PUBLICATIONS. Geophysical Research Letters

PUBLICATIONS Geophysical Research Letters RESEARCH LETTER Key Points: The 2011 flow depth was at least 1 m at the most landward tsunami deposit The revised estimate of the AD 869 Jogan earthquake magnitude is at least Mw 8.6 Paleoearthquake size can be estimated from tsunami deposits and flow depth Supporting Information: Readme Table S1 Table S2 Figure S1 Correspondence to: Y. Namegaya, yuichi.namegaya@aist.go.jp Citation: Namegaya, Y., and K. Satake (2014), Reexamination of the A.D. 869 Jogan earthquake size from tsunami deposit distribution, simulated flow depth, and velocity, Geophys. Res. Lett., 41, 2297 2303, doi:. Received 11 NOV 2013 Accepted 14 JAN 2014 Accepted article online 6 JAN 2014 Published online 1 APR 2014 Reexamination of the A.D. 869 Jogan earthquake size from tsunami deposit distribution, simulated flow depth, and velocity Yuichi Namegaya 1 and Kenji Satake 2 1 Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan, 2 Earthquake Research Institute, University of Tokyo, Tokyo, Japan Abstract The rupture parameters and magnitude of the A.D. 869 Jogan earthquake, a predecessor of the 2011 Tohoku earthquake, were previously estimated by matching tsunami deposit distributions with simulated inundation areas. The tsunami inundation associated with the 2011 Tohoku earthquake, however, extended farther inland than the sandy tsunami deposits. Numerical simulation of the 2011 tsunami indicated that flow depths and velocities were approximately 1 m and 0.6 m/s, respectively, at the most inland sand deposit sites on the Ishinomaki and Sendai plains. While these values depend on the assumed bottom roughness, we used these values to compare tsunami deposits and inundation simulation of the 869 Jogan earthquake from both uniform-slip and 2011-type variable-slip fault models. The results showed that the rupture length of the 869 Jogan earthquake was at least 200 km and its minimum moment magnitude was 8.6. 1. Introduction The 11 March 2011 Tohoku earthquake (M w 9.0) (Figure 1a) is the largest instrumentally recorded earthquake to occur in the Japanese islands, and it caused a devastating tsunami in the Tohoku region. The maximum coastal tsunami height was nearly 40 m at the Sanriku coast [e.g., Mori et al., 2012], and the maximum inundation distance from the coast exceeded 5 km on both the Ishinomaki and Sendai plains [e.g., Nakajima and Koarai, 2011]. Tsunami inundation areas computed with a fault model successfully reproduced the actual inundation areas mapped by using aerial photographs and field surveys [e.g., Satake et al., 2013]. Mapping of the modern tsunami deposits on these plains [Abe et al., 2012; Chague-Goff et al., 2012; Goto et al., 2011; Sawai et al., 2012; Shishikura et al., 2012], however, indicated that no sandy tsunami deposits were found near the inundation limit; in fact, the distance from the coast of tsunami inundation was on average 1.4 to 1.6 times the distance to the most landward sandy tsunami deposit. A similar distance exceedance ratio has been reported for the 1700 Cascadia earthquake [Hemphill-Haley, 1996], the 2009 Samoa earthquake [Apotsos et al., 2011], and the 1960 [Atwater et al., 2013] and 2010 Chile earthquakes [Morton et al., 2011] suggesting that there exist certain threshold values of tsunami flow depth and velocity for sand transport. The A.D. 869 Jogan earthquake in northeastern Japan was a predecessor of the 2011 Tohoku earthquake. According to a historical document reporting this disaster recorded near Sendai, the strong ground shaking and the ensuing tsunami caused 1000 fatalities [Imamura, 1934]. Tsunami deposits attributed to this earthquakehavebeenfoundontheishinomakiplain[sawai et al., 2012] and the Sendai Plain [Minoura and Nakaya, 1991; Minoura et al., 2001; Sawai et al., 2012; Sugawara et al., 2013] (Figures 1b 1d). The A.D. 869 tsunami sandy deposits commonly extend at least 1.5 km inland from the A.D. 869 shoreline, which is 1 1.5 km inland from the present shoreline and marked by the seaward limit of volcanic ash deposited in A.D. 915. The distribution of these tsunami deposits has been used to estimate the size and fault parameters of the