Source model for strong ground motion generation in the frequency range 0.1–10 Hz during the 2011 Tohoku earthquake
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The source model of the 2011 Tohoku earthquake, which is composed of four strong motion generation areas (SMGAs), is estimated based on the broadband strong ground motion simulations in the frequency range 0.1–10 Hz using the empirical Green’s function method. Two strong motion generation areas are identified in the Miyagi-oki region west of the hypocenter. Another two strong motion generation areas are located in the Fukushima-oki region southwest of the hypocenter. The strong ground motions in the frequency range 0.1–10 Hz along the Pacific coast are mainly controlled by these SMGAs. All the strong motion generation areas exist in the deeper portion of the source fault plane. The stress drops of the four SMGAs range from 6.6 to 27.8 MPa, which are similar to estimations for past M 7-class events occurring in this region. Compared with the slip models and aftershock distributions of past interplate earthquakes in the Miyagi-oki and Fukushima-oki regions since the 1930s, the SMGAs of the 2011 Tohoku earthquake spatially correspond to the asperities of M 7-class events in 1930s. In terms of broadband strong ground motions, the 2011 Tohoku earthquake is not only a tsunamigenic event with a huge coseismic slip near the trench but is also a complex event simultaneously rupturing pre-existing asperities.
Key words2011 Tohoku earthquake source model strong motion generation area empirical Green’s function method broadband strong ground motion simulation asperity
The 2011 Tohoku earthquake, which occurred at 14:46 on March 11, 2011 (JST = UTC + 9), rocked over the Japanese country. The hypocenter determined by the Japan Meteorological Agency (JMA) was 38.1035°N, 142.8610° E at a depth of 23.74 km beneath the Pacific Ocean off the eastern coast of northeastern Japan. Many earlier studies have reported that its moment magnitude was 9.0 (e.g., Hayes, 2011; Nettles et al., 2011) and it was the largest event to have occurred in Japan since instrumental observation started in the late 19th century. This event is characterized as a mega-thrust earthquake rupturing the plate boundary between the North American Plate and the subducting Pacific Plate. An enormous tsunami swept the Pacific coast of Tohoku and Kanto districts, northeastern Japan. A seismic intensity of 7 on the JMA intensity scale was observed at Tsukidate, Kurihara city, 175 km west of the epicenter, and a seismic intensity of 6+ was widely observed in the Tohoku and Kanto districts (Hoshiba et al., 2011). The nationwide digital strong motion seismograph networks, K-NET and KiK-net, both installed and operated by the National Research Institute for Earth Science and Disaster Prevention (NIED), Japan (Aoi et al., 2011), recorded the ground acceleration time histories at more than one thousand stations across Japan (Kunugi et al., 2012).
The kinematic heterogeneous slip histories on the source fault of this megathrust event were estimated in space and in time by inversion analyses of teleseismic data (e.g., Ammon et al., 2011; Hayes, 2011; Ide et al., 2011; Shao et al., 2011; Yagi and Fukahata, 2011), strong motion data (e.g., Suzuki et al., 2011; Yoshida et al., 2011a), both teleseis-mic and strong motion data (e.g., Yoshida et al., 2011b), and combined datasets of teleseismic, strong motion, and geodetic data (e.g., Koketsu et al., 2011). However, those studies used the seismic waves at strong motion stations in the frequency range lower than 0.1 or 0.125 Hz. It is not easy for those source models, which are constrained by the lower frequency data, to reproduce the observed broadband ground motions. In order to account for the observed strong ground motions of frequencies higher than 0.1 Hz, which are usually related to seismic damages on building and civil structures, constraints on the source process by higher frequency data are indispensable. It is useful for such an analysis to use the records of small events occurring close to the target event as empirical Green’s functions.
The use of empirical Green’s functions was originated by Hartzell (1978). Irikura (1986) developed a systematic methodology to simulate strong ground motions in a broadband frequency range based on the self-similar scaling law of fault parameters between large and small events and the ω−2 source spectral model. The waveform for the target event is simulated by summing up the observed waveform of a smaller event convolved with a filtering function or correction function, which corrects the difference in the slip velocity time function between the large and small events. Characterized source patch models give successful simulations using the empirical Green’s function method. Miyake et al. (2003) named this source patch the strong motion generation area (SMGA), and this is defined as the area characterized by a large uniform slip velocity within the total rupture area, which reproduces near-source strong ground motions up to about 10 Hz. The source process is represented by a source model which is composed of one or more SMGAs. For inland crustal earthquakes, Miyake et al. (2003) concluded that the SMGAs coincided with the large slip areas or the asperities of heterogeneous slip distributions derived from low-frequency (<1 Hz) waveform inversions, and they concluded that the near-source strong ground motions were controlled mainly by the size of the SMGA and the rise time there.
