IF we think the granitic or felsic magma in study is evolved from fractionation crystallization process and we wanna model this process. How to select the c0 and cL among your samples? Is it based mainly on the SiO2 contents, which directly can be seen from the Harker diagrams (I mean the maximum and minimum values of SiO2)? Or can we decide them on the log(incompatible) vs. log(compatible) diagrams(similarly, select the maximum and minimum values of compatible elements)? Which is accessible and what is the difference between the two? In addition, how to decide what the fractionated minerals are? Are they the same with the mineral assemblages in the thin section? I am new in this aspect, so can anyone give me a detailed reply with a few cases if possible? Thank you very much.
Dear colleague,
We have recently published a book dealing with numerical modelling of igneous petrogenesis. It also includes chapters on practical aspects you are asking about - so it perhaps could give you a head start::
Janoušek, V., Moyen, J. F., Martin, H., Erban, V. & Farrow, C. M. (2016). Geochemical Modelling of Igneous Processes – Principles and Recipes in R Language. Bringing the Power of R to a Geochemical Community. Springer-Verlag, Berlin, Heidelberg, 346 pp. doi:10.1007/978-3-662-46792-3
I trust that this helps,
Vojtech Janousek
http://blog.gcdkit.org/2015/10/book-on-geochemical-modelling-of.html
Dear Professor Janousek,
Thank you for your kind answer. Actually, I know this book and have read part of it.Since this book contains no tables of data, I am not sure whether my understanding is correct and I have a few puzzles when reading the book. So could you give a general answer to my question? Thank you for your time and concern.
Dear Houxiang Shan,
as you know, the book contains a great deal of solved exercises. The related datasets and the code are readily available from http://book.gcdkit.org/ (hardback), or just by clicking hyperlinks (electronic version).
For replies to more philosophical questions of yours, refer in particular to Part V ("Practical modelling") and for an example of a complete fractional crystallization model, to Chapter 26: "Differentiation of a Calc-Alkaline Volcanic Series: Example of the Atacazo-Ninahuilca Volcanoes, Ecuador".
Best wishes,
Vojtech Janousek
http://book.gcdkit.org/
http://link.springer.com/chapter/10.1007/978-3-662-46792-3_25
If you have trace-element and isotopic data, I would recommend the model by DePaolo, D.G., 1981, Trace elements and isotopic effects of combined wallrock assimilation and fractional crystallization: Earth and Planetary Science Letters, v. 53, p. 189-202.
We were able to apply this model to estimate fractional crystallization and assimilation indicated by trace-element and isotopic compositions of a series of intrusions of high-silica rhyolite-granite porphyries associated with the Climax and Red Mountain porphyry Mo deposits (Bookstrom, Carten, Shannon, and Smith, 1988, Origins of bimodal leucogranite-lamprophyre suites, Climaz and Red M
Dear Houxiang,
I suggest you to combine (i) least-square, mass balance modelling on major elements with (ii) trace element modelling. First you have to search on the internet for a software, or spreadsheet that does the least-square, mass balance calculations (I am sorry, I do not have one on my Mac). Then, choose the starting and final compositions amongst your samples; this is done by selecting the least and the highest SiO2 contents. Then insert in the spreadsheet the chemical compositions of the likely fractionated minerals, which can done taking the chemical analyses from the literature or from your own mineral chemical analyses. Then run the experiment. The lower the squared sum of the residuals, the best the experiment. The experiment will give you also the proportion of each fractionating phase. Take these proportions and use them to calculate the bulk partition coeficient (Kd) for the trace element modelling of fractionational crystallization and make some bi-log plots of your trace element data. You can also use single mineral partition coefficients for comparison. You should allways compare the petrography of your samples with the fractionating minerals of the modelling.
Good luck!
Elson P. Oliveira
Dear Professor Janousek,
Thanks a lot for the information you provided. I will study the book once again, especially the chapters you suggested. Thank you.
Houxiang
Dear Professor Arthur Bookstrom,
Thank you for your suggestion.I will refer to the model in this reference and have a try on my data. Thanks a lot.
Dear professor Oliveira,
Long time no see. How is everything going? Thank you for the detailed reply, in which you have answered some of my puzzles. what I am still not sure is that how to decide the likely fractionated minerals. Does it have any relationship with the mineral assemblages in my rock samples? Or do I have to try again and again？Do you have any tips for this? thank you very much.
Houxiang,
the fractionated minerals depend of the initial mineral composition. You probably have already an ideia of the type of granite series the studied granite belong. If you are dealing with a calc-alkaline series, the likely minerals to fractionate and end up with evolved granites are hornblende, biotite, Ca-plagioclase, and some accessories, such as magnetite, ilmenite, and epidote. Check this first, and then go to Rollinsons book to select the appropriate kds. Get some bi-log plots (e.g. Sr-Th, Ba-Sr, Zr-Sr) just to see how your data vary. Then for the same pair of trace elements, calculate the FC values for 10%, 20%, and 50% FC (see the formulas in Rollinsons book). When you use bi-log plots the initial composition is no longer relevant, for the size and direction of the vector will allways be the same.
Have a try. If you wish to send me the plots privately, my e-mail is [email protected]
Cheers,
Elson
Dear professor Oliveira,
Thanks a lot for the valuable tips you suggested. I will have a try.
Houxiang