JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, B01305, doi: /2010jb007900, 2011

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2010jb007900, 2011 Depth dependent stress field in and around the Atotsugawa fault, central Japan, deduced from microearthquake focal mechanisms: Evidence for localized aseismic deformation in the downward extension of the fault Kazutoshi Imanishi, 1 Yasuto Kuwahara, 1 Tetsuya Takeda, 2 Takashi Mizuno, 1,3 Hisao Ito, 4 Kiyoshi Ito, 5,6 Hiroo Wada, 5 and Yoshikatsu Haryu 2,6,7 Received 30 July 2010; revised 2 November 2010; accepted 22 November 2010; published 21 January [1] Focal mechanisms have been determined from P wave polarity data as well as body wave amplitudes for 154 microearthquakes that occurred around the Atotsugawa fault in central Japan between 2002 and While we found many microearthquakes with a pure strike slip mechanism that is similar to the faulting style of the Atotsugawa fault, a considerable number of microearthquakes with reverse faulting components are also occurring. Most of the P axes are horizontal and oriented in the WNW ESE direction, which conforms to the general tectonic trend in this area. In contrast, the T axes have a wide range of plunge, suggesting that reverse faulting type earthquakes as well as strike slip ones are occurring. The most conspicuous feature in the focal mechanism distribution is the depth dependence, where shallow earthquakes are primarily reverse faulting and strike slip earthquakes become predominant with depth. A stress tensor inversion reveals that the shallower part is characterized by a mixture of reverse and strike slip faulting regimes and that a pure strike slip faulting regime appears only around the bottom of the seismogenic zone. Together with other geophysical observational evidence for the fault, we suggest that the existence of a localized aseismic deformation below the Atotsugawa fault is the simplest scenario that can explain the observed stress fields. This scenario provides a stress accumulation mechanism of disastrous shallow inland earthquakes, in which the localized aseismic deformation accumulates stress onto the fault plane in the seismogenic zone during an earthquake cycle and the main shock would occur when the failure stress is reached on the fault. Citation: Imanishi, K., Y. Kuwahara, T. Takeda, T. Mizuno, H. Ito, K. Ito, H. Wada, and Y. Haryu (2011), Depth dependent stress field in and around the Atotsugawa fault, central Japan, deduced from microearthquake focal mechanisms: Evidence for localized aseismic deformation in the downward extension of the fault, J. Geophys. Res., 116,, doi: /2010jb Introduction [2] It is widely known that tectonic stress gradually accumulates in locked portions of plate boundaries, owing to relative plate motion, and that large interplate earthquakes 1 Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan. 2 National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan. 3 Now at Schlumberger Kabushiki Kaisha Integration Center, Sagamihara, Japan. 4 Center for Deep Earth Exploration, Japan Agency for Marine Earth Science and Technology, Yokohama, Japan. 5 Disaster Prevention Research Institute, Kyoto University, Uji, Japan. 6 Now at Hanshin Consultants Co., Ltd., Osaka, Japan. 7 Association for the Development of Earthquake Prediction, Tokyo, Japan. Copyright 2011 by the American Geophysical Union /11/2010JB occur when the accumulated stress exceeds the strength of the locked portions. In particular, recent seismic and geodetic observations of small repeating earthquakes [e.g., Nadeau and McEvilly, 1999; Igarashi et al., 2003; Uchida et al., 2007] and of episodic tremor and slip [e.g., Dragert et al., 2001; Obara, 2002; Shelly, 2010] contribute to a deeper understanding of the generation mechanism of large interplate earthquakes and provide a new way to monitor stress buildup at plate boundaries. In contrast, understanding of the generation mechanism of disastrous shallow inland earthquakes (intraplate earthquakes) has advanced slowly [e.g., Stein and Mazzotti, 2007]. Scholz [2002] classified shallow intraplate earthquakes into two types. The first type occurs in broad areas near plate boundaries (e.g., inland earthquakes in Japan and New Zealand) or in diffuse plate boundaries (e.g., the Basin and Range provinces of western North America, the Andes, and the Himalayan Tibetan Plateau). The second type occurs in stable continental areas 1of21

