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Volume 2018, Article ID 4968315, 18 pages
Research Article

Diagenetic Self-Organization and Stochastic Resonance in a Model of Limestone-Marl Sequences

Department of Physics, University of Ottawa, 598 King Edward Avenue, Ottawa, ON, Canada K1N 6N5

Correspondence should be addressed to Ivan L’Heureux; ac.awattou@ueruehli

Received 20 September 2017; Accepted 10 January 2018; Published 28 February 2018

Academic Editor: Qinghui Jiang

Copyright © 2018 Ivan L’Heureux. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Banded patterns in limestone-marl sequences (“rhythmites”) form widespread sediments typical of shallow marine environments. They are characterized by alternations of limestone-rich layers and softer calcareous-clayey material (marl) extending over hundreds of meters with a thickness of a few tens of meters. The banded sequences are usually thought to result from systematic variations in the external environment, but the pattern may be distorted by diagenetic nonlinear processes. Here, we present a reactive-transport model for the formation of banded patterns in such a system. The model exhibits interesting features typical of nonlinear dynamical systems: (i) the existence of self-organized oscillating patterns between a calcite-rich mode (“limestone”) and a calcite-poor one (“marl”) for fixed environmental conditions and (ii) bistability between these two modes. We then illustrate the phenomena of stochastic resonance, whereby the multistable system is driven by a small external periodic signal (the 100,000 years’ Milankovitch cycle comes to mind) that is too weak to generate oscillations between the states on its own. In the presence of random fluctuations, however, the system generates transitions between the calcite-rich and calcite-poor states in statistical synchrony with the external forcing. The signal-to-noise ratio exhibits many maxima as the noise strength is varied. Hence, this amplification effect is maximized for specific values of the noise strength.