Scaling relations of seismic moment, rupture area, average slip, and asperity size for M~9 subduction-zone earthquakes

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1 GEOPHYSICAL RESEARCH LETTERS, VOL. 4, 7 74, doi:1.12/grl.976, 213 Scaling relations of seismic moment, rupture area, average slip, and asperity size for M~9 subduction-zone earthquakes Satoko Murotani, 1 Kenji Satake, 1 and Yushiro Fujii 2 Received 21 August 213; revised 17 September 213; accepted 19 September 213; published 4 October 213. [1] Scaling relations for seismic moment M, rupture area S, average slip D, and asperity size S a were obtained for large, great, and giant (M w = ) subduction-zone earthquakes. We compiled the source parameters for seven giant (M w ~9) earthquakes globally for which the heterogeneous slip distributions were estimated from tsunami and geodetic data. We defined S a for subfaults exhibiting slip greater than 1. times D. Adding 2 slip models of 1 great earthquakes around Japan, we recalculated regression relations for 32 slip models: S = M 2/3, D = M 1/3, S a = M 2/3,andS a /S =.2, where S and S a are in square kilometers, M is in newton meters, and D is in meters. These scaling relations are very similar to those obtained by Murotani et al. (28) for large and great earthquakes. Thus, both scaling relations can be used for future tsunami hazard assessment associated with a giant earthquake. Citation: Murotani, S., K. Satake, and Y. Fujii (213), Scaling relations of seismic moment, rupture area, average slip, and asperity size for M~9 subduction-zone earthquakes, Geophys. Res. Lett., 4, 7 74, doi:1.12/grl Introduction [2] Three giant (M~9) megathrust earthquakes have occurred since 24: the 211 off the Pacific coast of Tohoku (211 Tohoku), 21 Maule (Chile), and 24 Sumatra- Andaman earthquakes (Figure 1). Many seismological studies have estimated the slip distributions of these earthquakes; yet, no scaling relations of source parameters have been proposed for M~9 earthquakes. Four other M~9 megathrust earthquakes occurred in the 19s and 196s: the 192 Kamchatka, 197 Aleutian, 196 Chile, and 1964 Alaska earthquakes. Although few high-quality seismic data are available for these earthquakes, their slip distributions and seismic moments have been estimated using tsunami waveforms and geodetic data [e.g., Fujii and Satake, 213]. Such inversions have been applied to the recent giant earthquakes [Fujii and Satake, 27, 213; Satake et al., 213], thus providing slip distributions for all seven giant earthquakes in the same format. [3] The ground motion and tsunami heights associated with giant earthquakes are controlled by the size and 1 Earthquake Research Institute, University of Tokyo, Bunkyo-ku, Tokyo, Japan. 2 International Institute of Seismology and Earthquake Engineering, Building Research Institute, Tsukuba, Ibaraki, Japan. Corresponding author: S. Murotani, Earthquake Research Institute, University of Tokyo, Yayoi, Bunkyo-ku, Tokyo , Japan. (s-muro@eri.u-tokyo.ac.jp) 213. American Geophysical Union. All Rights Reserved /13/1.12/grl distribution of asperities. Therefore, an understanding of the scaling relations between the various parameters of giant earthquakes is essential for accurate assessment of future earthquake hazards. In Japan, the tsunami damage caused by the 211 Tohoku earthquake (M w 9.) raised concerns regarding the possible occurrence of a giant earthquake along the Nankai Trough; accordingly, assessment of tsunami and strong ground motions that may result from such an earthquake has been initiated [e.g., Central Disaster Management Council; nankai_trough/nankai_trough_top.html]. Similarly, tsunami hazard maps have been prepared for a giant earthquake along the Cascadia subduction zone in the Pacific Northwest of the United States [e.g., Pacific Northwest Seismic Network; [4] Various scaling relations of rupture area and seismic moment have been proposed for heterogeneous slip distributions [e.g., Somerville et al., 1999]. For example, by characterizing source heterogeneity resulting from slip inversions, Murotani et al. [28] (hereafter referred to as M8) estimated the scaling relations for seismic moment (M in N m), rupture area (S in km 2 ), total average slip (D in m), and asperity area (S a in km 2 ) using 26 slip models of 11 plate-boundary earthquakes with M w in and around Japan. Blaser et al. [21] (hereafter B1) compiled the source parameters of 23 earthquakes with M w for global subduction zones, obtaining a slightly different relation between S (L W) and M w. Similarly, Strasser et al. [21] (hereafter S1) compiled the source parameters of 8 earthquakes with M w for global subduction zones, obtaining a scaling relation different from that in both M8 and B1. Both B1 and S1 attributed these differences in scaling relations to regional differences and the error of the inversion results, although the studies estimated S in different ways: M8 used only waveform and geodetic data inversion results, whereas B1 and S1 included data from aftershock areas. [] In this paper, we first compile the source parameters estimated by the inversion of tsunami waveforms and geodetic data for the seven M~9 earthquakes. Then, we redefined the rupture area S for these earthquakes and combined these data with the 2 earthquake source models with M w used by M8 and conduct regression analysis using this data set. We also compare the new scaling relations with those obtained previously by M8, B1, and S1. 2. Slip Models and Characterization [6] We examined the slip distributions of seven megathrust earthquakes: the 211 Tohoku earthquake (M w 9.), the 21 Maule earthquake in Chile (M w 8.8), the 24

