Validating slip distribution models of the 2011 Tohoku earthquake with diffracted tsunami and uplift-induced sea waves in the back-arc region

Transcription

1 Geophysical Journal International Validating slip distribution models of the Tohoku earthquake with diffracted tsunami and uplift-induced sea waves in the back-arc region Journal: Geophysical Journal International Manuscript ID GJI-S--0 Manuscript Type: Research Paper Date Submitted by the Author: 0-May- Complete List of Authors: Kim, SatByul; Pukyong National University, Division of Earth Environmental System Science Kang, Tae-Seob; Pukyong National University, Division of Earth Environmental System Science Rhie, Junkee; Seoul National University, School of Earth and Environmental Sciences Baag, So-Young; Seoul National University, School of Earth and Environmental Sciences Keywords: Japan < GEOGRAPHIC LOCATION, Tsunamis < GENERAL SUBJECTS, Earthquake dynamics < SEISMOLOGY, Numerical modelling < GEOPHYSICAL METHODS, Wave scattering and diffraction < SEISMOLOGY

2 Page of Geophysical Journal International Validating slip distribution models of the Tohoku earthquake with diffracted tsunami and uplift-induced sea waves in the back-arc region SatByul Kim, Tae-Seob Kang *, Junkee Rhie, and So-Young Baag Division of Earth Environmental System Science, Pukyong National University, Yongso-ro, Nam-gu, Busan, Republic of Korea School of Earth and Environmental Sciences, Seoul National University, Gwanak-ro, Gwanak-gu, Seoul 0, Republic of Korea Accepted: ; Received: ; in original form: Short title: Tohoku slip model validation using tsunami *Corresponding author: Tae-Seob Kang, Ph.D. Division of Earth Environmental System Science, Pukyong National University Yongso-ro, Nam-gu, Busan, Republic of Korea Phone: +---; Fax: +---; tskang@pknu.ac.kr - -

3 Geophysical Journal International Page of SUMMARY We investigate slip-distribution models of the Tohoku earthquake in terms of diffracted tsunamis and uplift-induced waves along the back-arc region of the Japanese Island Arc. The Tohoku earthquake tsunami turned to propagate around Kyushu Island before reaching the southern coast of Korea. Moreover, seafloor deformation by the earthquake also caused small sea waves with a short-period oscillation in the back-arc sea basin, which were recorded at several tidal gauges along the eastern coast of Korea. We performed tsunami simulations using seven previously defined slip distribution models of the Tohoku earthquake to examine whether the models can accurately reproduce synthetic waveforms similar to observations not only in the Pacific Ocean but also in the southern offshore region of Korea and the coastal back-arc region. To compare their accuracy in replicating Tohoku tsunami observations, we set three criteria: delay time of the first tsunami peak, mean normalized residuals, and mean normalized RMS misfits. The best performance model differed depending on the region where the tidal gauge was installed. This allows us to discriminate differences more clearly by comparing records from the southern coast of Korea and the coasts of the back-arc basin. Thus, we consider diffracted waves as one of the constraints on the models. Specifically, for the tsunami generated by the Tohoku earthquake, which occurred along the outer rim of the fore-arc sea basin of the Japanese Island Arc, uplift-induced sea waves in the sea basin can be used to constrain the extent and polarity of seafloor deformation, which is appropriate for a feasible finite-fault model. Keywords: Japan; Tsunamis; Earthquake dynamics; Numerical Modelling; Wave scattering and diffraction - -

4 Page of Geophysical Journal International Introduction Large subduction zone earthquakes like the Tohoku earthquake have heterogeneous slip distribution patterns (e.g., Kikuchi & Fukao ; Thatcher 0). Many slip distribution models have been presented to characterize the source of this earthquake using a variety of observation data, such as teleseismic waves (Hayes ; Lay et al. ; Polet & Thio ), strong ground motion (Suzuki et al. ), GPS (global positioning system) data (Iinuma et al. ), and tsunami records (Tajima et al. ). Some studies have also validated the accuracy of their models by comparing tsunami records and synthetic waveforms (e.g., Koketsu et al. ; Maeda et al. ; Fujii et al. ; Saito et al. ; Yamazaki et al. ; Satake et al. ). It is common to compare calculated results with tsunami observations in order to confirm the validity of the earthquake source model or numerical model when modeling a large earthquake source or developing a numerical tsunami propagation model. When a model is not realistic or not well constructed, it cannot reproduce results similar to the observations. Since Korea began instrumental sea-wave recording (i.e., tidal gauges) in the 00s, five tsunamis from Japan have reached Korean coasts. They are the Shakotan-oki tsunami, the Niigata tsunami, the Akita-oki tsunami, the southwest of Hokkaido tsunami, and the Tohoku-oki tsunami. The first four tsunamis occurred along the western coast of Tohoku and Hokkaido in Japan and directly propagated towards the Korean coast from the source regions. However, the Tohoku earthquake generated a large tsunami in the western Pacific Ocean and the main tsunamis propagated around Kyushu Island before reaching the southern coast of the Korean Peninsula. This diffracted wave was considerably attenuated during its propagation from the source region towards Korea and was perturbed by Kyushu Island. However, some diffracted waves cause as much damage as tsunamis that directly hit the land (Poisson et al. 0). It is important to understand how sea floor topography can affect different aspects of tsunami propagation as well as how the morphological features of ruptured faults, such as the location, extent, and geometry, dominate the characteristics of diffracted waves. The East Sea (Sea of Japan) contains three major deep (> km) basins, the Ulleung, Yamato, and Japan basins, all of which were formed under an extensional tectonic regime. Separation of the - -