Jogan earthquake. Sugawara et al. [2013] evaluated shear stresses on eroded surfaces of the tsunami deposits and concluded that a fault model 200 km long and 85 km wide with 6.1 m of slip (M w 8.3) could reproduce the estimated shear stresses. Sawai et al. [2012] examined various fault models (including an outer-rise normal fault, a tsunami earthquake [Kanamori, 1972] on the shallow plate interface near the Japan Trench, an active fault in Sendai Bay, and interplate faults) and concluded that an interplate fault, 200 km long by 100 km wide, that slipped 7 m (M w 8.4) could produce a tsunami inundation sufficient to cover the distribution of the known tsunami deposits. However, the model proposed by Sawai et al. [2012] might underestimate the magnitude of the A.D. 869 earthquake because of its assumption that the landward limit of the sandy tsunami deposits and the computed inundation limit are the same. NAMEGAYA AND SATAKE 2014. American Geophysical Union. All Rights Reserved. 2297

Figure 1 NAMEGAYA AND SATAKE 2014. American Geophysical Union. All Rights Reserved. 2298

Figure 2. (a) Comparison of calculated tsunami heights using n = 0.045 m 1/3 s with measured heights [Mori et al., 2012] of the 2011 tsunami on the Ishinomaki and Sendai plains. The locations used for the comparisons are shown in Figures 1b 1d. (b) Calculated flow depths (blue dots) at the most landward sandy deposits of the 2011 tsunami using n = 0.030, 0.040, 0.045, and 0.050 m 1/3 s. The error bars show range of the flow depths calculated from the computed values with n = 0.045 m 1/3 s and the error factor κ of 1.25. The flow depths (red dots) were also calculated at the most landward 869 tsunami deposits on the A.D. 869 topography from the 2011 earthquake model [Satake et al., 2013] using n = 0.030 and 0.040 m 1/3 s. (c) The geometric average K and geometric standard deviation κ [Aida, 1978] of the measured and calculated tsunami heights in Figure 2a for various Manning s roughness coefficients, n. The best match between the heights was obtained for n = 0.045 m 1/3 s(k = 1 and κ = 1.25). (d) Calculated depth-averaged velocities (blue dots) at the most landward sandy deposits of the 2011 tsunami using n = 0.030, 0.040, and 0.045 m 1/3 s. The flow velocities (red dots) were also calculated at the most landward 869 tsunami deposits on the A.D. 869 topography from the 2011 earthquake model [Satake et al., 2013] using n = 0.030 and 0.040 m 1/3 s. In this study, we first computed the tsunami inundation of the Sendai and Ishinomaki plains caused by the 2011 Tohoku earthquake and calculated the tsunami flow depths and velocities at the most landward 2011 sandy deposits. We estimated the threshold values of flow depth and velocity necessary to transport the sand forming the deposit. We next computed the tsunami inundations indicated by various fault models of the 869 Jogan earthquake and compared them with the distribution of the A.D. 869 tsunami deposits using the estimated threshold values of flow depth and velocity. Another way to conduct this comparison would be to Figure 1. (a) Slip distribution of the 2011 earthquake [Satake et al., 2013]. The blue rectangle shows the uniform-slip model for the 869 Jogan earthquake (a 200 km long fault with a top depth of 31 km). (b) Computed flow depths on Ishinomaki Plain using the 2011 earthquake model [Satake et al., 2013]. Locations of sandy deposits of the A.D. 869 (red circles) [Sawai et al., 2012] and 2011 tsunamis (blue circles) [Sawai et al., 2012; Shishikura et al., 2012] are also shown. Labels in red and blue indicate the transects for the A.D. 869 and 2011 tsunamis, respectively. Triangles indicate the locations of 2011 tsunami height measurements [Mori et al., 2012] more than 300 m from the shoreline and within 300 m of the A.D. 869 and 2011 transects. Calculated and measured tsunami heights at these locations are compared in Figure 2a. Black solid lines indicate the 2011 inundation limit [Nakajima and Koarai, 2011], and dashed lines indicated the shoreline in A.D. 869 [Sawai et al., 2012]. Orange lines are artificially elevated roads, such as the Sanriku expressway. Ground with an elevation of more than 10 m is defined as upland and colored gold. (c) Northern Sendai Plain. (d) Southern Sendai Plain. The color scales for flow depth are the same in Figures 1b, 1c, and 1d. (e) Transect Sa for the 2011 tsunami, showing the current topography and computed tsunami inundation. (f) Transect S1 for the A.D. 869 tsunami, showing the topography in A.D. 869 and the computed tsunami inundation. NAMEGAYA AND SATAKE 2014. American Geophysical Union. All Rights Reserved. 2299

