Dynamic source modeling of the 1978 and 2005 Miyagi oki earthquakes: Interpretation of fracture energy

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009jb006758, 2010 Dynamic source modeling of the 1978 and 2005 Miyagi oki earthquakes: Interpretation of fracture energy Takeshi Kimura, 1,2 Kazuki Koketsu, 1 Hiroe Miyake, 1 Changjiang Wu, 3,4 and Takashi Miyatake 1 Received 6 July 2009; revised 22 February 2010; accepted 16 March 2010; published 3 August [1] We constructed spontaneous dynamic rupture models of the 1978 and 2005 Miyagi oki, Japan, earthquakes, which occurred on the same plate boundary repeatedly with different magnitudes, to reproduce the slip and the rupture velocity predicted by kinematic source models. Comparison of the dynamic source parameters of these events enables us to consider the behavior of rupture dynamics during different source processes on the same fault. In particular, we compared the stress drop and the fracture energy, which can be evaluated stably, between two events. The maximum and average values of the stress drop over the whole fault plane and on an asperity that ruptured during both events are almost identical in the two models. On the other hand, the 1978 event, whose magnitude was larger than the 2005 event, has a fracture energy value larger than that of the 2005 event not only over the whole fault but also on the asperity that ruptured repeatedly. These results are consistent with previous studies of the scaling of fracture energy with the seismic moment. We also compared the fracture energy values with those of other inland events estimated for previous studies; our values for the Miyagi oki earthquakes are smaller. Differences in tectonic setting between shallow inland events and deep subduction zone events might cause this discrepancy. Citation: Kimura, T., K. Koketsu, H. Miyake, C. Wu, and T. Miyatake (2010), Dynamic source modeling of the 1978 and 2005 Miyagi oki earthquakes: Interpretation of fracture energy, J. Geophys. Res., 115,, doi: /2009jb Introduction [2] Accumulation of information on the source parameters of real earthquakes is important for understanding the physics of the source rupture process. Using seismic waves, geodetic data, tsunamis, and other information researchers have proposed a variety of kinematic source models [e.g., Kikuchi and Kanamori, 1982; Hartzell and Heaton, 1983; Satake, 1993; Wald and Heaton, 1994; Thatcher et al., 1997]. Based on these kinematic models, the dependencies of kinematic source parameters, such as fault size, slip, sliprate, and other characteristics on the seismic moment have been discussed [e.g., Kanamori and Anderson, 1975; Somerville et al., 1999; Mai and Beroza, 2000; Murotani et al., 2008]. [3] Contrary to the findings of kinematic source models, which might contain mechanical inconsistencies, dynamic ruptures propagate according to elastodynamic equations and friction laws on the fault. Numerous dynamic rupture 1 Earthquake Research Institute, University of Tokyo, Tokyo, Japan. 2 Now at National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan. 3 National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan. 4 Now at Japan Nuclear Energy Safety Organization, Tokyo, Japan. Copyright 2010 by the American Geophysical Union /10/2009JB models have been constructed that are consistent with the rupture physics identified by laboratory studies. Dynamic rupture models based on near source waveform or kinematic source models have been attempted for several real earthquakes: the 1979 Imperial Valley earthquake [Favreau and Archuleta, 2003], the 1992 Landers earthquake [Olsen et al., 1997; Peyrat et al., 2001], the 1994 Northridge earthquake [Nielsen and Olsen, 2000; Ma and Archuleta, 2006], the 2000 Tottori earthquake [Dalguer et al., 2003; Peyrat and Olsen, 2004], the 2001 Geiyo earthquake [Miyatake et al., 2004], the 2002 Denali earthquake [Dunham and Archuleta, 2004], and the 2004 Parkfield earthquake [Ma et al., 2008]. Dynamic rupture modeling enables us to consider the rupture physics more directly than kinematic source models do. Relationships among source parameters obtained from these dynamic source models have provided new insights into the physics of earthquakes [e.g., Tinti et al., 2005; Mai et al., 2006]. [4] In the Miyagi oki region (translated into English as the region off the coast of Miyagi Prefecture ) of northeastern Japan, the Pacific plate subducts beneath the continental plate. Historical records reveal that large offshore earthquakes with magnitudes of about 7.5 and recurrence interval of approximately 37.1 years have occurred repeatedly in the Miyagi oki region, as shown in Figure 1 [Earthquake Research Committee, 2005]. For the most recent two events that occurred in 1978 and 2005, several 1of12

