ALBERT

Description: Spectral analysis is a key tool for identifying periodic patterns in sedimentary sequences, including astronomically related orbital signals. While most spectral analysis methods require equallyspaced samples, this condition is rarely achieved either in the field or when sampling sediment cores. Here, we propose a method to assess the impact on the resulting power spectra of the uncertainty or error made in the measurement of sample stratigraphic position. 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 control of the mean and variance of the sample step distribution after randomisation. We test the Monte-Carlo procedure on two geological datasets and find that at 5 % uncertainty in the sample positions, the power of the spectral peaks is signifi cantly affected in all frequencies above ~1/3 of the Nyquist frequency. The randomisation process progressively affects the lower frequencies when increasing the level of uncertainty in the sample position. With 10 % sample position uncertainty, the change in relative power exceeds 10 % in all frequencies above ~1/5 of the Nyquist frequency. For robust applications of the power spectrum, we suggest strongly controlling the measurement of the sample position, keeping the variance of the sample distribution to a maximum of 10 % of the average sample step. In addition, the simulations indicate that taking at least 6-10 samples per precession cycle should allow calculation of robust power spectra estimates in the Milankovitch band.

Description: 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.