Scaling Relationships of Source Parameters of Inland Crustal Earthquakes in Japan based on Waveform Inversion of Strong Motion Data

1 Best Practices in Physics-based Fault Rupture Models for Scaling Relationships of Source Parameters of Inland Crustal Earthquakes in Japan based on Waveform Inversion of Strong Motion Data K. Miyakoshi 1, K. Somei 1, K. Irikura 2, K. Kamae 3 1 Geo-Research Institute (GRI), Osaka, Japan 2 Aichi Institute of Technology (AIT), Toyota, Japan 3 Kyoto University Research Reactor Institute (KURRI), Kumatori, Japan E-mail contact of main author: ken@geor.or.jp Abstract. Strong motion prediction has been effectively made using source fault models. Major parameters for the prediction are source area and seismic moment of the target earthquake. The seismic moment is given from a scaling relation between seismic moment and source area, as long as the source area is estimated from the geological and geomorphological investigations. A three-stage scaling model between source area and seismic moment of the inland earthquakes has been proposed by Irikura and Miyake (2011) and Murotani et al. (2015). The scaling relations have been originally constructed based on waveform inversion results using strong motion data and teleseismic data of inland earthquakes occurring mostly in California, USA, but including a few in Japan. After the 1995 Hyogo-ken Nanbu earthquake (M w 6.9) in Japan, dense strong ground motion networks were installed by NIED. Using strong ground motions near the source region, heterogeneous slip models are estimated by inversion analysis with high accuracy. Using the waveform inversion results of eighteen recent crustal earthquakes (M w 5.4-6.9) in Japan, we extracted the source parameters from the inverted heterogeneous slip distributions following the criterion of Somerville et al. (1999). We recognized that the scaling relationship of source area and seismic moment obtained in this study coincides with that of Irikura and Miyake (2011). However, the ratio for the combined area of asperities over the entire rupture area is about 0.16 in average for eighteen earthquakes, which is smaller than the previous result (0.22) by Somerville et al. (1999). Stirling et al. (2013) compiled a worldwide set of scaling relations of magnitude (or seismic moment) and source area and showed large differences of scaling relations in different tectonic environments. We recognized that the scaling relationship in this study coincide approximately with that of Hanks and Bakun (2008) in those compiled by Stirling et al. (2013). Key Words: Three-stage scaling model, waveform inversion, strong motion. 1. Introduction Strong motion prediction has been effectively made using source fault models. Major parameters for the prediction are the source area and seismic moment of the target earthquake. The seismic moment is given from a scaling relation between seismic moment and source area, as long as the source area is estimated from the geological and geomorphological investigations. The other parameters (asperity area, rise time and stress drop etc.) necessary for the prediction are given from scaling relations with the seismic moment. A three-stage scaling model between source area and seismic moment of the inland earthquakes has been initially proposed by Irikura and Miyake (2011) [1] and revised by Murotani et al. (2015) [2]. Fig.1 shows the schematic source model of each scaling stage. For the first stage, S is proportional to Mo 2/3 (self-similar scaling) for earthquakes smaller than around M w 6.5 (Somerville et al., 1999 [3] ). For the second stage, S is proportional to Mo 1/2 (the saturation of

2 Best Practices in Physics-based Fault Rupture Models for the thickness of seismogenic zone) for earthquakes between around M w 6.5 and 7.4 (Irikura and Miyake, 2011 [1] ). For the third stage, S is proportional to Mo (the saturation of the slip) for earthquakes larger than around M w 7.4 (Murotani et al., 2015 [2] ). Those scaling relations have been originally constructed based on waveform inversion results using strong motion data and teleseismic data of inland earthquakes that occurred mostly in California, USA, but including a few in Japan. After the 1995 Hyogo-ken Nanbu earthquake (M w 6.9) in Japan, the dense strong ground motion networks (K-NET, KiK-net) were installed with about 20 km intervals by NIED (National Research Institute for Earth Science and Disaster Prevention). Using strong ground motions near the source region, heterogeneous slip models are estimated by inversion analysis with high accuracy. So we extract the source parameters from the inversion results of recent crustal earthquakes in Japan and re-examine the relationship between source parameters and the proposed three-stage scaling model (Irikura and Miyake, 2011 [1] ; Murotani et al., 2015 [2] ). Stirling et al. (2013) [4] also compiled a worldwide set of scaling relations of magnitude (or seismic moment) and rupture source area and showed large differences of scaling relations in different tectonic environments. We compare the relationship in this study with the worldwide set of scaling relationships compiled by Stirling et al. (2013) [4]. FIG. 1. Schematic source model of each scaling stage. 2. Waveform Inversion Results Using the waveform inversion results of recent eighteen crustal earthquakes (M w 5.4-6.9) in Japan (see Fig.2), which occurred after the 1995 Hyogo-ken Nanbu earthquake, we extracted the source parameters from the inversion results using the same criterion as Somerville et al. (1999) [3]. These seismic magnitude ranges correspond to the first or second scaling stage. Fig.3 shows an example of the waveform inversion result of the 2004 Fukuoka-ken seiho-oki earthquake (Asano and Iwata, 2011 [16] ). Table 1 [5]-[25] shows analysis parameters of the waveform inversions of recent studies in Japan. Target period range of the waveform inversions is between about 0.5-10s. The fault plane is divided into a mesh with mesh size of about 1-4km 2. In order to develop appropriate Green s functions, one-dimensional velocity

3 Best Practices in Physics-based Fault Rupture Models for structure models for each station are constructed by modelling the aftershock waveforms in most recent studies (Asano and Iwata, 2011 [8] ). Table 2 shows the same parameters as Somerville et al. (1999) [3] for comparison of analysis parameters of the waveform inversions. In the analysis compiled by Somerville et al. (1999), target period range of the waveform inversions is between about 0.3-10s, the fault plane is divided into a mesh with mesh size of about 1-10km 2, and most studies used the common velocity structure model at each station. Because recent studies of waveform inversions in Japan used high accuracy Green s function (velocity structure model) and smaller mesh size, the results of the waveform inversion we compiled are more precise than those compiled by Somerville et al. (1999) [3]. FIG. 2. Distribution of 18 events and their focal mechanisms (F-net) compiled in this study. FIG. 3. Slip distribution on fault plane of the 2005 Fukuoka-ken seiho-oki earthquake (EQ.7; Asano and Iwata, 2006). The star indicates the hypocenter. Red line rectangles are asperities extracted from the final slip distribution using the same criterion as Somerville et al.(1999).