2 will clarify whether those source parameters depend on the location or whether the source parameters depend on the rupture process. Moreover, in order to understand the seismic cycle in the Miyagi oki region, it is important to clarify the relationship between the dynamic rupture processes of these events. [5] In this study, we construct dynamic source models for the 1978 and 2005 Miyagi oki earthquakes on the basis of the kinematic source models proposed by Wu et al. [2008, 2009]. Then we compare the dynamic source parameters between the two models. In particular, we analyze stress drop, Ds, and fracture energy, G C. These parameters can be evaluated more stably than other parameters, such as the strength excess and slip weakening distance, D C, from lowfrequency ground motion data [Guatteri and Spudich, 2000]. This evaluation of dynamic source parameters will offer a key to understanding not only the physics of earthquakes, but also the recurrence of large earthquakes in the Miyagi oki region. Moreover, it will provide an important constraint for the construction of a source model for prediction of strong ground motion, especially motion due to plate boundary events in a subduction zone. Figure 1. (a) Magnitudes for a series of Miyagi oki earthquakes determined by the Japan Meteorological Agency, JMA [Earthquake Research Committee, 2005]. (b) Slip distributions of the kinematic source models of the 1978 and 2005 Miyagi oki earthquakes [Wu et al., 2008]. The area represented by the black rectangle in the inset map is magnified in the main map. Gray and black contour lines represent the slip distributions of the 1978 and 2005 events, respectively. The contour interval is 0.5 m. Gray and black stars show the rupture nucleation points of the 1978 and 2005 events, respectively. kinematic source models were proposed [Yamanaka and Kikuchi, 2004; Okada et al., 2005; Yaginuma et al., 2007; Wu et al., 2008]. Previous studies reported that both events occurred on the plate boundary, and also that the large northern asperity (area exhibiting large slip) that ruptured during the 1978 event (M w 7.6) did not rupture during the 2005 event (M w 7.2). Wu et al. [2008] compared near source waveforms between the two events and inverted the source processes of them using teleseismic and near source waveform data. According to their results, 1) both events ruptured from almost the same hypocenter, 2) the 1978 event consisted of two southern asperities and a large northern asperity, and the 2005 event ruptured only the two southern asperities among them. Although these two events occurred on the same plate boundary in the same region, the seismic moment of the 1978 event was approximately four times larger than the 2005 event, and the rupture process of them were quite different in the northern part. Comparison of the dynamic source parameters of these two Miyagi oki events 2. Dynamic Source Modeling [6] The kinematic source models are described by spatiotemporal evolution of slip and generally estimated from observed data such as waveforms, tsunami, and geodetic data. However, they do not account for explicit rupture physics. On the other hand, the dynamic source models are constructed to satisfy the elastodynamic equations with rupture criterion on the fault plane. We modeled spontaneous dynamic rupture processes of the 1978 and 2005 Miyagi oki events to satisfy the slip distributions and rupture velocities of their kinematic source models. [7] In this study, we used kinematic source models estimated by Wu et al. [2008, 2009] as reference models because they analyzed both the 1978 and 2005 events in the same way and used near field ground motion data, which enable us to estimate detailed source processes. Several researchers have estimated kinematic source models of these two events. In the case of the 1978 event, Yamanaka and Kikuchi [2004] estimated the rupture process using the near field ground motion data. Wu et al. [2008] obtained results similar to that of Yamanaka and Kikuchi [2004]. In the case of the 2005 event, Wu et al. [2008] recovered two asperities although Okada et al. [2005] and Yaginuma et al. [2007] indicated a single asperity around the hypocenter. As mentioned by Wu et al. [2008], two distinct pulses in the strong motion data support