of crustal assimilation in magma genesis. The program also has two separate and user-modifiable sheets for storing D values of the elements for basic, intermediate and acid magmas, and storing up to 100 magmatic/crustal end-member compositions, which can be utilized in the modelling. By virtue of these features, the AFC-Modeler program can be used as a useful tool for both research and educational purposes.

Anahtar Kelimeler:

Petrological modelling, assimilation of crust, Excel spreadsheet, magma-crust interaction

AFC-Modeler: a Microsoft® Excel© workbook program for modelling assimilation combined with fractional crystallization (AFC) process in magmatic systems by using equations of DePaolo (1981)

Keywords:

Petrological modelling, assimilation of crust, Excel spreadsheet, magma-crust interaction,

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Aitcheson, S.J. & Forrest, A.H. 1994. Quantification of crustal contamination in open magmatic systems. Journal of Petrology 35, 461-488.
Allègre, C. J. & Minster, J.F. 1978. Quantitative models of trace element behavior in magmatic process. Earth Planetary Science Letters 38, 1-25.
Asimow, P.D. & Ghiorso, M.S. 1998. Algorithmic modifications extending MELTS to calculate subsolidus phase relations. American Mineralogist 83, 1127-1131
Bell, K. & Powell, J.L. 1969. Strontium isotopic studies of alkali rocks: the potassium rich lavas of the Birunga end Toro-Ankole regions, east and central equatorial Africa. Journal of Petrology 10, 536-572.
Bohrson, W.A. & Spera, F.J. 2001. Energy-constrained open-system magmatic processes II: Application of energy-constrained assimilation-fractional crystallization (EC-AFC) model to magmatic systems. Journal of Petrology 42, 1019-1041.
Bohrson, W.A. & Spera, F.J. 2003. Energy-constrained open-system magmatic processes IV: geochemical, thermal and mass consequences of energy-constrained recharge, assimilation and fractional crystallization (EC-RAFC). Geochemistry Geophysics Geosystems 4, 8002, doi:10.1029/2002GC000316.
Bowen, N.L. 1928. The Evolution of the Igneous Rocks, Princeton University Press, Princeton, 334 pp.
Calderon, M., Herve, F., Cordani, U. & Massonne, H.J. 2007. Crustmantle interactions and generation of silicic melts: insights from the Sarmiento Complex, southern Patagonian Andes. Revista Geologica De Chile 34, 249-275.
Cebriá, J.M., Martiny, B.M. López-Ruiz, J. & Morán-Zenteno, D.J. 20 The Parícutin calc-alkaline lavas: New geochemical and petrogenetic modeling constraints on the crustal assimilation process. Journal of Volcanology and Geothermal Research 201, 113-1 Conrad, W.K. 1987. A FORTRAN program for simulating major- and trace-element variations during Rayleigh fractionation with melt replenishment or assimilation. Computers & Geosciences 13, 1-12. doi:10.1016/0098-3004(87)90021-5.
Cribb, J.W. & Barton, M. 1996. Geochemical effects of decoupled fractional crystallization and crustal assimilation. Lithos 37, 293-30
DePaolo, D.J. & Wasserburg, G.J. 1979. Petrogenetic mixing models and Nd-Sr isotopic patterns. Geochimica Cosmochimica Acta 43, 615-627.
DePaolo, D.J. 1981. Trace element and isotopic effects of combined wall-rock assimilation and fractional crystallization. Earth and Planetary Science Letters 53, 189-202. doi: 10.1016/0012821X(81)90153-9.
D’Orazio, M. 1993. A Macintosh basic program for the interactive testing of combined assimilation and fractional crystallization.
Computers & Geosciences 19, 483-492. doi:10.1016/00983004(92)90003-A.
Ellam, R.M. & Harmon, R.S. 1990. Oxygen isotope constraints on the crustal contribution to the subduction-related magmatism of the Aeolian-islands, southern Italy. Journal of Volcanology and Geothermal Research 44, 105-122.
