ESTIMATION OF EFFECTIVE STRESS ON ASPERITIES IN INLAND EARTHQUAKES CAUSED BY LARGE STRIKE-SLIP FAULTS AND ITS APPLICATION TO STRONG MOTION SIMULATION

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1 ESTIMATION OF EFFECTIVE STRESS ON ASPERITIES IN INLAND EARTHQUAKES CAUSED BY LARGE STRIKE-SLIP FAULTS AND ITS APPLICATION TO STRONG MOTION SIMULATION Kazuo DAN, Takayoshi MUTO, Jun'ichi MIYAKOSHI, and Motofumi WATANABE Ohsaki Research Institute, Inc. Abstract Precise estimation of the effective stress on the asperities is essential for accurate strong motion prediction, but an estimation method has not been proposed for inland earthquakes caused by large strike-slip faults. Hence, we adopted two different methods to estimate the effective stress on the asperities. One was an estimation method based on the scaling law between the entire fault and the seismic moment proposed by Irikura and Miyake (2001) and on a circular crack model for evaluating the averaged stress drop. The other was an estimation method based on the model composed of a seismogenic layer and a visco-elastic basement proposed by Fujii and Matsu'ura (2000). We applied the estimates to strong motion simulation, compared the simulated peak ground velocities with those by the empirical attenuation relation by Si and Midorikawa (1999), and finally preferred the latter method. Introduction Strong motion pulses of about 1 second caused severe damage to structures in the 1995 Hyogo-Ken Nambu, Japan, earthquake of M JMA 7.3 (e.g., Tanaka et al., 1996; Editorial Committee for the Report on the Hanshin-Awaji Earthquake Disaster, 1998). For accurate strong motion prediction in a wide period range including these relatively short periods of 0.5 to 2 seconds, intensive studies have been carried out on characterized fault models, which are simple to capture the feature of the complexity of the fault rupture. In Japan, the asperity model proposed by Somerville et al. (1993) is often used as a characterized fault model for strong motion prediction (Earthquake Research Committee, 2004), and Irikura and Miyake (2001) compiled a procedure, called recipe for strong motion predication, for determining parameters of the characterized fault model. In the asperity model, the size of the asperity is proportional to the predominant period of the strong motion pulse (Miyatake, 1998), and the peak slip velocity on the asperity is proportional to the amplitude of the strong motion pulse (Matsushima and Kawase, 2000). The peak velocity is proportional to the effective stress (Brune, 1970), the effective stress on the asperity is almost equal to the stress drop on the asperity (Dalguer et al., 2002), and the stress drop on the asperity is evaluated by multiplying the averaged stress drop on the entire fault and the ratio of the entire fault area to the asperity area (Madariaga, 1979; Dan et al., 2002). Hence, the averaged stress drop on the entire fault or the effective stress on the asperity is a very important parameter for accurate prediction of the amplitude of the strong motion pulse.

