Multifractal measures of the 2021 earthquake swarm in Hualien, Taiwan

Abstract

An earthquake swarm occurred in Haulien, Taiwan, from April 7 to August 31, 2021. The epicenters are in the range from 23°47′ N to 24°04′ N and from 121°25′ E to 121°42′ E. Cq(r) and Cq(t) are the generalized correlation integral of r and t, respectively. From the events with local magnitudes ≥ 3 and focal depths ≤ 25 km, Cq(r) is calculated for the epicentral and hypocentral distribution (using the distance between two events, r) and Cq(t) for the time sequence (using the inter-event time between two events, t). The multifractal dimension Dq (q = 2, 3, …, 15) is the slope of the linear portion of the log–log plots of Cq(r) versus r as well as Cq(t) versus t. For the epicentral distribution, the linear pattern is in the range 0.5 ≤ log(r) ≤ 1.3. The measured values of Dq are all smaller than 2 that is the spatial dimension and monotonically decreases with increasing q. This indicates that the epicentral distribution of the swarm is multifractal. For the hypocentral distribution, a lack of a wide enough linear pattern on the log–log plot makes the hypocentral distribution be not multifractal. For the time sequence, the log–log plot of Cq(t) versus t shows a linear pattern in the range 0.5 ≤ log(t) ≤ 1.0. The values of Dq are all smaller than 1 that is the time dimension and monotonically decreases with increasing q, thus suggesting multifractality of the time sequence when t is shorter than the maximum inter-event time.