Ersoy, Y. & Helvacı, C. 2010. FC-AFC-FCA and mixing modeler: A Microsoft (R) Excel (c) spreadsheet program for modeling geochemical differentiation of magma by crystal fractionation, crustal assimilation and mixing. Computers & Geosciences 36, 383-3 DOI: 10.1016/j.cageo.2009.06.007
Faure, G., Bowman, J.R., & Elliot, D.H. & Jones, L.M. 1974. Strontium isotope composition and petrogenesis of the Kirkpatrick Basalt, Queen Alexandra Range, Antarctica. Contributions to
Mineralogy and Petrology 3, 153-169. Ghiorso, M.S. & Sack, R.O. 1995. Chemical mass-transfer in magmatic processes. 4. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevatedtemperatures and pressures. Contributions to Mineralogy and Petrology 119, 197-212. Doi: 10.1007/BF00307281.
Hagen, H. & Neumann, E.R. 1990. Modeling of trace-element distribution in magma chambers using open-system models.
Computers & Geosciences 16, 549-586. Halama, R., Marks, M., Brugmann, G., Siebel, W., Wenzel, T. & Markl, G. 200 Crustal contamination of mafic magmas: evidence from a petrological, geochemical and Sr-Nd-Os-O isotopic study of the Proterozoic Isortoq dike swarm, South Greenland. Lithos 74, 199-232. Doi: 10.1016/j.lithos.2004.03.004.
Huang, F., Gao, L. & Lundstrom, C.C. 2008. The effect of assimilation, fractional crystallization, and ageing on U-series disequilibria in subduction zone lavas. Geochimica et Cosmochimica Acta 72, 4136-4145.
Karacık, Z., Yılmaz, Y., Pearce, J.A. & Ece, I. 2008. Petrochemistry of the south Marmara granitoids, northwest Anatolia, Turkey. Int. J Earth Sci. (Geol Rundsch) 97, 1181–1200. Doi: 10.1007/ s00531-007-0222-y.
Keskin, M. 2002. FC-Modeler: a Microsoft ® Excel © spreadsheet program for modeling Rayleigh fractionation vectors in closed magmatic systems. Computers & Geosciences 28, 919-928.
Keskin, M., Genç, Ş.C. & Tüysüz, O. 2008. Petrology and geochemistry of post-collisional Middle Eocene-Oligocene volcanic units in North-Central Turkey: evidence for magma generation by slab-breakoff following the closure of the northern Neotethys Ocean. Lithos 104, 267-305. doi: 10.1016/j.lithos.2007.12.011.
Keskin, M., Pearce, J.A. & Mitchell, J.G. 1998. Volcano-stratigraphy and geochemistry of collision-related volcanism on the Erzurum-Kars Plateau, North Eastern Turkey. Journal of Volcanology and Geothermal Research 85, 355-404.
Keskin, M., Pearce, J.A., Kempton, P.D. & Greenwood, P. 2006. Magma-crust interactions and magma plumbing in a postcollisional setting: Geochemical evidence from the Erzurum-Kars volcanic plateau, eastern Turkey, In: Dilek, Y. & Pavlides, S. (eds), Postcollisional tectonics and magmatism in the Mediterranean region and Asia, Geological Society of America Special Paper 409, 475-505. doi: 10.1130/2006.2409(23).
Keskin, M., Ustaömer, T. & Yeniyol, M. 2010. Magmatic evolution and geodynamic setting of the Late Cretaceous volcanic sequences in the north of Istanbul, in Symposium on the Geology of Istanbul-III Proceedings book, 130-180 (in Turkish with English abstract).
Krienitz, M.S., Haase, K.M., Mezger, K., Eckardt, V. & ShaikhMashail, M.A. 2006. Magma genesis and crustal contamination of continental intraplate lavas in northwestern Syria. Contributions to Mineralogy and Petrology 151, 698-716. Doi: 1007/s00410-006-0088-1.
