The detection and illustration of regular sedimentary cycles using Walsh power spectra and filtering, with examples from the Lias of Switzerland

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Abstract
Power-spectral analysis provides an objective method for the detection of regular cyclicity in data recording some oscillating parameter (or time series). Digitization of measured stratigraphic sections is a convenient method for generating long time series, during the examination of pelagic sequences for cyclicity related to orbital variations or Milankovitch cycles. The application of Walsh power-spectral analysis to stratigraphic sections is outlined and band-pass filtering using the Walsh transform introduced. It is shown that variations in sedimentation rate, hiatuses, bioturbation and variations in compaction have the effect of damping or destroying spectral peaks. The wavelength ratios of spectral peaks are often used, during studies of Milankovitch cycles, to decide which orbital cycles are involved. However, in some circumstances hiatuses are able to alter wavelength ratios. Averaged Walsh power spectra were generated for three Liassic limestone/shale sequences from Breggia Gorge, Switzerland. The 21 000 year (21 ka) precession cycle was detected in all three cases, the 100 ka eccentricity cycle in two cases and the 41 ka obliquity cycle in one. Filtering revealed that the supposed 21 ka sedimentary cycles are grouped into packets of four or five small and large amplitude cycles. The packets reflect the 100 ka modulation of the 21 ka precession cycle. Local disruption of the packaging can be used to locate hiatuses in pelagic strata.