A decomposition approach to cyclostratigraphic signal processing

Sedimentary rocks can record signals produced by highly complex processes. These signals are generated by a progressive deposition of sediments which can be affected, mainly through the climate system, by regular astronomical cycles (i.e. Milankovitch cycles), and by irregular oscillations like the El Niño-Southern Oscillation. Also, usually through biological, chemical and/or physical post-depositional processes, the sedimentary records can be affected by pattern-creating heterogeneous processes. The noise in the signals further complicates the records, and the deposition rate (or sedimentation rate) can fluctuate, which greatly reduces the effectiveness of the classical stationary time-series analysis methods commonly used in cyclostratigraphy (i.e. the study of the cycles found in the sedimentary records). Faced with this multiplicity of processes, a common approach used in cyclostratigraphy is to reduce each signal to more manageable sub-signals, either over a given range of frequencies (e.g., by filtering), or by considering a continuum of constant frequencies (e.g., using transforms). This makes it possible to focus on the features of interest, commonly astronomical cycles. However, working with sub-signals is not trivial. Firstly, sub-signals have a certain amount of cross-cancellation when they are summed back to reconstruct the initial signal. This means that in filters and in transforms, wiggles that are not present in the initial signal can appear in the sub-signals. Secondly, the sub-signals considered often cannot be summed to reconstruct the initial signal: this means that there are processes affecting the signal which remain unstudied. It is possible to take cross-cancellation into account and to consider the entire content of a signal by dividing the signal into a decomposition: a set of sub-signals that can be added back together to reconstruct the original signal. We discuss here how to reframe commonly used time-series analysis techniques in the context of decomposition, how they are affected by cross-cancellation, and how adequate they are for comprehending the whole signals. We also show that decomposition can be carried out by non-stationary time-series methods, which can minimise cross-cancellation, and have now reached sufficient maturity to tackle sedimentary records signals. We present novel tools to adapt non-stationary decomposition for cyclostratigraphic purposes, based on the concepts of Empirical Mode Decomposition (EMD) and Instantaneous Frequency (IF), mainly: (1) a fast Ensemble Empirical Mode Decomposition (EEMD) algorithm, (2) quality metrics for decomposition, and (3) plots to visualise instantaneous frequency, amplitude and frequency ratio. We illustrate the use of these tools by applying them on a greyscale signal from the site 926 of the Ocean Drilling Program, at Ceara Rise (western equatorial Atlantic), especially to identify and characterise the expression of astronomical cycles. The main goal is to show that by minimising cross-cancellation, we can apply in real signals what we call the wiggle-in-signal approach: making the sub-signals in the decomposition more representative of the expression, wiggle by wiggle, of all the processes affecting the signal (e.g., astronomical cycles). We finally argue that decomposition could be used as a practical standard output for time-series analysis interpretation of cyclostratigraphic signals.

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astronomical cycles, cyclostratigraphy, time-series analysis, Empirical Mode Decomposition (EMD)