Langmuir, C.H., Vocke, R.D., Hanson, G.N. & Hart, S.R. 1978. A general mixing equation with applications to Icelandic basalts. Earth and Planetary Science Letters 37, 380-392.
Lightfoot, P.C., Sutcliffe, R.H. & Doherty, W. 1991. Crustal contamination identified in Keweenawan Osler group tholeiites, Ontario - a trace-element perspective. Journal of Geology 99, 739-760.
Marsh, J.S. 1989. Chemical constraints on coupled assimilation and fractional crystallization involving upper crustal compositions and continental tholeiitic magma. Earth and Planetary Science Letters 92, 70-80.
McBirney, A.R., Taylor, H.P. & Armstrong, R.L. 1987. Paricutin reexamined - a classic example of crustal assimilation in calcalkaline magma. Contributions to Mineralogy and Petrology 95, 4Myers, J.D., Sinha, A.K. & Marsh, B.D. 1984. Assimilation of crustal material by basaltic magma - strontium isotopic and traceelement data from the Edgecumbe volcanic field, SE Alaska. Journal of Petrology 25, 1-26.
Nielsen, R.L. 1985. EQUIL: a program for the modeling of low-pressure differentiation processes in natural mafic magma bodies. Computers & Geosciences 11, 531-546. doi:1016/0098-3004(85)90084-6.
Nielsen, R.L. 1988. TRACE FOR: A program for the calculation of combined major and trace-element liquid lines of descent for natural magmatic systems. Computers & Geosciences 14, 15-35. doi:1016/0098-3004(88)90050-7.
O’Hara, M.J. 1977. Geochemical evolution during fractional crystallization of a periodically refilled magma chamber. Nature 266, 503-507.
Ort, M.H., Coira, B.L. & Mazzoni, M.M. 1996. Generation of a crustmantle magma mixture: Magma sources and contamination at Cerro Panizos, Central Andes. Contributions to Mineralogy and Petrology 123, 308-322.
Pearce, J.A., Bender, J.F., De Long, S.E., Kidd, W.S.F., Low, P.J., Güner, Y., Şaroğlu, F., Yılmaz, Y., Moorbath, S. & Mitchell, J.G. 1990.
Genesis of collision volcanism in Eastern Anatolia, Turkey. Journal of Volcanology and Geothermal Research 44, 189-229. Powell, R. 1984. Inversion of the assimilation and fractional crystallization (AFC) equations; characterization of contaminants from isotope and trace element relationships in volcanic suites. Journal of Geological Society of London 141, 447-4
Reiners, P.W., Nelson, B.K. & Ghiorso, M.S. 1995. Assimilation of felsic crust by basaltic magma - thermal limits and extents of crustal contamination of mantle-derived magmas. Geology 23, 563-5
Reiners, P.W., Nelson, B.K. & Nelson, S.W. 1996. Evidence for multiple mechanisms of crustal contamination of magma from compositionally zoned plutons and associated ultramafic intrusions of the Alaska Range. Journal of Petrology 37, 2612
Rivalenti, G., Correia, C.T., Girardi, V.A., Mazzucchelli, M., Tassinari, C.C.G. & Bertotto, G.W. 2008. Sr-Nd isotopic evidence for crustal contamination in the Niquelandia complex, Goias, Central Brazil. Journal of South American Earth Sciences 25, 298-3 Doi: 10.1016/j.jsames.2007.08.007.
Schmidt, M.E. & Grunder, A.L. 2011. Deep mafic roots to arc volcanoes: Mafic recharge and differentiation of basaltic andesite at North Sister Volcano, Oregon Cascades. Journal of
Petrology 52, 603-641. doi:10.1093/petrology/egq094.
Spera, F.J. & Bohrson, W.A. 2001. Energy-constrained open-system magmatic processes I: General model and energy-constrained assimilation and fractional crystallization (EC-AFC) formulation. Journal of Petrology 42, 999-1018.
