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Empirical Relationships Between Aftershock Zone Dimensions and Moment Magnitudes for Plate Boundary Earthquakes in Taiwan by Wen-Nan Wu, Li Zhao, and Yih-Min Wu

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Empirical Relationships Between Aftershock Zone Dimensions and Moment Magnitudes for Plate Boundary Earthquakes in Taiwan by Wen-Nan Wu, Li Zhao, and Yih-Min Wu Bulletin of the Seismological Society of America, Vol. 103, No. 1, pp. 424–436, February 2013, doi: 10.1785/0120120173 Ⓔ Empirical Relationships between Aftershock Zone Dimensions and Moment Magnitudes for Plate Boundary Earthquakes in Taiwan by Wen-Nan Wu, Li Zhao, and Yih-Min Wu Abstract In this study, we establish the empirical relationships between the spatial M dimensions of the aftershock zones and moment magnitudes ( w) for the Taiwan region. The length (l) and width (w) of the aftershock zone of an earthquake is mea- sured by the major and minor axes, respectively, of the ellipse of a two-dimensional Gaussian distribution of one-day aftershocks. Our data is composed of 649 main- ≤ 70 M – shocks (depth km, w 4.0 7.6) between 1990 and 2011. The relationships be- M tween aftershock zone dimensions and w were obtained by least-squares method with the corresponding uncertainties estimated by bootstrap. Our study confirms that aftershock zone dimensions are independent of faulting types and the seismic moment l3 w=l M is proportional to . The ratio ( ) increases slightly with w and is independent of faulting types. Together with previous study, our results suggest that earthquakes of M 4:0 M ≥ 7:0 both small ( w ) and large ( w ) magnitudes have similar focal zone geo- M –S S metrical parameters. By using the w relation, where the aftershock zone area is estimated from l and w, we also provide an independent examination of the variations in the median stress drop. We find that the median stress drops of strike-slip earth- quakes are higher than those of thrust events. Moreover, the median stress drops are independent of the moment magnitudes for normal and strike-slip events but decrease for large thrust events. These results are consistent with the latest global observations. 6 ≤ M ≤ 7:6 Regardless of faulting types, the median stress drop decreases for larger ( w ) and relatively deep (depth ∼ 60–70 km) earthquakes. Online Material: Effect of up-dip rupture propagation on estimated maximum slip duration, details on teleseismic and geodetic stations, and figures of far-field displace- ments, temporal change in slip, and snapshots of the semblance-value distribution. Introduction Over the past several decades, the empirical relation- nitudes and/or faulting types has risen from these observa- ships between seismic moment (M0) or moment magnitude tions. A number of global and regional studies have sug- M ( w) and various earthquake faulting parameters (e.g., rup- gested that the rupture dimensions (rupture length, width, ture length, width, and displacement) have been studied by and area) are independent of moment magnitudes and/or a number of researchers on the basis of worldwide data faulting types (e.g., Wells and Coppersmith, 1994; Wang sets (e.g., Scholz, 1982; Bonilla et al., 1984; Scholz et al., and Ou, 1998; Hanks and Bakun, 2002, 2008; Kagan, 1986; Romanowicz, 1992; Wells and Coppersmith, 1994; 2002; Dowrick and Rhoades, 2004), indicating that we Pegler and Das, 1996; Wang and Ou, 1998; Mai and Beroza, can extrapolate from measurements of much more numerous 2000; Stock and Smith, 2000; Henry and Das, 2001; Hanks smaller earthquakes to those of the rare and devastating and Bakun, 2002, 2008; Kagan, 2002; Manighetti et al., greater events (Shaw, 2009). Several studies, however, have 2007; Blaser et al., 2010; Leonard, 2010; Strasser et al., drawn opposite conclusions (e.g., Bonilla et al., 1984; 2010) and regional data (e.g., Dowrick and Rhoades, Vakov, 1996; Mai and Beroza, 2000; Stock and Smith, 2000; 2004; Konstantinoua et al., 2005; Murotani et al., 2008; Hanks and Bakun, 2002, 2008; Manighetti et al., 2007; Yen and Ma, 2011). These scaling relationships provide Blaser et al., 2010; Leonard, 2010). For example, Mai not only useful empirical relationships for practical seismic and Beroza (2000) observed that the scaling relation is hazard analyses but also perspective on earthquake physics self-similar for dip-slip events but not for large strike-slip (Shaw, 2009). An ongoing debate on whether the physical events. Multiple magnitude-length scaling relations based processes of earthquakes are independent of moment mag- on fault segmentations have also been proposed (Manighetti 424 Empirical Relationships between Aftershock Zone Dimensions and Moment Magnitudes 425 et al., 2007). Furthermore, a self-similar model in which the Taiwan is located along a strongly oblique convergent seismic moment is proportional to the cube of the fault length zone. To the northeast, the Philippine Sea Plate subducts 3 (l)(M0 ∼ l ) has been suggested (e.g., Kanamori and Ander- northward beneath the Ryukyu Arc, where the Okinawa