4 Best Practices in Physics-based Fault Rupture Models for TABLE 1: LIST OF EARTHQUAKES USED IN THIS STUDY WITH THEIR INVERSION ANALYSIS CONDITIONS No. NAME Mech. Reference Mo (Nm) MW Target F.Q. sub fault Total number of No. Inversion F-net (F-net) Hz km 2 Time windows Green's function EQ.1 1995 Hyogo nanbu SS [5] 3.30E+19 3.30E+19 * 6.9 * 0.1-1.0 4.2 8 Rock & soil EQ.2 2008 Iwate-Miyagi nairiku RV [6] 2.76E+19 0.1-1.0 4.0 8 2.72E+19 6.9 [7] 2.73E+19 0.1-1.0 4.0 7 EQ.3 2007 Noto hanto RV [8] 1.57E+19 0.05-1.0 4.0 6 1.36E+19 6.7 [9] 1.10E+19 0.1-1.0 1.0 none EQ.4 2011 Fukushima hamadori NM [10] 1.14E+19 9.58E+18 6.6 0.03-0.8 4.0 6 [11] 1.62E+19 0.1-1.0 4.0 6 EQ.5 2007 Niigata chuetsu-oki RV [12] 1.00E+19 0.03-0.5 4.0 7 9.30E+18 6.6 [13] 6.50E+19 0.1-0.5 1.0 none Unknown [14] 1.62E+19 0.1-1.0 4.0 4 EQ.6 2000 Tottori seibu SS [15] 2.00E+19 8.62E+18 6.6 0.1-1.0 4.4 6 EQ.7 2005 Fukuoka seiho-oki SS [16] 1.15E+19 7.80E+18 6.6 0.05-1.0 4.0 6 EQ.8 2004 Niigata chuetsu RV [17] 1.07E+19 7.53E+18 6.6 0.05-1.0 4.0 6 EQ.9 2011Nagano-Niigata RV [18] 4.21E+18 2.13E+18 6.2 0.05-0.2 4.0 6 EQ.10 2003 Miyagi hokubu RV [19] 1.90E+18 1.53E+18 6.1 0.05-0.5 4.0 8 EQ.11 March 1997 Kagoshima hokuseibu SS [20] 1.73E+18 1.40E+18 6.1 0.1-2.0 1.0 5 EQ.12 May 1997 Kagoshima hokuseibu SS [21] 1.16E+18 1.22E+18 6.0 0.1-1.0 1.0 none EQ.13 2011Shizuoka tobu SS [22] 1.12E+18 8.38E+17 5.9 0.05-0.2 4.0 6 EQ.14 1998 Iwate nairiku hokubu RV [23] 6.10E+17 7.53E+17 5.9 0.1-0.5 4.0 2 EQ.15 1997 Yamaguchi hokubu SS [20] 5.10E+17 5.66E+17 5.8 0.1-2.0 1.0 4 EQ.16 2013 Tochigi hokubu SS [24] 7.10E+17 5.54E+17 5.8 0.1-1.0 1.0 6 EQ.17 2013 Awaji island RV [25] 5.33E+17 5.47E+17 5.8 0.05-0.2 4.0 8 EQ.18 2005 Fukuoka seiho-oki (Max. after shock) SS [16] 2.81E+17 1.31E+17 5.4 0.1-1.5 1.0 6 SS: Strike Slip, RV: Reverse Slip, NM: Normal Slip * [5] Sekiguchi et al.(2002) TABLE 2: LIST OF EARTHQUAKES COMPILED BY SOMERVILLE ET AL. (1999) WITH THEIR INVERSION ANALYSIS CONDITIONS Mo Target F.Q. Sub fault Total number of No. NAME Mech. Reference * (Nm) MW Hz km 2 time windows Green's function 1 1992Landers SS Wald et al.(1994) 7.50E+19 7.2 0.077-0.5 7.5 6 2 1978Tabas RV Hartzell and Mendoza (1991) 5.80E+19 7.1 0.15-2.0 20.3 3 3 1989Loma Prieta OB Wald et al.(1991) 3.00E+19 7.0 0.1-1.0 4.0 3 4 1995Kobe SS Wald(1996) 2.40E+19 6.9 0.05-0.5 8.3 6 Rock & Soil 5 1983Borah Peak NM Mendoza and Hartzell (1998) 2.30E+19 6.9-0.5 10.7 1 6 1985Nahanni(12/23) RV Hartzell et al.(1994) 1.50E+19 6.8 0.2-3.0 6.3 15 7 1994Northridge RV Wald et al.(1994) 1.10E+19 6.7 0.1-1.0 1.9 3 Rock & Soil 8 1985Nahanni(10/05) RV Hartzell et al.(1994) 1.00E+19 6.6 0.2-3.0 4.6 10 9 1971San Fernando(SM) RV Heaton(1982) 7.00E+18 6.5 0.0-0.125 3.6 1 10 1979Imperial Valley SS Hartzell and Heaton(1983) 5.00E+18 6.4 0.1-1.0 7.5 3 11 1987Superstition Hills 3 SS Wald et al.