5 Geophysical Journal International Page of Japanese Island Arc from the continent made the East Sea, an almost completely isolated sea basin, which has several straits, such as those connecting it to the East China Sea in the south-west and the Okhotsk Sea in the north-east. When the Tohoku earthquake generated a tsunami off the coast of Japan, the tsunami entered into the East Sea through the Tsugaru Strait separating Honshu and Hokkaido Island; this wave was captured by several tide gauges along the coast of the East Sea (Shevchenko et al. ; Murotani et al. ). When the tsunami turned around Kyushu Island, the wave was also able to penetrate into the East Sea through the Korea Strait, which is located between the Korean Peninsula and Kyushu Island. However, the diffracted tsunami was barely observable at tide gauges along the eastern coast of Korea. Meanwhile, immediately after the Tohoku earthquake, small waves with short-period oscillations appeared in the back-arc region (East Sea) of Japan. These waves were recorded at several tide gauges along the eastern coast of Korea. Such short-period components of a sea wave are unusual characteristics for a tsunami. The characteristics of wave diffraction and oscillation in a region of geometric shadow are controlled by source locations as well as any potential obstacles. In the case of tsunami generation, an earthquake source model described by several parameters such as rupture dimension, fault geometry, and slip distribution can be a variable, while the location and geometry of the obstacle are the given conditions. Therefore, the diffracted tsunamis and short-period oscillations in the back-arc region may be useful observables to evaluate the characteristics of various earthquake source models in tsunami observations. Some studies have already demonstrated the precise reproduction of tsunamis by earthquake models performing tsunami simulations with various earthquake slip distribution models (MacInnes et al. ; Ulutas ); however, they only compared synthetic results with observations close to the earthquake source region. This study compares seven different slip distribution models of the Tohoku earthquake by applying the most common numerical tsunami model, such as the nonlinear shallow water equation (e.g., Satake ), to explore how accurately the slip models reproduce diffracted tsunamis on the southern coasts of Korea and short-period waves off the coast of the back-arc basin of Japan. - -

6 Page of Geophysical Journal International Methods. Slip models and initial conditions We applied seven slip distribution models of the Tohoku earthquake to tsunami simulations to compare numerical waveforms with tsunami observations. The models were selected based on their inversion methods (Table ) and slip distribution patterns (Fig. ). Models M and M were derived from inversion of tsunami waveforms (Fujii et al. ; Satake et al. ). Models M, M, M, and M were derived from inversions using teleseismic P, SH, and long period surface waves (Shao et al. ; Hayes ). Model M was inferred from Table here teleseismic P waves, short-arc Rayleigh waves, and high-rate GPS data Fig. here (Ammon et al. ). Models M and M were derived from tsunami waveforms recorded at GPS tide gauges, coastal tide gauges, and deep-ocean bottom-pressure gauges (Fujii et al. ; Satake et al. ). For the inversion of both models, the Japan Meteorological Agency (JMA) hypocenter (.0 N and. E, depth = km) was applied. M was divided into 0 x sub-faults 0 km by 0 km. The parameters of each sub-fault (strike, rake, and dip ) were taken from the United States Geological Survey (USGS) W-phase moment tensor solution. M is an advanced version of M, which considers additional tsunami waveforms and temporal changes of slip. It consists of x subfaults measuring 0 km by 0 km, but two columns of sub-faults near the trench are km wide. This model has the same strike and rake as M whereas the dip varies depending on the depth of the subfaults. The maximum slip of M and M is approximately m and 0 m at the shallowest part of the source region, respectively. Models M, M, and M were suggested by Shao et al. () and created based on the finite fault inversion method of Ji et al. (0). The fault plane was determined by multiple double-couple analysis and used two different seismic datasets consisting of teleseismic body waves and long period surface wave observations, resulting in a strike of, a dip of 0, and a rake of. M was inferred using the USGS PDE hypocenter (. N and. E, depth = km). The dimensions of the fault plane are 00 km by 0 km and it consists of 0 sub-faults ( km by - -