2 Kanamori and Anderson (1975) applied the stress drop equation for a circular crack model derived by Eshelby (1957) to the relation between the entire fault area and the seismic moment to evaluate the averaged stress drop on the entire fault in large subduction earthquakes to be about 30 bars and the averaged stress drop on the entire fault in large inland earthquakes to be about 100 bars. Sato (1989) evaluated the averaged stress drop on the entire fault in large subduction and inland earthquakes in Japan to be about 50 bars. On the other hand, the scaling law of the entire fault area and the seismic moment changes between small earthquakes, where the rupture does not propagate to the upper and lower boundary of the seismogenic layer, and large earthquakes, where the rupture propagates to the upper and lower boundary of the seismogenic layer (Scholz, 1990). This change is that the seismic moment of large earthquakes is relatively larger for the area than that of small earthquakes. Watanabe et al. (1998) applied a semi-episoidal crack model to this scaling law, and explained this phenomenon by higher averaged stress drop of large earthquakes. Fujii and Matsu'ura (2000) introduced a model composed of a seismogenic layer and a visco-elastic basement, and explained this phenomenon by a constant averaged stress drop. Irikura and Miyake (2001) also discussed this change of the scaling law, and proposed a new scaling law for large inland earthquakes. However, they only showed the averaged stress drop on the entire fault and the effective stress on the asperities for small earthquakes after applying the stress drop equation for a circular crack model to the scaling law between the entire fault area and the seismic moment proposed by Somerville et al. (1999), but not for large earthquakes. Recently, Irikura and Miyake (2002) showed that the averaged stress drop on the entire fault is proportional to the 1/4 power of the seismic moment after applying the stress drop equation for a circular crack model to the new scaling law for large earthquakes. But, they also showed that the effective stress on the asperities is highest in the range of the moment magnitude M W of 6.6 to 6.8 and becomes rather smaller in the range of M W greater than 6.8 after they evaluated the effective stress on the asperities directly from the amplitudes of the strong motion pulses. These facts indicate that the averaged stress drop on the entire fault depends on the seismic moment while the effective stress on the asperities does not depend on the seismic moment and that a problem remains about the applicability of the stress drop equation for a circular crack model to large inland earthquakes where the rupture propagates to the upper and lower boundary of the seismogenic layer. In this paper, we adopted two different methods to estimate the effective stress on the asperities in large inland earthquakes, made two different characterized fault models based on these two different methods, carried out strong motion simulation, and compared the simulated peak ground velocities with those by the empirical attenuation relation by Si and Midorikawa (1999). The first method estimated the effective stress on the asperities based on the scaling law between the entire fault area and the seismic moment for large inland earthquakes proposed by Irikura and Miyake (2001) and on the stress drop equation for a circular crack model to evaluate the averaged stress drop on the entire fault as Irikura and Miyake (2002) did. In this model, the effective stress on the asperities is proportional to the 1/4 power of the seismic moment as mentioned above. The second method adopted the scaling law between the entire fault area and the seismic moment for large inland earthquakes based on the model composed of a seismogenic layer and a visco-elastic basement proposed by Fujii and Matsu'ura (2000). In this model, the averaged stress drop on the entire fault is constant as mentioned before, and the effective stress on the asperities is evaluated to be also constant based on this constant averaged stress drop. Procedure of determining parameters of the characterized fault model for strong motion prediction In this chapter, we explained the procedure of determining parameters of the

3 Figure 1. Procedure of determining parameters of the characterized fault model for strong motion prediction. characterized fault model for strong motion prediction, that is necessary for our study based on the two methods described in the previous chapter. In the recipe for strong motion prediction proposed by Irikura and Miyake (2001), consequently determined are causative faults, seismogenic zone, and locked area in Step 1, outer fault parameters (fault area, seismic moment, average slip, and short-period level) in Step 2, inner fault parameters (asperity area and slip and effective stress on the asperities) in Step 3, and other fault parameters (hypocenter, rupture propagation mode, and rupture propagation velocity) in Step 4, as shown in Figure 1.

4 Figure 2. Fault length and width of inland earthquakes caused by strike-slip faults (Wells and Coppersmith, 1994) Figure 2 shows the fault length L and width W of inland earthquakes caused by strike-slip faults (Wells and Coppersmith, 1994). The width is constant of about 15 km because of the thickness of the seismogenic layer for the fault length over about 30 km. Figure 2 also shows the following bilinear line proposed by Irikura and Miyake (2001) for modeling these data: W = 0.955L (L W /0.955) max (1) W max (W max / L). Here, W max is assumed to be 17 km because Irikura and Miyake (2001) obtained W max =16.6 km from the data of the source inversion results complied by Somerville et al. (1999) and the data compiled by Wells and Coppersmith (1994) and W max =17.1 km from the data of the source inversion results except the thrust faults compiled by Somerville et al. (1999). Figure 3 shows the entire fault area and the seismic moment (Abe,1990; Wells and Coppersmith, 1994). Scaling laws between the fault area and the seismic moment are also drawn by the straight lines for σ=10 bars and σ=100 bars, calculated by the following equation for a circular crack model (Eshelby, 1957): σ = 7 M 0 (2) 16 (S / π ) 1.5. The entire fault area and the seismic moment is located between the two lines for σ=10 bars and σ=100 bars for M W under 7 and is closer to the line for σ=100 bars for M W over 7. Considering this change of the scaling law, Irikura and Miyake (2001) proposed to use equation (3), derived by Somerville et al. (1999), for small earthquakes with the seismic moment M 0 less than dyne-cm and to use equation (4), derived by Irikura and Miyake (2001), for large earthquakes with M 0 larger than dyne-cm. S[km 2 ]= (M 0 [dyne-cm]) 2/3 (3) M 0 < dyne-cm S[km 2 ]= (M0[dyne-cm]) 1/2 (4) M dyne-cm Figure 3 shows two lines of equations (3) and (4) by the broken line and the dotted line, respectively. The lower bound of M 0 is dyne-cm according to Somerville et al. (1999), and the upper bound of M 0 is dyne-cm according to Irikura and Miyake (2001).

