Precession-constant test for a tuned record — test

Tests a tuned (time-domain) record with the precession constant k. Significant multi-taper (MTM) spectral peaks of the record, optionally pooled with other proxies on the same time scale, are assigned to the obliquity (k+s3, k+s6) and precession (k+g5, k+g2, k+g4) terms. Every combination of candidate peaks is tried over a wide range of k (no window is centred on a reference value), and the combinations in which all terms give one consistent k are kept. Because the terms share one k, a correct assignment gives the same k from every term. The result is compared with AstroGeo22 (Farhat et al. 2022) and a Devonian range, and combined with two further checks of the tuned record: the spectral peaks of the eccentricity, obliquity and precession terms, and the amplitude modulation (405 kyr from the 100 kyr envelope, 100 kyr from the precession envelope) against phase-randomised surrogates. This is the updated version of the test (version 3), which works better for Silurian/Devonian data than a search around the AstroGeo22 value.

Usage

test_tuned(
  URAN_time,
  others = NULL,
  tbw = 2,
  pad = 5,
  siglevel = 0.9,
  ftest = FALSE,
  tol = 0.04,
  scan = TRUE,
  scan_band = c(15, 23),
  scan_win = 200,
  scan_thr = 0.5,
  scan_min = 100,
  n_surr = 200,
  seed = 42,
  plot = TRUE,
  verbose = FALSE,
  age_ma = 386,
  k_ref = NULL,
  k_ref_range = NULL,
  k_dev = c(20.4, 21.6),
  k_search = c(19.5, 23.5),
  constraints = NULL
)

Arguments

URAN_time: Tuned record to test (required, no default): data frame or matrix with time in kyr in column 1 and the proxy value in column 2, e.g. the output of a tuning function. It is sorted, linearly interpolated to 1 kyr, detrended and standardised before the analysis.
others: Other tuned proxies on the same time scale (list of data frames/matrices with the same two-column layout as URAN_time, or NULL); they are cut to the time range of URAN_time and their peaks are pooled with those of URAN_time (a term found in several proxies adds support). Default=NULL.
tbw: Time-bandwidth product of the MTM spectrum (numeric, > 0; tbw of astrochron::mtm). It sets the resolution: the precession terms k+g5 and k+g2 only separate when tbw <= (record length in kyr) / 1600 (about 3 for 5.5 Myr). A larger tbw merges them into one broad peak and k cannot be measured (a warning is printed). At least 1.5 (two tapers; smaller values are raised to 1.5 with a warning), so records shorter than about 2400 kyr cannot separate k+g5 and k+g2. Default=2.
pad: Zero-padding factor of the MTM spectrum (numeric, >= 1; padfac of astrochron::mtm). Default=5.
siglevel: Confidence level a spectral peak must reach to be used (numeric, between 0 and 1): the AR1 confidence level at the peak (and, with ftest = TRUE, the harmonic F-test level). Only peaks with periods between 12 and 40 kyr are considered. Default=0.9.
ftest: Also require the harmonic F-test confidence level to reach siglevel (logical). The default FALSE uses the AR1 level only, because the F-test tests for a pure sinusoid and rejects broad, strong peaks of a tuned record. Default=FALSE.
tol: Half-width of the search window around each predicted term period, as a fraction of the period (numeric, e.g. 0.04 = +/- 4%). Default=0.04.
scan: Remove intervals with little precession imprint (set them to zero, with a 10-kyr cosine taper at the edges) before the spectrum is built (logical); the pre-scan is controlled by scan_band, scan_win, scan_thr and scan_min. Default=TRUE.
scan_band: Precession band of the pre-scan, in kyr (numeric vector c(shortest, longest) period); the record is band-passed (astrochron::taner) in this band and its Hilbert envelope gives the band variance. Default=c(15, 23).
scan_win: Length of the running window over which the precession-band variance is averaged, in kyr (numeric, > 0; at most a third of the record is used). Default=200.
scan_thr: An interval is weak when its averaged precession-band variance is below scan_thr times its median (numeric, >= 0). Default=0.5.
scan_min: Shortest piece kept or removed by the pre-scan, in kyr (numeric, >= 0): weak pieces shorter than this are kept and kept pieces shorter than this are removed. Default=100.
n_surr: Number of phase-randomised surrogates for the amplitude-modulation test (integer, > 0). Default=200.
seed: Seed of the random number generator (integer), so that the surrogates can be reproduced. Default=42.
plot: Draw the comparison figure with plot_test_k (logical). Default=TRUE.
verbose: Also print the peak tables and all peak assignments of the precession-constant test (logical, TRUE or FALSE); the compact report is always printed. Default=FALSE.
age_ma: Age of the record in Ma (numeric); the AstroGeo22 reference k and its envelope are taken at this age (astrogeo22) unless k_ref and k_ref_range are given. Default=386.
k_ref: Reference precession constant, as a period in kyr (numeric); used for the resolution check of tbw, the old search windows (k_search = NULL) and the plot. NULL uses AstroGeo22 at age_ma. Default=NULL.
k_ref_range: Range of the reference precession constant in kyr (numeric vector c(lower, upper)); the test passes when the 1-sigma interval of the estimate overlaps it (or the 20.70 kyr composite of Zeeden et al., 2023). NULL uses the AstroGeo22 envelope at age_ma. Default=NULL.
k_dev: Plausible range of k for the test verdict, in kyr (numeric vector c(lower, upper)); the default is the Devonian range. Default=c(20.4, 21.6).
k_search: Range of k in which peaks are searched, in kyr (numeric vector c(lower, upper)), independent of AstroGeo22. The search window of each term runs from its period at k_search[1] to its period at k_search[2] (plus or minus tol). NULL gives the old windows around the AstroGeo22 period, which can only return k within about 1 kyr of AstroGeo22 and so cannot test it. Default=c(19.5, 23.5).
constraints: Path to a CSV file of published constraints (character, or NULL for none), with columns set, observable, age_ma, a_RE, a_sd, lod_h, lod_sd, k_arcsec and k_sd, drawn in panels E-G of the figure. Default=NULL.

Value

Invisibly a list with the combined k (k, k_obliquity, k_precession, k_ranges), the peak assignment tables (k_terms, solutions), the verdicts and score of the three tests, and the spectra used for plotting.

References

Zeeden et al. (2023), see zeeden2023_table1. Farhat, M., Auclair-Desrotour, P., Boue, G., Laskar, J. (2022). The resonant tidal evolution of the Earth-Moon distance. Astronomy & Astrophysics 665, L1.

Examples

# \donttest{
# synthetic tuned record with a known precession constant (k = 21 kyr)
test_tuned_check(k_true = 21, tbw = 2, len = 3000)
#> true k 21.00 -> obliquity 20.85, precession 20.99, obliquity + precession 20.94
# }