Spera, F.J. & Bohrson, W.A. 2002. Energy-constrained opensystem magmatic processes 3. Energy-constrained recharge, assimilation, and fractional crystallization (EC-RAFC). Geochemistry Geophysics Geosystems 3, Art. No: 8001.
Spera, F.J. & Bohrson, W.A. 2004. Open-system magma chamber evolution: an energy-constrained geochemical model incorporating the effects of concurrent eruption, recharge, variable assimilation and fractional crystallization (ECE’RAcFC). Journal of Petrology 45, 2459-2480.
Sun, S.S., Tatsumoto, M. & Schilling, J.-G. 1975. Mantle plume mixing along the Reykjanes Ridge axis: lead isotopic evidence. Science 190, 143-149.
Taylor, H.P. 1980. The effects of assimilation of country rocks by magmas on 18 O/ 16 O and 87 Sr/ 86 Sr systematics in igneous rocks. Earth and Planetary Science Letters 47, 243-254.
Taylor, S.R. & McLennan, S.M. 1981. The composition and evolution of the continental crust: rare earth element evidence from sedimentary rocks. Philosophical Transactions of the Royal Society of London A301, 381-399.
Taylor, S.R. & McLennan, S.M. 1985. The continental crust: its composition and evolution, Blackwell Scientific Publications, Oxford, 312 pp.
Torres-Alvarado, I.S., Verma, S.P., Palacios-Berruete, H., Guevara, M. & González-Castillo, O.Y. 2003. DC_Base: a database system to manage Nernst distribution coefficients and its application to partial melting modeling. Computers & Geosciences 29, 119111
Velasco-Tapia, F. & Verma, S.P. 2012. Magmatic Processes at the volcanic front of Central Mexican Volcanic Belt: Sierra de Chichinautzin volcanic field (Mexico). Turkish Journal of Earth Sciences 21, in press, doi:10.3906/yer-1104-9
Verma, S.P. & Andaverde, J. 2007. Coupling of thermal and chemical simulations in a 3-D integrated magma chamber-reservoir model: a new geothermal energy research frontier. In: Ueckermann, H.I. (ed), Geothermal Energy Research Trends, New York, Nova Science Publishers, Inc. 149-189.
Verma, S.P. 1999. Geochemistry of evolved magmas and their relationship to subduction-unrelated mafic volcanism at the volcanic front of the central Mexican Volcanic Belt. Journal of Volcanology and Geothermal Research 93, 151-171.
Verma, S.P. 1998. Error propagation in geochemical modeling of trace elements in two component mixing. Geofísica Internacional 37, 327-3
Verma, S.P. 2000. Error propagation in equations for geochemical modelling of radiogenic isotopes in two-component mixing.
Proceedings of the Indian Academy of Sciences (Earth and Planetary Sciences) 109, 79-88. Verma, S.P. 2001. Geochemical and Sr-Nd-Pb isotopic evidence for a combined assimilation and fractional crystallisation process for volcanic rocks from the Huichapan caldera, Hidalgo, Mexico. Lithos 56, 141-164.
Vollmer, R. 1976. Rb-Sr and U-Th-Pb systematics of alkaline rocks: the alkaline rocks from Italy. Geochimica et Cosmochimica Acta 40, 283-295.
Weaver, B. & Tarney, J. 1984. Empirical approach to estimating the composition of the continental crust. Nature 310, 575-577.
Wenzel, T., Oberhansli, R. & Mezger, K. 2000. K-rich plutonic rocks and lamprophyres from the Meissen Massif (northern
Bohemian Massif): Geochemical evidence for variably enriched lithospheric mantle sources. Neues Jahrbuch fur Mineralogie-Abhandlungen 175, 249-293. YongSheng, L. & ZhaoChong, Z. 2011. Application of energyconstrained assimilation-fractional crystallization (EC-AFC) model for ultramafic magmatic systems: A case study of the Limahe intrusion associated with Cu-Ni sulfide ores, Sichuan
Province. Acta Petrologica Sinica 27, 2975-2983.