(1990) 3.50E+18 6.3 0.1-3.0 1.2 3 12 1984Morgan Hill SS Hartzell and Heaton(1986) 2.10E+18 6.2 0.2-5.0 1.9 3 13 1986North Palm Springs OB Hartzell(1989) 1.80E+18 6.1-0.5 3.8 1 14 1987Whitter Narrows RV Hartzell and Iida(1990) 1.00E+18 6.0 0.2-3.0 1.0 2 15 1979Coyote Lake SS Liu and Helmberger(1983) 3.50E+17 5.7 0.0-2.0 0.2 1 SS: Strike Slip, RV: Reverse Slip, NM: Normal Slip, OB: Oblique Slip *Somerville et al. (1999) [2] 3. Scaling relationships of Outer and Inner Fault Parameters 3.1 Outer Fault Parameters We extracted the source parameters from the inversion results using the same criterion as Somerville et al. (1999) [3]. Table 3 [5]-[25] shows the extracted source parameters of eighteen recent crustal earthquakes. Fig.4(a) shows the relation between rupture area and seismic moment. We also included earthquakes that were examined by Stirling et al. (2002) [26] used in Murotani et al. (2015) [2] in Fig.4(a). We recognized that the empirical scaling relationship with rupture area versus seismic moment in this study has a good agreement with those of Somerville et al. (1999) [3] (M w <6.5) and Irikura and Miyake (2011) [1] (M w >6.5), respectively. Fig.4(b) shows the relation between average slip on source fault and seismic moment. The results of earthquakes (M w >7.2) examined by Tajima et al. (2013) [27] are also plotted in Fig.4(b). We also recognized that the empirical scaling relationship with average slip in this study also has a good agreement with those of Somerville et al. (1999) [3] as shown in Fig.4(b).

5 Best Practices in Physics-based Fault Rupture Models for Seismic magnitude (Mo) in the long-term evaluations of earthquakes for seismic hazard analysis in HERP (Headquarters of Earthquake Research Promotion, 2009 [28] ) has been estimated from the empirical relation (L - M J ; M J is JMA magnitude) by Matsuda (1975) [29]. Applying the empirical relation of M J - Mo (Takemura, 1990 [30] ), the empirical relation of L - M J is converted into the one of L - Mo. Assuming this empirical relation of L - Mo (HERP, 2009 [28] )and the averaged width of source fault W=18 km from inland crustal earthquakes in Japan, Hashimoto (2007) [31] recognized that the transformed scaling relation of S (=LxW) - Mo is consistent with the scaling relation by Irikura and Miyake (2011) [1]. Fig.4(c) shows the length of source fault extracted from the waveform inversions using strong motion data in comparison with empirical scaling relationship (L-Mo) of Takemura (1998) [32] and HERP(2009) [28]. Earthquakes smaller than M w 6.5 coincide with the scaling relation of Takemura (1998) [32], whereas those larger than M w 6.5 is consistent with the scaling relation of HERP(2009) [28]. Outer fault parameters in this study extracted from the waveform inversion results of eighteen recent crustal earthquakes (M w 5.4-6.9) in Japan are consistent with the three-stage scaling model so far proposed (Irikura and Miyake, 2011 [1] ; Murotani et al. 2015 [2] ). We also included earthquakes examined by Stirling et al.(2002) [26], Murotani et al.(2015) [2] and Tajima et al.(2013) [27] in Fig.4(a), 4(b), 4(c). Most of these earthquakes occurred outside Japan. Fig.5 shows the worldwide regressions between rupture source area and seismic moment (S-Mo) compiled by Stirling et al. (2013) [4] in comparison with the relationship in this study. Rupture area is derived from the regressions of Mo L (rupture length), assuming a constant fault width of 15 km. We recognized that the scaling relationship in this study coincide with that of Hanks and Bakun (2008) [33] in those