7 Geophysical Journal International Page of km). The maximum slip is approximately m. In model M, the top side of the fault plane is placed nearest the trench axis. For the inversion, JMA s hypocenter was used but the depth was modified from km to km. The number of sub-faults was 0 x but the size of each sub-fault was the same as M; thus, the whole fault plane was smaller than M. Its large slip area was extended in the downdip direction to be distributed near the source point and the peak slip was approximately m. Model M was made using more station data and the weight of the surface waves was doubled. The number and size of sub-faults were the same as M. The large slip area was larger than in other models and extended along the trench axis as well as in the downdip direction. Model M used the modified strike ( ) and dip (0 ) of the early W-phase solution that better fits the Slab.0 global subduction interface model to the inversion (Hayes ). This model was derived from an inversion using the USGS source location (. E,. N) and a depth of km, which is approximately km deeper than the early USGS depth (approximately km) and more adjacent to the slab depth. The final dimension of this model was km (along strike) by 0 km (along dip), divided into segments of km by km. This model had the largest fault plane among the seven source models. Even if the same inversion method was used for M to M, we would expect different results from the tsunami simulation due to the different slip distribution generated by the moment tensor solution, hypocenter, and datasets. Model M was inferred using teleseismic P waves, short-arc Rayleigh waves, and threecomponent high-rate GPS ( s sampling rate) data. This model was composed of x sub-faults measuring km by km, which was the finest size of all seven models. The fault geometry was set to a strike of, a rake of, and a dip of for all sub-faults. The largest slip was distributed near the hypocenter whereas the asperities in the other models were located near the shallowest part of the trench. Using these seven models, we computed instantaneous seafloor displacement using Okada s formula (Okada ) and considered the horizontal movement of seafloor slope (Tanioka & Satake ; Fig. ). Results using M show large deformation near the hypocenter and larger uplift at the shallowest part of the fault plane. In all models, the largest slip is distributed along the trench axis. Models M, M, and M exhibit larger subsidence than other models. M displays uplift on the - -

8 Page of Geophysical Journal International northern side of the fault plane and subsidence on the western coast of Honshu, Japan. Values of total vertical seafloor deformation from the seven models were used as initial sea water amplitudes in the tsunami simulations. Fig. here. Numerical simulation To identify if the slip models accurately reproduce the diffracted tsunami waveforms and waves with short period components in the East Sea, we compared synthetic waveforms with observations from tide gauges that captured diffracted waves. For the numerical computation, we set the boundaries of the simulation region to E 0 E and N 0 N, which includes the northwest Pacific Ocean, the back-arc region of Japan, and the Korean coast (Fig. ). We used -arc-second bathymetry grid data provided by the General Bathymetric Chart of the Ocean (GEBCO; GEBCO_ Grid). The nonlinear long-wave equations were solved by the staggered leap-frog finite difference method (e.g., Satake ) with a time step of s. We also included inundation calculations by changing the boundary between land and water according Fig. here to water flow into the land area (e.g., Iwasaki & Mano ; Saito et al. ). The Tohoku tsunami was recorded at various gauges near the Japanese coast; some waves were also captured by several Korean tide gauges. In the Pacific Ocean, many DART buoys were operating when the earthquake generated the tsunami; we selected DART buoys 0,,, and for this study (Fig. ). In order to identify whether the slip models reproduce the waves that were diffracted around Kyushu Island and reached the southern coast of Korea, we collected tsunami data from the two stations, Moseulpo and Seogwipo, located along the Jeju coast, and the three stations, Goheung, Tongyeong, and Geomun-do, along the southern Korean coast. We also added a Japanese tide gauge, Akune, located in Kagoshima on Kyushu Island, which represents the region referred to here as the South Sea of Korea. Immediately after the Tohoku earthquake, some amplitude changes were observed at tide stations along the northwestern coast of Honshu, Japan (Shevchenko et al. ; Murotani et al. ), including short-period waves. We obtained tidal records from Wajima, Ogi, and Nezugaseki stations located on the northwest coast of Japan to - -

