Evolution of the multifractal parameters along different steps of a seismic activity. The example of Canterbury 2000–2018 (New Zealand)

The multifractal detrended fluctuation algorithm is applied to a series of distances and elapsed times between consecutive earthquakes recorded along the years 2000–2018 in the Canterbury region (New Zealand). The time evolution of several multifractal parameters (Hurst exponent, Hölder central and maximum exponents, spectral amplitude, asymmetry, and complexity index) is analyzed. Peaks of multifractal parameters, with statistical significance exceeding 95%, are associated with three earthquakes of notable magnitude (equaling or exceeding Mw = 5.7). Additionally, some other peaks are also associated with the swarm of earthquakes of moderate magnitude. Possible shortcomings created by this assignment to mainshocks or swarms can be removed by comparing the results corresponding to elapsed times and interevent distances between consecutive events. Additionally, the Buishand test, which is used to verify the statistical significance of the detected peaks, also discriminates between mainshocks of notable seismic magnitude and swarms of earthquakes with moderate magnitude. The obtained results, based on the multifractal structure of the seismic activity, could also represent some advances in predicting, with sufficient time, forthcoming mainshocks of high magnitude and mitigate their destructive effects.