Package index • WaverideR

Wavelet and superlet transforms

Continuous wavelet, superlet, adaptive and cross transforms, and their plots.

analyse_wavelet() analyze_wavelet(): Conduct the continuous wavelet transform on a time series/signal
analyse_superlet() analyze_superlet(): Conduct the superlet transform on a time series or signal
analyse_Awavelet() analyze_Awavelet(): Conduct the adaptive continuous wavelet transform on a time series or signal
analyse_Xwavelet() analyze_Xwavelet(): Conduct the cross wavelet transform on a time series or signal
analyse_Xsuperlet() analyze_Xsuperlet(): Conduct the cross superlet transform on a time series or signal
analyse_wavelet_coherence() analyze_wavelet_coherence(): Cross-wavelet coherence analysis
plot_wavelet(): Plots a wavelet scalogram
plot_superlet(): Plots a superlet scalogram
plot_Awavelet(): Plots a adaptive wavelet scalogram
plot_Xwavelet(): Plots a cross wavelet scalogram
plot_Xsuperlet(): Plots a cross superlet scalogram
plot_wavelet_coherence(): Plots a cross wavelet scalogram
plot_avg_wavelet(): Plot the average spectral power of a wavelet spectra
add_wavelet(): Add a wavelet plot
add_wavelet_avg(): Add a plot of a the average spectral power of a continous wavelet transform

Synchrosqueezing, chirplets and de-chirped spectra

Sharpened scalograms, chirp-matched spectra and checks of an age model in the de-chirped record.

analyse_wavelet_sst() analyze_wavelet_sst(): Wavelet synchrosqueezing transform
analyse_superlet_sst() analyze_superlet_sst(): Superlet synchrosqueezing: consensus of synchrosqueezed transforms with short and long wavelets
analyse_chirplet_sst() analyze_chirplet_sst(): Synchrosqueezed wavelet-chirplet transform
analyse_conceft() analyze_conceft(): Multitaper synchrosqueezing (ConceFT) of a record
analyse_chirp_wavelet() analyze_chirp_wavelet(): Chirp-matched wavelet scalogram with the astronomical template over rate and rate gradient
analyse_chirp_eha() analyze_chirp_eha(): Chirp-matched evolutive harmonic analysis (de-chirped windowed multitaper spectra)
chirp_eha_significance(): Significance of the lines of a (de-chirped) EHA map against warped noise
plot_chirp_eha(): Plot a chirp-matched EHA map, with or without the surrogate significance
rate_gram(): Rate-gram: the astronomical template as a spectrum over sedimentation rate, per window
analyse_dechirped(): De-chirped scalogram of any transform: the record warped to time with a track, transformed, mapped back to depth
plot_dechirped(): Plot a de-chirped scalogram
check_agemodel(): Check an age model against the de-chirped record: where do the astronomical cycles bend away?
plot_agemodel_check(): Plot an age-model check: the de-chirped maps, the rate corrections the cycles ask for and the flagged intervals
detect_transients(): Transient (impulsive) features of a record by transient extraction

Significance and uncertainty of spectra

wavelet_significance(): Significance of wavelet and superlet power: analytic and surrogate (Monte Carlo) levels
wavelet_band_significance() plot(<wr_band_significance>): Significance of scale-averaged wavelet power (Torrence and Compo, section 4d)
sst_significance(): Significance of synchrosqueezed (and other) scalograms against autocorrelated noise
model_red_noise_wt(): Models average spectral power based curves based on a red-noise signal generated using the characteristics of an input signal.
percentile_from_red_noise(): Calculate average spectral power from red noise curves for a given percentile
wavelet_uncertainty(): Calculate the uncertainty associated with the wavelet analysis based on the Gabor uncertainty principle
fft_uncertainty(): Calculate the uncertainty associated with a tracked cycle based on the frequency uncertainty of the FFT
fft_frequency_uncertainty(): Frequency uncertainty of the Fourier transform (FFT) for a record length
wr_coloured_noise() wr_brewer_palettes() wr_colored_noise(): Colour noise and palette helpers

Other spectral methods

Evolutive harmonic analysis, windowed FFT, MESA, multitaper, SWA, Bayesian and bispectral analysis.