9 Geophysical Journal International Page of investigate if the slip models reproduce the amplitude change that occurred immediately after the origin time. In addition, we obtained tidal data from tide gauges at Sokcho, Mukho, Pohang, and Hupo, located along the eastern coast of Korea to include the features of small waves with shortperiod oscillations in Korea.. Comparison of observations and simulated waveforms In order to quantify the performance of the different source models of the Tohoku earthquake, we investigated the following criteria: the delay time of the first peak, the mean normalized residuals, and the mean normalized root-mean-square (RMS) misfits. We cross-correlated the observations and synthetic waveforms for each station to calculate the lag time of the first peak and used this to investigate how precisely the source models predict the arrivals of the first peak. For the mean normalized residuals, we first define residual errors by subtracting the synthetic waveform,, from the observed one,, at time. Then, by dividing the mean residual error by the standard deviation of observations, the normalized residuals are estimated as follows: =, where is a sample point within the time window with a length of. The residual errors are resampled with iteration counts for the bootstrap estimate of the standard error. The size of the residuals depends on the amplitudes at each station. Thus, in order to make a fair comparison between all stations, we normalize the mean residual by the standard deviation of the observed amplitudes within each time window. Then, the mean normalized residuals are calculated as below: =, - -

10 Page of Geophysical Journal International where is the total number of iteration counts, which was 000 in this study. For the mean normalized RMS misfits, we define the mean RMS misfits as follows: =. The mean RMS misfits were again normalized by dividing by the standard deviation of the observed amplitudes for a fair comparison of misfits among stations to produce: =. Then, the mean normalized RMS misfits are calculated as below: =. After estimating the mean normalized residuals and the mean normalized RMS misfits of each station, we also applied the bootstrap approach for all stations to calculate the mean value of the normalized residuals and the RMS misfits 000 times. We termed these values the total mean normalized residuals and the total mean normalized RMS misfits, respectively.. DART buoys Here, we compare synthetic tsunami results and observations made in the western Pacific Ocean. As mentioned in the previous section, DART buoys 0,,, and were selected to verify that our tsunami simulations are reasonable. Tidal effects were removed from the - -

11 Geophysical Journal International Page 0 of observations by applying a low-pass filter with a corner frequency of 0.0 mhz or a period of approximately h. For the DART buoys, the lag time of the first peak between the observations and synthetic waveforms is small (Table ), which is also seen in Fig.. A time window of min, starting approximately min before the first arrival, was used for the observations of the four buoys to calculate mean normalized residuals and RMS misfits (Fig. ). Fig. (a) shows the mean normalized residual for all source models at each station and the average of all normalized residuals using all station s data. Most models predict lower amplitudes than that of tsunamis observations at the DART buoys while the total mean normalized residuals show that the Fig. here slip models overestimate wave amplitudes, except for model M. Models M, M, and M have almost the same trend at the four DART buoys. Fig. here Model M is slightly tilted towards the positive from zero, which means that model M shows the least bias at the DART buoy stations. Fig. a shows the mean normalized RMS misfit values for each DART buoy and model. Among the buoys, DART buoy is the closest to the earthquake source region, and we observe large wave heights (~. m) and the maximum peak arrival within min of the origin time (Fig. ). Model M has the lowest mean normalized RMS misfit of 0. while M has the highest value of.0. This is because model M results in a large negative secondary peak whereas the observation only shows a positive peak. At station, most models show a larger misfit than other DART buoys due to the absence of the observed secondary peak. Buoys 0 and are located to the north of the earthquake epicenter, and observations at those stations show that the tsunami amplitudes decrease due to the spreading tsunami wavefront from the source region. The maximum observed peak at both stations is 0. m and 0. m, respectively, and the simulation results also show much lower tsunami peaks than those at station. Model M produces the lowest mean normalized RMS misfit of 0., and at buoy, models M, M, and M produce similar low mean normalized RMS misfits. Model M shows the highest mean normalized RMS misfits at these two stations. At buoy, which is located to the south of the earthquake source, model M shows the best performance with an RMS misfit of 0.; M has the highest RMS misfit of 0.. M, M, and M also have low RMS misfits. We compared the mean normalized RMS misfits at DART buoys with the total mean - 0 -

