Confirmed detection of Palaeogene and Jurassic orbitally-forced sedimentary cycles in the depth domain using False Discovery Rates and Bayesian probability spectra

Abstract

It has been common practice to assume that power spectral backgrounds in cyclostratigraphy conform to a first-order autoregressive (AR1) model. Vaughan et al. (2011, Paleoceanography) argued that an unbiased approach to fitting the spectral backgrounds, as well as adjustment of confidence levels for multiple frequency testing, should be mandatory during the search in the depth domain for significant spectral peaks. To address these requirements Smoothed Window Averaging to find spectral backgrounds are combined with False Discovery Rates (FDR) for setting confidence levels and were applied to time series from seven Oligocene and Jurassic formations. Bayesian probability spectra provide an alternative method for detecting regular cyclicity. Pre-whitening the linearly detrended time series prior to calculation of Bayesian probabilities avoids confounding effects due to red noise.

In all seven formations there are sub-sections associated with spectral peaks exceeding the 5% FDR, in four formations they even exceed the 0.01% FDR.  Elevated Bayesian probability at the same frequencies as these significant power spectral peaks, supports the detection of regular cyclicity. This prevalence of detections conflicts with the assertion of Vaughan et al. (2011) that “almost certainly the vast majority of cycle detections … in the stratigraphy literature are false.” In previous publications spectral peaks exceeding the standard 95% level were considered significant so very high confidence levels were not reported. Nevertheless, the examples re-studied demonstrate that pre-Neogene cyclostratigraphic time series do indeed contain regular cycles most likely linked to orbital-forcing.