Cyclostratigraphy of Paleoproterozoic Sedimentary Records and Reconstruction of Earth-Moon System Parameters

The Paleoproterozoic represents a pivotal but poorly constrained interval in the tidal evolution of the Earth–Moon system. Quantifying Earth–Moon orbital parameters over this interval is fundamental for predicting the long-term dynamical evolution of the Earth–Moon system, yet direct geological evidence remains scarce. In this study, we conducted cyclostratigraphic analyses of the middle and upper members of the Dagushi Formation on the southern margin of the North China Craton, using high-resolution magnetic susceptibility (MS) and phosphorus (P) data as paleoclimate proxies. By employing two independent astrochronologic approaches—the main obliquity estimation method (k+s3) and Bayesian inversion (TimeOptMCMC)—we reconstructed key parameters of the Earth–Moon system, including the precession constant k, Earth–Moon distance, and length of day (LOD). The k+s3 approach yields k=98.12±1.07 arcsec/yr, from which the Earth–Moon distance is derived as 329,732 (+888/−877) km, with a LOD of 17.69±0.08 h. In contrast, the TimeOptMCMC method produces k=95.20±1.68 arcsec/yr, implying an Earth–Moon distance of 331,292 (+1446/−1418) km, with a LOD of 17.91±0.13 h. The MS and P indicators exhibit remarkable symmetry and phase synchronicity between their curves in both depth and time domains, serving as a robust indicator of stable sedimentation and primary depositional signals. These results provide direct geological constraints on Earth–Moon system parameters at ∼1787 Ma, contributing to a refined understanding of its tidal evolution during the Paleoproterozoic.