Joint determination of K decay constants and Ar∗/K for the Fish Canyon sanidine standard, and improved accuracy for Ar/Ar geochronology

⁴⁰Ar/³⁹Ar and K-Ar geochronology have long suffered from large systematic errors arising from imprecise K and Ar isotopic data for standards and imprecisely determined decay constants for the branched decay of ⁴⁰K by electron capture and β⁻ emission. This study presents a statistical optimization approach allowing constraints from ⁴⁰K activity data, K-Ar isotopic data, and pairs of ²³⁸U-²⁰⁶Pb and ⁴⁰Ar/³⁹Ar data for rigorously selected rocks to be used as inputs for estimating the partial decay constants (λ_ε and λ_β) of ⁴⁰K and the ⁴⁰Ar∗/⁴⁰K ratio (κ_FCs) of the widely used Fish Canyon sanidine (FCs) standard. This yields values of κ_FCs = (1.6418 ± 0.0045) × 10⁻³, λ_ε = (0.5755 ± 0.0016) × 10⁻¹⁰ a⁻¹ and λ_β = (4.9737 ± 0.0093) × 10⁻¹⁰ a⁻¹. These results improve uncertainties in the decay constants by a factor of >4 relative to values derived from activity data alone. Uncertainties in these variables determined by our approach are moderately to highly correlated (cov(κ_FCs, λ_ε) = 7.1889 × 10⁻¹⁹, cov(κ_FCs, λ_β) = −7.1390 × 10⁻¹⁹, cov(λ_ε, λ_β) = −3.4497 × 10⁻²⁶) and one must take account of the covariances in error propagation by either linear or Monte Carlo methods. ⁴⁰Ar/³⁹Ar age errors estimated from these results are significantly reduced relative to previous calibrations. Also, age errors are smaller for a comparable level of isotopic measurement precision than those produced by the ²³⁸U/²⁰⁶Pb system, because the ⁴⁰Ar/³⁹Ar system is now jointly calibrated by both the ⁴⁰K and ²³⁸U decay constants, and because λ_ε(⁴⁰K) < λ(²³⁸U). Based on this new calibration, the age of the widely used Fish Canyon sanidine standard is 28.305 ± 0.036 Ma. The increased accuracy of ⁴⁰Ar/³⁹Ar ages is now adequate to provide meaningful validation of high-precision U/Pb or astronomical tuning ages in cases where closed system behavior of K and Ar can be established.     

Statistical Methods for Jointly Estimating the Decay Constant of 40K and the Age of a Dating Standard

Mathematical Geosciences - To simultaneously evaluate the decay constant of 40K (λ) and the age of a standard (t std) using isotopic data from geologic materials, we applied a series of...     

Extensional deformation along the southern boundary of the Gyeonggi Massif,South Korea: structural characteristics,age constraints,and tectonic implications

The Permo–Triassic collision of the North and South China blocks caused the development of the Dabie–Sulu Orogen in China and Songrim Orogen in the Korean Peninsula. Extension after this collision is known from the Dabie–Sulu Orogen, but post-orogenic extension is not well defined in the Korean Peninsula. Extensional deformation along the southern boundary of the Gyeonggi Massif in Korea is characterized by top–down-to-the-south ductile shearing and subsequent brittle normal faulting, and was predated by regional metamorphism and north-vergent contractional deformation. Extension occurred between ~220 and 185 Ma based on the ages of pre-extensional regional metamorphism and post-extensional pluton emplacement. ⁴⁰Ar/³⁹Ar dating of syn-extensional muscovite in quartz–mica mylonite yields an age of 187.8 ± 5.6 (2σ) Ma, in agreement with constraints from structural relationships. Together with the extensional deformation identified along the northern boundary of the Gyeonggi Massif (~226 Ma), the extension along the southern boundary is probably related to the exhumation of the massif during late-orogenic or post-orogenic extension associated with the Songrim Orogeny of the Korean Peninsula and forms an important event in the Phanerozoic crustal evolution of East Asia.     

Statistical Methods for Jointly Estimating the Decay Constant of 40K and the Age of a Dating Standard

To simultaneously evaluate the decay constant of ⁴⁰K () and the age of a standard (t _std) using isotopic data from geologic materials, we applied a series of statistical methods. The problem of estimating the most probable intercept of many nonlinear curves in and t _std space is formulated by an errors-in-variables nonlinear regression model. Then a maximum likelihood method is applied to the model for a point estimate, which is equivalent to the nonlinear least square method when measurement error distributions are Gaussian. Uncertainties and confidence regions of the estimates can be approximated using three methods: the asymptotic normal approximation, the parametric bootstrap method and Bonferroni confidence regions. Five pairs of published data for samples with ages from 2 ka to 4.5 Ga were used to estimate and the age of Fish Canyon sanidine (t _FCs). The statistical procedure yields most probable estimates of (5.4755 ± 0.0170 × 10^–10 (1)/year) and t _FCs (28.269 ± 0.0661 (1) Ma) which are in between previously published values. These results indicate the power of our approach to provide improved constraints on these parameters, although the preliminary nature of some of the input data require further review before the values can be adopted.     

Geology of the 2018 Winter Olympic site,Pyeongchang, Korea

We review the geology of the Gyeonggi Massif, Gyeonggi Marginal Belt, and Taebaeksan Basin of the Korean Peninsula, which are relevant to the 2018 Winter Olympic sites. Neoarchaean–Palaeoproterozoic gneisses and schists of the Gyeonggi Massif underwent two distinct collisional orogenies at the Palaeoproterozoic (1.88–1.85 Ga) and Triassic (245–230 Ma). These basement rocks are structurally overlain by a suite of Mesoproterozoic to Early Permian supracrustal rocks of the Gyeonggi Marginal Belt, consisting primarily of medium-pressure schists and amphibolites metamorphosed at ~270–250 Ma. In contrast, sedimentary successions in the Taebaeksan Basin, commonly fossiliferous, consist primarily of Early Cambrian–Middle Ordovician Joseon Supergroup and Late Carboniferous–Early Triassic Pyeongan Supergroup. The ‘Great Hiatus’ between the two supergroups is characteristic for the North China Craton. The marked contrast in tectonometamorphic evolution between the Taebaeksan Basin and Gyeonggi Marginal Belt suggests an existence of major suture in-between, which is most likely produced by the Permian–Triassic continental collision between the North and South China cratons. Finally, recent tectonics of the Korean Peninsula is governed by the opening of East Sea/Sea of Japan during the Late Oligocene–Early Miocene. This back-arc rifting event has resulted in an exhumation of the Taebaek Mountain Range, estimated to be 22 ± 3 Ma on the basis of apatite (U–Th)/He ages. Thus, high topography in the 2018 Winter Olympic sites is the consequence of Tertiary tectonics associated with the opening of a back-arc basin.