Tsunami Simulation by Tuned Seismic Source Inversion for the Great 2011 Tohoku. Earthquake

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1 The final publication is available at Springer via View only version is available at this link Tsunami Simulation by Tuned Seismic Source Inversion for the Great 2011 Tohoku Earthquake A. Petukhin, K. Yoshida & K. Miyakoshi Geo-Research Institute, Japan 6F, Kokuminkaikan Sumitomoseimei Bldg., Otemae, Chuo-ku, Osaka JAPAN phone: K. Irikura Aichi Institute of Technology, Japan 1247 Yachigusa, Yakusa, Toyota, Aichi , Japan ABSTRACT: Seismic and tsunami waves were the most destructive phenomena during the 2011 Tohoku earthquake. Here we ask whether the same source model can be used to obtain equally good simulations of the observed strong ground motions and the tsunami waves. If so, we could use the same source modeling technique for predictions of both tsunami waves and strong ground motions. Long-period ( s) strong ground motion data were inverted to determine the rupture process of the 2011 Tohoku earthquake. The inverted slip distribution shows that large-slip area was extended around 150 km to North and 120 km to South from hypocenter and stretched between hypocenter and the trench. We estimated two slip models: without and with additional constraints. The first relatively rough slip model reproduced short-period tsunami wave (4-5 min). Due to better constraint by data of other kind and being relatively smooth the second model reproduces long-period tsunami wave (15-25 min), as well as keeps good fitting of the short-period tsunami, although short-period tsunami becomes underestimated. We used a fully nonlinear Boussinesq water wave model to model tsunami propagation, and used the results to tune the slip model. Finally, we developed a tuned slip model that combine the features of both the first and the second slip models and reproduced both the short- and long-period tsunami waves, while maintaining good fit of the seismic waveforms. Keywords: 2011 Tohoku earthquake, source inversion, fully nonlinear tsunami simulation 1

2 1. Introduction On 11 March 2011, an Mw9.0 earthquake occurred off the Pacific coast of Tohoku, Japan as a result of thrust faulting on the interface between the Pacific and North America plates. This earthquake generated a m extremely high runup in central and north Sanriku coast of Japan. High runup was associated with unusual short-period tsunami wave (e.g. Shimozono et al. 2014). This earthquake also generated strong ground motion of the order 1000 cm/s 2 in high-frequency range. It is one of the best geophysically recorded earthquakes among great earthquakes. Numerous source models have been generated by using teleseismic, GPS, strong ground motion, and tsunami data (e.g., Hayes 2011; Ide et al. 2011; Ito et al. 2011; Lay et al. 2011; Satake et al. 2013; see review Tajima et al. 2013). Here we ask whether the same source model can be used to obtain equally good simulations of the observed ground motions and tsunami waves. If so, it would be possible to use source modeling techniques that have been developed for strong-motion prediction, for modeling of tsunami sources and to predict possible tsunamis as well. For example, Irikura and Miyake (2011) employ source scaling for inland earthquakes based on seismic inversion results (see Somerville et al. 1999; Murotani et al. 2015, and references therein). For subduction earthquakes such scaling is developed by Murotani et al. 2008). Seismic source modeling is based on the determination of scaling relations between source parameters such as fault area, slip asperity (large slip) area, slip magnitude, and seismic moment (Murotani et al. 2008). These scaling relations are estimated by the generalization of seismic source inversion results. In this study, we applied a seismic source inversion technique for modeling tsunami sources and tested it on a megathrust earthquake (the 2011 Tohoku earthquake) by comparing simulated and observed tsunami waves. Inversion techniques using seismic wave data have been applied successfully to subduction earthquake source modeling (see Murotani et al and references therein), and inversion techniques have similarly used tsunami waveform data for source modeling (e.g., Satake 1993; Tanioka and Satake 2001; Fujii and Satake 2007; Fujii et al. 2011). In both cases, the accuracy of the models is assessed by the waveform fit between observed and simulated seismic and tsunami waves. 2

