Elsevier

Computers & Geosciences

Volume 119, October 2018, Pages 18-28
Computers & Geosciences

Research paper
Taner filter settings and automatic correlation optimisation for cyclostratigraphic studies

https://doi.org/10.1016/j.cageo.2018.06.005Get rights and content

Highlights

  • Automatic generation of an ensemble of correlation targets based on the La2004 astronomical solution.

  • Taner filter settings for the optimal extraction of astronomical components from geological datasets are established.

  • We present a method to automatically correlate a geological dataset to an ensemble of reference records.

Abstract

Cyclostratigraphy and astronomical tuning utilize the imprint of quasi-cyclic insolation changes in geological records to establish chronologies. In this context, filtering of time series in specific frequency bands is commonly applied to extract information on astronomical forcing from geological datasets. This approach is performed on specific insolation components (precession, obliquity or eccentricity) and sometimes also their amplitudes either in depth or time domain. In this study, we design and apply a simulation technique to determine the optimal Taner filter settings to extract precession-, obliquity- and eccentricity-related interference signals from astronomically tuned geological datasets. This is done by testing a variety of filter settings on several astronomical and artificial datasets. Based on our results, we propose specific filter settings (cut-off frequencies and roll-off rates) for the best extraction of astronomical (interference) signals from tuned geological datasets. Focus here lies on datasets shorter than ca. 1 million years and interference patterns between astronomical components.

A second step utilizes these filter settings for an automated alignment, where geological data on a tuned time scale are matched to a suite of astrochronologic correlation targets. This is done by aligning filter minima and maxima to astronomical targets. This approach is particularly useful for the determination of the relative contributions of astronomical parameters in a specific dataset and allows for the automatic determination of phase shifts between well expressed insolation components in datasets.

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.

References (62)

  • S.K. Hüsing et al.

    The upper Tortonian–lower Messinian at Monte dei Corvi (Northern Apennines, Italy): completing a Mediterranean reference section for the Tortonian stage

    Earth Planet Sci. Lett.

    (2009)
  • S. Kaboth et al.

    New insights into upper MOW variability over the last 150kyr from IODP 339 Site U1386 in the Gulf of Cadiz

    Mar. Geol.

    (2016)
  • J. Laurin et al.

    Frequency modulation reveals the phasing of orbital eccentricity during Cretaceous Oceanic Anoxic Event II and the Eocene hyperthermals

    Earth Planet Sci. Lett.

    (2016)
  • L.J. Lourens et al.

    Linear and non-linear response of late Neogene glacial cycles to obliquity forcing and implications for the Milankovitch theory

    Quat. Sci. Rev.

    (2010)
  • S.B. Marković et al.

    Danube loess stratigraphy—towards a pan-European loess stratigraphic model

    Earth Sci. Rev.

    (2015)
  • H. Pälike et al.

    Extended orbitally forced palaeoclimatic records from the equatorial Atlantic Ceara rise

    Quat. Sci. Rev.

    (2006)
  • W.G. Thompson et al.

    A radiometric calibration of the SPECMAP timescale

    Quat. Sci. Rev., Critical. Quat Stratigr

    (2006)
  • L. Valero et al.

    Long-period astronomically-forced terrestrial carbon sinks

    Earth Planet Sci. Lett.

    (2016)
  • L. Valero et al.

    20 Myr of eccentricity paced lacustrine cycles in the Cenozoic Ebro Basin

    Earth Planet Sci. Lett.

    (2014)
  • J.-F. Wotzlaw et al.

    High-precision zircon U–Pb geochronology of astronomically dated volcanic ash beds from the Mediterranean Miocene

    Earth Planet Sci. Lett.

    (2014)
  • C. Zeeden et al.

    Revised Miocene splice, astronomical tuning and calcareous plankton biochronology of ODP Site 926 between 5 and 14.4 Ma

    Palaeogeogr. Palaeoclimatol. Palaeoecol.

    (2013)
  • H.A. Abels et al.

    Orbital climate forcing in mudflat to marginal lacustrine deposits in the Miocene Teruel basin (Northeast Spain)

    J. Sediment. Res.

    (2009)
  • A. Berger et al.

    Stability of the astronomical frequencies over the Earth's history for paleoclimate studies

    Science

    (1992)
  • W.B. Curry et al.

    Leg 154

    Synth. Proc. ODP Initial Rep

    (1995)
  • Z.L. Ding et al.

    Stacked 2.6-Ma grain size record from the Chinese loess based on five sections and correlation with the deep-sea δ18O record

    Paleoceanography

    (2002)
  • S.E. Harris et al.
    (1997)
  • F. Hilgen et al.

    Integrated stratigraphy and pitfalls of automated tuning

    Earth Planet Sci. Lett.

    (2012)
  • F.J. Hilgen et al.

    Stratigraphic continuity and fragmentary sedimentation: the success of cyclostratigraphy as part of integrated stratigraphy

    Geol. Soc. Lond. Spec. Publ.

    (2015)
  • L.A. Hinnov

    New perspectives on orbitally forced stratigraphy

    Annu. Rev. Earth Planet Sci.

    (2000)
  • P. Huybers et al.

    Orbital tuning, eccentricity, and the frequency modulation of climatic precession

    Paleoceanography

    (2010)
  • K.P. Kodama

    Rock Magnetic Cyclostratigraphy

    (2015)
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