the existence of two asperities during the 2005 event. Even the empirical Green s function method obtained two asperities [Kamae, 2006; Suzuki and Iwata, 2007]. Therefore, we used the kinematic source models of Wu et al. [2008] in this analysis. [8] We assumed the linear slip weakening model [Ida, 1972; Andrews, 1976] applies on the faults (Figure 2). The linear slip weakening model is described with Ds, strength excess, and D C. According to this model, G C depends on these three parameters (gray area in Figure 2). The slip distribution determines the stress distribution and the rupture velocity determines the fracture energy. We modeled distributions of Ds, strength excess, and D C for the 2of12

3 Figure 2. Shear stress as a function of slip in the linear slip weakening model. First the stress increases from the initial stress, s 0, to the peak stress, s p, and then drops to the final frictional stress level, s f, over a critical slip, D C. The gray area shows the fracture energy, G C. Strength excess and stress drop, Ds, represent values of s p s 0 and s 0 s f, respectively. two Miyagi oki events to satisfy the kinematic source models. [9] Among the above source parameters, we assumed distributions of the stress drop on the basis of the slip distributions of the kinematic source models. We calculated the stress drop in a semi infinite homogeneous elastic medium using the method of Okada [1992], and then interpolated the stress drops on a finer grid (0.2 km for the 1978 event and 0.1 km for the 2005 event, respectively) bilinearly for the numerical simulations (Figures 3c and 3d). For simplicity, we considered the stress drop only for the dip slip component. The material properties are represented by the P wave velocity V P = 6.95 km/s, the S wave velocity V S = 3.96 km/s, and the density r = 2960 kg/m 3. These are values for a layer that includes the rupture nucleation points on the faults in the analyses of Wu et al. [2008]. We preserved the stress drop distributions calculated here through all the following dynamic simulations to reproduce the slip distributions of kinematic source models. [10] Second, we simulated spontaneous dynamic rupture processes with several sets of the strength excess and D C, and then selected models that satisfy the rupture velocity of the kinematic source models, particularly around asperities A, B, and C in Figures 3c and 3d. In this analysis, we defined the rupture start time as the time when the slip velocity exceeds the value of 0.1 m/s, not as the time when the stress exceeds the peak stress. Since we constructed the dynamic source models based on the kinematic source models estimated from the seismic wave data, the rupture start time should be defined with the slip velocity that is estimated directly by the waveform inversion, rather than the stress. [11] For simplicity, we started to model the strength excess and D C with assumptions that the S parameter and D C are spatially uniform over the fault plane in each event. The S parameter is the ratio of the strength excess to the stress drop introduced by Andrews [1976] and Das and Aki [1977]. Then we considered spatial variation in these parameters as necessary to match the rupture velocity of kinematic models. For the negative stress drop areas (Ds < 0), we assumed the strength excess to be 1.2Ds (>0) to preserve an even stress drop from the peak stress to the residual stress in those locations. [12] For calculating the dynamic rupture, we used the fourth order finite difference method (FDM) with a 3 D staggered grid [Virieux and Madariaga, 1982]. The fault plane was represented by the Stress Glut method [Andrews, 1976]. The grid intervals and the time increments are 0.2 km and 0.01 s for the 1978 event, and 0.1 km and s for the 2005 event, respectively. We forced the rupture to nucleate at t = 0 within a nucleation area whose size was calculated following Day [1982]. [13] We assumed an infinite elastic medium with the same properties as used in the stress drop calculation. Because the hypocentral depths of Miyagi oki earthquakes were 30 km [Wu et al., 2008] we did not include the free surface that would have little effect on our results. Miyagi oki earthquakes occurred on the plate interface in subduction zone. Therefore the dynamic rupture would be affected by the bimaterial effects [Weertman, 1980; Harris and Day, 1997, 2005; Ma et al., 2008; Ma and Beroza, 2008]. In this article, we did not take account of this effect because the main rupture directions during both events were same (the downdip