Statistics For Strontium Isotope Stratigraphy: A Robust Lowess Fit to the Marine Sr‐Isotope Curve For 0 to 206 Ma, With Look‐Up Table For Derivation of Numeric Age

Abstract

We provide a best‐fit curve to 1849 strontium isotope data for the period 0 to 206 Ma using the LOcally‐WEighted regression Scatterplot Smoother (LOWESS) method. This is a robust, nonparametric modern regression technique. Since it does not yield an explicit mathematical equation relating ⁸⁷Sr/⁸⁶Sr to time, a look‐up table to determine numeric age has been generated in steps of 1 × 10⁻⁶ in ⁸⁷Sr/⁸⁶Sr. The calibration uses the timescales of Shackleton and coworkers for 0‐7 Ma; Cande and Kent for 7‐72 Ma; Obradovich for 72‐95 Ma and Gradstein and coworkers for >95 Ma. The look‐up table includes 95% confidence intervals on the predictions of numeric age. When using this table, the uncertainty on the ⁸⁷Sr/⁸⁶Sr of the sample whose age is sought must be added to that inherent in the LOWESS regression. We show how to determine the uncertainty in ⁸⁷Sr/⁸⁶, i.e., how best to obtain the 95% confidence bounds on a single measurement of ⁸⁷Sr/⁸⁶ for a sample, and on the mean ⁸⁷Sr/⁸⁶ value for 2 or more replicate measurements of ⁸⁷Sr/⁸⁶ in the sample; these confidence intervals reflect analytical‐system reproducibility for routine samples (as opposed to that of standard control materials, e.g., NIST 987) and are necessary to establish the final upper and lower bounds on predicted numeric age.