| wavelet_uncertainty {WaverideR} | R Documentation |
Calculate the uncertainty associated with the wavelet analysis based on the Gabor uncertainty principle
Description
The wavelet_uncertainty function is used to calculate uncertainties associated
with the wavelet analysis based on the Gabor uncertainty principle applied to the
continuous wavelet transform using a Morlet wavelet. The calculated uncertainty is the underlying
analytical uncertainty which is the result of applying the Gabor uncertainty principle to the
continuous wavelet transform using a Morlet wavelet.
Usage
wavelet_uncertainty(
tracked_cycle = NULL,
period_of_tracked_cycle = NULL,
wavelet = NULL,
multi = 1,
verbose = FALSE,
genplot_time = FALSE,
genplot_uncertainty = FALSE,
genplot_uncertainty_wt = FALSE,
keep_editable = FALSE,
palette_name = "rainbow",
color_brewer = "grDevices"
)
Arguments
tracked_cycle |
Curve of the cycle tracked using the |
period_of_tracked_cycle |
period of the tracked curve (in kyr). |
wavelet |
wavelet object created using the |
multi |
multiple of the standard deviation to be used for defining uncertainty |
verbose |
Print text |
genplot_time |
plot time curves with a upper and lower uncertainty based on Gabor uncertainty principle applied to the
continuous wavelet transform using a Morlet wavelet, which uses which uses the omega number (number
of cycles in the wavelet) at one standard deviation to define the analytical uncertainty |
genplot_uncertainty |
Plot period curves with upper and lower uncertainty based on Gabor uncertainty principle applied to the
continuous wavelet transform using a Morlet wavelet, which uses which uses the omega number
(number of cycles in the wavelet) to define uncertainty at one standard deviation |
genplot_uncertainty_wt |
generate a wavelet plot with the uncertainty based on Gabor uncertainty
principle applied to the continuous wavelet transform using a Morlet wavelet superimposed on top of
original wavelet plot. The red curve is period of the tracked curve plus the analytical uncertainty.
The blue curve is period of the tracked curve min the analytical uncertainty.
The black curve is the curve tracked using the ' |
keep_editable |
Keep option to add extra features after plotting |
palette_name |
Name of the color palette which is used for plotting.
The color palettes than can be chosen depends on which the R package is specified in
the color_brewer parameter. The included R packages from which palettes can be chosen
from are; the 'RColorBrewer', 'grDevices', 'ColorRamps' and 'Viridis' R packages.
There are many options to choose from so please
read the documentation of these packages |
color_brewer |
Name of the R package from which the color palette is chosen from.
The included R packages from which palettes can be chosen
are; the RColorBrewer, grDevices, ColorRamps and Viridis R packages.
There are many options to choose from so please
read the documentation of these packages. " |
Value
Results pertaining to the uncertainty calculated based on the Gabor uncertainty principle.
If the genplot_time is TRUE then a depth time plot will be plotted with 3 lines, the mean age,age plus
x times the standard deviation and age minus x times the standard deviation .
If the genplot_uncertainty is TRUE then a curve will be plotted with the mean period, the tracked period plus
x times the standard deviation and the tracked period minus x times the standard deviation.
If the genplot_uncertainty_wt is TRUE a wavelet spectra will be plotted with the tracked period, the tracked period plus
x times the standard deviation,the tracked period minus x times the standard deviation and the area in between will be shaded in grey.
Returns a matrix with 8 columns.
The first column is called "depth" eg. depth
The second column is "period" of the originally tracked period.
The third column is "frequency" of the originally tracked period.
The fourth column "uncertainty in frequency FWHM" is the uncertainty in frequency based on the Gabor uncertainty principle defined as
(FWHM) full width at half maximum.
The fifth column "uncertainty in frequency x_times SD" is the uncertainty in frequency based on the Gabor uncertainty principle defined as
times x standard deviations.
The sixth column "time mean" is the mean time based on the tracked period.
The seventh column "time plus x_times sd" is the time based on the tracked period plus x times the standard deviation.
The eight column "time min x_times sd" is the time based on the tracked period min x times the standard deviation.
Author(s)
Code based on the analyze.wavelet function of the 'WaveletComp' R package and wt function of the 'biwavelet' R package which are based on the wavelet 'MATLAB' code written by Christopher Torrence and Gibert P. Compo (1998). 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
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
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
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
#calculate the Gabor uncertainty derived mathematical uncertainty of the
#magnetic susceptibility record of the Sullivan core 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)",
# palette_name="rainbow",
# color_brewer= "grDevices")
#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 = FALSE,
genplot = FALSE,
keep_editable=FALSE
)
mag_track_complete <- loess_auto(time_series = mag_track_complete,
genplot = FALSE, print_span = FALSE,keep_editable=FALSE)
uncertainty <- wavelet_uncertainty(
tracked_cycle = mag_track_complete,
period_of_tracked_cycle = 405,
wavelet = mag_wt,
multi=1,
verbose = FALSE,
genplot_time = FALSE,
genplot_uncertainty = FALSE,
genplot_uncertainty_wt = FALSE,
keep_editable=FALSE,
palette_name="rainbow",
color_brewer= "grDevices"
)