direction) and the bimaterial interface would affect two rupture processes in the same way. [14] For the 1978 event we simulated nine dynamic source models, shown in Table 1. In Table 1, we summarize the relationship between the constant source parameters, S and D C, and the secant rupture velocity (hypocentral distance divided by the rupture travel time [Day, 1982]) around asperities A and B (see Figure 3c). The propagation velocity of the first time window in the inversion analysis of Wu et al. [2008] is 3.2 km/s for the 1978 event, which corresponds well with the rupture times for asperities of their kinematic source model. As shown in Table 1, in all the models, the rupture velocities around asperity A exceeded the shear wave velocity and differed from that of the kinematic model greatly. We will consider source parameters around this asperity later. From the comparison of the rupture velocity around the other asperity, asperity B, between the dynamic and kinematic models, the model (S, D C )= (0.2, 0.4 m) was the best model in that the rupture velocity in asperity B stays at 3.2 km/s. Although the rupture velocity of the model (S, D C ) = (0.3, 0.3 m) is also close to that of the kinematic model, 3.2 km/s, it accelerates during the rupture of asperity B and reaches 3.7 km/s. The rupture velocities around asperity B in the other models differ from that of the kinematic source model by 0.5 km/s or more. Therefore, we selected the model with S and D C of 0.2 and 0.4 m as the best model, assuming that S and D C are constant. [15] Although the model with constant S of 0.2 and D C of 0.4 m was better than the other models with constant S and D C values, the rupture velocity around asperity A exceeded that of the kinematic source model and reached the supershear rupture velocity temporarily. Supershear rupture propagations have been reported for some large earthquakes [e.g., Archuleta, 1984; Wald and Heaton, 1994; Bouchon et al., 2000; Sekiguchi and Iwata, 2002; Bouchon and Vallee, 2003; Koketsu et al., 2004; Ellsworth et al., 2004; Dunham and Archuleta, 2004]. However, in the case of the 1978 Miyagi oki earthquake, any evidence of the supershear rupture was never reported. Moreover, not only the local rupture velocity but also the secant rupture velocity exceeded the rupture velocity of the kinematic 3of12

4 Figure 3. Slip distributions of the kinematic models and dynamic source parameters assumed for the dynamic rupture simulations. White stars indicate the rupture nucleation points. For Figures 3i and 3j, areas with slips of DC or less in the dynamic rupture models (see Figure 4) are masked. 4of12

5 Table 1. Secant Rupture Velocity in Asperities A and B, and the Source Parameters in Dynamic Source Models With Constant S and D C Values, for the 1978 Event a S A: > V S,B:>V S A: > V S,B:>V S A: km/s, B: ~3.7 km/s 0.2 A: > V S,B:>V S A: ~ V S,B:~3.2 km/s A: km/s, B: ~2.7 km/s 0.3 A: ~ V S, B: km/s A: ~ V S, B: km/s A: km/s, B: < 2.7 km/s a The cell in which values are written in bold indicates the best model. The rupture velocity of the kinematic model and the shear wave velocity are 3.2 km/s and 3.93 km/s, respectively. D C (m) model. Therefore, we modified the best model using constant S and D C values by assuming larger S and D C values only around asperity A (Figures 3e and 3g). In the case of (S, D C ) = (1.0, 0.8 m) around asperity A, we obtained a dynamic model in which the rupture propagates at subshear velocity, almost the same as the results of the kinematic source model (Figure 4). We will refer to this dynamic source model for the 1978 event as model M78. [16] For the 2005 event, we simulated three dynamic source models, shown in Table 2. The rupture velocity of the model with constant S and D C values of 0.1 and 0.3 m, respectively, is most similar to that of the kinematic source models, 3.4 km/s (bold text in Table 2). If we calculate the dynamic rupture with larger S or D C values as shown in Table 2, the rupture velocity will be markedly less than that of the kinematic source models or the rupture may terminate halfway because the fracture energy is larger. In the case of the 2005 event, the spatial variation of S and D C was not necessary. We will refer to the best model with constant S of 0.1 and D C of 0.3 m as model M05. [17] Comparisons of the slip rate functions between the dynamic and kinematic source models in each subfault of Figure 4. (a) Distributions of the fracture energy and (b) slip rate functions along the lines shown in Figure 4a. The contour interval in Figure 4b is 0.1 m/s. Gray lines in Figure 4b show the P and S wave velocities and rupture velocities assumed by Wu et al. [2008]. The zero on the lateral axis of Figure 4b represents the rupture nucleation point. 5of12

