Is Your Apatite Fission Track Annealing Parameter rmr0 Properly Calibrated?

The inter-laboratory comparison of fission track confined length and etch figure measurements of Ketcham et al. (2015; American Mineralogist; http://dx.doi.org/10.2138/am-2015-5167) reveals a frightening snapshot of the poor reproducibility of these parameters among participating analysts worldwide. Of 54 participants, an astounding 31 report that they do not measure standards, resulting in a very high degree of spread in reported means (fission track confined length and etch figure diameter parallel to c-axis D_par). Defining data spread as [standard deviation of reported means] divided by [average precision of the reported means], a spread value near 1 is expected for perfectly reproducible data, and a value <1 is unrealistic due to either incorrect calculation of precision or widespread analyst bias due to knowing the final numerical result during analysis. Ketcham et al. (2015) reported spread values ranging from 3.00-6.78 for mean lengths of single populations of fission tracks in Durango apatite (converted to mean reduced lengths where possible), and spread values for D_par ranging from 5.75-13.50, with absolute D_par values ranging from 1.26-2.39 µm. D_par is a popular proxy for apatite fission track annealing parameter r_mr0 (Carlson et al., 1999; American Mineralogist; https://doi.org/10.2138/am-1999-0901) indicating that most r_mr0 values and related thermal history modeling of apatite fission tracks in the published literature cannot be trusted.

To eliminate the need to use Dpar as a proxy, annealing parameter r_mr0 relative to apatite standard B2 (Carlson et al., 1999, American Mineralogist) is re-calibrated here (Patents Pending) using a combination of natural apatite mixtures from sandstones and selected standards. The standards include well-studied DR, FC, TI, and RN-like (Ca-F-apatite end-member) from Carlson et al. (1999). A machine learning approach is used that predicts r_mr0 based on independent chemical composition data from LA-ICP-MS.

The c-axis-projected, reduced mean length of partially annealed ²⁵²Cf-derived fission tracks is measured and converted to r_mr0 for each apatite grain studied. Absolute concentrations of Na, Mg, P, S, Cl, Ca, Mn, Fe, As, Sr, Y, 14 REEs, Th, U and relative concentrations of Al, Si, Sc, Br are determined for each grain by LA-ICP-MS using DR and other apatite species as matrix-matched standards. Of primary interest to r_mr0 is: absolute Cl, Mn, Fe, Sr, ΣREEs, and annealing state of natural FTs (pre-annealed or not; t-T path dependence?); of secondary interest is relative Br, absolute Y, Th, U, and Pb-corrected U-Pb age (t-T path dependence?); of tertiary interest is everything else including the concentrations of individual REEs.

Machine learning regression techniques fit the data including linear regression, random forests, dense neural networks, and support vector models. We compare the validation results between these regression techniques and examine the importance of each chemical composition feature as determined by the model training. The best-performing model identified so far is a random forest regressor, with a 5-fold cross-validation mean absolute error of 0.057 +/- 0.004 (1σ) on r_mr0.