extract_amplitude {WaverideR}

Extract amplitude from a signal

Description

Extracts the amplitude from a signal using the continuous wavelet transform using a Morlet wavelet. The extraction of the amplitude is useful for cyclostratigraphic studies because the amplitude of an astronomical cycle is modulated by higher order astronomical cycles.

Usage

extract_amplitude(
  signal = NULL,
  pts = 3,
  genplot = FALSE,
  remean = TRUE,
  ver_results = FALSE,
  keep_editable = FALSE
)

Arguments

signal

Input signal from which the amplitude is extracted any signal in which the first column is depth/time and the second column is the proxy record from which the amplitude is extracted

pts

The pts parameter specifies how many points to the left/right up/down the peak detect algorithm goes in detecting a peak. The peak detecting algorithm works by comparing the values left/right up/down of it, if the values are both higher or lower then the value a peak. To deal with error produced by this algorithm the pts parameter can be changed which can aid in peak detection. Usually increasing the pts parameter means more peak certainty, however it also means that minor peaks might not be picked up by the algorithm Default=3

genplot

If set to TRUE a plot with extracted amplitude will be displayed Default=FALSE.

remean

Prior to analysis the mean is subtracted from the data set to re-mean set Default=TRUE.

ver_results

To verify the amplitude extraction is representative of the amplitude extracted using the extract_amplitude function the results can be compared to the amplitude extracted using the Hilbert_transform if the mean difference is more then 5 whether the input contains a reliable enough signal with high a enough amplitude modulation to actually extract an amplitude from. Default=FALSE.

keep_editable

Keep option to add extra features after plotting Default=FALSE

Value

Returns a matrix with 2 columns. The first column is depth/time. The second column is the extracted amplitude

Author(s)

Code based on the reconstruct function of the 'WaveletComp' R package which is based on the wavelet 'MATLAB' code written by Christopher Torrence and Gibert P. Compo. The assignment of the standard deviation of the uncertainty of the wavelet is based on the work of Gabor (1946) and Russell et al., (2016)

References

Angi Roesch and Harald Schmidbauer (2018). WaveletComp: Computational Wavelet Analysis. R package version 1.1. https://CRAN.R-project.org/package=WaveletComp

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

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

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

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

Examples

#Extract amplitude of the 405 kyr eccentricity cycle from the the magnetic
# susceptibility data set of De pas et al., (2018)
#Perform the CWT on the magnetic susceptibility data set of Pas et al., (2018)

mag_wt <- analyze_wavelet(data = mag,
dj = 1/100,
lowerPeriod = 0.1,
upperPeriod = 254,
verbose = FALSE,
omega_nr = 10)

#Track the 405 kyr eccentricity cycle in a wavelet spectra

#mag_track <- track_period_wavelet(astro_cycle = 405,
#                                   wavelet=mag_wt,
#                                   n.levels = 100,
#                                   periodlab = "Period (metres)",
#                                   x_lab = "depth (metres)")

#Instead of tracking, the tracked solution data set mag_track_solution
#is used
mag_track <- mag_track_solution

mag_track_complete <- completed_series(
  wavelet = mag_wt,
  tracked_curve = mag_track,
  period_up = 1.2,
  period_down = 0.8,
  extrapolate = TRUE,
  genplot = FALSE
)

#Smooth the completed tracking of the 405 kyr eccentricity cycle in the wavelet spectra

mag_track_complete <- loess_auto(time_series = mag_track_complete,
genplot = FALSE, print_span = FALSE)




mag_405_ecc  <- extract_signal(
tracked_cycle_curve = mag_track_complete,
wavelet = mag_wt,
period_up = 1.2,
period_down = 0.8,
add_mean = TRUE,
tracked_cycle_period = 405,
extract_cycle = 405,
tune = FALSE,
plot_residual = FALSE
)

#extract the amplitude  of the 405 kyr eccentricity cycle
mag_ampl <- extract_amplitude(
signal = mag_405_ecc,
pts=3,
genplot = FALSE,
ver_results = FALSE,
keep_editable=FALSE)