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Aftershock Statistics of the 1999 Chi–Chi, Taiwan Earthquake and the Concept of Omori Times

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Aftershock Statistics of the 1999 Chi–Chi, Taiwan Earthquake and the Concept of Omori Times Pure Appl. Geophys. 170 (2013), 221–228 Ó 2012 Springer Basel AG DOI 10.1007/s00024-011-0445-5 Pure and Applied Geophysics Aftershock Statistics of the 1999 Chi–Chi, Taiwan Earthquake and the Concept of Omori Times 1,2 1 1,3 2 YA-TING LEE, DONALD L. TURCOTTE, JOHN B. RUNDLE, and CHIEN-CHIH CHEN Abstract—In this paper we consider the statistics of the after- the magnitude of the main shock and the largest shock sequence of the m = 7.65 20 September 1999 Chi–Chi, aftershock. This law states that the difference in Taiwan earthquake. We first consider the frequency-magnitude statistics. We find good agreement with Gutenberg–Richter scaling magnitude, Dm, between the main shock and its but find that the aftershock level is anomalously high. This level is largest aftershock is approximately constant inde- quantified using the difference in magnitude between the main pendent of the magnitude of the main shock shock and the largest inferred aftershock DmÃ: Typically, Dmà is in the range 0.8–1.5, but for the Chi–Chi earthquake the value is Dm ¼ mms À mmax as ð2Þ Dmà = 0.03. We suggest that this may be due to an aseismic slow- earthquake component of rupture. We next consider the decay rate where mms is the magnitude of the main shock and of aftershock activity following the earthquake. The rates are well m is the magnitude of the largest aftershock, approximated by the modified Omori’s law. We show that the max as distribution of interoccurrence times between aftershocks follow a typically Dm & 1.2 (BA˚ TH 1965). Many studies have nonhomogeneous Poisson process. We introduce the concept of been carried out regarding the statistical variability of Omori times to study the merging of the aftershock activity with Dm (VERE-JONES 1969;KISSLINGER and JONES 1991; the background seismicity. The Omori time is defined to be the mean interoccurrence time over a fixed number of aftershocks. TSAPANOS 1990;FELZER et al. 2002, 2003;CONSOLE et al. 2003;HELMSTETTER and SORNETTE 2003; Key words: Earthquakes, aftershocks, Omori times, SHCHERBAKOV and TURCOTTE 2004). Perhaps Console interoccurrence times. et al.(2003) developed a mathematical model showing a substantial dependence of Dm on the 1. Introduction magnitude thresholds chosen for the main shocks and the aftershocks. This partly explains the large Thebehaviorofaftershocksequenceshasbeen Dm values reported in the past. (3) Omori’s law for discussed widely (i.e. KISSLINGER 1996). There are the temporal decay of aftershocks (OMORI 1894), and three applicable scaling laws: (1) The Gutenberg– the modified Omori’s law (the Omori–Utsu law) Richter (GR) law for frequency-magnitude scaling of which was proposed by Utsu (1961). We will utilize aftershocks (GUTENBERG and RICHTER 1954). The the modified Omori’s law in the form proposed by number N of earthquakes with magnitudes greater than SHCHERBAKOV et al.(2004) or equal to m is well approximated by the relation: 1 1 raðt; mcÞ¼ p ð3Þ log10 NðmÞ¼ a À bðmÞ: ð1Þ saðmcÞ ½1 þ t=cðmcÞ where b is the b-value and a is a measure of seismic where ra(t,mc) : dN/dt is the rate of occurrence of intensity. (2) Ba˚th’s law for the difference between aftershocks with magnitudes greater than or equal to a lower cutoff mc, t is the time elapsed since the time of the main shock. In the limit t ? 0 we have -1 1 Department of Geology, University of California, Davis, ra = sa , the characteristic time sa(mc) is the reci- CA 95616, USA. E-mail: [email protected] procal of the initial (constant) rate of aftershock 2 Graduate Institute of Geophysics, National Central activity at early times. The characteristic time c(mc) University, Jhongli 320, Taiwan, ROC. 3 Department of Physics, University of California, Davis, is the time of transition from their rate to the power- CA 95616, USA. law decay of aftershock activity. 222 Y.- T. Lee et al. Pure Appl. Geophys. There are two limiting cases for the behavior of magnitude. The distribution of interoccurrence time Omori’s law. In the first it is assumed that c0 is a is well approximated by a nonhomogeneous Poisson constant and that sa(mc) depends on the cutoff mag- (NHP) process driven by the modified Omori’s law nitude mc. In the second it is assumed that s0 is a over a finite time interval T (SHCHERBAKOV et al. 2005, constant and that c(mc) depends on the cutoff mag- 2006). At the end of this paper, we introduce the nitude mc.NANJO et al. (2007) has discussed these concept of Omori times to analyze the interoccur- limits in some detail with applications to four Japa- rence times for the Chi–Chi aftershock sequence. We nese earthquakes. In this paper we will assume c0 to calculate the mean interoccurrence interval over a be constant and sa(mc) is determined from the data. In fixed number of aftershocks N = 25, 50, 100, 200, this limit the modified form of Omori’s law given in and compare the Chi–Chi aftershocks with a combi- Eq. (3) becomes nation of Omori decay and a steady-state background. 