12 Page of Geophysical Journal International normalized RMS misfits, and find that all models produce lower mean normalized RMS values at DART buoys than for region-wide values. Even though the maximum amplitudes of the simulated results differ slightly from the observations Fig. here depending on the source model, they are typically close to the observations. The first peak arrival times of the synthetic waveforms and the mean normalized RMS misfits demonstrate that our simulations are reasonable for direct tsunamis.. Southern offshore region of Korea We collected data from tide gauges Moseulpo, Seogwipo, Geomun-do, Goheung, and Tongyeong, which are located along the southern Korean coast. We also obtained tidal data from Akune station located on the western coast of Kagoshima, Kyushu. Unlike the DART buoys, these tide gauges are located in the port; thus, we used a band-pass filter to remove high frequency (periods < 0 min) and low frequency (periods > h) signals due to harbor oscillations and tidal effects. The delay times between observed and synthetic records became longer than those for DART buoys (Table ). The first peak arrivals of models M and M more closely match the observations than other models. Model M produces the longest delay time at Tongyeong station (~ min) whereas this model exhibits the smallest delay time at Moseulpo and Seogwipo stations. At Akune, the first peak arrival times of all models match well with the observations, even though the amplitudes are larger than the observations regardless of slip model (Fig. ). Fig. here For the mean normalized residuals and mean normalized RMS misfits, Table here we applied different duration time windows for each station due to the different times taken by the tsunamis to arrive at each station. We set a time window of 0 0 min for Akune, 0 0 min for Geomun-do, Seogwipo, and Moseulpo stations, and 0 0 min for Goheung and Tongyeong stations. The seven models show minimal differences in the mean normalized residuals and the general trend is a near zero systematic bias (Fig. b). At Goheung, all models have a larger bias than other stations in the South Sea of Korea, but they are still smaller than other offshore regions such as the northwestern coast of Japan. The mean normalized RMS misfits exhibit various differences with regard to source models and stations (Fig. b). Model M has lower - -

13 Geophysical Journal International Page of mean normalized RMS misfits than total mean normalized RMS misfits at all stations in the southern offshore region of Korea. At Tongyeong and Akune, all other models have higher normalized RMS misfit values than the region-wide mean normalized RMS misfit. The arrival times of the first peaks are in good agreement with the observations, but the synthetic waveforms are more amplified at these two stations. At Seogwipo and Moseulpo, located along the coast of Jeju Island, the synthetic waveforms are in good agreement with the observed waveforms, but the arrival time of the first peak is approximately 0 min faster than the observed one. The mean normalized RMS misfits also show that the simulation results at these two stations have the lowest and second lowest values among all the models. In the South Sea of Korea, the results of model M show the best fitting based on the three criteria.. Back-arc region of the Japanese Island Arc To study the unusual sea waves caused by the Tohoku earthquake in the back-arc basin of the Japanese Island Arc, we collected observed wave height data from the tide gauges at Nezugaseki, Ogi, and Wajima, located along the northwest coast of Honshu Island, Japan, as well as the tide gauges at Sokcho, Mukho, Pohang, and Hupo, located along the eastern coast of Korea. The records show short period oscillations (Fig. ) with different features than the tsunamis captured by the DART buoys and tide gauges in the southern sea of Korea. This may be because the East Sea, the back-arc basin of the Japanese Island Arc, was co-seismically disturbed when the Tohoku earthquake occurred. This is a similar phenomenon to when water in a bath experiences oscillations when the bath is impacted from the outside and can be further explained using rigorous approaches such as numerical simulations assuming a dynamic rupture model or elastic water wave propagation, which is beyond the scope of this study. Fig. here Before comparing observed and synthetic wave profiles, we applied a bandpass filter to the signals with corner periods of min and h to remove unwanted signals due to tidal and harbor effects. Nezugaseki and Ogi stations capture an increased amplitude and short period components right after the earthquake, and Wajima station shows a slight change in sea wave height about min later (Fig. a). There is less or no seafloor displacement near Wajima - -

14 Page of Geophysical Journal International compared with the other two stations; therefore, the sea level change is seen later at Wajima. Sokcho, Mukho, and Hupo stations also show the amplified amplitudes with short period oscillations about min after the earthquake origin time (Fig. b). We could not clearly determine the delay time between the observation data and synthetic data at these stations because waves caused by the earthquake were too small to detect. To calculate the mean normalized residuals and RMS misfits, we set a time window with a length of 0 min for Nezugaseki, Ogi, and Wajima. This time window covers the short period waves that occurred immediately after the earthquake but rules out any possible inclusion of the main tsunamis through the Tsugaru Strait. At these three stations, most of the source models overestimate wave amplitudes compared to the observations, except for model M (Fig. c). The seven models result in much higher mean normalized RMS misfits compared to the total mean normalized RMS misfit values. Meanwhile, model M in particular shows significantly higher misfit values at Nezugaseki than the other models (Fig. c). The synthetic results show a poor correlation to the observed waveforms (Fig. ). At the beginning of the wave profiles, model M produced an initial negative amplitude at Nezugaseki, while the other models produced positive amplitudes initially. This is due to model M largely producing initial seafloor subsidence in the back-arc region whereas other models show uplift predominantly (Fig. 0). The observed records at Sokcho, Mukho, Pohang, and Hupo tide Fig. here gauges, located along the eastern coast of Korea, were also bandpass Fig. 0 here filtered using corner periods of min and h and compared with synthetic tsunami waveforms produced by the seven slip models (Fig. ). For these Fig. here four stations, we used a time window duration of 0 min from the origin time to include waves generated off the northwest coast of Japan and exclude the main tsunamis that passed into the Tsugaru Strait from the origin source area. The mean normalized residuals show that model M tends to slightly underestimate amplitudes at Pohang and Mukho, but there are no systematic biases at Hupo and Sokcho. The other six models also underestimate tsunami heights with no significant discrepancy between stations (Fig. d). The mean normalized RMS misfits of the seven models are similar irrespective of the source model and station location. However, model M has a significantly higher - -

