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

Abstract

Spectral analysis is a key tool for identifying periodic patterns in sedimentary sequences, including astronomically related orbital signals. While most spectral analysis methods require equally spaced samples, this condition is rarely achieved either in the field or when sampling sediment core. Here, we propose a method to assess the impact of the uncertainty or error made in the measurement of the sample stratigraphic position on the resulting power spectra. We apply a Monte Carlo procedure to randomise the sample steps of depth series using a gamma distribution. Such a distribution preserves the stratigraphic order of samples and allows controlling the average and the variance of the distribution of sample distances after randomisation. We apply the Monte Carlo procedure on two geological datasets and find that gamma distribution of sample distances completely smooths the spectrum at high frequencies and decreases the power and significance levels of the spectral peaks in an important proportion of the spectrum. At 5 % of stratigraphic uncertainty, a small portion of the spectrum is completely smoothed. Taking at least three samples per thinnest cycle of interest should allow this cycle to be still observed in the spectrum, while taking at least four samples per thinnest cycle of interest should allow its significance levels to be preserved in the spectrum. At 10 and 15 % uncertainty, these thresholds increase, and taking at least four samples per thinnest cycle of interest should allow the targeted cycles to be still observed in the spectrum. In addition, taking at least 10 samples per thinnest cycle of interest should allow their significance levels to be preserved. For robust applications of the power spectrum in further studies, we suggest providing a strong control of the measurement of the sample position. A density of 10 samples per putative precession cycle is a safe sampling density for preserving spectral power and significance level in the Milankovitch band. For lower sampling density, the use of gamma-law simulations should help in assessing the impact of stratigraphic uncertainty in the power spectrum in the Milankovitch band. Gamma-law simulations can also model the distortions of the Milankovitch record in sedimentary series due to variations in the sedimentation rate.