compiled by Stirling et al. (2013) [4] with the exception for the magnitude range larger than around Mw7.4. Most earthquakes examined by Hanks and Bakun (2008) [33] occurred in California, USA. Source parameters extracted from the waveform inversion results of crustal earthquakes in Japan have a good accordance with regressions in USA. It is suggested that the difference of the regional tectonic environments between Japan and USA scarcely affects scaling relationship of source parameters. No. TABLE 3: OUTER AND INNER FAULT PARAMETERS EXTRACTED FROM THE INVERSION RESULTS OF RECENT CRUSTAL EARTHQUAKES NAME Reference Mo(F-net) Length Width Rupture Area Av. Slip Max. Slip Total Asperity Area Av. Asp. Slip Δσrup Δσasp No. Nm km km km 2 m m km 2 /Area m /Av.Slip MPa MPa EQ.1 1995 Hyogo nanbu [5] 3.30E+19 64 21 1303 0.79 4.01 244 0.19 1.74 2.20 3.1 * 16.6 EQ.2 EQ.3 2008 Iwate-Miyagi nairiku 2007 Noto hanto [6] 38 18 684 1.20 5.94 104 0.15 2.81 2.34 2.72E+19 39 18 702 1.31 6.07 112 0.16 3.22 2.45 [7] 40 18 720 1.44 6.20 120 0.17 3.68 2.56 [8] 30 16 480 1.09 5.07 84 0.18 2.32 2.13 1.36E+19 26 18 460 0.92 3.73 82 0.18 1.96 2.14 [9] 22 20 440 0.77 2.75 81 0.18 1.65 2.14 3.1 * 3.1 * 19.5 17.3 EQ.4 2011 Fukushima hamadori [10] 9.58E+18 40 16 640 0.52 2.51 144 0.23 1.25 2.40 3.1 * 13.8 [11] 30 24 720 0.91 2.68 64 0.09 2.13 2.34 [12] 30 18 540 0.56 2.66 92 0.17 1.44 2.57 EQ.5 2007 Niigata chuetsu-oki 9.30E+18 28 19 537 0.76 2.65 81 0.16 1.70 2.26 3.1* 19.5 [13] 25 17 425 0.54 2.12 100 0.24 1.27 2.35 [14] 28 18 504 1.22 3.28 72 0.14 2.16 1.77 EQ.6 2000 Tottori seibu [15] 8.62E+18 34 18 598 0.91 4.44 101 0.17 2.34 2.57 3.1 * 18.4 EQ.7 2005 Fukuoka seiho-oki [16] 7.80E+18 26 18 468 0.78 3.17 64 0.14 1.97 2.53 3.1 * 22.7 EQ.8 2004 Niigata chuetsu [17] 7.53E+18 28 18 504 0.67 3.08 84 0.17 1.38 2.06 3.1 * 18.6 EQ.9 2011Nagano-Niigata [18] 2.13E+18 22 14 308 0.43 1.19 72 0.23 0.88 2.05 1.0 4.1 EQ.10 2003 Miyagi hokubu [19] 1.53E+18 18 10 180 0.31 1.04 20 0.11 0.78 2.52 1.5 13.9 EQ.11 March 1997 Kagoshima hokuseibu [20] 1.40E+18 12 10 120 0.46 1.20 18 0.15 0.88 1.91 2.6 17.3 EQ.12 May 1997 Kagoshima hokuseibu [21] 1.22E+18 17 10 170 0.21 0.41 15 0.09 0.36 1.71 1.3 15.2 EQ.13 2011Shizuoka tobu [22] 8.38E+17 8 12 96 0.32 1.10 16 0.17 0.80 2.50 2.2 13.0 EQ.14 1998 Iwate nairiku hokubu [23] 7.53E+17 10 10 100 0.16 0.52 16 0.16 0.43 2.69 1.8 11.5 EQ.15 1997 Yamaguchi hokubu [20] 5.66E+17 8 14 112 0.14 0.83 18 0.16 0.41 2.93 1.2 7.2 EQ.16 2013 Tochigi hokubu [24] 5.54E+17 12 7 84 0.28 0.98 12 0.14 0.66 2.36 1.8 12.3 EQ.17 2013 Awaji island [25] 5.47E+17 10 6 60 0.20 0.71 12 0.20 0.46 2.30 2.9 14.3 EQ.18 2005 Fukuoka seiho-oki (Max. after shock) [16] 1.31E+17 8 8 64 0.14 0.51 9 0.14 0.33 2.36 0.6 4.4 * 3.1MPa: Fujii and Matsu'ura(2000) [53] Av.= 0.16 Av.= 2.33 Av.=13.2

6 Best Practices in Physics-based Fault Rupture Models for FIG.4(a). Relation between rupture area and seismic moment. Yellow symbols denote earthquakes included in this study. FIG.4(b). Relation between average slip and seismic moment. Yellow symbols denote earthquakes included in this study. FIG.4(c). Relation between length of source fault and seismic moment. Yellow symbols denote earthquakes included in this study.