15 Geophysical Journal International Page of normalized RMS value at Pohang, while the normalized RMS misfits for each station have smaller values than their region-wide averages (Fig. d). During the first 0 min, the initial subsidence in the back-arc region produced by model M caused a wave that appears to be out of phase with the observed wave heights, which caused the highest RMS misfits among the models to occur at Pohang. Model M shows noticeably different waveforms at the other three stations along the eastern coast of Korea while the other six models have analogous waveforms. The effect of the initial seafloor subsidence can also be seen to a smaller degree at Sokcho, Mukho, and Hupo (Fig. 0). At Mukho and Hupo, the observed wave height amplitudes increase slightly h after the earthquake origin time and the synthetic waveforms also marginally amplify due to sea waves generated on the eastern region of the East Sea. There are several aspects affecting this mismatch. Among them, the decisive factor is that the tidal gauges for the observed records are located within the port barrier, and the resolution of the complicated bathymetry and geometry inside the port is typically inappropriate for regional numerical simulations. Overall, the models effectively simulate the short-period oscillations generated in the back-arc basin by the Tohoku earthquake.. Discussion. Accuracy of source models according to source parameters We compare the slip models based on the results of tsunami simulations with regards to several details such as the distribution of slip and seafloor displacement, the amount of slip and seafloor displacement, the dimension of the fault, the size and number of sub-faults, and the location of the upper surface of the fault plane. Models Mand M, which were inverted using the tsunami waveforms, resulted in lower total mean normalized RMS misfits and shorter delay times than other models. The RMS values of the two models were low in most regions, but model M showed a better RMS misfit at stations along the coast of the South Sea of Korea. Several previous simulations of the Tohoku tsunami have been conducted using various source models, including model M used in this study, and their results also showed that tsunami waveform inversion model M matched the observations most closely (Ulutas ; MacInnes et al. ). Model M is the advanced tsunami waveform inversion model of M, - -

16 Page of Geophysical Journal International and it exhibited the lowest RMS value. A common characteristic of the two models is their moderate size, but the fault length of model M is longer than in model M. The upper limit of the fault is located near the shallowest trench and their maximum slip occurs in the middle of the fault tip. Model M had a larger average slip (. m) and produced better or similar RMS values at all stations. Models M to M were inverted from the finite fault inversion method (Shao et al. ). Model M showed a better mean normalized RMS misfit than models M and M for stations along the southern coast of Korea. These three models produced a similar amount of average slip, while models M and M generated larger maximum seafloor displacement (Table ), which was concentrated along the tip of the fault plane. Moreover, models M and M produced larger amplitudes than model M and even the observations. Model M had a higher RMS value at stations located along the northwest coast of Japan. This is because the fault planes of M and M are closer to the trench axis whereas that of model M is located further west than the other two models. The distribution of seafloor displacement shows that model M generated higher seafloor displacement along the northwest coast of Japan to produce larger amplitude wave profiles. Similar characteristics were shown by model M, in which the fault plane is further from the trench axis than in other models, leading to uplift over a broader area. Model M was inverted from the finite fault inversion method in the same manner as models M to M. The fault dimensions in model M were larger than in models M to M. The maximum seafloor displacement of model M (~. m) was smaller than that of models M to M (Table ), but the former showed a wider uplift area near the source region than the latter three models. As a result, model M produced better mean normalized RMS misfits than models M to M. On the other hand, model M was closest to the observations of all models despite its smaller fault dimensions and a larger seafloor displacement than model M. This implies that the fault dimensions and resulting seafloor displacement would not be the decisive factors in a finite-fault model accurately reproducing tsunami observations, especially when considering diffracted tsunamis. Model M exhibited a substantially larger mean normalized RMS value than the other six models. Specifically, it had a higher RMS misfit at several stations in the region of the South Sea and the northwest coast of Japan. The wave profile of model M was larger than other models and all - -