6 Table 2. Secant Rupture Velocity in Asperity C and Source Parameters for Dynamic Models With Constant S and D C Values, for the 2005 Event a D C (m) S C: ~3.4 km/s C: < 2.9 km/s 0.2 C: < 2.9 km/s a The cell in which values are written in bold indicates the best model. the kinematic models are shown in Figures S1 and S2 in the auxiliary material. 1 The slip rate functions of the dynamic models reproduce those of kinematic models, especially in subfaults with large amplitudes, such as asperities A, B and C. 3. Comparison of Source Parameters Between Models M78 and M05 [18] We compare the source parameters between models M78 and M05 below. All of the parameters discussed in this section are summarized in Figures 3 and 5. According to Wu et al. [2008], the hypocentral location of the 1978 and 2005 events was almost the same. Therefore, in Figures 3 and 5, we set origin at the hypocenter in each model, and in the strike direction the hypocenteral locations were aligned in order to make it easy to compare parameter distributions between two events Kinematic Source Parameters in Dynamic Source Models [19] In this section, we show the characteristics of the kinematic source parameters such as slip, slip rate, rupture velocity, and risetime, in the obtained dynamic source models. The slip distributions of the dynamic source models (Figures 5a and 5b) generally agree with those of the kinematic source models (Figures 3a and 3b) except in some regions of the 1978 event, where dynamic overshoots are found. Distributions of the peak slip rate are shown in Figures 5c and 5d. The peak slip rate increases with hypocentral distance in each area that has a large stress drop and decreases as the stress drop decreases. This behavior is similar to the results of Day [1982]. [20] We plotted the time at which the slip rate first exceeds 0.1 m/s to generate the rupture time distributions shown in Figures 5e and 5f. Although the stress exceeded the peak stress at the time of the S wave arrival around asperity B in model M78 and asperity C in model M05, the significant slip rate (>0.1 m/s) propagated with the subshear velocity as shown in Figure 4b. [21] Figures 5g and 5h show the risetime distributions of models M78 and M05. The risetime in the dynamic model is given by the time it takes for the slip to go from 10 to 90% of its final value at each point. In the case of model M78, the risetime is large around the rupture nucleation point and decreases with the hypocentral distance. These distributions are typical for a crack model with the linear slip weakening 1 Auxiliary materials are available in the HTML. doi: / 2009JB model [e.g., Day, 1982]. In model M05, we can see area with short risetime between the hypocenter and asperity C. This part has the large stress drop in a narrow area (Figure 3d) and pulse like rupture with short risetime and large slip rate (Figure 5d) would arise due to this geometrical factor [Day et al., 1998] Stress Drop and Fracture Energy on the Whole Fault [22] Stress drop distributions of models M78 and M05 are shown in Figures 3c and 3d, respectively, and distributions of the fracture energy are shown in Figures 3i and 3j. The maximum and average values of these parameters are presented in Figure 6a. We consider only the areas with slips of D C or larger to calculate the maximum and average values. [23] Although the seismic moment of the 1978 event is about four times as large as that of the 2005 event, the stress drop of these two models is almost the same. On the other hand, the fracture energy of model M78 is about five times larger than that of model M05 for the maximum value and 2.4 times larger for the average value. This fracture energy difference is caused by the difference in D C and the S parameters over the whole faults between models M78 and M05 and by quite large values of D C and the S parameter in asperity A of model M78, which are required to preserve the rupture velocity at the subshear level. [24] Consequently, while the two Miyagi oki earthquakes have similar stress drop values, the 1978 event has larger fracture energy values than the 2005 event, even though both events occurred in the same region. This result indicates that the fracture energy on the same fault plane can vary with the rupture process and magnitude Stress Drop and Fracture