The strong motion generation area and the empirical Green’s function method has been successfully applied to strong motion simulations of past subduction-zone in-terplate earthquakes (e.g., Kamae and Kawabe, 2004; Miyahara and Sasatani, 2004; Suzuki and Iwata, 2007; Takiguchi et al., 2011). Suzuki and Iwata (2007) analyzed the 2005 Miyagi-oki earthquake (MJMA 7.2) which occurred west of the epicenter of the 2011 Tohoku earthquake, and they confirmed that two SMGAs of the 2005 Miyagi-oki earthquake existed inside the asperities where relatively large slip was observed from the kinematic waveform inversions, but that the area size of these was significantly smaller than the asperity area. Takiguchi et al. (2011) modeled the SMGAs of two interplate events off Ibaraki on July 23, 1982, and May 8, 2008, which had occurred adjacent to the source area of the 2011 Tohoku earthquake. They concluded that the SMGAs of the 1982 and 2008 events were located close to each other but possibly did not overlap. The investigation on the repeatability of asperities and strong motion generation areas is one of the key issues for subduction-zone interplate earthquakes.
In this paper, we estimate a source model composed of SMGAs by analyzing the strong ground motion records observed at K-NET and KiK-net strong motion stations. We consider the three-dimensional geometry of the plate interface for locating SMGAs. The spatial relationships between the SMGAs of the 2011 Tohoku earthquake and the source regions of past interplate events in this subduction zone are discussed.
3. Locating the Rupture Starting Points of SMGAs on the Plate Interface
Here, we assume that each of the wave packets S1–S4 are generated from individual strong motion generation areas, SMGA1–SMGA4. We model those SMGAs in this study to explain the observed strong ground motions along the Pacific coast. The hypocenter is fixed at the location (38.1035°N, 142.8610°E, 23.74 km) determined by JMA. We assume that each SMGA is situated on the interface of the subducting Pacific plate. We refer to the depth of the upper surface of the Pacific slab determined by Nakajima and Hasegawa (2006) and Nakajima et al. (2009). They determined its configuration from the distribution of inter-plate earthquakes relocated using their own velocity structure model.
S-wave velocity structure model for calculating theoretical travel time and the ray path.
S-wave velocity (km/s)
The hypocentral information of events used as the empirical Green’s functions (EGF).
Origin time (JST)*
Seismic moment (N m)**
1.41 × 1018
2.32 × 1017
The location of the rupture starting point and the rupture time relative to the origin time for each SMGA.
Rupture starting point
Rupture time (s)
4. Construction of SMGA Source Model through Strong Motion Simulations in the Frequency Range 0.1–10 Hz
4.1 Brief introduction of the empirical Green’s function method
4.2 Source spectral ratios
The scaling parameters N and C are determined for each SMGA from the observed source spectral ratio by the source spectral fitting method (Miyake et al., 1999, 2003). This method derives these parameters by fitting the observed source spectral ratio between the large and small events to the theoretical source spectral ratio following the ω−2 source spectral model. The moment ratio M0/m0, and the corner frequency of the target and EGF events, are estimated by a grid search algorithm. Firstly, the observed source amplitude spectral ratio of the S-wave portion of each SMGA is calculated for each station. In this analysis, only records in which individual wave packets corresponding to each SMGA are isolated sufficiently to have the time windows for calculating Fourier amplitude spectra are used. The propagation path effects are corrected for geometrical spreading of the body waves and an attenuation factor. The frequency-dependent quality factor, Q(f) = 110 f0.69 obtained by Satoh et al. (1997) in this region is used to correct the attenuation factor. The S-wave velocity is assumed to be 4.46 km/s in this correction.
4.3 Estimation of SMGA source model
Search range, grid interval, and estimated value of model parameters in the grid search.
l = w (km)*
Estimated parameters of SMGAs.
M0 (N m)
4.57 × 1020
5.33 × 1020
3.07 × 1020
1.16 × 1020
1.41 × 1021
5.1 Comparison with other source models
All the strong motion generation areas exist in the deeper portion of the source fault plane, apart from the Japan Trench. The locations of these SMGAs are consistent with the high-frequency radiation estimated from the teleseis-mic back-projection analyses (e.g., Ishii, 2011; Meng et al., 2011) and strong seismic energy from regional back-projection analysis in the frequency range 0.05–0.5 Hz (Honda et al., 2011). For example, Meng et al. (2011) used teleseismic waveforms from 0.5 to 1 Hz and they highlighted the spatial complementarity between low- and high-frequency source properties of this event. The tsunami source was estimated in the shallower portion close to the Japan Trench (e.g., Fujii et al., 2011). Therefore, the main sources of strong ground motions and tsunamis of this earthquake are complementary to each other.