2 and is considered not to be associated with plate boundaries. The most famous example of this type is the New Madrid seismic zone in the central United States. During the last two decades, the aseismic deformation zone beneath the seismogenic layer came to be considered as a key for the occurrence of both types of large intraplate earthquakes, and some models incorporating a local stress accumulation mechanism have been proposed [e.g., Liu and Zoback, 1997; Kenner and Segall, 2000; Iio and Kobayashi, 2002a; Hasegawa et al., 2005]. Recent studies on the first type of intraplate earthquakes in Japan also support the existence of an aseismic deformation zone beneath the seismogenic layer, on the basis of high quality geophysical data and numerical simulation [Iio and Kobayashi, 2002b; Mizuno et al., 2005; Kawanishietal., 2009; Ando and Okuyama, 2010]. However, such observational results are still rare and the style of deformation (i.e., localized or widely distributed in volume) still remains open to discussion. Further observational constraints at various active faults are needed to better understand the stress accumulation mechanism of shallow inland earthquakes. [3] The Atotsugawa fault (Figure 1) in central Japan is probably the best field to study the stress accumulation mechanism of large inland earthquakes in Japan because of its high level of seismicity, high deformation rate, simple fault geometry, and the existence of many related studies [e.g., Ito and Wada, 2002; Hirahara et al., 2003; Mizuno et al., 2005; Kato et al., 2006]. Here, the Atotsugawa fault is categorized as being one of the first type of intraplate earthquakes, as defined by Scholz [2002]. Mizuno et al. [2005] suggested a possibility that localized aseismic slip occurs below the Atotsugawa fault by analyzing shear wave splitting across the fault. They found that the angle between the polarization direction of the leading shear wave (LSPD) and the strike of the fault decreases with approach to the fault. On the basis of the assumption that LSPD corresponds to the direction of the maximum horizontal stress [e.g., Crampin, 1978], they concluded that the spatial variation of LSPD can be explained by incorporating aseismic slip along the deep extension of the fault through numerical modeling. However, the assumption adopted by Mizuno et al. [2005] is not necessarily applicable each time, because LSPD may be affected by structural anisotropies such as fault zone fabric [e.g., Zinke and Zoback,2000;Balfour et al.,2005;boness and Zoback, 2006]. [4] If the deep extension of the fault slips aseismically, it might be possible to detect a depth dependence in the stress field caused by the stress concentration at the aseismic slip front. Among various stress indicators such as shear wave splitting, strain data, and others, earthquake focal mechanisms are thought to be the most effective means to detect the depth dependence, because they constrain the stress field at depths where earthquakes are actually occurring. Focal mechanisms are ordinarily determined from P wave polarity data. In the case of microearthquakes, however, it is difficult to obtain a unique focal mechanism solution, because the number of stations detecting events decreases and their azimuthal coverage becomes poor. One approach to overcoming this problem is to use S/P amplitude ratios [e.g., Kisslinger, 1980; Julian and Foulger, 1996; Hardebeck and Shearer, 2003] or absolute P and S amplitudes [e.g., Slunga, 1981; Nakamura et al., 1999; Igarashi et al., 2001]. These approaches have been successfully applied to microearthquakes and have been shown to be effective even if the number of P wave polarities is insufficient and the observation station coverage is poor. We prefer the latter approach for microearthquakes, because there are many seismograms in which only S wave amplitude can be used in the analysis owning to poor signal to noise ratio of P wave amplitude. [5] In this study, we investigate the depth dependence of the stress field along the Atotsugawa fault plane from numerous focal mechanism solutions. Because most of the earthquakes occurring in and around the Atotsugawa fault are smaller than 2 in magnitude, we carried out a dense temporary seismic observation around the fault and determined the focal mechanisms using P wave polarity data as well as absolute body wave amplitudes. On the basis of the estimated stress fields and other observational evidence, we discuss a possible stress accumulation mechanism of the Atotsugawa fault. 2. Seismological Setting [6] A number of active Quaternary faults are concentrated in the study region. They are conjugate sets, where one consists of right lateral strike slip faults trending in an ENE WSW to NE SW direction and the other consists of leftlateral strike slip faults trending in a NNW SSW to NW SE direction (Figure 1). The Atotsugawa fault system is located between Mt. Tateyama and Mt. Hakusan and is composed of three near vertical right lateral strike skip faults, the Atotsugawa, Ushikubi, and Mozumi Sukenobu faults [e.g., Takeuchi et al., 2003]. The Atotsugawa fault is traced geomorphologically for about 69 km with a strike of N60 E. The Ushikubi fault, with a length of about 54 km, runs almost parallel to the Atotsugawa fault about 6 km north of it. The Mozumi Sukenobu fault is about 23 km long and branches from the Atotsugawa fault at its eastern termination. Paleoseismic trenching data suggest that recurrence intervals of the Atotsugawa, Ushikubi, and Mozumi Sukenobu faults are about 2400 ± 100 years (Headquarters for Earthquake Research Promotion, Long term evaluation of the Atotsugawa fault (in Japanese), 2004, available at index.htm), 6050 ± 1050 years (Headquarters for Earthquake Research Promotion, Long term evaluation of the Ushikubi fault (in Japanese) 2005, available at and 13,500 ± 6300 years [Takeuchi et al., 2003], respectively. The most recent destructive earthquake in this area is the 9 April 1858 Hietsu earthquake (M7.0), which was considered to be a faulting on the Atotsugawa fault [Matsuda, 1966]. Takeuchi et al. [2003] suggested that the Mozumi Sukenobu fault was also active in the 1858 event. The average horizontal fault slip rate of the Atotsugawa fault inferred from the topographical offsets is 2 3 mm/yr (Headquarters for Earthquake Research Promotion, Longterm evaluation of the Atotsugawa fault (in Japanese), 2004, available at 04sep_atotugawa/index.htm). This slip rate falls within the fastest category in Japan [Research Group for Active Faults of Japan, 1991]. The average horizontal fault slip rates of 2of21

3 Figure 1. Overview of the Atotsugawa fault system and adjacent regions, central Japan. Active faults are represented by red lines and AGF represents the Atotsugawa fault. Two near vertical right lateral strike slip faults named the Ushikubi fault (UKF) and the Mozumi Sukenobu fault (MSF) are running near the Atotsugawa fault. Black circles represent earthquake locations shallower than 20 km determined by the Japan Meteorological Agency (JMA) during the period from January 2000 to December Earthquake locations in the X Y cross section are shown at the bottom. The thick orange line in the top left inset shows the concentrated deformation zone (Niigata Kobe Tectonic Zone, NKTZ). the Ushikubi and Mozumi Sukenobu faults are considered to be less than that of the Atotsugawa fault. [7] On the basis of his analyses of triangulation data compiled over the past 100 years, Hashimoto [1990] detected a zone with high strain rates from Niigata to the Kinki district, central Japan. This zone, with high strain rates, was also clearly identified in the recent observations from dense GPS arrays by the Geographical Survey Institute (Figure 1), and it was named the Niigata Kobe Tectonic Zone (NKTZ) [Sagiya et al., 2000]. The strain rate in the NKTZ was determined to exceed 10 7/yr, which is tenfold that of the average in Japan [Sagiya et al., 2000; Mazzotti et al., 2001]. There are many active Quaternary faults within this zone and large inland earthquakes have also occurred intensively. The Atotsugawa fault system is one of the active faults in the NKTZ. [8] Seismicity in the study region was investigated in detail by Mikumo et al. [1988], Ito and Wada [2002], and Ito et al. [2007]. Figure 1 shows seismicity in the study area 3 of 21

