WaverideR {WaverideR}

Extracting Signals from Wavelet Spectra

Description

The continuous wavelet transform enables the observation of transient/non-stationary cyclicity in time-series. The goal of cyclostratigraphic studies is to define frequency/period in the depth/time domain. By conducting the continuous wavelet transform on cyclostratigraphic data series one can observe and extract cyclic signals/signatures from signals. These results can then be visualized and interpreted enabling one to identify/interpret cyclicity in the geological record, which can be used to construct astrochronological age-models and identify and interpret cyclicity in past and present climate systems.

Details

Package: 'WaverideR'

Type: R package

Version: 0.3.2 (begin of 2023)

License: GPL (= 2)

Note

If you want to use this package for publication or research purposes, please cite:

Arts, M.C.M (2023). WaverideR: Extracting Signals from Wavelet Spectra. https://CRAN.R-project.org/package=WaverideR

Author(s)

Michiel Arts

Maintainer: Michiel Arts [e-mail]

References

The 'WaverideR' package builds upon existing literature and existing codebase. The following list of articles is relevant for the 'WaverideR' R package and its functions. Individual articles are also cited in the descriptions of function when relative for set function. The articles in the list below can be grouped in four subjects: (1) Cyclostratigraphic data analysis, (2) example data sets, (3) the (continuous) wavelet transform and (4) astronomical solutions). For each of these categories the relevance of set articles will be explained in the framework of the 'WaverideR' R package.

# 1. Cyclostratigraphic data analysis

Stephen R. Meyers, Cyclostratigraphy and the problem of astrochronologic testing, Earth-Science Reviews,Volume 190,2019,Pages 190-223,ISSN 0012-8252 doi:10.1016/j.earscirev.2018.11.015
The 'astrochron' R package is the most extensive R package with regards to cyclostratigraphic analysis. As such many of the functionalities of the 'WaverideR' R package are #' inspired/based on the 'astrochron' R package. The major difference between #' the 'astrochron' R package and the 'WaverideR' package is that the #' astrochron' R package relies on the Fast Fourier Transform whereas

S.R. Meyers, 2012, Seeing Red in Cyclic Stratigraphy: Spectral Noise Estimation for Astrochronology: Paleoceanography, 27, PA3228, doi:10.1029/2012PA002307
The article of Meyers (2012) explains how the (Multitaper method) MTM technique implemented into The 'astrochron' R package The MTM method can be used to assign confidence levels to spectral peaks and distinguish spectral peaks from harmonic spectral peaks.

Acycle: Time-series analysis software for paleoclimate research and education, Mingsong Li, Linda Hinnov, Lee Kump, Computers & Geosciences,Volume 127,2019, Pages 12-22,ISSN 0098-3004, doi:10.1016/j.cageo.2019.02.011
The 'Acycle' software package is a 'Matlab' based program, which is used for cyclostratigraphic studies. Acycle relies mostly on the Fast Fourier Transform. The 'Coco' and 'eCoco' functions from Acycle formed the inspiration for the flmw sum_power_sedrate functions of the ‘Waverider’ R package.

Tracking variable sedimentation rates and astronomical forcing in Phanerozoic paleoclimate proxy series with evolutionary correlation coefficients and hypothesis testing, Mingsong Li, Lee R. Kump, Linda A. Hinnov, Michael E. Mann, Earth and Planetary Science Letters,Volume 501, 2018,Pages 165-179, ISSN 0012-821X, doi:10.1016/j.epsl.2018.08.041
Li et al., (2019) introduces the Coco and eCoco functions of the Acycle software package. the 'Coco' and 'eCoco' function of the 'Acycle' software are able to estimate the sedimentation rate based on spectral characteristics of astronomical cycles. The 'Coco' and 'eCoco' function and form the inspiration for the flmw and sum_power_sedrate functions of the 'WaverideR' Package.

Wouters, S., Crucifix, M., Sinnesael, M., Da Silva, A.C., Zeeden, C., Zivanovic, M., Boulvain, F., Devleeschouwer, X., 2022, "A decomposition approach to cyclostratigraphic signal processing". Earth-Science Reviews 225 (103894).doi:10.1016/j.earscirev.2021.103894
Wouters et al., (2022) introduces the Empirical Mode Decomposition (EMD) as part of the 'DecomposeR' R package. EMD is a non-Fast Fourier Transform based spectral analysis technique. The Hilbert transform function inst.pulse of this package is used in WaverideR functions extract_amplitude and Hilbert_transform.

Wouters, S., Da Silva, A.-C., Boulvain, F., and Devleeschouwer, X.. 2021. StratigrapheR: Concepts for Litholog Generation in R. The R Journal. doi:10.32614/RJ-2021-039
Wouters et al., (2021) introduces the StratigrapheR R package. This package contains functions which format, process, and plot lithologs. The litholog format of Wouters et al., (2021) is used as the standardized input format to convert lithologs to a time series format using the lithlog_disc function. The time series can then be analysed for the imprint of cycles.