eha_log2(): Generate a log2 spaced EHA spectra
plot_eha_log2(): Plots an log2 spaced EHA spectra
win_fft(): Windowed fft based spectral analysis
plot_win_fft(): Plot windowed fft based spectral analysis results
mesa_spectrum(): Maximum entropy spectral analysis (MESA, Burg)
mesa_evolutive(): Evolutive maximum entropy spectral analysis (evolutive MESA)
mesa_average(): Average spectrum of an evolutive MESA
plot_mesa_spectrum(): Plot a maximum entropy (MESA) spectrum
plot_mesa_evolutive(): Plot an evolutive MESA
track_mesa(): Track a spectral peak through an evolutive MESA
amtm_spectrum(): Adaptive multitaper spectrum with background fit and periodic signal detection
amtm_prewhiten(): Autoregressive prewhitening of a series for aMTM analysis
plot_amtm_spectrum(): Plot an adaptive multitaper spectrum with background and detections
swa_spectrum(): Power spectrum with SWA background, chi-square and FDR confidence levels
swa_background(): Smoothed Window Average (SWA) spectral background
bayes_spectrum(): Bayesian probability spectrum
spectral_moments(): Sliding-window spectral moments (mean frequency and bandwidth)
plot_spectral_moments(): Plot the result of spectral_moments
bispectral_analysis(): Bispectral analysis: bispectrum, biphase and squared bicoherence
bispectral_surrogate(): FT and IAAFT surrogates for bispectral significance testing
plot_bispectral(): Plot the result of a bispectral analysis
cycle_band(): Period range implied by the frequency resolution of a record

Tracking cycles

Interactive and automatic tracking of the period of a cycle and of the sedimentation rate.

track_period(): Track the period of a cycle in a wavelet or superlet scalogram
track_period_wavelet(): Track the period of a cycle in a wavelet spectra
delpts_tracked_period_wt(): Remove tracking points which were tracked in a wavelet spectra
completed_series(): Complete the tracking of the period a cycle in a scalogram
retrack_wt_MC(): Re-track cycles using a Monte-Carlo simulation
loess_auto(): Perform an automatically loess based smoothing of a time series
track_ridge_hmm(): Continuous tracking of a cycle in a (synchrosqueezed) scalogram with a hidden Markov model
track_astro_hmm(): Astronomically constrained continuous tracking of the sedimentation rate in a scalogram
track_astro_auto(): Recommended workflow for continuous astronomical tracking of noisy records
track_astro_iterative(): Iterative (demodulated) astronomical tracking of the sedimentation rate
track_chirp_hmm(): Chirp-steered tracking of the sedimentation rate (rate and rate gradient as the hidden state)
plot_track(): Plot a continuous track on its scalogram
plot_astro_evidence(): Map of the astronomical evidence against sedimentation rate and depth
astro_periods_tracking(): Astronomical periods and weights for tracking, for any age
as_wr_track(): Build a track (depth, sedimentation rate, time) from a tracked period curve, a rate curve or an age model

Extracting signals and filtering

extract_signal(): Extract signal from a wavelet spectra using a traced period curve
extract_signal_stable(): Extract a signal/cycle from a wavelet spectra using a set period and boundaries
extract_signal_stable_V2(): Extract signal from a wavelet spectrum using a upper and lower period boundary
extract_signal_standard_deviation(): Extract a signal using standard deviation
dynamic_extraction(): Extract a signal in between tracked boundaries in a wavelet scalogram
extract_amplitude(): Extract the instantaneous amplitude (envelope) of a signal using the CWT
extract_power(): Extract power from a wavelet spectra
extract_power_stable(): Extract power from a wavelet spectra by using a constant period/duration
gaussian_bandpass(): Gaussian band-pass filter (Acycle)
dynamic_filter(): Dynamic (depth-varying) Gaussian band-pass filter
dynamic_filter_controls(): Build dynamic-filter control points from a tracked period curve
plot_dynamic_filter(): Plot the result of a dynamic filter
max_detect(): Detect and filter out all maxima in a signal
min_detect(): Detect and filter out all minima in a signal

