Multifractal Measures of M ≥ 3 Shallow Earthquakes in the Taipei Metropolitan Area


The generalized fractal dimensions are measured for M ≥ 3 shallow earthquakes with focal depths of ≤ 40 km in the Taipei Metropolitan Area (from 121.3 to 121.9°E and 24.8 to 25.3°N) over the 1973 - 2010 period based on spatial distribution (using epicentral and hypocentral distances between two events, r) and time sequence (using the inter-event time between two events, t). The multifractal measures are estimated from log-log plots of Cq(r) versus r and Cq(t) versus t, where Cq(r) and Cq(t) are the generalized correlation integral, respectively, of r and t at positive q. For the spatial distribution, Cq(r) is calculated based on the epicentral distance (i.e., the 2D measure) and hypocentral distance (i.e., the 3D measure). Under both 2D and 3D measures, the log-log plot of Cq(r) versus r shows a linear distribution when log(ro) ≤ log(r) ≤ log(rub) and roll-over when r > rub. For all cases log(ro) is 0.3, and log(rub) are 1.7 and 1.4 for the 2D and 3D measures, respectively. Dq, which is the slope of the linear portion, monotonically decreases with increasing q, thus indicating that the epicentral and hypocentral distributions of earthquakes are multifractal. The values of Dq are lower than 2 and 3, respectively, for the 2D and 3D measures. For the time sequence of the events in study, Cq(t) is calculated based on the inter-event time between two events. The log-log plot of Cq(t) versus t does not seem able to show a linear relationship in a large range of log(r) or r and the value of Dq cannot be evaluated, thus suggesting that the time sequence of M ≥ 3 shallow earthquakes in the Taipei Metropolitan Area (TMA) is not multifractal.

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