17 Geophysical Journal International Page of observations were smaller at the DART buoys except for station. The biggest differences between this model and the other models were the higher distribution of slip along the down-dip direction from the upper limit of the fault and the greater distance from the trench axis of the area showing large seafloor displacement. This model is composed of the largest number and the smallest size of sub-faults among all the models considered in this study; thus, it may be able to describe slip distribution in more detail.. Comparison of station mean normalized RMS misfits to total mean normalized RMS There are several stations where the source models resulted in worse mean normalized RMS misfits than the region-wide average; namely, Akune and Tongyeong stations, which are located in the South Sea of Korea, and three stations along the northwestern coast of Japan: Nezugaseki, Ogi, and Wajima. Fig. compares the locations of Tongyeong and Akune and Moseulpo and Seogwipo, which had the lowest RMS misfits along the southern Korean coast. Tongyeong and Akune are located in narrow channels between two islands whereas Moseulpo and Seogwipo are located along uninterrupted coastline. In this study, we used arc-second bathymetry data for the tsunami simulations, which may not have sufficient resolution to represent the complicated coastline and obtain synthetic waveforms similar to the observations. On the other hand, while Nezugaseki, Ogi, and Wajima stations are located along a linear coast, their mean normalized RMS misfits were among the highest in the region. In this region, the seven models produced waveforms with larger amplitudes than the observations. Fig. 0 shows the complicated contour line of the Fig. here total vertical displacement offshore of northwest Japan; this synthetic seafloor displacement generated larger amplitude and shorter period synthetic wave profiles. - -

18 Page of Geophysical Journal International Conclusions The tsunami caused by the Tohoku earthquake reached the southern sea of Korea by diffracting around Kyushu Island. It also co-seismically induced small waves with short period oscillations in the back-arc region of Japan, which were captured at several tide gauges along the eastern coast of Korea. The tsunami propagated indirectly into Korea because of the geographical features of the Japanese Island Arc. In this study, we performed tsunami simulations using seven different slip distribution models of the Tohoku earthquake to examine whether the slip models were able to accurately reproduce synthetic waveforms similar to the observations made in the western Pacific Ocean, the southern offshore region of Korea, and the coastlines of the back-arc region between Korea and Japan. The models reproduce reasonable waveforms at four DART buoys,, 0,, and. The seven models tend to slightly overestimate amplitudes and produce either earlier or the same arrival times compared to observations. The mean normalized RMS misfits of all models at these four stations are lower than the total mean normalized RMS misfit as well as stations in other regions. We compared synthetic waveforms with observations of six tide gauges located along the coasts of southern Korea and one tide gauge on the western coast of Kyushu Island for the diffracted tsunami. Overall, the slip models reproduce synthetic waveforms that agree well with the observations, except that their first arrival times are faster than the observations. Synthetic results at seven tide gauges located along the coast of the back-arc basin of Japan also show short period waves, which were co-seismically excited by the Tohoku earthquake, despite the difficulty of waveform matching due to the low resolution of coastlines and bathymetry in the near-shore region. To determine which source model shows the best performance in the tsunami simulations, we set three criteria; the delay time between observations and synthetic waveforms, the mean normalized residuals, and the mean normalized RMS misfit. Based on these three criteria, we conclude that model M reproduces the best results among the seven models. Most of the existing slip-distribution models of the Tohoku earthquake are applicable for tsunami simulations according to a comparison of the synthetic waveforms with observation records from the open sea, i.e. the DART buoys. This leads to a non- - -

19 Geophysical Journal International Page of uniqueness problem because the slip-distribution models have been developed independently using various data and methods. For example, a slip model with smaller fault dimensions and larger seafloor displacement may produce a comparable result to one with larger fault dimensions and smaller seafloor displacement. A comparison of tsunamis that propagate directly to DART buoys in the open sea cannot properly determine the most appropriate simulation model. In this case, diffracted tsunamis, which depend on the location and geometry of the fault, can be used as a constraint on the models. Specifically, for the tsunami generated by the Tohoku earthquake, which occurred along the outer rim of the back-arc sea basin of the Japanese Island Arc, uplift-induced sea waves in the sea basin constrain the extent and polarity of seafloor deformation, which is appropriate for a feasible finite-fault model. ACKNOWLEDGMENTS The authors thank the General Bathymetric Chart of the Ocean (GEBCO), Geospatial Information Authority of Japan (GSI), National Oceanic and Atmospheric Administration (NOAA), and Korea Hydrographic and Oceanographic Agency (KHOA) for making their data available. Figures were drawn using the Generic Mapping Tools (Wessel & Smith ) and Matplotlib package of Python (Hunter 0). ObsPy v..0 (Beyreuther et al. 0) was used to process the data. To plot the trench line and contours of subduction, we used data from Kita et al. (0), Nakajima & Hasegawa (0), and Nakajima et al. (0). This work was funded by the Korea Meteorological Administration Research and Development Program under Grant KMIPA