Sedimentation rates and astronomical testing

TimeOpt with noise correction, COCO and eCOCO, and other estimates of the sedimentation rate.

astro_sedrate_test(): Test sedimentation rates with noise-corrected TimeOpt, likelihood and COCO scores
plot(<astro_sedrate_test>): Plot an astro_sedrate_test result
astro_sedrate_multi(): Combined astronomical test for several proxies and sections
plot(<astro_sedrate_multi>): Plot an astro_sedrate_multi result
astro_tune_test(): Test a minimal tuning: multi-band rate tracking with surrogates run through the whole chain
plot(<astro_tune_test>): Plot an astro_tune_test result
win_timeOpt(): Windowed timeOpt sedimentation rate estimation
plot_win_timeOpt(): plot the windowed timeOpt sedimentation rate estimation
win_timeOpt_multi(): Windowed timeOpt with precession, short-eccentricity and obliquity interpretations
plot_win_timeOpt_multi(): Plot the fits of win_timeOpt_multi side by side
flmw(): Fit linear models to spectral peaks extracted from the wavelet spectra to astronomical cycles multiplied by sedimentation rate x
flmw_path(): Smooth sedimentation rate curve with uncertainty from a flmw score matrix
plot_sed_model(): Plot sedimentation modelling results
sum_power_sedrate(): Calculate sum of maximum spectral power for sedimentation rates for a wavelet spectra
coco_classic(): COCO analysis (Li et al. 2018)
plot(<coco_classic>): Plot a COCO result (Li et al. 2018 method)
coco_adaptive(): Adaptive COCO
plot(<coco_adaptive>): Plot an adaptive COCO result
coco_adaptive_evaluate(): Evaluate Adaptive COCO for a batch of spectra (cocoAdaptiveEvaluate.m)
coco_prepare_regular_data(): Prepare a depth series for COCO (cocoPrepareRegularData.m)
coco_target_fixed(): Fixed-weight astronomical target spectrum (Fixed-target COCO)
coco_fixed_target_weights(): Fixed sinusoid-amplitude weights for a COCO target (cocoFixedTargetWeights.m)
coco_target_from_periods(): Target periodogram from a list of orbital periods (period2spectrum.m)
coco_target_from_series(): Target periodogram from an astronomical time series (e.g. La2004 ETP)
cvcoco(): Cross-validated correlation coefficient (cvCOCO) analysis
plot_cvcoco(): Plot a cvCOCO result
ecoco_classic(): Evolutionary COCO (Li et al. 2018)
plot(<ecoco_classic>): Plot an eCOCO result (Li et al. 2018 method)
ecoco_adaptive(): Adaptive eCOCO
plot(<ecoco_adaptive>): Plot an adaptive eCOCO result
ecoco_blocked(): Blocked eCOCO (cross-fitted evolutionary correlation coefficient)
ecoco_interleaved(): Interleaved eCOCO (odd/even cross-validated evolutionary COCO)
plot_ecoco_cv(): Plot Blocked / Interleaved eCOCO maps
ecoco_best_per_window(): Best sedimentation rate per eCOCO window
ecoco_track(): Track sedimentation-rate solutions through eCOCO peak maps
ecoco_track_ridge(): Track a smooth sedimentation-rate ridge through an eCOCO score map
track_ecoco(): Track the sedimentation rate through an eCOCO map

Age models and tuning

curve2time(): Convert the tracked curve to a depth time space
curve2time_unc(): Convert the re-tracked curve results to a depth time space with uncertainty
curve2time_unc_anchor(): Convert the re-tracked curve results to a depth time space with uncertainty
curve2tune(): Convert data from the depth to the time domain
curve2sedrate(): Convert a tracked tracked to a sedimentation rate curve
sedrate2tune(): Use a sedimentation curve to convert data to the time domain
minimal_tuning(): Create an age model using minimal tuning
anchor2time(): Convert a proxy record to the time domain using anchor points
astro_anchor(): Anchor proxy record to an astronomical solution
plot_astro_anchor(): Plot proxy record anchored to an astronomical solution
astro_anchor_interactive(): Interactively tie a proxy record to an astronomical solution (random order, tie and untie, inspect)
astro_anchor_app(): Interactive Shiny app to tie a proxy record to an astronomical solution (tune live while tying)
dur_gaps(): calculate the duration of stratigraphic gaps using astronomical cycles
expSedRamp(): exponentially ramped sedimentation rate model to convert time to stratigraphy

