[M-TT42] Frontiers in Geochemistry

[MTT42-10] Element abundance modeling method with the gamma distribution for quantitative balance calculations

*Sanshiro Enomoto^1,2, Kenta Ueki³, Tsuyoshi Iizuka⁴, Nozomu Takeuchi⁵, Akiko Tanaka⁶, Hiroko Watanabe⁷, Satoru Haraguchi⁵ (1.Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo, 2.University of Washington, 3.Japan Agency for Marine-Earth Science and Technology, 4.University of Tokyo, 5.Earthquake Research Institute, University of Tokyo, 6.National Institute of Advanced Industrial Science and Technology, 7.Research Center for Neutrino Science, Tohoku University)

Keywords:geochemical modeling, continental crust, geoneutrino

Rocks display highly variable trace element abundances, even those with similar major element compositions. To estimate the trace element compositions of geochemical reservoirs containing various rocks, such as the continental crust, trace element distributions must be modeled. Normal and log-normal distributions have been widely adopted to model trace element data of rocks and the median has been widely used as a representative value of trace element abundance. However, such modeling or treatment does not preserve the mean value of the distribution, leading to biased results of mass balance calculations. On the other hand, it is often impossible to directly use the mean of the samples because of sample imperfections due to analytical detection limits, outliers, and other reasons. Here we present a method to model unknown true distributions without causing a bias on the means, combined with proper treatment of sample cutoffs. We show that the new method preserves the mean values of ideal samples of any distributions and is robust against actual sample imperfections. Although the method was primarily developed for geoneutrino analysis in Japan, for which mass and energy balance calculations among the crust, mantle, and the whole Earth are essential, it is applicable to many balance calculations that require the conservation of mean values.