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24 Page of Geophysical Journal International 0 Table Source parameters of the seven slip distribution models. Seismic Size of subfaults Max.* Max. Width Length Number of subfaults Model moment Epicenter slip/ave. slip Disp. (km) (km) (Nm) (km²) (m) (m). M (Fujii et al..0n,.e. x x 0 0 x 0 /.. ) (JMA). M (Satake et al..0n,.e. x x /0 x 0 /.. () (JMA). M (Shao et al..n,.e. x x x /.. ) (preliminary USGS). M (Shao et al..0n,.0e. x x x /.. ) (JMA). M (Shao et al..0n,.0e. x x x /.. ) (JMA) - - Inversion methodology (dataset) Tsunami inversion (tsunami wave) Tsunami inversion (tsunami wave) Seismic inversion (teleseismic P, SH, and surface wave) Seismic inversion (teleseismic P, SH, and surface wave) Seismic inversion (teleseismic P, SH, and surface

25 Geophysical Journal International Page of 0. M (Hayes et al.. x 0.N,.E ) (USGS). M (Ammon et.n,.e. x 0 al. ) (USGS) *Maximum amount of slip Average amount of slip Maximum amount of total vertical displacement 0 x x /.. 00 x x / wave) Seismic inversion (teleseismic P, SH, and surface wave) Seismic and GPS inversion (teleseismic P and Rayleigh wave, hrgps)

26 Page of Geophysical Journal International 0 Table Delay between observations and synthetic wave profiles of the seven source models. Delay time (min) Station M M M M M M M DART DART DART DART Geomun-do Goheung Moseulpo Seogwipo Tongyeong Akune

27 Geophysical Journal International Page of N N (a) E Fujii et al. () E M M M M M M M Figure. Seven slip distribution models of the Tohoku-oki earthquake. Solid line shows the depth of the subducting Pacific plate and the interval is km. Dark gray solid line is the plate boundary. - - (c) (g) E E E E Slip [m]

28 Page of Geophysical Journal International N N N N (a) (e) E E E E M M (b) (f) M E E E E E E M Figure. Total vertical seafloor displacement of seven source models. Red and blue colors represent uplift and subsidence, respectively. Gray solid and dotted lines are the contour lines of uplift and subsidence at. m intervals, respectively. Star symbol represents the epicenter of each source model. - - (c) (g) E E E E M M (d) Disp. [m] M

29 Geophysical Journal International Page of Figure. Tsunami simulation region. Star represents the epicenter of the Tohoku earthquake and triangles indicate the station locations of observation data used in this study. Yellow triangle symbols are DART buoys and light orange triangles are tide gauges. - -

30 Page of Geophysical Journal International Figure. Plots of simulated and observed tsunami waveforms at the DART buoys. Gray region represents the duration of the time window. - -

31 Geophysical Journal International Page of (a) (c) Figure. (a) Mean normalized residuals of the DART buoy stations, (b) tide gauges in the southern offshore region of Korea, (c) tide gauges on the northwest coast of Japan, and (d) tide gauges on the east coast of Korea. Gray rectangle is the total mean normalized residual for each model. - - (b) (d)

32 Page of Geophysical Journal International (a) (c) Figure. (a) Mean normalized RMS misfit of the DART buoy stations, (b) tide gauges in the southern offshore region of Korea, (c) tide gauges on the northwest coast of Japan, and (d) tide gauges on the east coast of Korea. Gray rectangle is the total mean normalized RMS misfit for each model. (b) (d) - -

33 Geophysical Journal International Page of Figure. Comparison of synthetic waveforms and observations at stations on located the south coast of Korea and the west coast of Kyushu Island. Gray region represents the duration of the time window. - -

34 Page of Geophysical Journal International (a) Figure. (a) Observations at Nezuegaseki, Ogi, and Wajima stations along the northwest coast of Japan. (b) Observations at Sokcho, Mukho, Hupo, and Pohang stations along the eastern coast of Korea. - - (b)

35 Geophysical Journal International Page of Figure. Comparison of synthetic waveforms and observations at stations located on the southwest coast of Honshu, Japan. Gray region represents the duration of the time window. - -

36 Page of Geophysical Journal International (a) (b) M M M M (e) (f) M M M Figure 0. Total vertical seafloor displacement throughout the back-arc basin. The contour line has an interval of cm. Note that the dark blue color ranges from -0. m to -0. m. The range from -0. to is plotted using the same color. - - (c) (g) (d) Disp. [m]

37 Geophysical Journal International Page of Figure. Comparison of synthetic waveforms and observations at stations located on the east coast of the Korean Peninsula. Gray region represents the duration of the time window. - -