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Cycle pathology

West Bay.jpg

In the search for stratigraphic cyclicity, false positives may be the norm, says Simon Vaughan*

Geoscientist Online 24 November 2011

Image: Toarcian sands showing 'cyclic' sedimentation pattern frequently ascribed to orbitally induced climatic fluctuations.  Photo: Ted Nield, from the Society's Online Photolibrary.

Detecting Milankovitch-band (orbitally-forced) cyclicity in stratigraphic data holds out the tantalising possibility of time calibration. Most of such detections derive from statistical analyses of power spectra; but in a new paper Vaughan, Bailey and Smith1 demonstrate that many (perhaps the majority) of those in the literature (generated by procedures that have become the standard) are false.

Stratigraphic data suitable for spectral analysis comprise measurements of rock properties taken at regularly-spaced intervals. The key question concerns the nature of the peaks in the ‘red noise’ power spectra that these data display. Do the peaks represent cycles, or chance fluctuations from the noise? Significance tests are then used to answer the question: “How unlikely is it that a peak in the observed spectrum was generated by the noise?”


One problem in the detection of quasi-periodic (M-) forcing in stratigraphic data is the generally unknown relationship between stratal thickness and geological time. The question thus becomes: “Are there any cycles in the data?” Answering this means testing each of perhaps hundreds of frequencies in the spectrum; but despite using the canonical p < 0.05 threshold for detection, the multiple testing methods commonly used will result in false positives for almost any reasonably-sized dataset. This fact is easily demonstrated with cycle-free synthetic, random data. There are simple methods to correct for the effect of multiple tests, but these are not routinely applied in cyclo-stratigraphic analysis.

The result of the significance test is conditional on the null hypothesis model adopted for the noise in the data series. Apparent ‘detections’ will arise wherever the noise model differs significantly from the data, whether or not this difference arises as a result of cyclic variations or an undiagnosed mismatch between the noise model and the noise spectrum in the data.

The model most often used in cyclo-stratigraphic work is the autoregressive AR(1), a simple process characterised by only two parameters. It would be surprising if a wide range of different and complex sedimentary systems all generated variations with such simple statistical properties. Vaughan et al. demonstrate that real datasets often display power spectra rather different from the simplistic AR(1) case. This data-model mismatch is another source of spurious cycle detections, and goes unnoticed because model checking is not routinely applied in stratigraphic spectral analysis.

Vaughan et al. analysed four well-known datasets for which cyclicities have been claimed, applying model checking and accounting for multiple tests. The cyclicity detections were reproduced, in only one case. This suggests that the majority of published reports of regular Milankovitch-band cyclicities (eg in Paleogene, Mesozoic, and older strata), and the resultant astrochronological time calibrations, are based on statistically unsound detections. On a positive note, the more general approaches outlined by Vaughan et al. allow for the investigation of a wider range of spectral features than considered by the standard approaches.


  • Vaughan, S, Bailey R J and Smith D G (2011): Detecting cycles in stratigraphic data: Spectral analysis in the presence of red noise. Paleoceanography, 26, PA4211, doi:10.1029/2011PA002195.
  • See also Robin Bailey’s recent Soapbox article in Geoscientist, "Spare me the cycles".
* Dept. Physics & Astronomy, University of Leicester, Leicester, LE1 7RH, UK E: [email protected]