Bayesian age-depth models

Radioisotopic dates combined with a floating astrochronology (astroMCBchron), and a pure-R modifiedBChron.

astroMCBchron(): Joint Bayesian age-depth model of radioisotopic dates and a floating astrochronology (astroMCBchron)
plot(<astroMCBchron>): Plot an astroMCBchron model
predict(<astroMCBchron>): Predict ages at new positions from an astroMCBchron model
modBchron(): Run a modified version of the Bchronology algorithm from the R package "Bchron" (Haslett and Parnell, 2008)
modBchron_predict(): Predict ages at new positions from a modBchron (or modifiedBChron) model
upb_grain_loglik(): Eruption-age likelihoods from single-zircon U-Pb dates (for astroMCBchron)

Sedimentary noise and change points

dynot(): Dynamic noise after orbital tuning (DYNOT)
plot_dynot(): Plot DYNOT results
pda(): Power decomposition analysis (strict evolutionary MTM band-power ratio)
pda_legacy(): Legacy power decomposition analysis (Acycle PDA menu / DYNOT core)
rho1_evolutive(): Evolutionary lag-1 autocorrelation coefficient (rho1)
lag_1(): lag-1 autocorrelation coefficient
bayes_changepoint(): Bayesian change point analysis (Ruggieri, 2013)
bayes_changepoint_r2(): R-squared of the Bayesian change point model as a function of the maximum number of change points
plot_bayes_changepoint(): Plot the result of bayes_changepoint

Precession constant, astronomical periods and the Earth-Moon system

Astronomical periods for any age, tests of the precession constant and Earth-Moon parameters.

ctest(): CTest: astronomical parameters from interpreted spectral peaks
plot(<ctest>): Plot the CTest posterior distributions
print(<ctest>): Print a CTest result
ctest_input(): Build the CTest input table from interpreted cycle wavelengths
ctest_combine(): Combine several CTest results by multiplying their densities
ctest_earthmoon(): Earth-Moon distance, length of day and obliquity for CTest samples
astro_ctest(): Consistency-test inversion (the estimator used in the paper)
astro_from_peaks(): Astronomical parameters from spectral peaks
print(<astro_from_peaks>): Print an astro_from_peaks result
astro_from_periods(): Astronomical parameters from a tuned record (cycles already in kyr)
astro_invert(): Joint inversion of several measured terms, with Monte Carlo uncertainty
astro_mc(): Monte Carlo consistency test for tuned (time-domain) or depth-domain cycles
plot_astro(): Six-panel summary of an inversion
astro_terms(): The menu of named astronomical terms at a given age
astro_term_search(): Which term could a measured period be?
astro_obliquity(): Obliquity at a given age, from AstroGeo22 if available, else today's value
astrogeo22(): Earth-Moon state from the AstroGeo22 model at a given age
orbit9(): Nine principal astronomical terms for a given precession constant
orbit9_at_age(): Nine orbital periods (kyr) at age_ma
orbital_periods(): All principal astronomical periods for a given precession constant
calculate_orbit9(): Nine astronomical periods at a given age
la2004_extrap(): La2004 polynomial extrapolation (Laskar et al. 2004, eqs. 39-40) Strictly valid only over a few hundred Myr; shown for comparison.
k_from_bundling(): Precession constant from bundling: precession cycles per eccentricity bundle
k_from_cycles(): Precession constant from one or more single-valued cycles
k_from_period(): Precession constant implied by one measured cycle period
k_from_ratio(): Precession constant from the RATIO of two cycles in one section
k_hypotheses(): Which precession term is that peak? One k per hypothesis.
k_scan(): Scan k and count how many measured windows a single k can satisfy
cycles_to_k(): Precession constant implied by an observed obliquity or precession cycle
bundling_ratios(): Precession cycles per eccentricity bundle, predicted
compare_published(): Compare a measured precession constant with published models
term_sensitivity(): Sensitivity of every cycle to each fundamental frequency
chaos_scenario(): Shift the fundamental frequencies and see what every cycle does
resonance_state(): Which secular resonance state does a record show?
test_tuned(): Precession-constant test for a tuned record
test_tuned_check(): Check the precession-constant test on a synthetic record
plot_test_k(): Comparison figure of the precession-constant test
earthmoon_state(): Full Earth-Moon state from any one observable
earthmoon_from_precession(): Invert the AstroGeo22 precession curve: Earth-Moon state for a measured precession frequency / period.
em_state(): Full Earth-Moon state from a precession constant
earth_moment_of_inertia(): Earth's polar moment of inertia at spin rate omega (Farhat et al. 2022, A.3)
earth_omega(): Earth's angular velocity from the length of day
earthmoon_angular_momentum(): Earth-Moon system angular momentum (spin + lunar orbit), kg m^2 s^-1
precession_frequency(): Luni-solar precession frequency (Farhat et al. 2022, eq. A.7)
lod_hours(): Length of day from Earth's angular velocity
lod_from_moon_distance(): Length of day implied by an Earth-Moon distance (angular momentum conserved)
moon_distance_from_lod(): Earth-Moon distance implied by a length of day (angular momentum conserved)
moon_distance_from_months(): Earth-Moon distance from the number of lunar months per year (the observable of tidal rhythmites)
months_per_year(): Lunar mean motion and months per year from the Earth-Moon distance (Kepler's third law, n^2 a^3 = G(M_E + M_M), as in Farhat et al. 2022 Table D.2)
omega_from_moon_distance(): Earth's spin rate implied by an Earth-Moon distance, assuming the Earth-Moon angular momentum is conserved (solar tidal drain neglected).
days_per_year(): Days in a year for a given solar day length
zeeden2023_table1(): Devonian reference values of Zeeden et al. (2023), EPSL 621, 118348, Table 1
example_pridoli(): The Pridoli example: the four terms resolved at Cellon (Carnic Alps) on the astrochronozone time scale of Arts and Da Silva.