4 occurring in the area are strike slip faulting, reverse faulting, or a mixture of these. The JMA earthquake catalog is insufficient to discuss the general tectonic stress prevailing over the Atotsugawa fault system, since there are few focal mechanisms near the fault system. Mikumo et al. [1988] and Koizumi et al. [1993] reported about 10 focal mechanisms of earthquakes with magnitudes greater than 3 that occurred during the period from 1977 to 1984 and from 1978 to 1990, respectively. Most of these moderate size earthquakes have almost a strike slip mechanism with a NWN ESE orientation of P axis, which is similar to the faulting style of the Atotsugawa fault system. There are also a few events with a reverse faulting or normal faulting component. Together with a temporary seismic observation, focal mechanisms of earthquakes smaller than M3 could be determined by using the P wave first motions [Wada et al., 2003; Ito et al., 2007; Katsumata et al., 2010]. The result shows that earthquakes with reverse faulting and normal faulting components are certainly occurring around the Atotsugawa fault system, implying a spatial variation of the local stress field. Figure 2. Spatial distribution of focal mechanism solutions shallowerthan20kmdeterminedbythejmaduringthe period from October 1997 to December Focal mechanisms are projected onto the lower hemisphere using the equalarea projection. M j denotes the magnitude reported by the JMA. The M j 4.1 earthquake of 24 March 2005 is shown by an arrow. during the period from January 2000 to December 2009 as routinely determined by the Japan Meteorological Agency (JMA). A linear distribution of high seismic activity can be recognized along the Atotsugawa fault, which was first reported by Wada and Kishimoto [1974]. Linear trends of seismicity along the Mozumi Sukenobu and Ushikubi faults can also be identified, although the activity on the faults is lower than that on the Atotsugawa fault. A cross section along the Atotsugawa fault system is shown at the bottom of Figure 1. A spatial nonuniformity of seismicity is clearly recognized, in which seismicity rate on the northeast side near the central part of the fault is significantly low. The seismicity cutoff depth decreases gradually from the central part of the Atotsugawa fault to both ends. This concave shape could be explained by the change in thermal structure, because there are active volcanoes at both ends of the Atotsugawa fault [Ito and Wada, 2002]. The cross sections perpendicular to each fault indicate that the seismicity along the faults occurs in a nearly vertical zone without intersecting each other [Ito et al., 2007]. [9] Figure 2 shows focal mechanisms of earthquakes that occurred during the period from October 1997 to December 2009 at depths shallower than 20 km. These mechanisms were routinely determined by the JMA on the basis of the observation of P wave first motion polarities, which are listed in the JMA earthquake catalog since October JMA generally reports focal mechanisms of earthquakes with magnitudes greater than 3. Most of the earthquakes 3. Data [10] We conducted temporary observations around the Atotsugawa fault at 8 stations from July to November 2002, 23 stations from May to October 2003, and 14 stations from May to October 2004 (Figure 3). Seismometers employed in the temporal observations were three component velocity geophones having a natural frequency of 2 Hz (L22 E, Mark Product Inc.) and fixed on a hard rock surface with Plaster of Paris. The events were recorded on REF TEK 72A (Refraction Technology, Inc.) and LS7000 data loggers (HAKUSAN Corp.) with GPS clocks at sample rates of 250 or 200 Hz in offline continuous mode. In Figure 3, we also show the distribution of the permanent stations used in our study; these are operated by the Disaster Prevention Research Institute (DPRI, Kyoto University), Earthquake Research Institute (ERI, University of Tokyo), Nagoya University, JMA, National Research Institute for Earth Science and Disaster Prevention (NIED), and Geological Survey of Japan (GSJ, National Institute of Advanced Industrial Science and Technology). Each station is equipped with a set of three component velocity geophones having a natural frequency of 1 or 2 Hz. Seismometers operated by the NIED and GSJ are installed at the bottom of a borehole at a depth of several hundred meters. Figure 4 shows an example of vertical component seismograms recorded by temporal stations (black lines) and surrounding permanent stations (shaded lines). [11] We analyzed 481 earthquakes that occurred in and around the Atotsugawa fault during the period of the temporary observations. The hypocenters were determined by applying a maximum likelihood estimation algorithm [Hirata and Matsu ura, 1987] to manually picked arrival times. The P wave velocity model used in our investigation is shown in Figure 5, which is the same as that of Ito and Wada [2002]. The S wave models are p ffiffiffi assumed by scaling the P wave velocities by a factor of 1/ 3. The P and S wave arrival times were identified manually using the WIN system developed by Urabe and Tsukada [1991]. We first located the hypocenters of all events that occurred in 2003 without station corrections. We then relocated these events 4of21

5 Figure 3. Distribution of temporary and permanent seismic stations used for the relocation and focal mechanism determination. The shaded circles represent earthquake locations determined in this study. Active faults are represented by solid lines. by introducing the station correction, which was obtained using the average of the differences between observed and theoretical travel times at each station. We repeated the above procedure three times and obtained final locations as well as station corrections at individual stations. The rootmean square (RMS) values of the residuals decreased from 0.14 to 0.07 s for the P wave and from 0.20 to 0.11 s for the S wave. The locations of all events that occurred in 2002 were determined using the same velocity structures and station corrections. For the 2004 observations, there were an additional five stations that were not deployed in We first determined the locations of all events that occurred in 2004 on the basis of the same velocity structures and station corrections without these five stations. We then calculated the station corrections at those five stations by averaging the differences between the observed and theoretical travel times. Finally, we relocated the 2004 events incorporating the newly determined station corrections. Magnitudes ranged from 1.2 to 3.0, which were determined from the maximum velocity amplitude data of seismograms by the method of Watanabe [1971]. The average spatial errors calculated by the maximum likelihood estimation algorithm [Hirata and Matsu ura, 1987] were 122 m in the horizontal direction and 235 m in depth, which is sufficient for the purpose of the present study. There are 259 events among our data set that were used for a 3 D seismic travel time tomography study [Takeda et al., 2004]. We compared the locations determined in the present study with those determined by the 3 D model and found that the average spatial differences are 274 m in the horizontal direction and 376 m in depth. This comparison demonstrates that our procedure based on the 1 D velocity model with station corrections gives reasonable estimates of earthquake locations. The general feature of the seismicity along the Atotsugawa fault 5of21

