Proterozoic Milankovitch cycles and the history of the solar system

Abstract

The geologic record of Milankovitch climate cycles provides a rich conceptual and temporal framework for evaluating Earth system evolution, bestowing a sharp lens through which to view our planet's history. However, the utility of these cycles for constraining the early Earth system is hindered by seemingly insurmountable uncertainties in our knowledge of solar system behavior (including Earth-Moon history), and poor temporal control for validation of cycle periods (e.g., from radioisotopic dates). Here we address these problems using a Bayesian inversion approach to quantitatively link astronomical theory with geologic observation, allowing a reconstruction of Proterozoic astronomical cycles, fundamental frequencies of the solar system, the precession constant, and the underlying geologic timescale, directly from stratigraphic data. Application of the approach to 1.4-billion-year-old rhythmites indicates a precession constant of 85.79 ± 2.72 arcsec/year (2σ), an Earth-Moon distance of 340,900 ± 2,600 km (2σ), and length of day of 18.68 ± 0.25 hours (2σ), with dominant climatic precession cycles of ∼14 ky and eccentricity cycles of ∼131 ky. The results confirm reduced tidal dissipation in the Proterozoic. A complementary analysis of Eocene rhythmites (∼55 Ma) illustrates how the approach offers a means to map out ancient solar system behavior and Earth-Moon history using the geologic archive. The method also provides robust quantitative uncertainties on the eccentricity and climatic precession periods, and derived astronomical timescales. As a consequence, the temporal resolution of ancient Earth system processes is enhanced, and our knowledge of early solar system dynamics is greatly improved.

Keywords: Bayesian inversion; Earth–Moon history; Milankovitch cycles; astrochronology; fundamental frequencies.

Fig. 1.

TimeOptMCMC results for the ∼1.4 Ga Proterozoic Xiamaling Formation Cu/Al data (9) and the ∼55 Ma Eocene Walvis Ridge a* (red/green) data (10). (A) Xiamaling Cu/Al data versus stratigraphic height. (B) Astronomically tuned Xiamaling Cu/Al data, using the TimeOptMCMC derived posterior mean sedimentation rate (Table 2). The data series has been standardized to unit variance, and a linear trend has been removed. (C) Xiamaling Cu/Al data precession envelope (red line) for the posterior mean sedimentation rate, and precession filter output (blue line). The black line illustrates the TimeOpt reconstructed eccentricity model. (D) Xiamaling Cu/Al data power spectrum (squared Fourier transform) using the posterior mean sedimentation rate. The vertical dashed red lines indicate the reconstructed target periods (mean posterior values in Table 2) for climatic precession and eccentricity, and the blue line illustrates the frequency response of the bandpass filter for precession modulation evaluation. (E) Eocene Walvis Ridge a* data versus meters composite depth (mcd). (F) Astronomically tuned Walvis Ridge a* data, using the TimeOptMCMC derived posterior mean sedimentation rate (Table 2). The data series has been standardized to unit variance, and a linear trend has been removed. (G) Walvis Ridge a* data precession envelope (red line) for the posterior mean sedimentation rate, and precession filter output (blue line). The black line illustrates the TimeOpt reconstructed eccentricity model. (H) Walvis Ridge a* data power spectrum (squared Fourier Transform) using the posterior mean sedimentation rate. The vertical dashed red lines indicate the reconstructed target periods for climatic precession and eccentricity (Table 2), and the blue line illustrates the frequency response of the bandpass filter for precession modulation evaluation.

Fig. 2.

Summary of TimeOptMCMC prior and posterior distributions for the ∼1.4 Ga Proterozoic Xiamaling Formation Cu/Al data (9), and the ∼55 Ma Eocene Walvis Ridge Site 1262 a* (red/green) data (10). (A–F) Prior (red line) and posterior (histogram) probability distributions for Xiamaling Formation sedimentation rate, precession constant, length of day, long eccentricity period, short eccentricity periods, and climatic precession periods (C). (G–L) Prior (red line) and posterior (histogram) probability distributions for Eocene Walvis Ridge Site 1262 sedimentation rate, precession constant, length of day, long eccentricity period, short eccentricity periods, and climatic precession periods (I). See Table 1 for the relationship between g, k, and observed astronomical periods. See Table 2 for the mean posterior values associated with each distribution shown in this figure.

Fig. 3.

TimeOptMCMC reconstructed Earth–Moon distance, compared with two tidalite-based estimates and two models. Uncertainties in Earth–Moon distance are ±2σ and age uncertainties span minimum and maximum values. The Bayesian posterior TimeOptMCMC estimates for the Proterozoic Xiamaling Formation and Eocene Walvis Ridge are indicated with blue symbols. Note the significant improvement in precision between posterior (blue) and prior estimates for the Xiamaling data (prior = 319,743 to 380,309 km; 2σ). Age uncertainties for the Xiamaling and Walvis Ridge results fall within the size of the blue symbols. Tidalite estimates from the Big Cottonwood Formation (∼900 Ma; ref. 22) and Elatina Formation and Reynell Siltstone (∼620 Ma; ref. 23) are shown with dark green symbols (based on the updated analyses of ref. 16). The light green Big Cottonwood Formation estimate (364,192 km) is an alternative value reported by ref. with uncertainties from the 348,884-km estimate (dark green symbol). The ocean model (red line), and a model using the present rate of tidal dissipation (black line), derive from ref. .