Geological time scale and lithology

geo_col(): Generate standard color codes for the Geological Time Scale
geo_loc(): Generates ages for the boundaries of a geochronological subdivision
geo_mid(): Generate the mean age of a geological subdivision
GTS_info: Information of the Geological timescale 2020
lithlog_disc(): Discriticizes lithologs

Example data

WaverideR_Datasets: Example data sets for the 'WaverideR' package
Bisciaro_XRF: XRF records of the Bisciaro Fm
Bisciaro_al_wt_track: Period of the short kyr ecc cycle in the Al record of the Bisciaro Fm
Bisciaro_ca_wt_track: Period of the short kyr ecc cycle in the Ca record of the Bisciaro Fm
Bisciaro_Mg_wt_track: Period of the short kyr ecc cycle in the Mg record of the Bisciaro Fm
Bisciaro_Mn_wt_track: Period of the short kyr ecc cycle in the Mn record of the Bisciaro Fm
Bisciaro_sial_wt_track: Period of the short kyr ecc cycle in the si/Al record of the Bisciaro Fm
anchor_points_Bisciaro_al: XRF records of the Bisciaro Fm
grey: Grey scale record IODP 926 of Zeeden et al., (2013)
grey_track: Tracking points of the precession (22 kyr cycle) IODP 926 grey scale (154-174m) record of Zeeden et al., (2013)
age_model_zeeden: Age model of Zeeden et al., (2013) for the (154-174m) interval of the IODP 926 grey scale record
anchor_points_grey: Example anchor points for the grey scale data set of Zeeden et al., (2013)
mag: Magnetic susceptibility data of the Sullivan core of Pas et al., (2018)
mag_track_solution: Period of the 405 kyr ecc cycle in the magnetic susceptibility record of the Sullivan core
TSI: Total solar irradiation data (0-9400ka) of steinhilber et al., (2012)
astrosignal_example: An ETP astronomical solution
depth_rank_example: An example depth rank series

Package

WaverideR-package WaverideR: Extracting Signals from Wavelet Spectra