2 Figure 1. Plate-boundary earthquakes of M w 8. (white stars) that have occurred since 19 from USGS and the seven earthquakes compiled in this paper (black stars). Solid lines indicate transform and spreading plate boundaries. Dashed lines represent subduction boundaries. Sumatra-Andaman earthquake (M w 9.1), the 1964 Alaska earthquake (M w 9.1), the 196 Chile earthquake (M w 9.2), the 197 Aleutian earthquake (M w 8.6), and the 192 Kamchatka earthquake (M w 8.7) (Figure 1 and Table 1). For these earthquakes, inversion of tsunami waveforms or joint inversion of tsunami and geodetic data was made to estimate the slip distributions. The moment magnitude of the 196 Chile earthquake (M w 9.2) is somewhat lower than that estimated from seismic data (M w 9., e.g., Kanamori [1977], as discussed in Fujii and Satake [213]). [7] We first defined the rupture area S as the area of subfaults with slip greater than m, estimated according to the non-negative least-squares method. Inversion analysis typically includes some uncertainties and has produced different slip distributions in different studies; however, the rupture area is similar [e.g., Beresnev, 23]. M8 derived scaling relations using 26 slip models of plate-boundary earthquakes following the procedure given by Somerville et al. [1999], in which the rupture area is trimmed to estimate fault size and the asperity regions are defined from the slip distribution. However, the subfault size adopted in the tsunami and geodetic inversion method is relatively large and sometimes variable, making it difficult to apply the trimming procedure. Here, the average slip D and the total seismic moment M were computed using the rigidity assumed in the original literature (see Table 1). [8] Next, we examined the slip distribution on each subfault. The largest slip (38 m) occurred for the 211 Tohoku earthquake, followed by the 196 Chile earthquake (3 m), and the 24 Sumatra-Andaman earthquake (2 m). In fact, the slip distributions of these earthquakes exhibit exponential decay (Figure 2) when they are arranged in descending order. We also obtained similar distribution for large and great earthquakes in M8, which may indicate that all earthquakes exhibit self-similar structure regardless of size. The maximum slip of each earthquake was 2 to 4 times the average slip D. Moreover, the total area of subfaults with average slip or greater ranged 2 2% of S, and that with slip of more than 1. D was 16 32%. [9] We defined the asperity area S a for subfaults with slip greater than 1. D. M8 demonstrated that such definition resulted in a good fit for the complex asperities of a plateboundary earthquake. Figure 3 presents examples of the definition of rupture area and asperity area for the 211 Tohoku and 197 Aleutian earthquakes. For the 211 Tohoku earthquake (Figures 3a and 3b), 44 subfaults were considered, each with dimensions of km km. However, seven of these subfaults were found to exhibit zero slip; therefore, it can be assumed that the rupture area consisted of 37 subfaults with an average slip of 1.6 m. Ten subfaults exhibited slip of more than 1.9 m ( m); these subfaults were defined as the asperity region. For the 197 Aleutian earthquake, the rupture area can be separated into three discontinuous regions (Figures 3c and 3d). Of the 13 subfaults studied (including 11 large and 2 small subfaults with dimensions of 1 km 1 km and km 7 km, respectively), 6 subfaults exhibited zero slip; therefore, the rupture area consisted of 7 subfaults with an average slip of 3.1 m. Two subfaults exhibited slip greater than 4.7 m ( m), and these were defined as the asperity region in this study. The source parameters defined in this manner for all seven earthquakes are compiled in Table 1. We also applied the same procedure to 2 models of large and great earthquakes (M w ) compiled by M8, except for the 1968 Tokachi-oki earthquake, for which subfaults data were unavailable. 3. Scaling Relations for M9 Earthquakes [1] We conducted regression analyses for the source parameters of the entire data set, which includes both the Table 1. Fault Parameters Obtained From Tsunami and Geodetic Inversion Earthquake Data a Sori b S c M d 211 Tohoku T Maule T, G Sumatra-Andaman T Alaska T, G Chile T, G Aleutian T Kamchatka T M w e D f S a g μ h Reference i a T: tsunami data, G: geodetic data. b Rupture area originally adopted by the tsunami and geodetic data inversion (1 3 km 2 ). c Rupture area (1 3 km 2 )isdefined in this paper. d Seismic moment (1 22 Nm)isdefined in this paper. e Moment magnitude is defined in this paper. f Average slip (m) is defined in this paper. g Asperity area (1 3 km 2 )isdefined in this paper. h Rigidity (GPa) assumed in the references. i 1, Satake et al. [213]; 2, Fujii and Satake [213]; 3, Fujii and Satake [27]; 4, Johnson et al. [1996];, Johnson et al. [1994]; and 6: Johnson and Satake [1999]. 71

