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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 delta O-18 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 similar to 760 million year cycle over the 4.4 billion years of Earth's history. Wavelet coherence analysis shows that the U-Pb age and delta O-18 systems are coupled in significant in-phase coherence for a cycle of similar to 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(beta) scaling behavior that persists beta similar to 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 similar to 670,000 U-Pb ages and similar to 6,000 delta O-18 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 delta O-18 isotope systems are coupled in significant in-phase coherence with a strong persistent similar to 760Ma cycle throughout geological time similar to 4.4Ga. 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.