6 Figure 4. Example of vertical component seismograms recorded by temporary stations (black lines) and surrounding permanent stations (shaded lines). (e.g., a concave shape of the cutoff depth of seismicity and a very low seismicity rate on the northeast side) is the same as those in previous studies [e.g., Mikumo et al., 1988; Ito and Wada, 2002]. 4. Focal Mechanism Solution of Microearthquakes Using Body Wave Amplitudes [12] In the present study, we determined focal mechanism solutions of microearthquakes using absolute P and SH wave amplitudes as well as P wave polarity. The same approach was used by Imanishi et al. [2006a, 2006b] and Imanishi and Kuwahara [2009], and was shown to be effective for microearthquakes. We analyzed earthquakes having at least eight P wave polarities. After correcting the instrumental response, we determined the spectral levels and corner frequencies of the spectra by fitting the w 2 model [Boatwright, 1978] with an attenuation correction. The spectral levels for lower frequencies were used as observed amplitudes. Theoretical amplitudes were calculated from the 6of21

7 Figure 5. P wave velocity (V p ) structure models used for hypocenter determination. The S wave models arep assumed ffiffi by scaling the P wave velocities by a factor of 1/ 3. far field solutions for a shear point source dislocation in a homogeneous infinite medium, with corrections of the incident angles at the surface and geometrical spreading. The best fit solution of each event was determined by minimizing the residual between the observed and theoretical amplitudes, where a grid search approach was applied for strike, dip, and slip angles at 5 intervals. We first determined focal mechanisms and seismic moments of all events that occurred in We then redetermined them by introducing the amplitude station correction, which was obtained using the logarithmic average of the ratios between the theoretical and observed amplitudes at each station. Focal mechanisms and seismic moments of all events that occurred in 2002 were determined by using the same amplitude station corrections. For the 2004 observations, as mentioned, there were an additional five stations that were not deployed in Therefore, we first determined the focal mechanisms and seismic moments of all events that occurred in 2004 on the basis of the same amplitude station corrections without these five stations. We then calculated the amplitude station corrections at those five stations using the logarithmic average of the ratios between the theoretical and observed amplitudes. Finally, we redetermined the focal mechanisms and seismic moments of the 2004 events incorporating the newly determined amplitude station corrections. The stability of the solution was checked by plotting all focal mechanisms whose residual was less than 1.1 fold the minimum residual value. We rejected ambiguous solutions where multiple solutions were possible. In total, we obtained 154 focal mechanisms whose moment magnitudes ranged from 0.7 to 3.1. It should be noted that during the same period there are no routinely determined first motion mechanisms by the JMA or moment tensor solutions determined by the NIED. We also evaluated focal mechanism uncertainties for each event from the average of Kagan angles [Kagan, 1991] between the best fitting solution and all the solutions whose residual is within 1.1 fold that of the minimum residual. Here, the Kagan angle becomes zero when the two mechanisms are the same, and becomes 120 when they differ most. The average uncertainty of all the focal mechanisms was [13] Figure 6 shows an example of focal mechanism determination for an earthquake (M w 0.8) that occurred at 1754 LT (Japan standard time) on 5 August As is evident from Figure 6, P wave first motion polarity alone cannot constrain the mechanism of this earthquake. The first motion P wave polarities are perfectly explained not only by a pure reverse faulting type mechanism but also by a pure strike slip one. On the other hand, absolute amplitudes and the polarity observations require the strike slip faulting type mechanism. All of the single event focal mechanism solutions determined in our study are shown in Figure 7 together with the first motion polarities. The estimated solutions explain the first motion polarities well. [14] The focal mechanisms are plotted on maps in Figure 8a, where different colors are used according to the faulting types; reverse (green), strike slip (red), and normal (blue) faulting mechanisms. Following Frohlich [1992], we classified reverse events as those having T axis plunges of less than 40, and strike slip and normal fault earthquakes as those having B and P axis plunges of less than 30, respectively. All remaining events were defined as other. The numbers of reverse, strikeslip, normal, and other events are 37, 64, 0, and 53, respectively. All events are plotted by open circles in a color triangle diagram (Figure 8a, bottom right), which suggests that most of the other events are a mixture of reverse and strike slip components. As was the case with the results obtained by Wada et al. [2003], Ito et al. [2007], and Katsumata et al. [2010], our results reveal that many earthquakes with large reverse components are also occurring. In order to investigate the spatial pattern of focal mechanisms, we plotted their faulting types by means of colored circles in the cross section (Figure 8b). Here, the color is based on the color triangle diagram in Figure 8a. The most conspicuous feature is the depth dependence in the western half of the entire fault, where the shallow earthquakes are primarily reverse faulting and the strike slip earthquakes dominate at the bottom of the seismogenic zone. We also found that the strike slip and reverse type earthquakes are mixed in all depth ranges near the center of the fault. These features had not been reported in previous studies. The directions of the P and the T axes are shown in Figure 9, where different colors are used to denote different plunge angles. Most of the P axes are horizontal and oriented in the WNW ESE direction, which conforms to the general tectonic trend in this area [e.g., Tsukahara and Kobayashi, 1991; Townend and Zoback, 2006]. The T axes have a wide range of plunge, suggesting that reverse faulting type earthquakes as well as strike slip ones are occurring in the area. [15] Katsumata et al. [2010] found 10 normal faulting microearthquakes that occurred in a small cluster near the central part of the Atotsugawa fault and at depths greater than 8 km. The majority of those events occurred within one month after the occurrence of the M j 4.1 earthquake of 24 March 2005, where M j is the magnitude reported by the JMA. As shown in Figure 3, the focal mechanism of the M j 4.1 earthquake is a strike slip faulting type. There are some observations that a strike slip earthquake produced a 7of21

