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 degrees E and 24.8 to 25.3 degrees 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 C-q(r) versus r and C-q(t) versus t, where C-q(r) and C-q(t) are the generalized correlation integral, respectively, of r and t at positive q. For the spatial distribution, C-q(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(r(0)) <= log(r) <= log(rub) and roll-over when r > r(ub) For all cases log(r(0)) is 0.3, and log(r(ub)) are 1.7 and 1.4 for the 2D and 3D measures, respectively. D-q, 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 D-q are lower than 2 and 3, respectively, for the 2D and 3D measures. For the time sequence of the events in study, C-q(t) is calculated based on the inter-event time between two events. The log-log plot of C-q(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 D-q cannot be evaluated, thus suggesting that the time sequence of M >= 3 shallow earthquakes in the Taipei Metropolitan Area (TMA) is not multifractal.