Fig. 3: Power ratio relationship between ~20-kyr and ~100-kyr components in linear and nonlinear threshold systems.

A 1E1T-1P curve over the past 34 Ma, generated by normalizing and averaging variations in eccentricity (E), tilt (T), and reversed precession (P) based on La04 solution⁷⁴. B, C The ~20-kyr and ~100-kyr spectral power ratios of the 1E1T-P datasets, displaying an in-phase correlation between them. D 0E0T-1P curve over the past 34 Ma, with the weight of E, T, P being 0, 0, and -1, based on La04 solution⁷⁴. E the clipped/rectified 0E0T-1P with a threshold setting of 0. F, G The ~20-kyr and ~100-kyr spectral power ratios of the clipped 0E0T-1P, exhibiting a nearly anti-phase correlation between them. H, I The 2π-MTM spectra of 0E0T-1P and the clipped 0E0T-1P. The clipping effect can amplify the ~100-kyr power ratio in the datasets, and induce prominent 405-kyr component, which is absent in the marine benthic δ¹⁸O and ice volume curve. J the relationship between threshold used to clip the 0E0T−1P curve, and the resulting ~100-kyr power ratios in the corresponding clipped 0E0T-1P curves. The precession parameter poses a negative effect on the strength of northern hemisphere summer insolation; thus, a more negative threshold value indicates a stronger threshold effect. With the increase in threshold (more negative), the ~100-kyr power ratio increases, whereas an upper limitation exists (<0.2).