8 Figure 6. Example of focal mechanism determination for an earthquake (M w 0.8) that occurred at 1754 LT on 5 August (top left) A map of the epicenter (open star) and station distribution. (top right) A unique focal mechanism solution cannot be determined by using P wave polarity data alone, while (bottom) it is possible to determine a unique solution (pure strike slip faulting) by using absolute P and SH amplitudes and P wave polarity. Focal mechanism solutions are projected onto the lower hemisphere using equal area projection, where circles and triangles represent compressional and dilatational first motions, respectively. The size of each symbol is proportional to the logarithmic amplitude. number of normal faulting aftershocks [e.g., Polat et al., 2002]. It seems probable that the normal faulting events were caused by a local stress perturbation due to the M j 4.1 strike slip faulting earthquake and they do not reflect the general stress state around the Atotsugawa fault. 5. Stress Field in and Around the Atotsugawa Fault [16] Using the focal mechanism solutions determined in the present study, we calculated the stress field around the Atotsugawa fault by applying the inversion method of Michael [1984]. The inversion solves the orientation of the three principal stress axes and the relative magnitude of the principal stresses defined by =(S 2 S 3 )/(S 1 S 3 ), where S 1, S 2, and S 3 are the maximum, intermediate, and minimum compressive principal stresses, respectively. We applied the bootstrap resampling technique to calculate confidence regions for the stress tensor by assuming that a certain percentage of the planes are picked incorrectly [Michael, 1987]. In the present study, we assumed for the bootstrap that each nodal plane had the same probability of being chosen during the resampling. On the basis of this assumption, we used 2000 bootstrap samples to obtain the Figure 7. Focal mechanism solutions of all events determined in the present study (lower hemisphere of equal area projection). The circles and triangles represent compressional and dilatational first motions, respectively. Origin time (LT), event number, and moment magnitude are shown above each beach ball. The letter in the top left corner indicates the subarea (see Figure 10) in which the earthquake is included. Letter O denotes an earthquake that is not included in any subarea. 8of21

9 Figure 7 9of21

10 Figure 7. (continued) 10 of 21

11 Figure 8. (a) Spatial distribution of focal mechanism solutions in seven different depth ranges (lower hemisphere of equal area projection), where different colors are used to differentiate reverse (green), strike slip (red), and normal (blue) faulting mechanisms. The numbers adjacent to each beach ball correspond to the event number in Figure 7. A triangle diagram [Frohlich, 1992] with color scale is shown on the right. Each focal mechanism is plotted by open circles. (b) Types of estimated focal mechanism solutions in the X Y cross section. The color is based on the triangle diagram in Figure 8a. 95% confidence region, which is adequate to produce stable confidence regions up to the 95% level [Michael, 1987]. We used earthquakes whose epicenters are within 3 km away from the approximate surface trace of the Atotsugawa fault, and we divided the data set into eastern and western areas in the analysis. In order to investigate the depth dependence of the stress field, the western area was further divided into three depth intervals as shown in Figure 10. The subarea W3 11 of 21

12 Figure 9. P axis and T axis distributions of focal mechanism solutions. Different colors are used to indicate different plunge angles. corresponds to the bottom of the seismogenic zone. For the eastern area, we cannot study the depth dependence of the stress field due to the low seismicity rate in the shallower part, so the stress field estimated in this area is considered to be that around the bottom of the seismogenic zone. The numbers of focal mechanisms for areas W1, W2, W3, and E are 22, 23, 22, and 31, respectively. It is noted that the data near the center of the fault are included in areas W1 W3, although a different stress field around the center might be suggested by a different pattern of focal mechanism distribution there. It is considered that more data volume is necessary to distinguish the different stress field around the center. [17] The results of the stress tensor inversion are shown in Figure 11. For every area, the maximum principal stress S 1 is clearly differentiated from S 2 and S 3, trending horizontally WNW ESE. The directions of S 2 and S 3 are, on the other hand, nonuniform along the Atotsugawa fault, which gives rise to a depth dependence in the stress field. The 95% confidence regions of S 2 and S 3 form a girdle and trend roughly NNE SSW for areas W1 and W2. Together with the observation of a relatively low stress ratio, 0 0.3, these confidence regions suggest that the principal stresses S 2 and S 3 differ only slightly in their magnitude and that the style of faulting is a mixture of reverse and strike slip faulting. In contrast, the stress fields in areas W3 and E are characterized by a pure strike slip faulting regime, where the orientations of the principal stress axes are nearly vertical for S 2 and horizontal for S 1 and S 3. The stress ratio is near 0.5 for both areas, implying that the magnitude of S 2 is close to (S 1 + S 3 )/2. This result of nonuniformity distribution of S 2 and S 3 is discussed in section 6. [18] Lund and Townend [2007] demonstrated that the direction of maximum horizontal compressive stress (S Hmax ) is not always equal to the trend of the larger of the Figure 10. Definition of subareas used in the stress tensor inversion (rectangles). White circles represent focal mechanisms used in the inversion, in which their locations are within about 3 km of the surface trace of the AGF. Earthquakes shown by crosses are not used in the stress tensor inversion, because they are too far from the fault plane. A tomographic P wave velocity cross section along AGF is also shown. The velocity is contoured with intervals of 0.1 km/s. 12 of 21