3 Average x 1. Average 1 1 newly compiled data set for the seven giant earthquakes and the recompiled data set for the 2 large and great earthquakes. We plotted these data for comparison with the scaling relations derived by M8 (Figure 4). [11] Figure 4a illustrates the relation of seismic moment and rupture area. First, we conducted a regression analysis for logm and logs and achieved the following result: logs = 8.97 (±.82) +.62 (±.4) logm. The slope (i.e., the exponent of M ) is very close to 2/3, suggesting Figure 2. Slip distribution for the seven giant earthquakes compiled in this paper. The subfaults for each earthquake are rearranged with slip amounts in descending order. that the rupture area was proportional to two-thirds the power of seismic moment; this agrees with results presented in Somerville et al. [1999] and M8. The constrained regression line can be defined as S = M 2/3, with a standard deviation SD (±σ) of 1.4. Six of the studied earthquakes are plotted below the regression line; however, except for the 196 Chile and 211 Tohoku earthquakes, all earthquakes are within SD of the regression line. M8 obtained a regression coefficient of 1.48 and SD of 1.61, which are similar to those obtained in the present study. Alternatively, if we substitute the M8 coefficient (1.48) into our data set, the SD becomes 1., which is almost identical to the value obtained in this study. [12] Figure 4b illustrates the scaling relation of seismic moment and average slip. The regression analysis for logm and logd yielded logd = 7.7 (±.96) +.3 (±.4) logm. The slope is very close to 1/3, suggesting that the rupture area is proportional to one-third the power of seismic moment. The constrained regression line can be represented by D = M 1/3 with SD of In this case, six earthquakes are plotted above the regression line and all are within SD except the 211 Tohoku earthquake. Furthermore, the coefficient (1.66) is similar to that obtained by M8 (1.48), and the calculated SD is almost identical to that obtained by M8 (1.66). [13] Figure 4c presents the scaling relation of seismic moment and asperity area. The regression analysis for logm and logs a yielded logs a = 1.98 (±1.6) +.69 (±.) logm. Constraining the slope to 2/3 produced a regression line that can be defined as follows: S a = M 2/3, with SD of Here, all of the studied earthquakes except the 197 Aleutian earthquake were plotted within SD. It is notable that relatively few subfaults were associated with the 197 Aleutian earthquake; accordingly, the definition of the asperity area is associated with relatively large errors (see Figure 2). Regardless, the coefficient obtained here (2.81) and by M8 (2.89) are very similar, with almost identical values of SD for the two coefficients. [14] Figure 4d illustrates the scaling relation of rupture area and asperity area. The regression line can be represented by slip(m) 2km (b) 2km (c) Alaska 8 (a) Japan Japan 2km (d) Slip > m Slip > D x 1. m Alaska Slip > m Slip > D x 1. m 2km slip(m) Figure 3. Examples of slip distributions of the 211 Tohoku and 197 Aleutian earthquakes. (a and c) The slip distributions obtained by Satake et al. [213] and Johnson et al. [1994], respectively. (b and d) The rupture areas (slip > m) and asperity areas (slip > 1. times D) defined in the present study. White stars indicate the epicenters. 72

4 Figure 4. Scaling relations of the source parameters of M~9 and smaller earthquakes using the method adopted in the present study (red lines) and those obtained by M8 using only smaller earthquakes. (a) Rupture area S versus seismic moment M.(b) Average slip D versus seismic moment M. (c) Asperity area S a versus seismic moment M. (d) Asperity area S a versus rupture area S. Black lines represent the regression lines of M8. Open circles indicate the earthquakes used in M8 with rupture and asperity areas delineated using the new definitions. Red dashed lines represent the standard deviation on a log-log scale. S a /S =.2, with SD of All seven earthquakes were plotted very close to the regression line, although the 197 Aleutian and 196 Chile earthquakes were plotted slightly outside the range of SD. The ratio and SD obtained are identical to those obtained by M8. [1] The regression coefficients of the scaling relations estimated in the present study are almost the same as those given by M8, although our standard errors are slightly smaller (Table 2). Moreover, the differences in the definition of rupture area S and asperity area S a between our method and that of M8 appear to have little effect on the obtained scaling relations, suggesting that the scaling relations determined previously for large and great (i.e., M w = ) earthquakes are applicable to our entire data set, including the seven giant earthquakes. 4. Discussion [16] We have compared the scaling relations of seismic moment and rupture area obtained in the present study (which are almost identical to those presented by M8) with those obtained by B1 and S1 (Figure ). The regression lines obtained by B1 and S1 were plotted below that obtained by M8, indicating that B1 and S1 predict smaller source areas for earthquakes of the same size. Moreover, the slope of the regression line varies between Table 2. Scaling Relations and Standard Deviations Original Regression of Murotani et al. [28] New Regression of This Study SD S = /3 M S = /3 M 1.4 D = /3 M D = /3 M 1.64 S a = /3 M S a = /3 M 1.72 S a /S = S a /S = Magnitude range, M w SD M a a Standard deviation of M8 used 26 earthquakes for M -S and M -D and 14 earthquakes for M -S a and S-S a, respectively. b Standard deviation calculated for the 32 earthquakes (seven giant earthquakes in this paper and 2 earthquakes of M8 with definitions of this paper) with the fixed coefficients as those estimated by M8. 73 SD M32 b