Energy in an Asperity Ruptured Repeatedly [25] According to the analysis of Wu et al. [2008], the two southern asperities of the 1978 event were ruptured again during the 2005 event. We compare the stress drop and fracture energy in the asperities that ruptured during both events. The eastern asperity of them includes the rupture nucleation area. The rupture nucleation area was introduced artificially for the dynamic rupture calculation and we cannot evaluate the dynamic parameters there precisely. Therefore, we analyze only the western asperity (asperities B and C in Figures 3c and 3d, respectively) in this study. [26] In Figure 6b, we summarize the maximum and average values of the stress drop and the fracture energy in asperity B of model M78 and asperity C of model M05. Both of these asperities have similar stress drop values. On the other hand, the maximum fracture energy value of asperity B is slightly larger than that of asperity C (about 1.6 times), and the average fracture energy value of asperity B is about twice as large as that of asperity C. We will discuss this difference of fracture energy in greater detail in section 4. [27] According to the kinematic models of Wu et al. [2008], asperity C was ruptured during the 2005 event. However, Okada et al. [2005] and Yaginuma et al. [2007] showed kinematic models without the rupture in asperity C as mentioned in section 2. Therefore we cannot discuss on the difference of the fracture energy in the same asperity when we refer their source models. However, in this article 6of12

7 Figure 5. Comparison of the dynamic source models for the (a, c, e, and g) 1978 (M78) and (b, d, f, and h) 2005 (M05) events. For the rupture time distributions and the risetime distributions, areas where the slip rate value did not exceed 0.1 m/s are masked. 7of12

8 1978 event. However, this possibility does not affect our result. That is, the fracture energy on the same area was different during two events Source Models for Test [30] We constructed two other dynamic source models and simulated the spontaneous dynamic rupture of them for the validation of the fracture energy difference between asperities B and C. One assumes that the dynamic parameters are same as for model M78, but in asperity B only, S and D C values are 0.1 and 0.3 m. These values are the same with those in model M05. In this model (model M78 ), the fracture energy values only in asperity B are smaller than those in model M78, and they are as large as those in asperity C of model M05 (Figure 7a). The maximum and average values of the fracture energy in asperity B of model M78 are 0.60 and 0.36 MJ/m 2, respectively. Since the stress drop is not same with in asperity C of model M05, the fracture energy value is not exactly same. M78 is a model with the same stress drop and the fracture energy with model M78 except that the fracture energy in asperity B is similar to that in asperity C of model M05. [31] The other model assumes that the stress drop, S, and D C values are the same as for model M05, but in asperity C only, S and D C values are 0.2 and 0.4 m. These values are the same as in model M78. We will refer to this model as model M05. The maximum and average fracture energy values in asperity C of model M05 are 0.82 and 0.40 MJ/m 2, respectively. [32] By the comparison of the rupture velocity in asperity B between models M78 and M78 and in asperity C between models M05 and M05, we examined how the rupture velocity changes if the repeatedly ruptured asperity has the fracture energy similar to each other. Figure 6. Comparison of the stress drop and the fracture energy between (a) models M78 and M05, and (b) asperities B and C. White and gray bars represent the maximum and average values, respectively. we analyzed based on the results of Wu et al. [2008] for the reasons mentioned in section Numerical Test on Difference of Fracture Energy in a Repeatedly Ruptured Asperity [28] As mentioned in section 3.3, we obtained the fracture energy difference between repeatedly ruptured asperities B and C. In this section, we examined how large an effect this difference of the fracture energy between asperities B and C has on the rupture velocity of dynamic source models. [29] We did not examine effects of the uncertainty of the asperity size because reliable resolution analyses were conducted by Wu et al. [2008]. The size of asperity C was smaller than that of asperity B and it is possible that the 2005 event ruptured only a part of the asperity B during the 4.2. Comparison of Rupture Velocity [33] Figures 7a and 7b show the fracture energy distribution and the slip rate function along the line D D of models M78 and M05, respectively. In the case of model M78, the rupture in asperity B begins earlier than that of model M78, and the secant rupture velocity reaches the shear wave velocity. This difference in the rupture velocity between models M78 and M78 is large and the rupture velocity in model M78 is not consistent with the kinematic model which has the subshear rupture velocity. In the case of M05, we can see a large delay of rupture in asperity C from the rupture velocity of the kinematic model and model M05, which is about five seconds. [34] In the inversion analysis of Wu et al. [2008], the authors searched for the best rupture velocity values by comparing the waveform fits for different maximum rupture velocities. The rupture velocity differences between models M78 and M78 and between models M05 and M05 evaluated in this section will be significant. Asperity B of model M78 should have a larger fracture energy value than asperity C of model M05. Therefore the 1978 Miyagi oki earthquake (M w 7.4) had larger fracture energy values than the 2005 event (M w 7.2) not only on the whole fault as shown in section 3.2, but also on the asperity which ruptured repeatedly as shown in this section. These differences of the fracture energy on the same fault and same asperity might be caused by the change of the state on the fault plane 8of12

9 Figure 7. (a) Distributions of the fracture energy of models M78 and M05. Rectangles show areas where values of the strength excess and D C were different from those of models M78 and M05. Areas with slip of D C or less are masked. (b) Slip rate functions along lines shown in Figure 7a. The contour interval in Figure 7b is 0.1 m/s. Gray lines in Figure 7b show the P and S wave velocities and rupture velocities assumed by Wu et al. [2008]. The zero on the lateral axis of Figure 7b represents the rupture nucleation point. during the coseismic rupture in 1978 event or at some point between the 1978 and 2005 events. Another possible reason is the fracture energy scaling with seismic moment. Tinti et al. [2005] and Mai et al. [2006] suggested that the fracture energy estimated by them includes not only surface energy but also dissipative processes around the crack tip. Our results showing that the fracture energy on a fault plane and in an asperity was larger during larger event agree with their interpretation. 5. Discussion 5.1. Seismic Cycle of the Miyagi oki Earthquakes [35] By the construction of the dynamic source models of recent two Miyagi oki earthquakes, we obtained information on dynamic source parameters during the coseismic slip in the seismic cycle of the Miyagi oki earthquakes. Along the subduction zone in northeastern Japan including Miyagioki region, some asperities repeatedly generated large interplate earthquakes [Yamanaka and Kikuchi, 2004]. Especially in the Miyagi oki region, events with the magnitude of about 7 occurred repeatedly with the interval of about 37.1 years (see Figure 1). However, the rupture processes of the 1978 and 2005 events were quite different. During the 1978 event three asperities were ruptured. Among the asperities, the northern asperity was not ruptured during the 2005 event. Moreover, according to Kanamori et al. [2006], the 1936 Miyagi oki event and other two large events there in the 1930s would not also rupture asperity A. These variations of the rupture process might be caused by the spatial variation of the source parameters. [36] As modeled in section 2, asperity A demands larger G C values than other areas during the 1978 event in order to keep the rupture velocity at subshear levels. The behavior of stress during the dynamic rupture is important to consider the seismic cycle. However, we cannot directly determine the strength excess from our analysis because of the tradeoff between it and D C. 9of12