13 Figure 11. Stress tensor inversion results in each area. (left) Principal stress axes with their 95% confidence regions plotted on lower hemisphere stereonets. The shaded lines on the stereonets indicate the orientation of the Atotsugawa fault. (middle) Misfit angles for the data with respect to the best stress tensor determined by the stress tensor inversion. Here, the misfit angle represents the angle between the tangential traction predicted by the best solution and the observed slip direction on each plane determined from the focal mechanism. (right) Frequency of the stress ratio, which belongs to the 95% confidence region. 13 of 21

14 Figure 12. Frequency of the true axis of S Hmax in each subarea computed from the 95% confidence regions of the stress tensor inversion results using the algorithm by Lund and Townend [2007]. The shaded vertical line corresponds to the strike of the Atotsugawa fault. two subhorizontal principal stresses. The difference depends not only on the plunges of the principal stress axes but also on the stress ratio. Following the method of Lund and Townend [2007], we computed the true axis of S Hmax from the four stress parameters determined by the stress tensor inversion (the directions of the three principal stresses and the stress ratio ). Figure 12 shows the frequency of S Hmax computed from the stress parameters that are within the 95% confidence regions. Here, 180 is subtracted from azimuth, if necessary, to ensure that all orientations can be plotted in the range of 0 to 180. The range of S Hmax within the 95% confidence regions is generally consistent with that of the regional one [e.g., Tsukahara and Kobayashi, 1991; Townend and Zoback, 2006]. It seems that the S Hmax direction in area W3 is slightly different from those in other areas. However, we cannot statistically exclude a possibility of uniform S Hmax direction across the entire region, because the 95% confidence regions of S Hmax overlap each other. For all areas, the orientation of S Hmax relative to the fault trend is less than the predicted lock up angle for standard friction coefficients of about 0.6 [Sibson and Xie, 1998], suggesting that the orientation of S Hmax is under the condition for reactivating the Atotsugawa fault. [19] Except for the present research, the study by Katsumata et al. [2010] is the only one that has carried out a stress tensor inversion in and around the Atotsugawa fault system. They divided the region containing the Toyama plain as well as the Atotsugawa fault system into 9 subareas, in which each area had a size of 18 and 23 km in the NS and EW directions, respectively. Although the subareas for the stress tensor computation are different from each other, the S 1 directions determined in this study agree well with those determined by Katsumata et al. [2010]. This suggests that the S 1 direction is stable over the region and its estimate is not influenced by the definition of subareas. For the stress ratio, it is not appropriate to compare both results, because we found that it changes with subareas. However, the stress ratios near the Atotsugawa fault estimated by Katsumata et al. [2010] vary from 0.23 to 0.57, which are within our estimates. 6. Inferred Model for the Stress Field [20] It is common to assume that one principal stress is vertical and its magnitude is the overburden pressure (S v ) calculated from the density and depth [e.g., Zoback, 1992]. If this is the case, the present study indicates that the minimum horizontal stress (S hmin ) has almost the same magnitude as S v at depths shallower than about 8 km in the western area. Because the reverse faulting type earthquakes are dominant at the shallower depth (Figure 8), S hmin should be slightly larger than S v in that depth range. On the other hand, S hmin becomes less than S v around the bottom of the seismogenic zone, so strike slip earthquakes are generated. The stress field in area E is almost the same as that in area W3, suggesting that the bottom of the seismogenic zone is characterized by a similar stress field, although the depth Figure 13. (a) Aseismic slip model in a vertical cross section. The aseismic slip accumulates stress onto the fault plane at the seismogenic zone during an earthquake cycle, and the main shock will occur when the failure stress is reached on the fault. The present study alone cannot constrain the depth range of the aseismic slip zone. (b) Schematic view of principal stress profile at the Atotsugawa fault. 14 of 21

15 Figure 14. Perspective view of the model used in the numerical simulation. The fault plane is completely locked and its deep extension is stably sliding. The X and Y axes correspond to East and North directions, respectively. dependence of the stress field is not clarified, owning to a low seismicity rate in the shallower part. We infer that the depth dependence of the stress field is caused by the aseismic deformation with right lateral strike slip faulting in the downward extension of the fault as suggested by Mizuno et al. [2005]. In this case, a stress concentration occurs above the aseismic deformation, resulting in the increase in S Hmax (maximum horizontal stress) and the decrease in S hmin at the bottom of the seismogenic zone. As described above, S hmin should be slightly larger than S v in most of the seismogenic zone, so the depth dependent change in the stress field can occur as observed in this study. Figure 13 shows a schematic view of the proposed principal stress profile, where we assume, for the sake of simplicity, that S Hmax and S hmin are zero at the surface. [21] In order to confirm the validity of the present model, we numerically compute the stress field in and around the Atotsugawa fault by the superposition of a stress change due to aseismic slip in the downward extension of the fault and variously assumed external stress fields around the fault. In this section, we define s 1 e, s 2 e, and s 3 e as maximum, intermediate, and minimum compressive principal stresses for the external stress fields, respectively, to avoid confusion with symbols used in the stress tensor inversion as well as that described above. [22] Following Mizuno et al. [2005], we assume that (1) the seismogenic zone of the Atotsugawa fault is completely locked and its deep extension is stably sliding, (2) the deep extension of the fault extends from the bottom of the seismogenic zone at a depth of 12 km to the bottom of the lower crust at a depth of 28 km, and (3) the relative displacement rate of the aseismic slip is 3 mm/yr, which is comparable to the average fault slip rate along the Atotsugawa fault (Headquarters for Earthquake Research Promotion, Long term evaluation of the Atotsugawa fault (in Japanese), 2004, available at 15 of 21