son, 1975; Wells and Coppersmith, 1994; Kagan, 2002). Trough, a back-arc basin, is developing, whereas in the south Specifically, because the depth extent of earthquake rupture the Eurasia Plate subducts eastward beneath the Luzon Arc is limited by the finite seismogenic thickness for great earth- (Angelier, 1990; Sibuet et al., 1998; Hsu and Deffontaines, quakes, the seismic moment is proportional to the fault 2009; Fig. 1). This results in an active and complicated length (M0 ∼ l)(Romanowicz, 1992, 1994; Romanowicz tectonic environment, including subduction, collision, and M ∼ 2 and Ruff, 2002), or the square of the fault length back-arc rifting. Earthquakes from small ( w ) to large M ∼ l2 M > 6 ( 0 )(Scholz, 1982, 1994a,b; Scholz et al., 1986). Re- magnitude ( w ) with various faulting types (thrust, cently, Leonard (2010) proposed scaling relations between normal, and strike-slip focal mechanisms) occur frequently. M ∼ l3 the moment magnitude and fault length of w and To the best of our knowledge, however, the study of the em- M ∼ l2:5 w , respectively, for events smaller and larger than pirical relations between focal zone geometrical parameters M 5 w on the basis of a compilation of global data sets. and magnitudes for earthquakes in Taiwan in particular Yen and Ma (2011) suggested that the relations between the has not received as much attention. Therefore, in this study 2 3 seismic moment and fault length are M0 ∼ l and M0 ∼ l , we aim to establish a set of empirical relationships between M 7 respectively, for events smaller and larger than w aftershock zone dimensions and moment magnitude for the based on slip models mostly from the Taiwan region. Taiwan region. (a) Distribution of Stations (c) Normal Events TSMIP 801 26°N CWBSN 262 26°N JMA 41 OBS 11 24°N 24°N Eurasia Plate 22°N 22°N Philippine Sea Plate 120°E 122°E 124°E 120°E 122°E 124°E Thrust Events Strike-slip Events (b) (d) 26°N 26°N 24°N 24°N 22°N 22°N 120°E 122°E 124°E 120°E 122°E 124°E 0 10203040506070 Focal Depth (km) Mw= 45 6 7 Figure 1. (a) Tectonic environment of Taiwan and seismic stations used in the relocation of earthquakes in Wu et al. (2009).(b–d) Dis- ≤ 70 M ≥ 4 tributions of shallow and relatively large (depth km, w ) earthquakes with thrust, normal, and strike-slip faulting types, respec- tively. Mainshocks that meet the criteria for data selection and are used in scaling-relation regressions, circles. 426 W.-N. Wu, L. Zhao, and Y.-M. Wu In establishing the empirical source scaling relations, a Furthermore, the stress drop (Δσ), the difference between common way to estimate the earthquake rupture size is to the average state of stress on the fault plane before and after an rely on the distributions of either the coseismic slip (e.g., earthquake (Allmann and Shearer, 2007), is one of the most Somerville et al., 1999; Mai and Beroza, 2000; Murotani important earthquake source parameters. The issue of whether et al., 2008; Yen and Ma, 2011) or the aftershock locations the stress drop is magnitude dependent or depth dependent (e.g., Wells and Coppersmith, 1994; Henry and Das, 2001; is still open to debate (Allmann and Shearer, 2007, 2009; Kagan, 2002; Konstantinoua et al., 2005; Leonard, 2010; Hardebeck and Aron, 2009). There have been many efforts Strasser et al., 2010). The major drawbacks of these ap- to resolve these controversies, mainly by improving the reli- proaches, however, are that the solution in the coseismic slip ability and stability of the earthquake source spectra (e.g., inversion is often not unique (Beresnev, 2003; Zahradník and Mayeda and Walter, 1996; Prieto et al., 2004; Allmann Gallovič, 2010), and the definition of the aftershock zone can and Shearer, 2007, 2009; Mayeda et al., 2007). In this study, be subjective (Tajima and Kanamori, 1985a,b; Kagan, 2002; we relate the stress drop to our derived relations between the Tajima and Kennett, 2012). These ambiguities introduce moment magnitude and aftershock zone area. Our approach large uncertainties in delineating the rupture size and estab- is free from the limitation of using earthquake source spectra lishing the empirical source scalings. Although the after- to retrieve the stress drop, and we can provide an indepen- shock mapping method has the weakness of subjective dent examination of the scaling behavior for the stress drop. judgment, it allows for a lower moment magnitude threshold in the mainshocks selection and, therefore, enables us to use Data and Analysis a greater number of events to derive empirical relationships. Earthquake Catalogs and Data Selection A large number of available events are favorable for the empirical relationship regression study, especially in the case To derive the scaling relationships of aftershock zone where data are further divided to examine the dependence on dimensions with moment magnitude for the Taiwan region, the magnitudes and focal mechanisms of earthquakes as well a latest high-quality seismicity catalog between 1990 and as other earthquake source parameters. We, thus, adopt a 2011 is used.
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