7 Best Practices in Physics-based Fault Rupture Models for FIG.5. Three stage scaling model (black solid line) in comparison with regressions of Mo S (rupture area) compiled by Stirling et al. (2013). 1 st.-stage, Somerville et al. (1999); 2 nd.-stage, Irikura and Miyake (2011); 3 rd.-stage, Murotani et al. (2015). Rupture area is derived from the regression of Mo L (rupture length), assuming a constant fault width of 15 km [A22(ST), A23 & D2(WS n), and B1 & B2(NT)]. Identifiers (A, B, and D) in the legend correspond to the tectonic regime classification by Stirling et al. (2013). Abbreviation in parentheses refer to authors of the regressions: HB, Hanks and Bakun (2008); YM, Yen and Ma (2011); ST, Stirling et al. (2008); WS, Wesnousky (2008); NT, Nuttli (1983); JST, Johnston (1994); and VL, Villamor et al. (2001). Slip types: all, all slip type; n, normal; ds, dip-slip. Yellow squares, circles and triangle denote compiled earthquakes in this study (RV - Reverse, SS - Strike, NM - Normal). Blue circles denote earthquakes compiled by Somerville et al. (1999). Gray circles denote earthquakes compiled by Stirling et al. (2002) used in Murotani et al. (2015). Crosses denote large earthquakes compiled by Murotani et al. (2015). 3.2 Inner Fault Parameters Fig.6 shows the relation between combined area of asperities and seismic moment (Sa-Mo). We recognized that the slope for the scaling relationship of the combined area of asperities and seismic moment (Sa-Mo) in this study coincides with that of Somerville et al. (1999) [3]. However, the combined area of asperities are slightly smaller than the empirical scaling relationships of Somerville et al.(1999) [3]. The average ratio of the combined area of asperities to the rupture area (Sa/S) is about 0.16 (SD=0.04), which is smaller than the ratio of 0.22 by Somerville et al.(1999) [3]. Recent waveform inversions using high accuracy Green s function (velocity structure model) improve resolution of source models. It is suggested that improvement of the resolution of source model lowered the average ratio of Sa/S. Next we discuss the difference of the ratio of Sa/S for three categories: strike-slip (SS), reverse-slip (RV), and normal-slip (NM). The ratio of Sa/S is 0.15(SD=0.03) for strike-slip, 0.17(SD=0.04) for reverse-slip, and 0.23 for normal-slip, respectively. Only one earthquake with normal-slip was analyzed, so the standard deviation cannot be estimated. We do not recognize the large difference of the ratio of Sa/S for three categories faults (SS, RV, and NM). Next we compare the combined area of asperities with SMGAs (Strong Motion Generation Areas) estimated from the Empirical Green s Function method (EGF method; Irikura, 1986 [34] ). The target period range of the inversion analysis is long period (T > around 1s), while that of the EGF method is short period (T < around 1s). Table 4 [35]-[50] shows the inner fault parameters extracted from the EGF method. Unfortunately we could not collect SMGA models of two earthquakes (EQ.9, EQ.10 in Table 4 [35]-[50] ) in this study. Fig.7 shows a comparison of the combined area of asperities with that of SMGAs. We recognized that the

8 Best Practices in Physics-based Fault Rupture Models for combined area of asperities is consistent with SMGAs. So it is suggested that the broadband strong motion is generated from SMAGs for the seismic magnitude range from M w 5.4 to 6.9. FIG.6. Relation between combined area of asperities and seismic moment. Yellow symbols denote earthquakes included in this study. TABLE 4: INNER FAULT PARAMETERS EXTRACTED FROM THE FORWARD MODELING USING THE EGF METHOD No. NAME Reference Mo(F-net) SMGA Stress drop Stress drop Total SMGA Num. of (km 2 ) (MPa) (MPa) SMGA No. (Nm) km 2 SMGA1 SMGA2 SMGA3 SMGA1 SMGA2 SMGA3 average EQ.1 1995 Hyogo nanbu [35] 3.30E+19 * 304.0 3 176 64 64 8.6 16.3 8.6 10.6 EQ.2 2008 Iwate-Miyagi nairiku [36] 2.72E+19 92.5 2 46.24 46.24 13.8 13.8 13.8 [37] 52.7 2 39.69 12.96 25.8 10.3 EQ.3 2007 Noto hanto [38] 69.2 3 27.0 27.0 15.2 46.9 37.5 46.9 1.36E+19 85.0 [39] 146.0 2 98.01 48.00 9.4 15.6 20.5 [40] 97.9 3 51.84 23.04 23.04 20.0 20.0 10.0 EQ.4 2011 Fukushima hamadori [41] 9.58E+18 79.0 2 39.5 39.5 14.6 14.6 14.6 EQ.5 2007 Niigata chuetsu-oki [42] 85.9 3 30.25 30.25 25.40 23.7 23.7 19.8 9.30E+18 89.0 [43] 92.3 3 36.00 36.00 20.25 19.5 14.8 19.5 19.9 EQ.6 2000 Tottori seibu [44] 8.62E+18 57.6 2 28.8 28.8 28.0 14.0 19.8 EQ.7 2005 Fukuoka seiho-oki [45] 7.80E+18 41.8 1 41.82 10.7 10.7 EQ.8 2004 Niigata chuetsu [46] 7.53E+18 91.0 2 75 16 7.0 20.0 11.8 EQ.9 2011Nagano-Niigata None 2.13E+18 None EQ.10 2003 Miyagi hokubu None 1.53E+18 None EQ.11 March 1997 Kagoshima hokuseibu [47] 1.40E+18 42.0 1 42 17.0 ** 17.0 ** EQ.12 May 1997 Kagoshima hokuseibu [47] 1.22E+18 24.0 2 12 12 23.9 ** 23.9 ** 23.9 ** EQ.13 2011Shizuoka tobu [48] 8.38E+17 26.6 1 26.63 16.9 16.9 EQ.14 1998 Iwate nairiku hokubu [47] 7.53E+17 16.0 1 16 20.3 ** 20.3 ** EQ.15 1997 Yamaguchi hokubu [47] 5.66E+17 14.4 1 14.4 20.5 ** 20.5 ** EQ.16 2013 Tochigi hokubu [49] 5.54E+17 17.6 1 17.6 16.4 16.4 EQ.17 2013 Awaji island [50] 5.47E+17 8.1 1 8.12 9.0 9.0 EQ.18 2005 Fukuoka seiho-oki (Max. aftershock) [45] 1.31E+17 15.8 1 15.75 1.4 1.4 * Sekiguchi et al. (2002) [5] Av. = 13.6 ** Estimated stress drop