Point events spectrum

This module, using the “circular spectral analysis” method (e.g. Lutz 1985) is used to search for periodicity in point event series such as earthquakes, volcanic eruptions, and mass extinctions (e.g. Rampino & Caldeira 2015). A single column of event times (e.g. dates of eruptions in millions of years) is required. The event times do not need to be in sequential order.

The method works by wrapping the time line around a circle with a circumference corresponding to a trial period P. If points are P-periodic, they will cluster at a certain angle corresponding to the phase.

As in directional statistics, the mean sines and cosines are computed and converted to a mean vector magnitude (Rayleigh statistic) R and a phase t0R and t0 are computed for P ranging from the average waiting time up to 1/3 of the total duration of the series, giving a full spectrum.

A 95% significance line for R is computed by a Monte Carlo procedure with 1,000 replicates. Random event times are computed by a gamma distribution for waiting times. The shape parameter should be set to k=1 (i.e. exponential distribution) for a null model with no interactions between events (Poisson process). If closely spaced points are expected to be rare, you can set k=2 or k=3.

Wrapping correction: Lutz (1985) described a correction for non-integer number of wraps causing some points to be over-represented. This correction, optional in Past, gives a jagged appearance of the spectral curve and seems to work best for relatively large numbers of points (N>20).

Harmonics: This method is as plagued by harmonics as traditional Fourier analysis. A spectral peak for a period P will be accompanied by strong peaks also on harmonics, i.e. at P/2, P/3 etc. It is important to take this into account when interpreting the spectrum.


Lutz, T.M. 1985. The magnetic reversal record is not periodic. Nature 317:404-407.
Rampino, M.R. & K. Caldeira. 2015. Periodic impact cratering and extinction levels over the last 260 million years. Monthly Notices of the Royal Astronomical Society 454:3480-3484.

Published Aug. 31, 2020 9:23 PM - Last modified Aug. 31, 2020 9:23 PM