5 Figure. Comparison of the scaling relation of seismic moment and rupture area between M8 (blue line, extended to M w 9.2), B1 (gray line and squares), S1 (black line), and this study (green circles). The line obtained in the present study is almost identical to that obtained by M8. The definition of rupture area is different for B1, S1, M8, and the present study. The data set used by M8 includes only earthquakes around Japan. studies: we obtained a slope of 2/3, whereas S1 and B1 obtained slopes of.637 and.713, respectively. Because of this difference, the lines obtained by M8 and S1 are closer at a smaller M w (~6.), whereas those obtained by B1 and S1 are closer at a larger M w (~9). We believe that the differences between the results obtained by B1, S1, and M8 likely originated from the use of different data sets (i.e., M8 and the present study used only Japanese data for smaller M w ) and different definitions of source area (i.e., M8 and the present study used only slip distribution, whereas B1 and S1 also included aftershock areas). [17] Scaling relations such as those described in this study can be used to assess the tsunami hazard associated with future giant earthquakes. For example, the rupture area S can be estimated based on these scaling relations if the size of the earthquake (either M w or M ) is known. Conversely, earthquake size can be estimated from a possible source area. D and S a can also be estimated using these scaling relations, although the locations of asperities cannot; therefore, asperities must be located after considering seismotectonic features or must be placed randomly at various locations within the source area. Once all fault parameters (including asperity location) have been specified, coastal tsunami heights can be computed through numerical tsunami simulation [e.g., Satake, 27]. [18] Scaling relations for giant earthquakes may not be applicable for source parameters used in the prediction of short-period (i.e., less than a few seconds), strong ground motion. For example, the strong motion generation areas of the 211 Tohoku earthquake were located at a deeper location along the plate interface closer to land, which is separated from the large slip area [Asano and Iwata, 212]. Furthermore, the magnitude (M J ) of the 211 Tohoku earthquake was estimated from seismic waves by the Japan Meteorological Agency to be only 8.4, which is much smaller than M w 9.. That is, the strong motion from this giant earthquake can be estimated by assuming a great earthquake of M J Conclusions [19] We examined scaling relations for large, great, and giant (M w = ) earthquakes. In particular, we redefined the rupture area S and asperity region S a for seven giant (M~9) earthquakes and 2 models of large and great (M w = ) earthquakes and conducted regression analyses for the source parameters S, M, D, ands a. The regression lines correspond very closely to scaling relations obtained previously for large and great plate-boundary earthquakes (see M8); moreover, the standard deviations obtained in this study are almost identical to those obtained using the regression coefficients given by M8. This suggests that such scaling relations are insensitive to the definition of rupture and asperity areas and, perhaps most importantly to earthquake size. Both scaling relations are applicable to M~9 megathrust earthquakes, indicating that they can be used for tsunami modeling, particularly for the prediction of tsunami height or inundation areas associated with giant megathrust tsunamigenic earthquakes. [2] Acknowledgments. We are grateful to P. G. Somerville and H. Miyake, who read the manuscript and provided valuable comments. We thank the editor and two anonymous reviewers for improvements made to the manuscript. Figures were produced using GMT [Wessel and Smith, 1998]. This research was supported by the Special Project for Research on earthquake and tsunami off the Pacific coast of Tohoku from the Ministry of Education, Culture, Sports, Science and Technology and KAKENHI (grants and ) from the Japan Society for the Promotion of Science. [21] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper. References Asano, K., and T. Iwata (212), Source model for strong ground motion generation in the frequency range.1 1 Hz during the 211 Tohoku earthquake, Earth Planets Space, 64, Beresnev, I. A. (23), Uncertainties in finite-fault slip inversions: To what extent to believe? (A critical review), Bull. Seismol. Soc. Am., 93, Blaser, L., F. Krüger, M. Ohrnberger, and F. 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