Testing astronomically tuned age models

Abstract

Astrochronology is fundamental to many paleoclimate studies, but a standard statistical test has yet to be established for validating stand-alone astronomically tuned time scales (those lacking detailed independent time control) against their astronomical insolation tuning curves. Shackleton et al. (1995) proposed that the modulation of precession's amplitude by eccentricity can be used as an independent test for the successful tuning of paleoclimate data. Subsequent studies have demonstrated that eccentricity-like amplitude modulation can be artificially generated in random data, following astronomical tuning. Here we introduce a new statistical approach that circumvents the problem of introducing amplitude modulations during tuning and data processing, thereby allowing the use of amplitude modulations for astronomical time scale evaluation. The method is based upon the use of the Hilbert transform to calculate instantaneous amplitude following application of a wide band precession filter and subsequent low-pass filtering of the instantaneous amplitude to extract potential eccentricity modulations. Statistical significance of the results is evaluated using phase-randomized surrogates that preserve the power spectrum structure of the data but have randomized amplitude modulations. Application of the new testing algorithm to two astronomically tuned data sets demonstrates the efficacy of the technique and confirms the presence of astronomical signals. Additionally, it is demonstrated that a minimal tuning approach using (at maximum) one precession cycle per~100 kyr eccentricity cycle does not introduce systematic frequency modulations, even when a narrow band-pass filter is applied, allowing direct comparison of data amplitudes and orbital eccentricity.

Reinforcing the North Atlantic backbone: revision and extension of the composite splice at ODP Site 982

“…Initially, a minimal tuning strategy was applied (similar to Holbourn et al, 2007), where δ 18 O minima were correlated to E+T-P maxima using 20 tie 5 points (green lines - Figure 5; Supplementary Figure 3 and Table 7). The correlation was restricted to approximately one tie point per ~100 kyr cycle, as recommended by Zeeden et al (2015) to avoid the introduction of frequency modulation through the astronomical tuning process. Finally, following a fine-tuning strategy, an additional 41 tie points were added between the E+T-P maxima and δ 18 O minima (orange lines - Figure 5; Supplementary Table 7).…”

Stratigraphic continuity and fragmentary sedimentation: the success of cyclostratigraphy as part of integrated stratigraphy

“…Nevertheless, given that real data amplitudes (and not frequencies introduced by the tuning process) are investigated, amplitudes of precession-related signals filtered from a geological record can be compared to orbital eccentricity, which modulates the precession amplitude. A reasonable fit between the amplitude of a precession-related component from a geological record and eccentricity is a very convincing argument for the orbital forcing of a geological time series (Zeeden et al 2013). Datasets showing real amplitudes corresponding to amplitudes of Milankovitch parameters can be interpreted as astronomically forced.…”

“…The eccentricity modulation of the precession signal can be investigated in these records (e.g. Hinnov 2000) although with caution (Huybers & Aharonson 2010;Zeeden et al 2013). Such distortions also point to the problem of false negatives rather than that of false positives in the spectral analysis of palaeoclimatic records.…”

“…These real amplitude variations are not introduced by the tuning process but are an attribute of the climate proxy data themselves. Such variations can thus be used to test whether a tuned time series is consistent with an astronomical target, as was performed by, for example, Pälike & Shackleton (2000), Pälike et al (2004Pälike et al ( , 2006b), Shackleton & Crowhurst (1997), Shackleton et al (1999), Westerhold et al (2007) and Zeeden et al (2013). Complex amplitude demodulation provides the statistical means to use amplitude for testing an astronomical tuning in the time domain (Shackleton & Crowhurst 1997).…”

Testing the impact of stratigraphic uncertainty on spectral analyses of sedimentary series

“…Linking sedimentary cycles to orbital cycles or assessing the quality of an orbital tuning procedure often requires a good matching between the sedimentary period ratios and the orbital period ratios (Huang et al, 1993;Martinez et al, 2012;Meyers and Sageman, 2007) and/or the determination of the amplitude modulation of the orbital cycles Moiroud et al, 2012;Zeeden et al, 2015). On average, stratigraphic uncertainties trigger a decrease in the power spectrum of the main significant frequencies while distributing the power spectrum to the surrounding frequencies.…”