16 Figure 15. Computed stress fields (superposition of the stress change due to the aseismic slip and regional stress field) at a depth of 8 11 km. S Hmax directions calculated by the algorithm of Lund and Townend [2007] are plotted with 5 km spacing. The same color triangle diagram as that used in Figure 8a is employed to differentiate stress fields. See text for the assumption regarding the regional stress field. chousa/04sep_atotugawa/index.htm) (Figure 14). Because the last large earthquake along the Atotsugawa fault, the Hietsu earthquake, occurred about 150 years ago in 1858 [Matsuda, 1966], the total aseismic slip becomes 0.45 m. We computed the stress change associated with the aseismic slip in an elastic half space following Okada [1992] by assuming a shear modulus of 32 GPa and a Poisson s ratio of The slip is linearly tapered as shown in Figure 14 to avoid unrealistic stress concentrations at the edges of the fault. [23] For external stress fields, we assumed that s 1 e is horizontal and oriented to N105 E. This assumption is consistent with the present study as well as other seismic observations [e.g., Townend and Zoback, 2006; Katsumata et al., 2010]. It is also reasonable to assume that the orientation of s 3 e is vertical, because except for the bottom of the seismogenic zone, the stress field around the Atotsugawa fault is generally characterized by a reverse faulting regime. The magnitude of s e 3 corresponds to the overburden pressure (S v ). Under the assumption of the s e e 1 and s 3 orientations, s e 2 is horizontal and oriented to N15 E. We also assumed a uniform differential stress (s e 1 s e 3 ) of 150 MPa in the seismogenic depth range. This value approximately corresponds to a depth averaged stress level of the upper crust in a reverse faulting stress regime predicted for optimally oriented, cohesionless faults under conditions of hydrostatic pore pressure and a friction coefficient of 0.6 [e.g., Zoback and Townend, 2001]. Since there is no information about the magnitude of s e 2 (or s e 2 s e 3 ), we tried to constrain it by comparing the stress fields deduced from the stress tensor inversion with theoretically calculated ones. [24] Through the numerical simulation, we found that the spatial distribution in the faulting style (strike slip or reverse 16 of 21

17 faulting) strongly depends on the magnitude of (s e 2 s e 3 ). Figure 15 shows computed stress fields (superposition of the stress change due to the aseismic slip and assumed external stress fields) at the depth of 8 11 km for four examples of (s e 2 s e 3 ), where S Hmax directions calculated by the algorithm of Lund and Townend [2007] are plotted with 5 km spacing. The same color triangle diagram as that used in Figure 8 is employed to differentiate stress fields. Figure 15 suggests that the difference in the magnitude of s e e 2 and s 3 can be constrained within some range to produce a strikeslip faulting regime only at the bottom of the seismogenic zone. On the basis of numerous forward modeling, we conclude that the magnitude of s e 2 s e 3 should be in the range of about 0.5 to 1 MPa. We reach the same conclusion as long as the magnitude of s e 1 is at least 1 MPa larger than that of s e 2 as well as s e 3, through calculations of various magnitudes of the external differential stress (s e 1 s e 3 ). If the magnitude of s e 1 does not meet the condition, the orientations of computed maximum principal stress scatter significantly and become inconsistent with the result of the stress tensor inversion. [25] We also compared the computed stress ratios with the results of the stress tensor inversion. The computed stress ratios have a value of less than 0.01 in the shallower part and about 0.5 at the bottom of the locked region for the preferred stress state in Figure 15. This is owing to the fact that the stress change caused by the right lateral aseismic slip becomes predominant in the deeper part, while the stress change by the aseismic slip does not reach the shallower part and the external stress field becomes predominant there. It seems probable that the computed stress ratio in the shallower part is somewhat lower than the result of the stress tensor inversion, though it is within the 95% confidence region (Figure 11). The external differential stress (s e 1 s e 3 ) of 5 MPa, for instance, gives a computed stress ratio in the shallower part of about , which seems to explain the results of the stress tensor inversion better. It should be noted that such a small external differential stress requires a significantly small friction coefficient of less than 0.1 to cause earthquakes in the seismogenic depth zone. It is still controversial whether the friction coefficient in and around fault zones is governed by Byerlee s [1978] law with a friction coefficient of about 0.6 (e.g., see review by Townend [2006]). For example, there is extensive evidence showing a lower friction coefficient at the San Andreas fault and at several other large strike slip faults and subduction zones [e.g., McGinty et al., 2000; d Alessio et al., 2003; Hardebeck and Michael, 2004]. Scholz [2006] indicates that except for the creeping section, the San Andreas fault has a strength consistent with a friction coefficient of 0.6 comparable to that of the adjacent crust. For an inland active fault that caused the 1995 Hyogo ken Nanbu (Kobe) earthquake, which is categorized as the same type of intraplate earthquake as that of the Atotsugawa fault, Yamashita et al. [2004] estimated a friction coefficient of 0.6 by combining in situ stress measurements with the static stress change caused by the main shock. In contrast, Spudich et al. [1998] concluded the complete opposite on the basis of slip rake rotations with time. The present study alone cannot constrain which value of the friction coefficient or external differential stress explains the observations better, although it provides a clue toward better understanding of a large earthquake occurrence. 7. Discussion [26] We consider that the depth dependence of the stress field is related to the aseismic deformation with right lateral strike slip faulting in the downward extension of the fault. In addition to observations of shear wave splitting and the present study, there is other observational evidence that supports the existence of the aseismic deformation below the Atotsugawa fault. We show, in Figure 10, a tomographic P wave velocity along the fault that was obtained by applying a double difference tomography method [Zhang and Thurber, 2003] to arrival time data during the period from April 1995 to December 2004 [Takeda et al., 2004]. The P wave velocity is found to decrease with increasing depth around the bottom of the seismogenic zone. The P and S wave velocity structures below the bottom of the Atotsugawa fault were imaged by Matsubara et al. [2008], who determined 3 D wave velocity structures beneath the whole of the Japan Islands. Figure 16 shows P wave velocity perturbation and V p /V s at a depth of 15 km constructed from their numerical data, suggesting that the low velocity as well as a low V p /V s anomaly also exist below the Atotsugawa fault. This pattern seems to continue down to a depth of at least 25 km. According to Takei [2002], low V p and low V p /V s reflect the presence of water filled cracks with a large aspect ratio. Laboratory experiments of rock friction suggest that high pore water pressure reduces the strength and tends to promote an anelastic deformation [e.g., Scholz, 1998], supporting the existence of aseismic deformation below the Atotsugawa fault. [27] Hirahara et al. [2003, 2007] obtained the crustal deformation around the Atotsugawa fault on the basis of dense GPS array observations. They proposed a model without aseismic deformation below the fault, in which two elastic blocks with a thickness of 15 km are obliquely colliding with each other along the Atotsugawa fault in an E W direction. On the other hand, Sagiya et al. [2008] redetermined a crustal deformation pattern around the fault by incorporating newly deployed GPS stations and suggested the possibility of existence of a concentrated deformation at the deeper extension of the fault. Because the average fault slip rate of the Atotsugawa fault is estimated to be 2 3 mm/yr (Headquarters for Earthquake Research Promotion, Long term evaluation of the Atotsugawa fault (in Japanese), 2004, available at it is reasonable to assume that the relative displacement rate of the aseismic slip is of the same order. In this case, the displacement rate observed at the surface is less than 1 mm/yr, so it may be difficult to distinguish which model explains the observations better on the basis of GPS observations over a decade. Our model predicts that the longer term GPS observations will observe a signal caused by the aseismic deformation in the downward extension of the fault. [28] It is now widely considered that aseismic deformation below the seismogenic zone plays an important role for an inland large earthquake occurrence [e.g., Iio and Kobayashi, 2002a]. For an improved understanding of the stress accumulation mechanism, it is important to know the style of 17 of 21