3 In fact, however, there is a trade-off inherent in inversion techniques between the Green s function used and the resulting modeled slip distribution. That is, uncertainty of Green s function due to the simulation method and the seismic velocity or bathymetry model used disturbs the source model in a specific way to obtain a good waveform fit. As a result, models obtained by inverting seismic and tsunami data are not necessarily same. To reduce the influence of this trade-off, Yoshida and Koketsu (1990) have proposed joint inversion of different kinds of data, for example, seismic waveforms and geodetic data. Yokota et al. (2011) applied this method to the 2011 Tohoku earthquake, and they also used tsunami data, although the waveform fit of tsunamis is poor. Gusman et al. (2012) used this method by combining tsunami and GPS data and succeeded in getting a good fit with both kinds of data. As for the real-time tsunami forecasting, on the example of 2011 Tohoku earthquake Wei et al. (2014) demonstrate critical role of the deep-ocean measurements of tsunami in addition to seismic and GPS data for the source validation and high-quality forecasting. Another effect of the uncertainty of the Green s function is that the slip distribution in the inversion result is noisy (e.g. Fig. B1 in Lee et al. 2006). To reduce the noise component, a smoothing constraint is applied during inversion, and various criteria are applied to regulate the strength of this constraint, such as an information criterion (Yoshida 1989, Sekiguchi et al. 2000). The same smoothing constraint is applied to the whole source area. The disadvantage of this approach in the case of the 2011 Tohoku earthquake is that large slip concentrated near the trench, which may have been responsible for the large short-wavelength tsunami generated by the earthquake (e.g. Fujii et al. 2011), might be smoothed out and not appear in the inversion result. Source inversion methods that employ pre-calculated Green s functions for the summation of waveforms from different subsources assume linearity. This assumption is valid for seismic waves and geodetic displacement. In the case of tsunami data, it may be valid for offshore water pressure and floating GPS gauge data, but it is questionable for onshore observations, because wave breaking and run-up processes are highly nonlinear. In this study, we first used a linear seismic inversion method, and then tuned the source slip distribution by trial and error to get a better tsunami waveform fit. We 3

4 used results obtained with a fully nonlinear tsunami simulation model of Wei et al. (1995) and Kirby (2003) for this tuning. In this way, we obtained a single source model that could explain the observed tsunami and seismic waveforms equally well. Tsunami waveforms from the 2011 Japan tsunami, observed by GPS floating gauges (see Fig. 1) can be interpreted as a set of two wave types: a long-period tsunami wave (15 25 min) overlapped by a short-period tsunami wave (4 5 min). Because the amplitude of the long-period wave increased from north to south along the Tohoku coast, and the amplitude of the short-period wave increased in the opposite direction, we can infer that the source of the long-period wave was the southern part of Tohoku, whereas the source of the short-period wave was the northern part. Hayashi et al. (2011) estimated the source location of the short-period wave by tsunami crest inversion to be near the trench at 39.5 N on the northern part of the fault. Many studies have inferred that the devastating short-period large-amplitude tsunami wave was generated by large slip concentrated near the trench (e.g. Fujii et al. 2011). Here we tried to construct a source model that explained both the short-period and long-period tsunami waves in target area shown in Fig Seismic Source Modeling As a first step of the source modeling, we performed a multi-time window linear waveform inversion of the rupture process of the 2011 Tohoku earthquake. Accurate seismic Green s functions can be estimated by tuning of 1D velocity structure model at each site using waveforms of small point earthquake (e.g. Ichinose et al. 2005, Yoshida et al. 2017). Knowledge of the rise time is necessary in this case. Source rise time can be estimated from the width of velocity pulse of a near source record. Modern dense observation networks allow applying this method to inland earthquakes. However, for off-shore earthquakes, both the getting of rise time information and the validity of 1D velocity structure approximation in a short period range is problematic. Instead, we used very long-period ( s) strong ground motion data. In this period range, the effects of the complicated 3D velocity 4