5 Figure 3. Fault area and seismic moment of inland earthquakes caused by strike-slip faults (Abe, 1990; Wells and Coppersmith, 1994) and the empirical relation by Irikura and Miyake (2001). Figure 4. Fault area and seismic moment of inland earthquakes caused by strike-slip faults (Abe, 1990; Wells and Coppersmith, 1994) and the empirical relation by Fujii and Matsu'ura (2000). Irikura and Miyake (2001) showed that the averaged stress drop σ was 23 bars for equation (3) using equation (2), and Irikura and Miyake (2002) showed that the averaged stress drop σ became larger with M W and about 100 bars for M W of 8 using equation (2) again. On the other hand, Irikura et al. (2002) and Dan et al. (2002) showed that the effective stress σ asp on the asperity was calculated by the following equation (5) from the entire fault area S, the asperity area S asp, and the averaged stress drop σ: σ asp = S σ. (5) S asp Here, the effective stress σ asp on the asperity is assumed to be equal to the stress drop σ asp on the asperity (Dalguer et al., 2002). Since Somerville et al. (1999) obtained the empirical relation of S asp /S=0.22, the effective stress σ asp on the asperity is calculated to be 105 bars for σ=23 bars and to become larger with M 0 to be about 400 bars for M W of 8.

6 Scaling law of the outer fault parameters and evaluation of the effective stress on the asperities In the previous chapter, we showed the scaling law between the fault area and the seismic moment described in equation (3) for small earthquakes and in equation (4) for large earthquakes. On the other hand, Fujii and Matsu'ura (2000) explained this change of the scaling law by the visco-elastic basement bellow the seismogenic layer. The thick lines in Figure 4 show the scaling law of the following equation proposed by Fujii and Matsu'ura (2000): σ S 2 M 0 =. (6) as + bw max Here, a= km, b=1.0, S=L W max, and L 30 km. Fujii and Matsu'ura (2000) showed W max =12 km and σ=18 bars for plate-boundary inland earthquakes and W max =15 km and σ=31 bars for intra-plate inland earthquakes. Fujii and Matsu'ura (2000) noted that they applied equation (6) to intra-plate earthquakes while they had no evidence of the visco-elastic basement under the seismogenic layer in intra-plate zone. Figure 5 shows the averaged stress drop for equation (3) by Somerville et al. (1999) and for equation (4) by Irikura and Miyake (2001), evaluated by equation (2) for a circular crack model. It also shows the averaged stress drop for intra-plate inland earthquakes by Fujii and Matsu'ura (2000) as inland earthquakes in Japan are intra-plate earthquakes (e.g., Earthquake Research Committee, 1999). The averaged stress drop for equation (4) by Irikura and Miyake (2001) is found to become drastically large from about 20 bars to about 100 bars for large M W, while the averaged stress drop for equation (3) by Somerville et al. (1999) and for equation (6) by Fujii and Matsu'ura (2000) is constant of 23 bars and 31 bars, respectively. Figure 6 showed the effective stress on the asperities calculated by equation (5) from the averaged stress drop in Figure 5. Here, S asp /S in equation (5) is assumed to be constant of 0.22 based on the data obtained by Somerville et al. (1999) and Miyakoshi (2002). The effective stress on the asperities based on the scaling law by Fujii and Matsu'ura (2000) is found to be constant of 141 bars, while the effective stress on the asperities based on the scaling law by Irikura and Miyake (2001) is found to become larger with M W to be about 400 bars for M W of 8. In order to examine if the estimated effective stress on the asperities is consistent with strong motion records, we compared the short-period level (flat level of the acceleration source spectrum in the short-period range:dan et al., 2001) evaluated from the effective stress shown in Figure 6 with that evaluated from the variable-slip rupture models obtained by source inversion for inland earthquakes caused by strike-slip faults. The short-period level A is evaluated by the following equation from the effective stress on the asperities σ asp and the asperity area S asp : A=4 πr σ asp β 2, πr 2 =S asp. (7) Here, β is the S-wave velocity at the source, and the short-period seismic waves generated on the background are assumed to be negligible compared with those generated on the asperity. Figure 7 shows the short-priod level evaluated from the effective stress shown in Figure 6. Here, β is assumed to be 3.5 km/s. Also shown are the short-period level obtained from the variable-slip rupture models for the 1999 Kocaeli, Turkey, earthquake inverted by Sekiguchi and Iwata (2002) and for the 1997 Kagoshima-Ken Hokuseibu earthquake inverted by Miyakoshi and Petukhin (2002) and the short-period level for the four earthquakes caused by strike-slip faults obtained by Dan et al. (2001).

