Cyclicity and Persistence of Earth's Evolution Over Time: Wavelet and Fractal Analysis

Accessing the cyclicity and persistence of geological records with time series analysis deepens our understanding of Earth's long‐term evolution. In this study, time series from recent global zircon U‐Pb age and δ18O databases are analyzed using wavelet transform from a fractal perspective. Continuous wavelet transform of the local fractal sequences of both zircon records indicates a strong, persistent ~760 million year cycle over the 4.4 billion years of Earth's history. Wavelet coherence analysis shows that the U‐Pb age and δ18O systems are coupled in significant in‐phase coherence for a cycle of ~760 million year, implying synchronization between the two underlying processes. This study also demonstrates that the variation in the time series records manifests as 1/f β scaling behavior that persists β ~ 1.8 over the entire interval. This 1/f fractal scaling nature furnishes evidence for the conjecture that rather than being an equilibrium system, Earth's long‐term evolution follows a self‐organized pattern. Plain Language Summary Determining the cyclicity and persistence of Earth's long‐term evolution can provide important clues for understanding the formation and growth of the continental crust. Significant obstacles to address the above questions include a lack of adequate data for global geological records over the course of Earth history and the sophistication of the time series analysis of these data. The recently improved global database of ~670,000 U‐Pb ages and ~6,000 δ18O isotope analyses from zircon grains allows the periodicity analysis of geological time series by a popular method of wavelet transform, form a fractal perspective. We found that the U‐Pb age and δ18O isotope systems are coupled in significant in‐phase coherence with a strong persistent ~760 Ma cycle throughout geological time ~4.4 Ga. We also demonstrate the harmonically (1/f) fractal nature of zircon time series, which provides evidence for the conjecture that the Earth's long‐term evolution is a self‐organized, far from equilibrium system. Key Points A persistent ~760 Ma cycle is identified in global zircon records across 4.4 Ga U‐Pb age and δ18O systems are coupled in in‐phase coherence for an ~760 Ma cycle Earth's long term evolution is demonstrated with 1/f fractal nature