Figure 3. Flow depths and velocities calculated from the A.D. 869 uniform-slip models with a fault depth of 31 km. (a) Assumed fault models. The fault parameters of the subfaults are summarized in Table S2. Black blocks indicate rupture areas (lengths of 100, 200, 300, and 400 km) with slip amounts of 6, 9, and 12 m. (b) Calculated flow depths at each most landward sandy deposit of the A.D. 869 tsunami. If the computed flow depth was less than 0.01 m or the tsunami did not inundate that site, symbols are plotted at 0.01 m. (c) Calculated depth-averaged flow velocities at the most landward sandy deposits of the A.D. 869 tsunami. use the distance exceedance ratio in the numerical simulation. However, we cannot assume that the distance exceedance ratios were the same for the A.D. 869 and 2011 tsunamis because many variables were different, such as the coastline locations, the roughness due to vegetation and buildings in the tsunami s path, and particularly the topography along the inundation profile as shown in Figures 1e and 1f. Finally, on the basis of our findings, we reexamined the fault parameters and magnitude of the 869 Jogan earthquake. 2. Flow Depth and Velocity for the 2011 Tsunami We calculated the tsunami inundation of the Sendai and Ishinomaki plains from a 2011 fault model estimated by inversion of tsunami waveforms [Satake et al., 2013] as the initial condition. We calculated the flow depth and velocity, important parameters for the physics of sediment transport, at the location of the farthest inland sandy deposits (Figures 1b 1d) [Sawai et al., 2012; Shishikura et al., 2012]. For the tsunami computation, we used basically the same method as Goto et al. [1997] (summarized in Table S1). Flow velocities at the locations of tsunami sandy deposits are strongly dependent on the assumed bottom friction [Jaffe et al., 2012]. We assumed 21 different spatially constant values of Manning s roughness coefficient, n, ranging from 0.030 to 0.050 m 1/3 s. We compared measured [Mori et al., 2012] and computed tsunami heights (above sea level at the time of the tsunami arrival) at 101 sites on the plains by using the geometric average K and geometric standard deviation κ (used as the error factor) [Aida, 1978]. The best match between the measured and computed heights of the 2011 tsunami was obtained by using n = 0.045 m 1/3 s, for which K and κ were calculated as 1.01 and 1.25, respectively (Figures 2a and 2c). The inundation simulations using n = 0.045 m 1/3 s indicated that the flow depth and velocity were at least 1.0 m and 0.6 m/s, respectively, at the most landward sandy deposits of 2011 tsunami (Figures 2b and 2d) along 15 transects (Figures 1b 1d). Given the error factor of 1.25, the possible range of the computed flow depths varies along each transect (bars in Figure 2b), roughly corresponding to n = 0.05 to 0.04 m 1/3 s. We also computed using smaller and often-used values of Manning s roughness coefficient (n = 0.03 m 1/3 s) and found that they produce larger flow depths and velocity (Figures 2b and 2d). NAMEGAYA AND SATAKE 2014. American Geophysical Union. All Rights Reserved. 2300

