Unveiling Geological Patterns: Bayesian Exploration of Zircon-Derived Time Series Data

For its immunity to post-formation geological modifications, zircon is widely utilized as chronological time capsule and provides critical time series data potential to unravel key events in Earth’s geological history, such as supercontinent cycles. Fourier analysis, which assumes stationary periodicity, has been applied to zircon-derived time series data to find the cyclicity of supercontinents, and wavelet analysis, which assumes non-stationary periodicity, corroborates the results of Fourier Analysis in addition to detecting finer-scale signals. Nonetheless, both methods still prognostically assume periodicity in the zircon-derived time-domain data. To stay away from the periodicity assumption and extract more objective information from zircon data, we opt for a Bayesian approach and treat zircon preservation as a composite stochastic process where the number of preserved zircon grains per magmatic event obeys logarithmic series distribution and the number of magmatic events during a geological time interval obeys Poisson distribution. An analytical solution was found to allow us to efficiently invert for the number and distribution(s) of changepoints hidden in the globally compiled zircon data, as well as for the zircon preservation potential (encoded as a model parameter) between two neighboring changepoints. If the distributions of changepoints temporally overlap with those of known supercontinents, then our results serve as an independent, mathematically robust test of the cyclicity of supercontinents. Moreover, our statistical approach inherently provides a sensitivity parameter the tuning of which allows to probe changepoints at various temporal resolution. The constructed Bayesian framework is thus of significant potential to detect other types of trend swings in Earth’s history, such as shift of geodynamic regimes, moving beyond cyclicity detection which limits the application of conventional Fourier/Wavelet analysis.