Fractal and Morlet-wavelet analyses of M ≥ 6 earthquakes in the South-North Seismic Belt, China

Abstract

The M ≥ 6 earthquakes occurred in the South-North Seismic Belt, Mainland China (longitudes from 98 -107°E and latitudes from 21 -41°N) during 1900 -2016 are taken to measure the multifractal dimensionsspatial distribution and time sequence of events and the dominant periods. The multifractal dimensions, D q , are measured from the log-log plots of C q (r) versus r and C q (t) versus t, where C q (r) and C q (t) are the generalized correlation integrals for the epicentral distribution and time sequence of events, respectively. r and t are the epicentral distance and inter-event time, respectively, at positive q. The log-log plot of C q (r) versus r shows a linear portion when log(r l ) ≤ log(r) ≤ log(r u ). The r l and r u values are, respectively, 120 and 560 km for M ≥ 6 events, 100 and 560 km for M ≥ 6.5 events, and 63 and 560 km for M ≥ 7 events. The r l value decreases with the lower-bound magnitude. D q monotonically decreases with increasing q. The D q values are between 1.618 and 1.426 for M ≥ 6 events, between 1.562 and 1.108 for M ≥ 6.5 events, and between 1.365 and 0.841 for M ≥ 7 events. The log-log plot of C q (t) versus t show a linear distribution when log(t l ) ≤ log(t) ≤ log(t u ), where t l and t u are, respectively, 5 and 50.1 years for M ≥ 6 events, 5 and 50.1 years for M ≥ 6.5 events, and 16 and 63.1 years for M ≥ 7 event, thus suggesting that the time sequences of earthquake in the study region are multifractal. The D q values are between 0.830 and 0.703 for M ≥ 6 events, between 0.835 and 0.820 for M ≥ 6.5 events, and between 0.786 and 0.685 for M ≥ 7 events. The Morlet wavelet technique is applied to analyze the dominant periods of temporal variations in numbers of yearly earthquakes for the three magnitude ranges, i.e., M ≥ 6, M ≥ 6.5, and M ≥ 7. The resultant dominant period is 2.94 years for M ≥ 6 events and cannot be evaluated for M ≥ 6.5 and M ≥ 7 events.

Dominant periods and memory effect of the 2021 earthquake swarm in Hualien, Taiwan

“…Since the methods applied in this study have been explained in details in several articles (e.g., Chen et al 2015;Wang et al 2017), only simple descriptions are given below. The detailed description about the technique can see Torrence and Compo (1998).…”

“…Numerous authors (e.g., Kagan and Knopoff 1976;Wang 2013;Wang et al 2017; and cited references therein) assume that the occurrences of earthquakes with M ≥ 7 are the pure Poisson process or the Poisson process with a weak memory effect. The degree of memory effect may increase from larger-sized earthquakes to smaller-sized events (e.g., Wang 2013;Wang et al 2017). For the earthquake sequence of the Hualien swarms, the magnitude ranges from 3.0 to 6.2.…”