Research paperTaner filter settings and automatic correlation optimisation for cyclostratigraphic studies
Introduction
Cyclostratigraphy relates quasi-cyclic patterns in sediments to astronomical characteristics which in turn are used for time scale reconstructions (e.g. Hinnov, 2000; Hinnov and Hilgen, 2012; Hilgen et al., 2015). These are then further aided by other dating techniques (i.e. Ar/Ar and U/Pb dating). Generally, the quasi-cyclic patterns are extracted from geological datasets by filtering the data in the depth or time domain (e.g. Valero et al., 2014, 2016; Martinez and Dera, 2015; Da Silva et al., 2016). During the Neogene, direct astronomical tuning is often possible at the scale of precession (∼20 kyr; e.g. Shackleton and Crowhurst, 1997; Lourens et al., 2001; Abels et al., 2009; Zeeden et al., 2014). In particular, precession filtering of geological data and the extraction of their respective amplitudes have been used to reconstruct the astronomical imprint within geological datasets (e.g. Ding et al., 2002; Lourens et al., 2010). These filtered data patterns and amplitudes are also applied to test tuned time scales (Shackleton et al., 1995; Meyers, 2015; Zeeden et al., 2015). Yet, filter settings are commonly chosen quite arbitrarily, and we are aware of only one study which systematically investigates the effect of filter settings (Li et al., 2018).
Hence, we focus on filtering individual precession-obliquity and eccentricity cycles in a most representative way. We highlight that the filter settings suggested in this study are unsuitable for extracting amplitude variations of cycles, as for such investigations the full span of astronomical forcing must be included (see e.g. Hinnov, 2000), and wider filters must be applied (Zeeden et al., 2015).
Here, we focus on two different aspects related to cyclostratigraphy and time scale reconstructions: (1) Taner filters and (2) automated alignment of filter extremes to correlation targets. We focus on Taner filters (Taner, 1992) as they (a) are available in the ‘astrochron’ R package (a widely used method in cyclostratigraphy; Meyers, 2014; R Core Team, 2017) and in matlab (http://mason.gmu.edu/∼lhinnov/cyclostratigraphytools.html), and allow for automated application to various datasets, (b) their filter properties such as high and low filter cut-off frequencies and the roll-off rate, a parameter for the steepness of the filter boundaries, can easily be adjusted, and (c) they enjoy increasing popularity in the cyclostratigraphic community, (e.g. Wu et al., 2013; Boulila et al., 2014, 2015; Meyers, 2015; Laurin et al., 2016; Martinez et al., 2017). An intuitive visualisation of the Taner filter and its properties is given in Kodama (2015; their Fig. 4.5). Comparing filters of geological data and astronomical targets, and especially their amplitudes, can give a direct (visual) impression of similarity.
Automated correlation is often regarded as a helpful tool and several methods have been proposed and published (Olea, 1994; Lisiecki and Lisiecki, 2002; Pälike, 2002; Huybers and Aharonson, 2010; Lin et al., 2014; Kotov et al., 2016; Edwards et al., 2018), and used (e.g. Lisiecki and Raymo, 2005; Pälike et al., 2006b; Necula and Panaiotu, 2008; Lang and Wolff, 2011; Liebrand et al., 2011). Generally, these methods aim at a high-resolution correlation based on an initial time scale. However, they do not enjoy great popularity within the geosciences community. This may be because no-easy-to-use open source application was made available for cyclostratigraphic and geochronologic applications until recently (Kotov et al., 2016), while also care must be taken to take additional constraints from integrated stratigraphy into account (Hilgen et al., 2012) to avoid errors in automated correlation. The fear of geoscientists to be replaced by algorithms may also contribute to limit the application of such methods.
We suggest that automatic correlation approaches become especially useful when their freedom in changing sedimentation rates is limited, and an initial (tuned) time scale is the basis for further improvements. Here we describe and provide algorithms that (a) create an ensemble of tuning targets based on variable contributions of the individual astronomical parameters as well as variable phase relationships between them (Laskar et al., 2004), and (b) automatically optimise a correlation between a geological record and a specific target or an ensemble of tuning targets by aligning filtered data extremes (i.e., minima and maxima) to those in the targets.
Section snippets
Taner filter settings for cyclostratigraphy: concept
To find the best Taner filter settings for astrochronologic applications, we test the frequency range and steepness of various Taner filter settings. This is done by using the precession, obliquity and eccentricity from the La2004 astronomical solution (Laskar et al., 2004). In addition, a set of signal- and time-distortions are imposed on the solution, and the extraction of astronomical signals is tested on these datasets (see Table 1 for an overview). The details of these tests are outlined
Filter settings and generation of correlation targets
Table 1 summarizes the results from the experiments investigating different filter settings for precession and Supplementary Tables 1 and 2 contain the results for obliquity and eccentricity. Please note that these results are partly based on resampling procedures and noise generation from specified distributions. To make results reproducible we set a seed in the R code. For all experiments, we investigate whether the ideal filter properties represent real optima in the settings, or if these
Filter settings
Here we suggest specific filter settings for the optimal reconstruction of astronomical parameters from geological datasets. We propose to use cut-off frequencies of 0.043 and 0.054 [1/kyr] for filtering precession related signals and 0.022 and 0.029 [1/kyr] for obliquity. For eccentricity, the filter results (0.003 and 0.012 [1/kyr]) describe the periodicities around 100 kyr well. In case of lower and very low frequency eccentricity components (e.g. Boulila et al., 2012; Martinez and Dera, 2015
Conclusions
Here we propose specific Taner filter settings to extract astronomical scale variations from geological tuned time series. Our experiments suggest the following filter properties for Quaternary and Neogene studies: For precession, filter boundaries are optimally set at frequencies of 0.043 and 0.054 using a roll-off rate of 1028. These consistently perform well in a set of experiments with artificial data. For obliquity, we suggest setting upper and lower filter limits at 0.022 and 0.029 and
Author contributions*
*CZ carried out the programming and designed the study. SK helped applying methods to several test datasets, discussed these, and ensured suitable implementation. FH and JL oversaw the study and discussed the implementation and documentation. All authors contributed to the manuscript creation by writing, discussing changes for clarity and technical usefulness and correctness.
Computer Code Availability
All computer code described here is available as code in the R language in supplementary materials. It was designed by C. Zeeden, IMCCE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Lille, 75014 Paris, France. Phone: +33 1 4051 2038. The code requires a decent computer, and the R software including the ‘astrochron’ package installed.
Competing interests statement
No author has a competing interest.
Acknowledgements
CZ is financed through an PSL post-doctoral fellowship. All datasets used in this study are available in the Pangaea database, computer code is available as supplementary information. Four reviewers are thanked for their constructive comments which helped to improve this study.
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