using Circular Crack Model (Eshelby, 1957 [52] ) in this study We also estimated stress drop on asperity (Δσ asp ), as shown in Table 3 [5]-[25], using the following expression. Δσ asp = (S/Sa) x Δσ rup ( Madariaga, 1979 [51] ) For the first stage of self-similar scaling (M w <6.5), we calculated average stress drop (Δσ rup ) on entire source fault using Circular Crack Model (Eshelby, 1957 [52] ). Above the second stage (M w >6.5), the estimation of the stress drop assuming circular crack model might not be appropriate because the aspect ratio L/W is more than 2. Therefore, we calculate the stress drop following the model proposed by Fujii and Matsu ura (2000) [53]. Then average stress drop (Δσ rup ) is estimated to be 3.1MPa. Because they assumed only strike-slip fault type (SS)

9 Best Practices in Physics-based Fault Rupture Models for of crustal earthquake, 3.1MPa is the provisional stress drop for the exception fault type (RV; reverse-slip, NM; normal-slip) in this study. Fig.8(a) shows the comparison of average stress drop between in the combined area of asperities and in SMGAs. Average stress drop (13.2MPa) in the combined area of asperities roughly follows that (13.6MPa) in SMGAs. Fig.8(b) shows the stress drop contrast of asperities to SMGAs. The stress drop contrast is varying within about 0.5 to 2. The average ratio of the combined area of asperities to the rupture area (Sa/S) is smaller (0.16) than previous result (0.22; Somerville et al., 1999 [3] ). The averaged stress drop (13.2MPa) in the combined area of asperities also follows that (13.6MPa) in SMAGs. These are assumed to be caused by the progress of inversion analysis after the Hyogo-ken Nanbu earthquake not only with dense-network of strong motion observation sites (K-NET, KiK-net) but also using smaller mesh size (1-4km 2 ) and higher accuracy Green s function (velocity structure model) for waveform inversion. FIG.7. Comparison between combined area of asperities with that of SMGAs. FIG.8(a). Left: Average stress drop in combined area of asperities (red symbol) or in SMGAs (black symbol) for each earthquake. Vertical bar shows the standard deviation. Right: Average stress drop in combined area of asperities (red rhombus) or in SMGAs (black rhombus) for all earthquakes.

10 Best Practices in Physics-based Fault Rupture Models for FIG.8(b). Stress drop contrast between stress drop in combined area of asperities with that in SMGAs. 4. Conclusion Using the waveform inversion results of eighteen recent crustal earthquakes (M w 5.4-6.9) in Japan, which occurred after the 1995 Hyogo-ken Nanbu earthquake, we extracted the source parameters (entire rupture area (S) and the asperity area (Sa)) from the inverted heterogeneous slip distributions using the criterion of Somerville et al. (1999) [3]. We recognized that source parameters have a good agreement with the three-stage scaling model so far proposed (Irikura and Miyake, 2011 [1] ; Murotani et al. 2015 [2] ). The combined area of asperities over the entire rupture area (Sa/S) is about 0.16 in average for eighteen earthquakes, which is smaller than previous result (0.22) by Somerville et al. (1999) [3]. We compared the three stage scaling model with the worldwide regressions of Mo S (rupture area) compiled by Stirling et al. (2013) [4]. We also recognized that the scaling relationship in this study coincide approximately with that of Hanks and Bakun (2008) [33]. Most earthquakes examined by Hanks and Bakun (2008) [33] occurred in California, USA. Source parameters extracted from the waveform inversion results of crustal earthquakes in Japan have a good accordance with regressions in USA. It is suggested that the difference of the regional tectonic environments between Japan and USA scarcely affects scaling relationship of source parameters. 5. Acknowledgements We use the hypocentral information catalog of JMA (Japan Meteorological Agency), and the source information by F-net provided by NIED (National Research Institute for Earth Science and Disaster Prevention). We would like to thank Dr. Asano (DPRI), Dr. Sekiguchi (DPRI), Prof. Iwata (DPRI), Dr. Horikawa (AIST), Dr. Suzuki (NIED), Dr. Aoi (NIED), and Dr. Hikima (TEPCO) for provision of waveform inversion results. We also would like to thank Dr. Kurahashi (AIT), and Dr. Ikeda (Tobishima Co.) for provision of EGF modeling. This study was based on the 2014 research project 'Improvement for uncertainty of strong ground motion prediction' by the Nuclear Regulation Authority (NRA), Japan. References