18 Figure 16. Tomographic imaging below the seismogenic zone [Matsubara et al., 2008]. (left) P wave velocity perturbation and (right) V p /V s ratio at a depth of 15 km are shown in these examples. deformation, whether it is localized in a narrow zone [e.g., Stuart et al., 1997; Iio and Kobayashi, 2002a] or widely distributed in volume [e.g., Kenner and Segall, 2000]. In geologic studies of exhumed fault zones, there is much evidence for localized ductile shear zones in the lower crust [e.g., Shigematsu et al., 2004; Cole et al., 2007]. In addition, geophysical evidence for a localized slip below the seismogenic zone has recently been found at other faults. On the basis of deep borehole heat flow measurements around the Nojima fault that caused the 1995 Kobe earthquake, Iio and Kobayashi [2002b] obtained the temperature profile down to a depth of 30 km. They compared the seismicity cutoff depth in and around the Nojima fault with the brittle ductile transition depth estimated from the temperature profile and found that the cutoff depth can be explained by the assumption of a localized aseismic deformation with a width of 100 m or less. Kawanishi et al. [2009] found a spatial change in the stress field in and around the eastern part of the seismic belt along the Japan Sea coast and showed that it can be explained by a localized aseismic deformation with a width of 5 km or less. For the Atotsugawa fault, the stress ratio determined by the stress tensor inversion largely changes at the bottom of the seismogenic zone (Figure 11). In addition, the orientation of S Hmax derived from the shear wave splitting suddenly decreases within 1 km of the fault [Mizuno et al., 2005]. These observations seem to support a localized slip model in the case of the Atotsugawa fault and the width of the localized slip should be less than 1 km. [29] It should be noted that except at the bottom of the seismogenic zone, the stress field is different from the faulting style of the Atotsugawa fault. This is considered to be for the following reasons. Because the recurrence interval of large earthquakes on the fault is estimated to be 2500 years [Research Group for Active Faults of Japan, 1991] and the 1858 M7.0 Hietsu earthquake is considered to be due to a faulting along the fault [Matsuda, 1966], the Atotsugawa fault is now in an early stage in the earthquake cycle. We suggest that the influence of the stress concentration caused by the aseismic deformation will gradually spread upward with time and that the shallower part will also become a strike slip faulting regime in the future. [30] Finally, we discuss lateral variations of stress fields along the fault. As mentioned in section 2, the seismicity rate on the northeast side near the central part of the Atotsugawa fault is extremely low (Figure 1). In this area, the Geographical Survey Institute of Japan [2000] observed a right lateral creeplike movement at a rate of about 1.5 mm/yr on the basis of repeated electronic distance measurement (EDM). Figure 10 suggests that the area of Region_C characterized by creeplike movement and low seismicity rate is roughly consistent with a low V p zone. Kato et al. [2007] revealed that the area is also characterized by low V p /V s values and inferred that the low seismicity rate and creep like movement are induced by high pore water pressures. If this is the case, a stress concentration will occur adjacent to the creep region and strike slip earthquakes will dominate there. In fact, there is a tendency for earthquakes with a large strike slip component to be dominant at the eastern edge of areas W1 and W2 (see 19, 30, 32, 123, 143, 146, and 153 in Figure 8a) as described in section 4. However, the present data set is not necessarily sufficient to conclude that the creep like movement actually occurs along the fault. Further studies are needed to clarify the existence of the creep like movement on the basis of long term dense seismic and geodetic observations. 8. Conclusion [31] Stress fields in and around the Atotsugawa fault in central Japan have been investigated on the basis of numerous focal mechanism solutions of microearthquakes. We con- 18 of 21