Sr-isotope chronology of carbonate rocks: Quantifying the uncertainty of inversion

Wan, Ruoqi; Liu, Wenjian; McArthur, John M.; Wang, Zhengrong

Abstract

The ages of carbonate rocks can be determined by comparing their 87Sr/86Sr ratios with the well-established seawater 87Sr/86Sr curve. Current models and databases provide no explicit solution to the problem of accurately assigning uncertainties to derived ages when the 87Sr/86Sr ratios of carbonate rocks contain analytical uncertainties. This is particularly concerning as significant amount of 87Sr/86Sr ratios are being measured by multi-collector inductively-coupled-plasma mass-spectrometry (MC-ICP-MS) which typically has a lower precision (1σ is typically several tens of ppm) compared with thermo-ionization mass-spectrometry (TIMs, 1σ can be as low as several ppm) used for calibrating the seawater 87Sr/86Sr curve. Deriving ages from carbonate 87Sr/86Sr ratios with large analytical uncertainties could introduce significant, sometimes asymmetric uncertainties in age estimates following a non-Gaussian distribution. More importantly, uncertainties in age estimates around the local maximum/minimum and saddle points on the Phanerozoic seawater 87Sr/86Sr curve are difficult to examine using conventional methods. In this study, we developed a rigorous mathematical framework (including perturbation and probability density methods) to estimate the 95% confidence interval (or any confidence interval of interest) of the derived age with any given analytical uncertainty. We applied this method to estimating uncertainties in derived ages for one version of the Phanerozoic seawater 87Sr/86Sr curve, assessing their sources and amplitudes. Our results indicates this method has the potential to be widely applied to estimating the uncertainties in ages derived from inversions using an empirical relationship. A Matlab program is presented that can calculate the age of carbonate rocks (based on their 87Sr/86Sr ratios and analytical uncertainties), the duration of intervals between ages, and the confidence interval of choice over the last 509 Ma (Version1 is available from [e-mail] upon request).

Citation

Wan, R., Liu, W., McArthur, J. M., & Wang, Z. (2019). Sr-isotope chronology of carbonate rocks: Quantifying the uncertainty of inversion. In M. Montenari (Ed.), Stratigraphy & Timescales (35-72). Elsevier. https://doi.org/10.1016/bs.sats.2019.08.003

• Online Publication Date: Nov 9, 2019
• Publication Date: 2019
• Deposit Date: Jun 12, 2023
• Publisher: Elsevier
• Pages: 35-72
• Series Title: Case Studies in Isotope Stratigraphy
• Series ISSN: 2468-5178
• Book Title: Stratigraphy & Timescales
• Chapter Number: 2
• ISBN: 978-0-12-817552-1
• DOI: https://doi.org/10.1016/bs.sats.2019.08.003