11 Best Practices in Physics-based Fault Rupture Models for [1] IRIKURA, K., and MIYAKE, H., Recipe for predicting strong ground motion from crustal earthquake scenarios, Pure Appl. Geophys., 168(2011), 85-104. [2] MUROTANI, S., et al., Scaling relation of source parameters of earthquakes on inland crustal mega-fault systems, Pure Appl. Geophys., 172(2015), 1371-1381. [3] SOMERVILLE, P., et al., Characterizing crustal earthquake slip models for the prediction of strong ground motion, Seism. Res. Lett., 70(1999), 59 80. [4] STIRLING, M., et al., Selection of earthquake scaling relationships for seismic-hazard analysis, Bull. Seism. Soc. Am., 103(2013), 1-19. [5] SEKIGUCHI, H., et al., Source inversion for estimating the continuous slip distribution on a fault-introduction of Green's functions convolved with a correction function to give moving dislocation effects in subfaults, Geophys. J. Int., 150(2002), 377-391. [6] ASANO, K. and IWATA, T., Characterization of stress drops on asperities estimated from the heterogeneous kinematic slip model for strong motion prediction for inland crustal earthquakes in Japan, Pure Appl. Geophys., 168(2011), 105-116. [7] SUZUKI, W., et al., Rupture process of the 2008 Iwate Miyagi Nairiku, Japan, earthquake derived from near-source strong-motion records, Bull. Seism. Soc. Am., 100(2010), 256-266. [8] ASANO, K. and IWATA, T., Source-rupture process of the 2007 Noto Hanto, Japan, earthquake estimated by the joint inversion of strong motion and GPS data, Bull. Seism. Soc. Am., 101(2011), 2467-2480. [9] HORIKAWA, H., Characterization of the 2007 Noto Hanto, Japan, earthquake, Earth Planets Space, 60(2008), 1017-1022. [10] HIKIMA, K., Rupture process of the April 11, 2011 Fukushima Hamadori earthquake (Mj7.0) -Two fault planes inferred from strong motion and relocated aftershocks-, ZISIN2 (J. Seismol. Soc. Jpn.), 64(2012), 243-256 (in Japanese). [11] AOI, S., et al., Source process of the 2007 Niigata-ken Chuetsu-oki earthquake derived from near-fault strong motion data, Earth Planets Space, 60(2008), 1-5. [12] HIKIMA, K. and KOKETSU, K., Source process of the 2007 Chuetsu-oki earthquake inferred from far and near field waveforms and geodetic data, Japan Geoscience Union, Chiba(2008), S146-015 (in Japanese). [13] HORIKAWA, H., The 2007 Chuetsu-oki, Japan, Earthquake: rupture over a complicated fault system, Japan Geoscience Union, Chiba(2008), S142-P0025. [14] MIYAKOSHI, K. et al., Source modeling of the 2007 Niigata-ken Chuestu-oki earthquake, 7th General Assembly of Asian Seismological Commission and Seismological Society of Japan, Tsukuba(2008), X4-059. [15] IWATA, T. and SEKIGUCHI, H., Source model of the 2000 Tottori-ken seibu earthquake and near-source strong ground motion, The 11th Japan Earthquake Engineering Symposium, Tokyo(2002), 125-128. [16] ASANO, K. and IWATA, T., Source process and near-source ground motions of the 2005 West Off Fukuoka Prefecture earthquake, Earth Planets Space, 58(2006), 93-98. [17] ASANO, K. and IWATA, T., Source rupture process of the 2004 Chuetsu, Mid-Niigata Prefecture, Japan, earthquake inferred from waveform inversion with dense strong-

12 Best Practices in Physics-based Fault Rupture Models for motion data, Bull. Seism. Soc. Am., 99(2009), 123-140. [18] JMA, 12 March 2011 Nagano-ken hokubu earthquake, -Source process estimated from near-field strong motions-, Tokyo(2012), (in Japanese). http://www.data.jma.go.jp/svd/eqev/data/sourceprocess/event/20110315near.pdf [19] HIKIMA, K. and KOKETSU, K., Source processes of the foreshock, mainshock and largest aftershock in the 2003 Miyagi-ken Hokubu, Japan, earthquake sequence, Earth Planets Space, 56(2004), 87-93. [20] MIYAKOSHI, K. et al., Source modeling of inland earthquakes for the intermediate period range -Case study of the 1997 Kagoshima-ken Hokuseibu (March) and the 1997 Yamaguchi-ken Hokubu earthquakes-, Seismological Society of Japan, Fukuoka(2004), P065 (in Japanese). [21] HORIKAWA, H., Earthquake doublet in Kagoshima, Japan: rupture of asperities in a stress shadow, Bull. Seism. Soc. Am., 91(2001), 112-127. [22] JMA, 15 March 2011 Shizuoka-ken Tobu earthquake, -Source process estimated from near-field strong motions-, Tokyo(2012), (in Japanese). http://www.data.jma.go.jp/svd/eqev/data/sourceprocess/event/20110315near.pdf [23] MIYAKOSHI, K. et al., Source characterization of inland earthquakes in Japan using source inversion results, 12th World Conference on Earthquake Engineering, Auckland (2000), 1850(CD-ROM). [24] SOMEI, K. et al., Source model and strong ground motion simulation for the 2013 Northern Tochigi prefecture, Japan, earthquake, Japan Geoscience Union, Yokohama(2014), SSS23-P19 (in Japanese). [25] JMA, 13 April 2013 Awaji island earthquake, -Source process estimated from nearfield strong motions-, Tokyo(2013), (in Japanese). http://www.data.jma.go.jp/svd/eqev/data/sourceprocess/event/20130413near.pdf [26] STIRLING, M. D., et al., Comparison of earthquake scaling relations derived from data of the instrumental and preinstrumental era, Bull. Seism. Soc. Am., 92(2002), 812-830. [27] TAJIMA, R. et al., Comparative study on scaling relations of source parameters for great earthquakes in inland crusts and on subducting plate-boundaries, ZISIN2 (J. Seismol. Soc. Jpn.), 66(2013), 31-45 (in Japanese). [28] HEADQUARTERS FOR EARTHQUAKE RESEARCH PROMOTION (HERP), Predicting strong ground motions for identified earthquake scenarios (RECIPE), (2009), (in Japanese). http://www.jishin.go.jp/main/chousa/09_yosokuchizu/g_furoku3.pdf. [29] MATSUDA, T., Magnitude and recurrence interval of earthquakes from a fault, ZISIN (J. Seismol. Soc. Jpn.), 28(1975), 269-283 (in Japanese). [30] TAKEMURA, M., Magnitude-Seismic moment relations for the shallow earthquakes in and around Japan, ZISIN2 (J. Seismol. Soc. Jpn.), 43(1990), 257-265 (in Japanese). [31] HASHIMOTO, T., The surface length of earthquake fault and the moment magnitude, Japan Geoscience Union, Chiba(2007), S 145-013 (in Japanese).

