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

  • Author(s): Jeen-Hwa Wang, Kou-Cheng Chen, and Kao-Hao Chang
  • DOI: 10.3319/TAO.2017.01.25.01
  • Keywords: Multifractal dimension, Earthquake sequence, Epicenter, Inter-event time, Morlet wavelet technique, Dominant period
  • Citation: Wang, J.-H., K.-C. Chen, and K.-H. Chang, 2017: Fractal and Morlet-wavelet analyses of M ≥ 6 earthquakes in the South-North Seismic Belt, China. Terr. Atmos. Ocean. Sci., 28, 799-814, doi: 10.3319/TAO.2017.01.25.01
  • To evaluate the multifractal dimensions of epicentral distributions
  • To evaluate the multifractal dimensions of earthquake sequences
  • To evaluate the dominant periods of sequences of M≥6 earthquakes
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, Dq, are measured from the log-log plots of Cq(r) versus r and Cq(t) versus t, where Cq(r) and Cq(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 Cq(r) versus r shows a linear por­tion when log(rl) ≤ log(r) ≤ log(ru). The rl and ru 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 rl value decreases with the lower-bound magnitude. Dq monotonically decreases with increasing q. The Dq 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 Cq(t) versus t show a linear distribution when log(tl) ≤ log(t) ≤ log(tu), where tl and tu 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 Dq 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.

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