1 1 raðt; mcÞ¼ p ð4Þ saðmcÞ ½1 þ t=c0 2. Scaling of Chi–Chi Aftershock Sequences For all values of time t the values of the after- shock rate ra(t, mc) for different mc are related by The Chi–Chi earthquake struck central Taiwan on 20 September 1999 at 17:47UTC. It ruptured along raðt; mc1Þ saðmc2Þ ¼ ð5Þ the Chelungpu fault, and the moment magnitude, mw, raðt; mc2Þ saðmc1Þ was 7.65. The hypocenter of the Chi–Chi earthquake However, the rates of aftershock occurrence for was located at 23.853°N, 120.816°E, at a depth of different values of mc satisfy the GR law. From 8 km. In this paper we study the aftershock sequence Eq. (1) we obtain of this earthquake. We combine three catalogs from 1994 to 2008 for our analyses. These three catalogs raðt; mc1Þ ¼ 10Àbðmc1Àmc2Þ ð6Þ include: (1) the Central Weather Bureau seismic r ðt; m Þ a c2 network (CWBSN) catalog from the Central Weather Combining Eqs. (5) and (6) we find Bureau (CWB) of Taiwan, (2) the Taiwan Strong Motion Instrumentation Program (TSMIP) (CHANG saðmc2Þ ¼ 10Àbðmc1Àmc2Þ ð7Þ et al. 2007) which provides good coverage for early s ðm Þ a c1 aftershocks, and (3) the Centroid-Moment-Tensor We will obtain a b-value from GR scaling and (CMT) catalog for large aftershocks. We use the will then fit aftershock statistics for several values of TSMIP catalog for the first hour of Chi–Chi after- mc to obtain preferred values of c0, p, and the sa(mc). shocks and the CMT catalog for aftershocks m [ 5. We illustrate it in the Sect. 2. The completeness magnitude for the area analyzed is In this study, we analyze the scaling laws for the m C 2.0. We combine these catalogs and then define aftershock sequence from the m = 7.65 20 Septem- the Chi–Chi aftershock region. ber 1999 Chi–Chi, Taiwan earthquake. The In Fig. 1 we define the spatial window for the aftershocks are in good agreement with the Guten- Chi–Chi aftershocks. We compare the spatial distri- berg–Richter law for frequency–magnitude scaling bution of seismic activity in Taiwan for 1,000 days and the aftershock decay rates satisfy the modified after the Chi–Chi earthquake with the activity for Omori’s law. An interesting result in this paper is that 1,000 days before the Chi–Chi earthquake. We we find that the Chi–Chi earthquake triggered an choose the area with the largest change in seismic anomalously large number of aftershocks. We also activity as the Chi–Chi aftershock region. Our pur- consider the statistics of interoccurrence times for pose is to exclude the region of high seismicity to the Chi–Chi aftershocks. The observed statistics of east. The epicenter of the mainshock is shown as a interoccurrence times for the Chi–Chi earthquake black star. The dashed lines show the region of sequence has a power-law dependence on the times seismic activity we associate with the Chi–Chi between successive aftershocks over several orders of aftershocks. During the 1,000 day time interval after Vol. 170, (2013) Aftershock Statistics of the 1999 Chi–Chi, Taiwan Earthquake 223 Figure 1 The spatial distribution of seismicity activity for 1,000 days before the 20 September 1999 Chi–Chi earthquake in (a), and 1,000 days after the Chi–Chi earthquake in (b). The magnitude of these earthquakes are great than 2.0. The epicenter of the Chi–Chi earthquake is shown as a black star. The black line shows the surface rupture of the Chi–Chi earthquake. The dash line shows the region of the aftershocks for the statistic of Chi–Chi aftershocks. EP Eurasian Plate, and PSP Philippine Sea Plate the Chi–Chi earthquake, 42,952 aftershocks were 6 recorded with magnitudes m C 2.0, and nine of the y=-0.84x+6.4 aftershocks had magnitudes m C 6.0. A comparison 5 of Fig. 1a with b indicates that less than 5% of the earthquakes in our region were not aftershocks and 4 less than 5% of the aftershocks occurred outside the chosen region. Since the majority of aftershocks have N) ( 10 3 been included we therefore expect the minor differ- g o ence in the spatial extent does not affect the following L analysis. 2 First, we consider the frequency–magnitude scal- ing for the Chi–Chi aftershock sequence.
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