10 Figure 8. Average fracture energy versus seismic moment. White circles and white squares show the average values of the fracture energy in areas with slips of D C or larger and those evaluated according to Mai et al. [2006], respectively. Black circles and the gray line show values estimated by Tinti et al. [2005] and the empirical scaling relationship by Mai et al. [2006], respectively. [37] If only the southern part of the 1978 event ruptured during the events in the 1930s as indicated by Kanamori et al. [2006] and the plate boundary had been 100% coupled [Mazzotti et al., 2000; Nishimura et al., 2004] from the 1930s events to the 1978 event, asperity A would be closer to the rupture than other areas just before the 1978 event. Therefore the strength excess in asperity A would be less than that in other areas during the 1978 event. This suggests that during the 1978 event the strength excess in asperity A would be smaller than that in model M78. And instead of the strength excess, D C would be larger than that in model M78 to preserve the fracture energy value. To verify this suggestion, analysis of higher frequency waveforms than those of Wu et al. [2008] during the coseimic rupture need to be conducted [Guatteri and Spudich, 2000] Comparison of Fracture Energy With Inland Events [38] As mentioned in section 3.2, we obtained fracture energy values of the 1978 and 2005 Miyagi oki earthquakes. In this section, we compare the fracture energy values of our models with other studies. In previous studies, realistic dynamic source models of interplate earthquakes in subduction zones, such as the Miyagi oki earthquakes, had not been constructed. Therefore in this section, we compared our models, which are the first results for the interplate events in subduction zones, with dynamic source models of inland events constructed in previous studies [Tinti et al., 2005; Mai et al., 2006]. [39] Figure 8 shows the relations between the seismic moment and the fracture energies of models M78 and M05. We also show the values estimated by Tinti et al. [2005] and the empirical relationship estimated by Mai et al. [2006]. The regression line of Mai et al. [2006] is about ten times larger than our values for the Miyagi oki earthquakes. Moreover, the values of Tinti et al. [2005] are approximately times larger than our values. This discrepancy of the fracture energy between our results and those for inland events suggests that the 1978 and 2005 Miyagi oki events were anomalous earthquakes or it is possible that the scaling relationships of the fracture energy are different between deep interplate events in subduction zones and shallow inland events. [40] The rupture velocity and stress drop affect the fracture energy estimation explicitly. However, we could not recognize significant difference of the rupture velocities and the average value of the stress drop between our models and models of M7 class events by Mai et al. [2006]. It is possible that the difference of the tectonic setting between interplate events in subduction zones and inland events causes the fracture energy discrepancy. In paticular, the fault depth and shapes determined by the width of the seismogenic zone are quite different. These factors might affect the difference of fracture energy. 6. Conclusions [41] The 1978 and 2005 Miyagi oki earthquakes occurred repeatedly on the same plate boundary in a subduction zone, and their magnitudes were different. In this study, we constructed spontaneous dynamic source models of the 1978 and 2005 Miyagi oki earthquakes on the basis of kinematic source models. In the dynamic model of the 1978 event, the fracture energy in the northern asperity that did not rupture during the 2005 event was larger than in the other areas, and this difference in dynamic source parameters may cause the complex recurrence of the interplate events in the Miyagioki region. From the comparison of the dynamic source parameters between the 1978 and 2005 events, we obtained similar values of stress drop not only for the whole fault but also in an asperity ruptured repeatedly. On the other hand, the fracture energy of the 1978 event is significantly larger than that of the 2005 event both on the whole plane and on the re ruptured asperity. These results support the hypothesis that the fracture energy estimated for the real earthquake is a mesoscopic parameter consisting of the surface energy and other dissipative processes in the volume around the crack tip and it scales with the magnitude. 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12 Yamanaka, Y., and M. Kikuchi (2004), Asperity map along the subduction zone in northeastern Japan inferred from regional seismic data, J. Geophys. Res., 109, B07307, doi: /2003jb T. Kimura, National Research Institute for Earth Science and Disaster Prevention, 3 1, Tennodai, Ibaraki, Tsukuba , Japan. (tkimura@ bosai.go.jp) K. Koketsu, H. Miyake, and T. Miyatake, Earthquake Research Institute, University of Tokyo, 1 1 1, Yayoi, Bunkyo ku, Tokyo , Japan. C. Wu, Japan Nuclear Energy Safety Organization, Kamiyacho MT Building, , Toranomon, Minato ku, Tokyo , Japan. 12 of 12