5 structure in the subduction zone (accretionary prism and basin effects near the observation site) are negligible. For this reason, the accurate and computationally effective discrete wavenumber method of Bouchon (1981) combined with the 1D propagator matrix algorithm of Kennet and Kerry (1979) can be used to calculate the Green s functions. Velocity records from seismic stations of the nationwide F-net and KiK-net networks (Okada et al. 2004), and Hokkaido University seismic network, located on very hard bedrock sites, were used for inversion. Two models were estimated. The first model is the model inverted by Yoshida et al. (2011). For more details see also (Yoshida et al., 2012). It is assumed a single planar fault model with a length of 475 km in the strike direction and a width of 240 km in the dip direction, and it was based on the first day's aftershock distribution. Yoshida et al. (2011) used eight smoothed ramp functions, each with duration of 16 s and separated by 8-s intervals to represent the slip history of each subfault of size 12 x 12 km. To suppress instability and excessive complexity, a smoothing constraint was introduced to reduce differences in the moment release values of subfaults situated close together in space. The smoothing constraint parameter used in the inversion was determined so that the total slip would agree with that indicated by the geodetic data (e.g., 24 m off the coast of Miyagi Prefecture; Sato et al. 2011, Fujita et al. 2006). The rupture velocity was inferred to be slower than 2.5 km/s at this early stage of the rupture process. The seismic moment of this model was estimated as Nm (Mw = 9.0). Large slip covers an area between hypocenter and trench and extended around 150 km to North and 120 km to South from hypocenter. The inverted slip distribution is heterogeneous and showed two small patches of very large slip with a maximum slip of 47 m located on the shallow part of the fault plane, slightly northeast of the epicenter (Fig. 2), as well as some other secondary heterogeneities along the boundary of area of large slip (see heterogeneities along green-blue boundary in Fig.2). This source model is consistent with some other source models for the 2011 Tohoku earthquake (e.g., Ide et al. 2011; Lay et al. 2011). The first model reproduces well the seismic waveforms used for the inversion (Fig. 3). Petukhin et al. (2012) used this model also for tsunami simulation. Forward tsunami simulations have reproduced well the short-period waves along the northern Tohoku coast and the tsunami runups along 5

6 the southern coast. Unfortunately, this model strongly underestimated the tsunami wavelength along the southern coast, and the tsunami amplitude at the northernmost gauge (number 807) was underestimated: ratio of observed-to-simulated peak amplitudes is around 1.5. Moreover, the model showed limited agreement with the seafloor GPS data (Sato et al. 2011). For these reasons, we revised the seismic inversion as below. With the new seafloor GPS and tsunami constraints at hand we revised source inversion. The second model similarly assumed a single planar fault model. The fault plane of this model, which was based on the aftershock distribution over 6 months, extended further north than the first model; its length was 540 km in the strike direction, and its width was 240 km in the dip direction. We used 12 time windows (smoothed ramp functions) and a revised smoothing constraint. The smoothing constraint parameter used in the second inversion was determined so that the slip distribution would agree with that indicated by the seafloor GPS data and the tsunami wavelength along the southern part of the Tohoku coast. The rupture trigger velocity was increased to 3.0 km/s. The seismic moment of the second model was estimated to be Nm (Mw = 9.05), which is similar to the first model. Similarly to the first model, large slip cover an area between hypocenter and trench and extended 150 km to North and 120 km to South from hypocenter. In contrast to the first model, the inverted slip distribution shows less slip near the trench and almost evenly distributed slip in a wide area between trench and hypocenter (Fig. 4). The maximum slip decreased to 25 m. Some other source inversion results (e.g., Suzuki et al. 2011; Yagi and Fukahata 2011) support this model. Naturally for inversion result, this model also reproduce well the seismic waveforms used for the inversion (Fig. 5). 3. Tsunami Simulation Numerical simulations of tsunamis require three components: (1) a tsunami source model, i.e. the sea surface elevation; (2) information on ocean bathymetry and coastal topography; and (3) a tsunami propagation and inundation model. 6