#'Huang, Norden E., Zhaohua Wu, Steven R. Long, Kenneth C. Arnold, Xianyao Chen, and Karin Blank. 2009. "On Instantaneous Frequency". Advances in Adaptive Data Analysis 01 (02): 177–229. doi:10.1142/S1793536909000096
The Hilbert transform function inst.pulse of the 'DecomposeR' R package is based on the work of Huang et al., (2009).

Cleveland, W. S. (1979) Robust locally weighted regression and smoothing scatter plots. Journal of the American Statistical Association. 74, 829–836. doi:10.1080/01621459.1979.10481038
Cleveland (1979) explains how the robust locally weighted regression works and how it can be used to smooth data sets. This theory is applied in the loess_auto function of the ‘WaverideR’ package.

#'Hurvich, C.M., Simonoff, J.S., and Tsai, C.L. (1998), Smoothing Parameter Selection in Nonparametric Regression Using an Improved Akaike Information Criterion. Journal of the Royal Statistical Society B. 60, 271–293 doi:10.1111/1467-9868.00125
Hurvich et al., (1998) explains how the Improved Akaike Information Criterion can be used to optimally smooth data sets This theory is applied in the loess_auto function of the ‘WaverideR’ package.

#'Golub, G., Heath, M. and Wahba, G. (1979). Generalized cross validation as a method for choosing a good ridge parameter. Technometrics. 21, 215–224. doi:10.2307/1268518
Golub et al., (1979) explains how the Generalized cross validation can be used to optimally smooth data sets. This theory is applied in the loess_auto function of the ‘WaverideR’ package.

# 2. Example data sets

Damien Pas, Linda Hinnov, James E. (Jed) Day, Kenneth Kodama, Matthias Sinnesael, Wei Liu, Cyclostratigraphic calibration of the Famennian stage (Late Devonian, Illinois Basin, USA), Earth and Planetary Science Letters, Volume 488,2018,Pages 102-114,ISSN 0012-821X, doi:10.1016/j.epsl.2018.02.010
The data set of Pas et al, (2018) is a magnetic susceptibility data measured on the Fammennian aged shales of the from the Illinois basin in the USA. The data set contains the imprint of astronomical cycles in the a Paleozoic succession making it a good example for times (250Ma) when no astronomical solutions are available.

Steinhilber, Friedhelm & Abreu, Jacksiel & Beer, Juerg & Brunner, Irene & Christl, Marcus & Fischer, Hubertus & Heikkilä, U. & Kubik, Peter & Mann, Mathias & Mccracken, K. & Miller, Heinrich & Miyahara, Hiroko & Oerter, Hans & Wilhelms, Frank. (2012). 9,400 Years of cosmic radiation and solar activity from ice cores and tree rings. Proceedings of the National Academy of Sciences of the United States of America. 109. 5967-71. 10.1073/pnas.1118965109. doi:10.1073/pnas.1118965109
The Total Solar Irradiance record of Steinhilber et al., (2012) is a Holocene record of normalized Total Solar Irradiance in the time domain. The data set is a good example for studying/extracting sub-Milankovitch 5000yr from a relatively (geologically) speaking young record.

Christian Zeeden, Frederik Hilgen, Thomas Westerhold, Lucas Lourens, Ursula Röhl, Torsten Bickert, Revised Miocene splice, astronomical tuning and calcareous plankton biochronology of ODP Site 926 between 5 and 14.4Ma, Palaeogeography, Palaeoclimatology, Palaeoecology,Volume 369,2013,Pages 430-451,ISSN 0031-0182, 10.1016/j.palaeo.2012.11.009
The record of Zeeden et al., (2013) consists of a grey scale record from Miocene sediment cores from offshore Brazil. The record contains a clear imprint of astronomical cycles as such it is a good Neogene example data set to demonstrate the functionalities of the 'WaverideR' R package

# 3. The (continuous) wavelet transform

Morlet, Jean, Georges Arens, Eliane Fourgeau, and Dominique Glard. "Wave propagation and sampling theory—Part I: Complex signal and scattering in multilayered media. " Geophysics 47, no. 2 (1982): 203-221. https://pubs.geoscienceworld.org/geophysics/article/47/2/203/68601/Wave-propagation-and-sampling-theory-Part-I
Morlet et al., (1982a) together with Morlet et al., (1982b) are the original publications which explain the use of the wavelet to analyse signal.