7 Figure 5. Averaged stress drop and seismic moment of inland earthquakes caused by strike-slip faults. Figure 6. Effective stress on the asperities and seismic moment of inland earthquakes caused by strike-slip faults. Here, S asp /S is assumed to be Figure 7. Short period level and seismic moment of inland earthquakes caused by strike-slip faults. Here, S asp /S is assumed to be 0.22, and β is assumed to be 3.5 km/s.

8 The short-period level based on the scaling law by Fujii and Matsu'ura (2000) is consistent with that evaluated from the variable-slip rupture models, and the short-period level based on the scaling law by Irikura and Miyake (2001) and on the stress drop equation of a circular crack model is almost equal to that based on the scaling law by Fujii and Matsu'ura (2000) for M W of 7 while it is three times larger for M W of 8. Examples of the characterized fault models and strong motion simulation In this chapter, we carried out strong motion simulation from two different characterized fault models determined by a method based on the scaling law proposed by Irikura and Miyake (2001) and on the stress drop equation of a circular crack model for evaluating the averaged stress drop and a method based on the model composed of a seismogenic layer and a visco-elastic basement proposed by Fujii and Matsu'ura (2000). Actual strong motion simulation was performed for 160 km-long strike-slip fault composed of 6 segments. Here, we assumed two cases of asperity number according to Irikura and Miyake (2001): one asperity in each segment and two asperities in each segment. We located these asperities in the middle depth of the seismogenic layer because we compared the results of the strong motion simulation with the peak ground velocities calculated by the existing empirical attenuation relation. A method based on the scaling law by Irikura and Miyake (2001) and on the stress drop equation for a circular crack model Figures 8(a) and 8(b) show two examples of the characterized fault models determined by the method based on the scaling law proposed by Irikura and Miyake (2001) and on the stress drop equation for a circular crack model. Here, the fault width is assumed to be 17 km according to Irikura and Miyake (2001), the S-wave velocity in the seismogenic layer 3.5 km/s, and the density 2.7 g/cm 3. The entire fault area is 2,720 km 2, M W 7.7, the effective stress on the asperities 321 bars, and the averaged slip on the largest asperity 1,020 cm in the model with one asperity in each segment and 1,245 cm in the model with two asperities in each segment. The total seismic moment is distributed into each segment proportionally to the square of the segment area based on equation (4). Figure 8(c) and 8(d) show peak ground velocities on the engineering bed rock (S-wave velocity 600m/s) simulated by the stochastic Green's function method. Figure 8(c) is the result for the characterized fault model with one asperity in each segment, and Figure 8(d) is the result for the characterized fault model with two asperities in each segment. Here, the stochastic Green's function method was taken from Dan et al. (2000). The stochastic Green's functions were generated for the SH-wave and the SV-wave with the hypocenter at the center of the fault. The radiation pattern was assumed to be theoretical one in the frequency range below 3 Hz, to be isometric one in the frequency range over 6 Hz, and to be interpolated in logarithmic scale in the frequency range from 3 to 6 Hz according to Satoh (2002). The Fourier phase was assumed to be common for the SH-wave and the SV-wave in the frequency range below 3 Hz, and to be independent for the SH-wave and the SV-wave in the frequency range over 3 Hz. The quality factor Q was assumed to be Q(f)=60f for f 0.8 Hz taken from Amaike et al. (2003) and Q(f)=48 for f 0.8 Hz. The f max was assumed to be 6 Hz according to the f max for the 1995 Hyogo-Ken Nambu, Japan, earthquake (Tsurugi et al. 1997). The soil amplification was evaluated from the impedance ratio between the seismogenic layer (S-wave velocity 3.5 km/s and density 2.7 g/cm 3 ) and the engineering bed rock (S-wave velocity 600 m/s and density 2.2 g/cm 3 ). Figures 8(c) and 8(d) indicate that the peak ground velocities based on the characterized fault model with one asperity in each segment are not different from those based on the characterized fault model with two asperities in each segment.

