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Transient (impulsive) features of a record by transient extraction

Source: R/detect_transients.R
detect_transients.Rd

Finds the positions in a record where energy over many periods arrives at the same instant: the signature of an impulsive feature such as a hiatus (a phase jump of all cycles), an erosion surface, a turbidite or a spike. The wavelet coefficients are reassigned along the record to their group delay (the time-reassigned synchrosqueezing / transient-extracting transform, He et al. 2019; Yu et al. 2023), only the coefficients that lie on their own group delay are kept, and their energy is summed over the periods. The sum is compared with a running median and peaks above threshold times the median are reported, which can be passed as jump_depths to track_astro_hmm or track_astro_auto.

Usage

detect_transients(
  data,
  lowerPeriod,
  upperPeriod,
  dj = 1/20,
  omega_nr = 6,
  threshold = 4,
  min_distance = NULL,
  window = NULL
)

Arguments

data

Record to scan (matrix or data frame): depth in column 1 and the proxy in column 2; incomplete rows are dropped, the rows sorted, the record linearly interpolated to its median spacing and standardised. Required, no default.

lowerPeriod

Shortest period of the Morlet wavelet transform, in depth units (numeric, > 0; at least twice the sample spacing). Required, no default.

upperPeriod

Longest period of the transform, in depth units (numeric, larger than lowerPeriod); it also sets the defaults of min_distance and window. Required, no default.

dj

Spacing of the periods of the transform, in octaves (numeric, > 0; 1/20 gives 20 periods per doubling). Default=1/20.

omega_nr

Central angular frequency (omega_0) of the Morlet wavelet (numeric, > 0); small values give short wavelets, which localise transients best. Default=6.

threshold

Detection threshold (numeric, > 1): positions where the reassigned (transient) energy exceeds this multiple of the running median of the energy are reported as transients. Default=4.

min_distance

Minimum distance between two reported transients, in depth units (numeric, >= 0); of candidates closer together only the strongest is kept. NULL uses upperPeriod / 4. Default=NULL.

window

Length of the running median that forms the baseline of the energy, in depth units (numeric, > 0). NULL uses 2 * upperPeriod. Default=NULL.

Value

A list with profile (data frame: depth, energy, ratio to the running median) and transients (data frame: depth, ratio of the detected peaks, strongest first).

Details

The transform cannot see a jump of the sedimentation rate itself (the cycles stay continuous); it sees the phase jumps that a gap in time causes.

References

He, D., Cao, H., Wang, S. and Chen, X. (2019). Time-reassigned synchrosqueezing transform: the algorithm and its applications in mechanical signal processing. Mech. Syst. Signal Process. 117, 255-279.

Yu, G. et al. (2023). Synchro-transient-extracting transform for the analysis of signals with both harmonic and impulsive components. arXiv:2306.01320.

Examples

set.seed(2)
t <- seq(0, 2000, by = 0.5)
x_t <- sin(2 * pi * t / 23.7) + 0.6 * sin(2 * pi * t / 41) + 0.4 * cos(2 * pi * t / 405)
keep <- !(t > 800 & t < 900) & !(t > 1500 & t < 1550)        # two gaps in time (hiatuses)
z <- seq(0, by = 2, length.out = sum(keep))
x <- x_t[keep] + rnorm(length(z), sd = 0.5)
tr <- detect_transients(data.frame(z, x), lowerPeriod = 20, upperPeriod = 400)
tr$transients
#> [1] depth ratio
#> <0 rows> (or 0-length row.names)