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

Abstract

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 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 C q (r) versus r shows a linear distribution when log(r o ) ≤ log(r) ≤ log(r ub ) and roll-over when r > r ub . For all cases log(r o ) 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.

Strong Ground Motions Generated by the February 11, 2014 Tatunshan Earthquake in the Taipei Metropolitan Area

“…1). From the epicentral distributions, several authors (Tsai et al 1973;Wang et al 1983Wang et al , 2006Wang 1988;Chen and Yeh 1991;Chen et al 1995;Chen et al 2005;Kim et al 2005;Konstantinou et al 2007) showed lower seismicity in the TMA than other areas in northern Taiwan and a low correlation between seismicity and the recognized faults.…”

“…Except for July 3, 1988 M 5.3 earthquake, seismicity in the TMA was low (Wang et al 2006(Wang et al , 2012a. In 2005 three felt earthquakes (M L = 3.8, 3.2, and 3.7) occurred near the eastern part of the basin, about 3 km to the south of Taipei 101, the tallest building in the world.…”

Elucidating the geometry of the active Shanchiao Fault in the Taipei metropolis, northern Taiwan, and the reactivation relationship with preexisting orogen structures

“…Although confirmed to be active in the Holocene [ C.‐T. Chen et al ., ] with several inferred paleoearthquake events [ Huang et al ., ], the crustal geometry of the Shanchiao Fault remained uncertain since no outcrop has been identified, and direct imaging of the fault is prevented by the lack of both seismic profiling and clustering of (micro) seismicity [ Wang et al ., ] (Figure a). The only inference on the Shanchiao Fault crustal configuration is its structural inversion relationship with a former thrust, the Hsinchuang Fault, deduced from regional geological synthesis [ Wu , ; Chiu , ; Teng et al ., ].…”

“…The Taipei Basin, containing the Taipei metropolis in northern Taiwan with more than 8 million inhabitants, is geologically a half graben formed through the successive slips of the Shanchiao Fault during the late Quaternary (Figure 1). Although confirmed to be active in the Holocene [C.-T. with several inferred paleoearthquake events [Huang et al, 2007], the crustal geometry of the Shanchiao Fault remained uncertain since no outcrop has been identified, and direct imaging of the fault is prevented by the lack of both seismic profiling and clustering of (micro) seismicity [Wang et al, 2006] (Figure 2a). The only inference on the Shanchiao Fault crustal configuration is its structural inversion relationship with a former thrust, the Hsinchuang Fault, deduced from regional geological synthesis [Wu, 1965;Chiu, 1968;Teng et al, 2001].…”

Heterogeneous Slip Distribution Self-Similarity on a Fault Surface

“…Mandelbrot (1983) proposed another concept, fractal geometry, and stated that a fractal dimension can describe the scale invariance of natural phenomena. This concept has been widely applied to describe the spatial distribution and time series of earthquakes (Turcotte 1989(Turcotte , 1997Ogata and Abe 1991;Hirabayashi et al 1992; Papadopoulos and Dedousis 1992; Koyama et al 1995;Wang 1996;Wang and Lee 1997;Wang et al 2014) and fault activities (cf. Okubo and Aki 1987;Lee and Schwarcz 1995).…”