J. Morlet, G. Arens, E. Fourgeau, D. Giard; Wave propagation and sampling theory; Part II, Sampling theory and complex waves. Geophysics 1982 47 (2): 222–236. https://pubs.geoscienceworld.org/geophysics/article/47/2/222/68604/Wave-propagation-and-sampling-theory-Part-II
Morlet et al., (1982a) together with Morlet et al., (1982b) are the original publications which explain the use of the wavelet to analyse signal.

Torrence, C., and G. P. Compo. 1998. A Practical Guide to Wavelet Analysis. Bulletin of the American Meteorological Society 79:61-78. https://paos.colorado.edu/research/wavelets/bams_79_01_0061.pdf
'Torrence and Compo (1998) shows how the continuous wavelet transform can be used to analyse cyclicity in paleo-climatic data-sets. The equations in this publication forms the basis for many wavelet based packages/software applications.

Gouhier TC, Grinsted A, Simko V (2021). R package biwavelet: Conduct Univariate and Bivariate Wavelet Analyses. (Version 0.20.21), https://github.com/tgouhier/biwavelet
Gouhier et al., (2021) is the implementation of equations of Torrence and Compo (1998) in the form of the 'biwavelet' R package

Angi Roesch and Harald Schmidbauer (2018). WaveletComp: Computational Wavelet Analysis. R package version 1.1. https://CRAN.R-project.org/package=WaveletComp
Roesch and Schmidbauer et al., (2018) is the article of the 'WaveletComp' R package which is a built upon the functionalities of the 'biwavelet' R package

Russell, Brian, and Jiajun Han. "Jean Morlet and the continuous wavelet transform. " CREWES Res. Rep 28 (2016): 115. https://www.crewes.org/Documents/ResearchReports/2016/CRR201668.pdf
Russell and Han (2016) gives a concise summary of the work of Morlet et al., (1982a) and Morlet et al., (1982b) and the developments since then. The publication also describes how the Gabor uncertainty principle (Gabor 1946) affects the frequency uncertainty of the wavelet which can be used to calculate the analytical uncertainty of a given wavelet spectra.

Gabor, Dennis. "Theory of communication. Part 1: The analysis of information." Journal of the Institution of Electrical Engineers-part III: radio and communication engineering 93, no. 26 (1946): 429-441. http://genesis.eecg.toronto.edu/gabor1946.pdf
Gabor (1946) describes the Gabor uncertainty principle which states how the uncertainty in time and frequency are related in time series analysis.

# 4. Astronomical solutions

J. Laskar, P. Robutel, F. Joutel, M. Gastineau, A.C.M. Correia, and B. Levrard, B., 2004, A long term numerical solution for the insolation quantities of the Earth: Astron. Astrophys., Volume 428, 261-285. doi:10.1051/0004-6361:20041335
Laskar et al., (2004) is an astronomical solution which can be used to anchor geological data to absolute ages.

Laskar, J., Fienga, A., Gastineau, M., Manche, H., 2011a, La2010: A new orbital solution for the long-term motion of the Earth: Astron. Astrophys., Volume 532, A89 doi:10.1051/0004-6361/201116836
Laskar et al., (2011a) is an astronomical solution which can be used to anchor geological data to absolute ages.

Laskar, J., Gastineau, M., Delisle, J.-B., Farres, A., Fienga, A.: 2011b, Strong chaos induced by close encounters with Ceres and Vesta, Astron: Astrophys., Volume 532, L4. doi:10.1051/0004-6361/201117504
Laskar et al., (2011b) is an astronomical solution which can be used to anchor geological data to absolute ages.

J. Laskar,Chapter 4 - Astrochronology,Editor(s): Felix M. Gradstein, James G. Ogg, Mark D. Schmitz, Gabi M. Ogg,Geologic Time Scale 2020,Elsevier,2020,Pages 139-158,ISBN 9780128243602, 'doi:10.1016/B978-0-12-824360-2.00004-8
Laskar et al., (2019) explains how astronomical solutions are created and how they should/can be used

Zeebe, Richard E. "Numerical solutions for the orbital motion of the Solar System over the past 100 Myr: limits and new results." The Astronomical Journal 154, no. 5 (2017): 193. doi:10.3847/1538-3881/aa8cce
Zeebe (2017) is an astronomical solution which can be used to anchor geological data to absolute ages.

Richard E. Zeebe Lucas J. Lourens ,Solar System chaos and the Paleocene–Eocene boundary age constrained by geology and astronomy.Science365,926-929(2019) doi:10.1126/science.aax0612
Zeebe and Lourens (2019) is an astronomical solution which can be used to anchor geological data to absolute ages.

Zeebe, R. E. and Lourens, L. J. Geologically constrained astronomical solutions for the Cenozoic era, Earth and Planetary Science Letters, 2022 doi:10.1016/j.epsl.2022.117595
Zeebe and Lourens (2022) is an astronomical solution which can be used to anchor geological data to absolute ages.