Stochastic model for the deposition of varves in glacial Lake Barlow–Ojibway, Ontario, Canada

Abstract

Various methods of time series analysis have been applied to thickness data obtained from eight measured sequences of varves belonging to the Pleistocene glacial Lake Barlow–Ojibway in northern Ontario. Both sedimentological evidence and the results of the statistical analysis support Kuenen's model for varve deposition by turbidity currents.Proximally, individual varves merge with the crossbedded deltaic sands and gravel of eskers. Distally, they change successively from sandy to silty, and then to diamictic facies. Both the silt (summer) and the clay (winter) layers in a varve couplet show an approximately exponential decrease in thickness away from the icefront. This trend is more conspicuous in the silt. The genetic difference between the silt (deposited by turbidity currents) and the clay (deposited out of suspension) is reflected in marked differences in the statistical behavior of their thickness-time series.The thickness variations of both silt and clay layers can be considered as the sum of a gradual, systematic variation (signal) and a random variation (noise). When the effect of the thinning away from the icefront and that of the superimposed noise are eliminated, both the silt and clay residual thickness data satisfy a Markov model of the second order. This model is shown to be related to variations in the rate of retreat of the icefront. Besides the second-order Markov process, two weakly-developed short-term cycles have also been detected.