Four SMGAs have nearly identical spatial dimensions. The spatial dimensions of these SMGAs are much smaller than the large slip area resolved by the kinematic waveform inversions using the low-frequency strong motion records (e.g., Koketsu et al., 2011; Suzuki et al., 2011; Yoshida et al., 2011a, b). The slip amount in SMGA itself is consistent with the slip model from those studies. Since most of the current source inversion studies on this event use very coarse grids (~30 km) over the entire source fault, which is almost the scale of SMGAs, and low-frequency seismic waves mostly less than 0.1 Hz. There are no prominent peaks corresponding to these SMGAs in low-frequency waveforms analyzed in those kinematic source inversion studies. Localized high-slip velocity SMGAs found in this study may not be captured well in those studies.
SMGAs for this event are also studied in other earlier studies (e.g. Kurahashi and Irikura, 2011; Kawabe et al., 2011). The major differences between our source models and theirs are the source fault geometry, and the velocity structure model, to locate the SMGAs on the fault. The details in the analysis are somewhat different among those studies. These studies did not consider the three-dimensional geometry of the plate interface. Our study also considered a one-dimensional velocity structure model in locating SMGAs, and in the strong motion simulations using the empirical Green’s function method as explained in the previous sections. We searched the best model objectively by a grid search approach, whereas other studies determined their source models by a trial and error method and they described some source parameters by empirical relationships. Some differences in the obtained source parameters might arise from such differences in the modeling procedures. Nevertheless, Kurahashi and Irikura (2011) and Kawabe et al. (2011) also similarly found two SMGAs in the Miyagi-oki region, west of the epicenter and two or three SMGAs in the Fukuhima-oki and Ibaraki-oki regions. None of the studies found any SMGA in the shallow portion of the source fault near the trench. Hence, the overall features of the obtained source model regarding the strong motion generation are consistent with these studies.
5.2 Spatial relationship between SMGAs and past in-terplate events
In the Miyagi-oki region (off Miyagi), which is the vicinity of SMGA1 and SMGA2 of the 2011 Tohoku earthquake, M 7-class interplate earthquakes occurred in 1933, 1936, 1937, 1978, 1981, and 2005. In the Fukushima-oki region (off Fukushima), three M 7-class interplate earthquakes occurred in 1938.
Yamanaka and Kikuchi (2004) collected the paper seis-mograms recorded by the mechanical strong-motion seismometers of JMA since the 1900s, and they analyzed the kinematic source process of eight interplate earthquakes, which occurred after 1930 in northeastern Japan, by the waveform inversion of these paper seismograms. They found that the typical size of individual asperities in northeastern Japan was M 7-class, and an M 8 earthquake could be caused when the ruptures of multiple asperities were synchronized. Based on their analyses, they proposed an asperity map in this subduction zone. Umino et al. (2007) relocated the mainshocks and aftershocks of six earthquake sequences in the Miyagi-oki region occurring in 1933, 1936, 1937, 1939, 1978, and 1981 by using S –P times from the Seismological Bulletin of JMA and original smoked-paper seismograms observed at several seismic stations in the To-hoku district.
Figure 9(b) spatially compares SMGA1 and SMGA2 with the source regions of interplate events in this area on June 19, 1933 (MJMA 7.1), November 3, 1936 (MJMA 7.4), July 27, 1937 (MJMA 7.1), and October 11, 1939 (MJMA 6.9). The hypocenters of the mainshocks and aftershocks of these events are also from Umino et al. (2007). The slip distributions of the 1936 and 1937 Miyagi-oki events have been estimated by Yamanaka and Kikuchi (2004). They did not analyze the 1933 and 1939 events. The SMGA1 corresponds to the large slip area, or asperity, of the 1936 Miyagi-oki earthquake, and the SMGA2 is located inside the aftershock area of the 1933 Miyagi-oki earthquake. These SMGAs are spatially included in the anticipated Miyagi-oki earthquake evaluated by the Headquarters for Earthquake Research Promotion.
