Extract power from a wavelet spectra — extract

Extracts the spectral power from a wavelet spectra in the depth domain using a traced period and boundaries surround the traced period. The extraction of spectral is useful for cyclostratigraphic studies because the spectral power of an astronomical cycle is modulated by higher order astronomical cycles. The spectral power record from an astronomical cycle can thus be used as a proxy for amplitude modulating cycles The traced period result from the track_period_wavelet function with boundaries is used to extract spectral power in the depth domain from a wavelet spectra.

Usage

extract_power(
  tracked_period_curve = NULL,
  scalogram = NULL,
  period_up = 1.2,
  period_down = 0.8,
  tracked_cycle_period = NULL,
  extract_cycle_power = NULL,
  ...
)

Arguments

tracked_period_curve: Tracked period of the cycle along the record (matrix or data frame: depth/time in column 1, period in column 2, in the depth/time unit of the scalogram), e.g. the output of track_period_wavelet or track_period completed with completed_series, optionally smoothed with loess_auto. Rows with NA are dropped and the curve is linearly interpolated (and extrapolated) to the depth/time axis of the scalogram. Required (Default=NULL).
scalogram: Wavelet or superlet object (list of class analyze.wavelet or analyze.superlet) created with analyse_wavelet or analyse_superlet, whose power is summed. Required (Default=NULL).
period_up: Upper boundary of the band whose power is summed, as a factor of the (rescaled) tracked period (numeric, > period_down). Default=1.2.
period_down: Lower boundary of the band whose power is summed, as a factor of the (rescaled) tracked period (numeric, > 0). Default=0.8.
tracked_cycle_period: Period of the tracked cycle, e.g. 405 for the 405-kyr eccentricity cycle (numeric, > 0), in the same unit as extract_cycle_power. The tracked curve is multiplied by extract_cycle_power / tracked_cycle_period. Required (Default=NULL).
extract_cycle_power: Period of the cycle whose power is extracted (numeric, > 0), in the same unit as tracked_cycle_period (both in time or both in depth). Use the same value as tracked_cycle_period to extract the tracked cycle itself. Required (Default=NULL).
...: Old argument names of earlier versions: wavelet (used as scalogram) and completed_series (used as tracked_period_curve).

Value

Returns a matrix with 3 columns. The first column is depth/time. The second column is extracted power. The third column is extracted power/total power.

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

Routines for astrochronologic testing, astronomical time scale construction, and time series analysis <doi:10.1016/j.earscirev.2018.11.015>

Author

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) The functionality of this function is is inspired by the integratePower function of the 'astrochron' R package.

Examples

#Extract the power 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 <- analyse_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(
  scalogram = 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)

#extract the spectral power of the 405 kyr eccentricity cycle
mag_power <- extract_power(
tracked_period_curve = mag_track_complete,
scalogram = mag_wt,
period_up = 1.2,
period_down = 0.8,
tracked_cycle_period = 405,
extract_cycle_power = 405
)