Figure 4. Flow depths and velocities calculated from the A.D. 869 variable-slip models. (a) Assumed fault models based on the slip distribution of the 2011 Tohoku earthquake [Satake et al., 2013]. Slip amounts outside the green rectangles were set to zero. (b) Calculated flow depths at the most landward sandy deposits of the A.D. 869 tsunami. If the calculated flow depth was less than 0.01 m or the tsunami did not inundate the site, symbols are plotted at 0.01 m. (c) Calculated depthaveraged velocities at the most landward sandy deposits of the A.D. 869 tsunami. 3. Tsunami Inundation Modeling of the 869 Jogan Earthquake We computed tsunami flow depths and velocities at the most landward sandy deposits of the A.D. 869 tsunami [Sawai et al., 2012] along eight transects (Figures 1b 1d). Sawai et al. [2012] ranked these data according to their reliability as Present and Probable, but we treated both types of data equally. As initial conditions, we used two types of fault model with various magnitudes. The first type was a uniform-slip model, which we used with different fault lengths, slip amounts, and fault depths (Figures 3a and S1a). For this type, we considered a total of 24 fault models (Table S2), consisting of combinations of four different fault lengths (100, 200, 300, and 400 km), three different slip amounts (6, 9, and 12 m), and two different fault depths (15 and 31 km). The fault width was fixed at 100 km in all models, yielding different stress drops (Table S2). The second type was a variable-slip model (Figure 4a). For this type, we considered models of the entire fault (model 2011) and of subfaults of the 2011 Tohoku earthquake [Satake et al., 2013]. For the subfaults, we assumed 100 km 50 km faults (models 100a, 100b, and 100c) and 200 km 100 km faults (models 200a and 200b) with different depths, a 300 km 150 km fault (model 300); a 400 km 150 km fault (model 400); and a 550 km 150 km fault (model 550). We assumed an average rigidity of 4 10 10 N/m 2 for the calculations of the moment magnitude. The original fault model of Satake et al. [2013] considered the temporal as well as the spatial slip distribution; hence, a delayed rupture was also considered for the 2011 model (model 2011r) and the largest subfault (model 550r). For the other models, an instantaneous rupture was assumed. We used the same computational method as Sawai et al. [2012], but we also considered the effect of horizontal displacement [Tanioka and Satake, 1996] in the variable-slip models, because the slip amounts close to the trench axis were large. Bottom friction represented by Manning s roughness coefficients is one of uncertainties. The range of n estimated from the comparisons of measured and computed heights of the 2011 tsunami was 0.04 0.05 m 1/3 s (Figure 2b). The bottom friction is expected to be lower in 869 than 2011 because of fewer artificial structure; hence, we basically adopt the lower value of n =0.04m 1/3 s. We then computed flow depths and velocities on the A.D. 869 topography from the 2011 model and found that they are similar to the results of the 2011 tsunami NAMEGAYA AND SATAKE 2014. American Geophysical Union. All Rights Reserved. 2301

on the 2011 topography using n = 0.045 m 1/3 s, except for the flow depths at two sites (I2 and S3). For these two sites, computations using lower values of n (0.03 m 1/3 s) produce flow depths similar to those computed at the neighboring sites of 2011 tsunami deposit. Therefore, we used n =0.03m 1/3 s for these sites. 4. Reexamination of the Magnitude of the 869 Jogan Earthquake The uniform-slip models with a fault depth of 31 km (Figure 3a) required a fault length of 200 km or longer, a fault slip of 12 m, and a minimum moment magnitude of 8.6 to produce flow depths of >1 m at the most landward tsunami sandy deposit sites (Figure 3b). The flow velocities from these models exceeded 1 m/s. The computed flow depths were <1 m for all the transects of the 100 km long fault models (M w 8.2, 8.3, and 8.4). The flow depths and velocities calculated for a fault depth of 15 km (Figure S1) produced similar results except for Site I3 where the computed flow depths and velocities become much smaller than those from 31 km deep fault. For the fault length of 300 km and 400 km at both depths, the flow depths on most transects are almost same for the large slips of 9 m and 12 m, indicating that the tsunami inundation was not sensitive to fault lengths beyond 300 km. The variable-slip models (Figure 4a) required a fault length of 300 km and a moment magnitude of 8.8 to produce a flow depth of >1 m at the most landward tsunami deposits on all transects (Figure 4b). The corresponding flow velocities were also calculated to be > 1 m/s (Figure 4c). For the 2011 Tohoku earthquake and the 550 km long fault models (M w 9.0 and 8.8), both simultaneous