Figure 9(c) shows the spatial comparison of SMGA3 and SMGA4 with the source regions of three interplate events in the Fukushima region occurring in 1938. The first event (MJMA 7.0) occurred on May 23, 1938. The second (MJMA 7.3) and third (MJMA 7.5) events occurred on November 5, 1938. No large interplate earthquake occurred in this region after the events of 1938. Abe (1977) estimated the fault dimensions and dislocations of those interplate events of 1938, based on the aftershock distribution, tsunami source area, and forward modeling of regional long-period seismograms using the Haskell-type source model. The 1982 and 2008 Ibaraki-oki interplate events are also shown on the map. The SMGA3 is included in the source region of the 1938 events analyzed by Abe (1977), and is outside the source area of the 1982 and 2008 Ibaraki-oki events. Murotani et al. (2004) and Uetake et al. (2006) also analyzed the regional paper seismograms to obtain the slip models for the 1938 Fukuhina-oki sequences, and their results suggest the possibility that SMGA3 is spatially included in the source area of an MJMA 7.5 event at 19:50 on November 5, 1938 (Nov. #2 event in Fig. 9(c)). As for SMGA4, it is difficult to relate this with past inter-plate events.
From spatial comparisons presented above, the rupture of SMGA1, SMGA2, and SMGA3 are possibly presumed to be the reactivation of pre-existing asperities, or strong motion generation areas, of past M 7-class interplate events in the 1930s. In the 1930s, those asperities ruptured separately, but they ruptured simultaneously within three minutes during the 2011 Tohoku earthquake. However, the spatial extent of SMGAs for the 2011 Tohoku earthquake is significantly larger than SMGAs of other M 7-class interplate events in northeast Japan estimated in the previous studies (Suzuki and Iwata, 2007; Takiguchi et al., 2011). Thus, the SMGAs of the 2011 Tohoku earthquake are supposed not to have the same source dimensions with repeating M 7-class events which ruptured in the 1930s. It is likely that the size of the SMGA depend on the magnitude of an earthquake, as do asperities and the total rupture area, even if the location is nearly the same between M 7 and M 9 events. However, there is a possibility that SMGAs estimated in this study still have heterogeneity on a smaller scale, which is not considered in the present study since uniform slip and slip-velocity distributions are assumed within SMGA. Further studies on the hierarchy of SMGA and asperity are necessary to clarify this issue.
The source model composed of four strong motion generation areas of the 2011 Tohoku great subduction earthquake was estimated based on the broadband strong ground motion simulations using the empirical Green’s function method. Two strong motion generation areas (SMGA1 and SMGA2) are identified in the Miyagi-oki region west of the hypocenter. Another two strong motion generation areas (SMGA3 and SMGA4) are located in the Fukushima-oki region southwest of the hypocenter. The broadband strong ground motions (0.1–10 Hz) along the Pacific coast are mainly controlled by these SMGAs. All the strong motion generation areas exist in the deeper portion of the source fault plane. The stress drops of four SMGAs range from 6.6 to 27.8 MPa, which are similar to estimations for past M 7-class events in this region. Compared with the slip models and aftershock distributions of past interplate earthquakes in the Miyagi-oki and Fukushima-oki regions since the 1930s, the rupture of strong motion generation areas of the 2011 Tohoku earthquake is presumed to be the reactivation of asperities of past events, which ruptured separately as M 7-class events in the 1930s. In terms of broadband strong ground motions, the 2011 Tohoku earthquake is not only a tsunamigenic event with huge coseismic slip over a wide area along the trench, but also a complex event rupturing pre-existing asperities. These findings are quite important for the assumption of source models for strong motion predictions from such huge interplate earthquakes. They also provide an insight into the rupture physics of this great interplate event in terms of the hierarchy of the source model.
We use the strong-motion records of K-NET and KiK-net operated by NIED and hypocentral information catalog of JMA, and the moment tensor catalog by Global CMT Project. We would like to thank the staff in these institutes for their continuous effort toward maintaining the system to obtain high-quality data. The digital data of the geometry of the Pacific plate is compiled and provided via the Internet by Dr. Fuyuki Hirose at the Meteorological Research Institute of JMA. The slip data of past events are provided by Prof. Yoshiko Yamanaka at Nagoya University. All of figures are drawn by using the Generic Mapping Tools (Wessel and Smith, 1998). The comments from Dr. Yasuhiro Yoshida, Prof. Kuo-Fong Ma, and the associate editor Prof. Tomomi Okada improved the manuscript. This work is partially supported by the Grant-in-Aid for Young Scientists (B) 22710172 from the Japan Society for the Promotion of Science and by the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan under the Observation and Research Program for Prediction of Earthquakes and Volcanic Eruptions.