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GEOLOGY BY NUMBER: solving petrology problems with quantitative skills Jennifer M. Wenner Geology Department University of Wisconsin Oshkosh GEOLOGY BY NUMBER µ = µinf Ea/RT e * [1+A(mT + -2.5 b)] The research question: • How is continental crust formed? (especially in continental arcs since they best approximate “average continental crust”) Observations Continental arcs are sites of voluminous continental crustal addition Observations The major rock type in continental arcs is granodiorite (although there are close associations of mafic and felsic rocks). Observations Field and chemical observations suggest that two (or more) distinct magmas were interacting to generate a variety of different rocks QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Hypothesis Average continental crust is formed by mixing basaltic magmas and granitic magmas to make GRANODIORITE! Problems (perceived?) Early calculations suggested that physical properties (melting temperature, viscosity and density) limit the abilities of magmas to mix. QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. VISCOSITY CALCULATIONS µ =µ0(1+A)-2.5(Marsh, 1981) § = mT + b (empirical data) § § µ = µ0[1+A(mT + b)]-2.5 µ0 = µinf eEa/RT (theoretical -- Arrhenius) § µ = µinf eEa/RT * [1+A(mT + b)]-2.5 VISCOSITY CALCULATIONS-students need to be able to: § µ =µ0 (1+A)-2.5 • Manipulate others’ (Marsh, 1981) = mT + b • • § µ = µ0[1+A(mT + b)]-2.5 § § µ0 = µinf eEa/RT µ = µinf eEa/RT * [1+A(mT + b)]-2.5 • • equations Use and evaluate empirical data Assess a model’s assumptions Discern rate and order of magnitude Use tools such as Excel GEOCHEMICAL ANALYSIS GEOCHEMISTRY -students need to be able to: Read and interpret graphs Recognize and assess sources of error Approximate slope / shape of data Articulate meaning of data with reference to quantitative chemical concepts (i.e., KD values, µ, eNd) Use computer programs (i.e., Excel, etc.) Petrology and Petrography QuickTime™ and a Photo - JPEG decompressor are needed to see this picture. Petrology and Petrography-students need to be able to: Express scale (including features at a variety of scales) Assess changes/ contrasts in rates (i.e., cooling/crystallization, tectonic, diffusion) Recognize different orders of magnitude Field work Field work -Students need to be able to: Approximate distances / height / scale Estimate slope Calculate angles and plot structural data on a map Determine magnetic declination Visualize 3-D from a 2-D map Important quantitative skills Approximation and/or estimation of: Rates Slope / shape of curve Distances / angular relationships Order of magnitude Appreciation of the power of graphical solutions Assessment of assumptions Spatial relations Statistics, sources of error, data analysis Use of technologic tools such as Excel Others?