Multifractal Measures of Time Series of Earthquakes.

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  • Multifractal Measures of Time Series of

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The generalized fractal dimensions are measured for the time series based on two complete earthquake catalogues: one with M≥6 earthquakes occurring in the north-south seismic belt of mainland China during the 1900-1990 period published by Ma et al. (1992) and the other with M≥5.5 earthquakes occurring in southern California, USA during the 1915-1994 period compiled by Press and Allen (1995). The log-log plot of Cq versus t, where Cq(t) is the generalized correlation integral and t is the interoccurrence time in years between two events, at positive q shows a linear istribution when t<tc. Dq is the slope of this linear portion. The value of tc decreases from 50.1 to 39.8 years for Chinese earthquakes and from 50.1 to 31.6 years for southern California events as q is increased from 0 to 15. For M≥6 Chinese earthquakes, the well-distributed, monotonically decreasing function of Dq, with increasing q would imply that such earthquakes have formed a multifractal time series. In contrast, the M≥5.5 southern California earthquakes might have not yet formed a complete multifractal time series or the number of these events is too small to accurately estimate the multifractal dimensions, especially for large qs. Different degrees of complexity of fault distributions in the two seismic regions might also be a factor in causing the difference in the Dq-q relations. In addition, the results also suggest that a Dq-q relation is better than the first three commonly-used values of Dq to completely represent a multifractal time series.

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