and delayed rupture, the flow depths exceeded 1 m on all transects. The similar flow depths for both simultaneous and delayed 550 km long ruptures indicate that the effect of a delayed rupture on the flow depth is insignificant on the Ishinomaki and Sendai plains. The flow depths estimated with the variable-slip models required a moment magnitude of M w 8.8 for the 869 Jogan earthquake. However, the flow depths on each transect were similar for models with a fault length of more than 300 km. The tsunami inundation computations using the 2011 earthquake models indicated that the offshore slip near the Japan Trench axis does not contribute to the inundation on the Ishinomaki and Sendai plains [Satake et al., 2013]. From these results and the tsunami deposit distribution in the Sendai and Ishinomaki plains, we cannot exclude the possibility that the size and slip distribution of the 869 Jogan earthquake were the same as those of the 2011 Tohoku earthquake (M w = 9.0). 5. Discussion Most of physical parameters of tsunami sediment transport are considered to be similar between A.D. 869 and 2011. Although the shoreline locations are different, the background bathymetry and topography are basically the same. The compositions of the 869 and 2011 tsunami deposits can be considered similar. The nonlinear effects of the tsunami inundation also can be similar except for the effects of bottom roughness. Therefore, we only change topography including the shoreline locations and Manning s roughness coefficients for the inundation computations of 869 and 2011 tsunamis. We assumed that a threshold flow depth of 1 m, estimated from the 2011 Tohoku earthquake tsunami data, can be applied to the 869 Jogan tsunami at the locations of the most inland tsunami sandy deposits. Although this assumption is valid for both the Sendai and Ishinomaki plains, these values may not be applicable elsewhere. A different flow depth may be appropriate, for instance, for the 17th century tsunami deposits in eastern Hokkaido, associated with an unusually large earthquake along the southern Kuril Trench [Nanayama et al., 2003]. The current estimate of the size of the Kuril earthquake, M w 8.5 [Satake et al., 2008], may be too small if, as near Sendai, the tsunami outran its sandy deposits. If both source models and the distribution of modern tsunami sandy deposits are known, as in Thailand [Jankaew et al., 2008], Samoa [Apotsos et al., 2011], and Chile [Morton et al., 2011], we can use them to estimate the minimum flow depth necessary to lay down a tsunami sandy deposit, as demonstrated in this paper. If modern analogues are not available, the value estimated in this paper might be usable for similar environments, that is, a coastal plain with a large (~4 km) inundation limit. The approach presented here is based solely on tsunami sands. Ongoing research is examining the inland extent of fine sediments and geochemical and microfossil evidence beyond the inland limit of visible sandy deposits [Chague-Goff et al., 2012; Goto et al., 2011]. Use of multiple types of data for inundation estimates is NAMEGAYA AND SATAKE 2014. American Geophysical Union. All Rights Reserved. 2302

important for assessing the validity of each approach. In addition, this work is based solely upon the presently known sandy deposits of the A.D. 869 tsunami on the Ishinomaki and Sendai plains. If additional deposits are identified to the north or south or farther landward, then the estimated earthquake magnitude might change. Acknowledgments We thank B. Atwater, J. Goff, K. Goto, and M. Shishikura for discussions and constructive comments. We also thank an anonymous reviewer, who provided us valuable comments. Y. N. calculated the tsunami inundations and drafted the manuscript. K.S. contributed to the overall design of the tsunami computations, the choice of models, and finetuning of the manuscript. Most figures were generated using the Generic Mapping Tools [Wessel and Smith, 1998]. The Editor thanks one anonymous reviewer for his/her assistance in evaluating this paper. References Abe, T., K. Goto, and D. 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American Geophysical Union. All Rights Reserved. 2303