9 (a) Slip in the characterized fault model with one asperity in each segment (unit=cm; =rupture initiation point) (b) Slip in the characterized fault model with two asperities in each segment (unit=cm; =rupture initiation point). (c) Peak ground velocities simulated by stochastic Green's function method based on the characterized fault model with one asperity in each segment. (d) Peak ground velovities simulated by the stochastic Green's function method based on the characterized fault model with two asperities in each segment. Figure 8. Characterized fault models determined by the method based on the scaling law by Irikura and Miyake (2001) and on the stress drop equation for a circular crack model and its application to the strong motion simulation.

10 (a) Slip in the characterized fault model with one asperity in each segment (unit=cm; =rupture initiation point). (b) Slip in the characterized fault model with two asperities in each segment (unit=cm; =rupture initiation point). (c) Peak ground velocities simulated by the stochastic Green's function method based on the characterized fault model with one asperity in each segment. (d) Peak ground velocities simulated by the stochastic Green's function method based on the characterized fault model with two asperities in each segment. Figure 9. Characterized fault models determined by the method based on the model composed of a seismogenic layer and a visco-elastic basement by Fujii and Matsu'ura (2000) and its application to the strong motion simulation.

11 For comparison, Figures 8(c) and 8(d) show the empirical attenuation of peak ground velocities (mean and mean±one standard deviation) by Si and Midorikawa (1999). Although the data base of Si and Midorikawa (1999) contained no peak ground velocities of inland earthquakes of M W 8 caused large strike-slip faults, the peak ground velocities simulated by the stochastic Green's function method are much larger than those estimated by this empirical attenuation. A method based on the model composed of a seismogenic layer and a visco-elastic basement by Fujii and Matsu'ura (2000) Figures 9(a) and 9(b) show two examples of the characterized fault models determined by the method based on the model composed of a seismogenic layer and a visco-elastic basement proposed by Fujii and Matsu'ura (2000). Here, the fault width is assumed to be 15 km according to Fujii and Matsu'ura (2000). The entire fault area is 2,400 km 2, M W 7.6, the effective stress on the asperities 141 bars, and the averaged slip on the largest asperity 1,076 cm in the model with one asperity in each segment and 1,201 cm in the model with two asperities in each segment. The total seismic moment is distributed into each segment proportionally to the function of the segment area based on equation (6). Figures 9(c) and 9(d) show peak ground velocities on the engineering bedrock (S-wave velocity 600 m/s) simulated by the stochastic Green's function method based on the characterized fault models and the empirical attenuation of peak ground velocities (mean and mean±one standard deviation) by Si and Midorikawa (1999). The peak ground velocities simulated by the stochastic Green's function method indicate rather steep attenuation, but show a good agreement with those by the existing empirical attenuation. Conclusions We estimated the effective stress on the asperities by the following two methods for large inland earthquakes caused by long strike-slip faults, where the rupture propagated to the upper and lower boundary of the seismogenic layer, determined the parameters of the characterized fault models based on these two methods, and carried out strong motion simulation. The first method estimated the averaged stress drop on the entire fault based on the scaling law between the entire fault area and the seismic moment for large inland earthquakes proposed by Irikura and Miyake (2001) and on the stress drop equation for a circular crack model. The effective stress on the asperities was estimated to be 321 bars, and the peak ground velocities simulated by the stochastic Green's function method were much larger than those evaluated by the empirical attenuation. The second method used the averaged stress drop on the entire fault in the scaling law between the entire fault area and the seismic moment for large inland earthquakes based on the model composed of a seismogenic layer and a visco-elastic basement proposed by Fujii and Matsu'ura (2000). The effective stress on the asperities was estimated to be 141 bars, and the peak ground velocities simulated by the stochastic Green's function method were in a good agreement with those evaluated by the existing empirical attenuation. We concluded that the method based on the model composed of a seismogenic layer and a visco-elastic basement was preferred in a viewpoint of the generated strong motions. Acknowledgments This study was supported by Special Coordination Funds, titled "Study on the master model for strong ground motion prediction toward earthquake disaster mitigation," of the Ministry of Education, Science, Sports, and Culture, Japan.

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