Geological records reveal chaotic diffusion during the Late Paleozoic Ice Age

Chaotic diffusion arising from the long-term gravitational interactions between Earth and Mars has increasingly been recognized as a fundamental part of the chaotic behavior of the Solar system, yet investigations into chaotic orbital modulation during deep-time icehouse intervals remain poorly constrained by geological evidence. Here, high-resolution gamma-ray (GR) datasets from marine (Lower Wolfcamp Formation in the Permian Basin) and terrestrial (Lucaogou Formation in the Junggar Basin) successions record chaotic diffusion during the Late Paleozoic Ice Age (LPIA). Multitaper spectral analyses of the tuned GR series reveal prominent Milankovitch-scale periodicities. Million-year-scale modulation is assessed using the amplitude modulation (AM) spectrum of short eccentricity and the power spectra of eccentricity and obliquity band-power series, revealing modulations near ∼1.5 Myr and ∼1.0 Myr, respectively. These modulations agree with theoretical predictions of Earth-Mars secular interactions ( g 4 - g 3 , s 4 - s 3 ), suggesting a persistent chaotic diffusion throughout the LPIA. Despite differences in paleogeography, lithology, and depositional age, both sedimentary archives capture these long-period orbital cycles, indicating that chaotic orbital behavior exerted a sustained influence on astronomical forcing. In addition, intervals marked by enhanced short-eccentricity modulation and elevated obliquity-band power broadly coincide with glacial expansions and sea-level fluctuations, implying that chaotic diffusion may have amplified climate oscillations and ice-sheet variability. These findings provide further geologic evidence of chaotic behavior of the Solar system during the LPIA, deepening our understanding of how chaotic drift in planetary orbits influences large-scale icehouse conditions.