13 Best Practices in Physics-based Fault Rupture Models for [32] TAKEMURA, M., Scaling law for Japanese intraplate earthquakes in special relations to the surface faults and damages, ZISIN2 (J. Seismol. Soc. Jpn.), 51(1998), 211-228 (in Japanese). [33] HANKS, T. C. and BAKUN, W. H., M log A observations of recent large earthquakes, Bull. Seism. Soc. Am., 98(2008), 490-494. [34] IRIKURA, K., Prediction of strong acceleration motions using empirical Green's function, The 7th Japan Earthquake Engineering Symposium, Tokyo(1986), 151-156. [35] KAMAE, K. and IRIKURA, K., Source model of the 1995 Hyogo-ken Nanbu earthquake and simulation of near-source ground motion, Bull. Seism. Soc. Am., 88(1998), 400-412. [36] KAMAE, K., Source model of the 2008 Iwate-Miyagi nairiku earthquake(m J 7.2) for estimating broad-band strong ground motion, Osaka(2008), (in Japanese). http://www.rri.kyoto-u.ac.jp/jishin/iwate_miyagi_1.html [37] KURAHASHI, S. et al., Source model of the 2007 Noto-Hanto earthquake(m W 6.7) for estimating broad-band strong ground motion, Earth Planets Space, 60(2008), 89-94. [38] MAEDA, T. et al., Source parameters of the 2007 Noto Hanto earthquake sequence derived from strong motion records at temporary and permanent stations, Earth Planets Space, 60(2008), 1011-1016. [39] YOSHIMI, M. and YOSHIDA, K., Site amplification and strong ground motion of the 2007 Noto Hanto, Japan, earthquake estimated from aftershock observation, Earth Planets Space, 60(2008), 161-167. [40] KAMAE, K. et al., Source model of the 2007 Noto hanto earthquake(m J 6.9) for estimating broad-band strong ground motion, Osaka(2007), (in Japanese). http://www.rri.kyoto-u.ac.jp/jishin/eq/notohantou/notohantou.html [41] SOMEI, K. et al., Estimation of Source Model and Strong Motion Simulation for the 2011 East Fukushima Prefecture Earthquake using the Empirical Green s Function Method, Seismological Society of Japan, Shizuoka(2011), P2-29 (in Japanese). [42] KURAHASHI, S. et al., Source model of the 2007 Niigata-ken Chuetu-oki earthquake using empirical Green s function (SE-dip model), Japan Geoscience Union, Chiba(2014), S146-P017 (in Japanese). [43] YAMAMOTO, Y. and TAKENAKA, H., Source modeling of the 2007 Niigataken Chuetsu-oki earthquake using the empirical Green s function method, ZISIN2 (J. Seismol. Soc. Jpn.), 62(2009), 47-59 (in Japanese). [44] IKEDA, T. et al., Source characterization and strong ground motion simulation of the 2000 Tottori-ken Seibu earthquake using the empirical Green s function method, J. Struct. Constr. Eng., AIJ, 561(2002), 37-45 (in Japanese). [45] SUZUKI, W. and IWATA, T., Source model of the 2005 west off Fukuoka prefecture earthquake estimated from the empirical Green's function simulation of broadband strong motions, Earth Planets Space, 58(2006), 99-104. [46] KAMAE, K. et al., Source model composed of asperities for the 2004 Mid Niigata Prefecture, Japan, earthquake (M JMA =6.8) by the forward modeling using the empirical Green's function method, Earth Planets Space, 57(2005), 533-538.

14 Best Practices in Physics-based Fault Rupture Models for [47] MIYAKE, H. et al., Source characterization for broadband ground-motion simulation: kinematic heterogeneous source model and strong motion generation area, Bull. Seism. Soc. Am., 93(2003), 2531 2545. [48] SOMEI, K. et al., Source model of the 2011 East Shizuoka prefecture, Japan, earthquake by using the empirical Green s function method, Japan Geoscience Union, Chiba(2012), SSS26-P27 (in Japanese). [49] SOMEI, K. et al., Source model and strong ground simulation for the 2013 Northern Tochigi prefecture, Japan, earthquake, Japan Geoscience Union, Yokohama(2014), SSS23-P19 (in Japanese). [50] KURAHASHI, S., Source model of the 2013 Awaji island earthquake (M J 6.3) by using the empirical Green s function method, personal com. [51] MADARIAGA, R., On the relation between seismic moment and stress drop in the presence of stress and strength heterogeneity, Journal of Geophysical Research, 84(1979), 2243-2250. [52] ESHELBYE, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proceedings of the Royal Society, A241(1957), 376-396. [53] FUJII, Y. and MATSU URA, M., Regional difference in scaling laws for large earthquakes and its tectonic implication, Pure Appl. Geophys., 157(2000), 2283-2302.