7 Seafloor displacement was modeled as the sum of the displacement from all subsources, which are classical dislocation point sources, of the seismic source model. This sum combines slip motions occurring on an oblique fault plane embedded in a semi-infinite elastic medium (Okada 1985). A shear modulus of kg/ms 2 was assumed. The sea surface elevation was assumed to be similar to the seafloor elevation. We used time-dependent slip-rate functions estimated by multi-time-window source inversion on each subfault. We also considered the time delay of subsources due to rupture propagation. Although rupture velocity (~2.5 km/s, e.g. Yoshida et al. 2011) was much higher than the tsunami wave velocity (~500 m/s for deep water around the trench), a slight tsunami delay due to rupture propagation is possible, particularly for the short-period tsunami waves observed during the 2011 Tohoku tsunami. The ocean bathymetry (Fig. 6) was compiled from a bathymetric data set with a 500-m grid spacing (J-EGG500) from the Japan Oceanographic Data Center, and the coastal topography model was based on a digital elevation model with a 250-m grid spacing provided by the Geospatial Information Authority of Japan. The 500-m resolution of the bathymetric data is adequate for detecting tsunami propagation in an offshore area. An important source of tsunami wave amplification is wave propagation along or above submarine ridges (waveguides, e.g. Levin and Nosov, 2016). The reduction of wave velocity just above a ridge, together with higher velocities in neighboring valleys, causes the amplitude of the tsunami wave to increase. Among the potential waveguides in the study area (see dashed arrows in Fig. 6), the northern-most waveguide, which would draw wave energy southward, may account for the underestimation of amplitude at gauge 807 by the first source model. We prevented this effect by extending the fault plane of the second source model northward. To model tsunami propagation and inundation we used a Boussinesq water wave model developed by Wei et al. (1995) and Kirby (2003) (FUNWAVE program). This model was originally designed for simulating coastal and nearshore waves, but it was later successfully applied to a variety of tsunami case studies, including of coseismic tsunamis (Grilli et al. 2007; Ioualalen et al. 2007; Tappin et al. 2008; Karlsson et al. 2009; Grilli et al. 2010). The model is fully nonlinear and dispersive, retaining information relating to all orders of nonlinearity a/h, where a is wave amplitude and h is 7

8 water depth. The program considers both bottom dissipation and wave breaking, without which the wave would be artificially amplified at the coast. Simulation of the land inundation is achieved by means of a fully validated moving shoreline algorithm for short-wave shoaling, breaking and run-up. Further, the model has been calibrated to provide a stable model of tsunami run-up, and has been successfully used to simulate several regional earthquake tsunamis, including the devastating 2004 Indian Ocean tsunami (e.g., Ioualalen et al. 2007). For the 2011 Tohoku tsunami simulation, we used a 500 m finite difference grid and the area within E and N for the simulation domain. We should notice that including a dispersion term is especially important to compute the short-period tsunami (e.g. Saito et al. 2011). From another side, in contrast to the previous paper (Petukhin et al., 2012), here we simulate tsunami at the off-shore gauges and nonlinearity of the simulation model looks a superfluous. However, near-shore nonlinearity may be important to reproduce reflected and refracted waves. For this reason we keep using nonlinear model. 4. Simulation Results We compared the tsunami simulation results with the offshore floating gauge waveform data of the Nationwide Ocean Wave information network for Ports and HArbourS (NOWPHAS, Many coastal tide gauges on the Tohoku coast were broken by the first tsunami wave. Two offshore floating GPS wave gauges (numbers 804 and 802 deployed in area of 200 m water depth) and two seafloor pressure gauges (Maeda et al. 2011) recorded an unusual overlapped tsunami wave (Fig. 1). After arrival of the long-period tsunami wave, the water level gradually increased to 2 m during the first 10 min, and then an impulsive tsunami wave, having higher amplitude and a shorter period, on the order of 4-5 min, was observed. Amplitudes of the min long-period tsunami wave tended to decrease from south (gauge 801) to north (gauge 807), whereas amplitudes of the 4-5 min short-period tsunami wave increased in the same direction. 8

9 The first source model accurately simulated the open ocean propagation of short-period tsunami waves (Fig. 8), as well as of the land inundation (Fig. 4 in Petukhin et al., 2012). In general, the simulated waveforms reproduced well the observed waveforms of the 4-5 min short-period direct wave and the min long-period reflected/refracted later waves in the offshore area (Fig. 8). The min long-period component of the direct waves, however, was underestimated. We inferred that the short-period wave was a result of high uplift of the ocean surface at the edge of the seismic source near the trench (see Fig. 7). This inference is supported by a back projection analysis of tsunami arrival times performed by Hayashi et al. (2011) and by Tappin et al. (2014), who showed that the primary crests of the short-period tsunami waves were generated in an area near the trench, but north of the high uplift in our model. In the second source model, the area of large slip was smoother and broader, while slip near the trench is smaller (see also Fig. 12 below for the sea surface uplift). As a result, the amplitudes of the short period waves were smaller (Fig. 9). We infer that difference in heterogeneity of the tsunami source (compare Fig.7a to Fig.12a) is result of difference in heterogeneity of seismic slip, which in turn is result of difference of smoothing strength. Effectiveness of smoothing strength is demonstrated by Figure 8 of Sekiguchi et al. (2000) for example. Generally, weak smoothing constraint results in smaller misfit of inverted data (seismic waveforms) but produce heterogeneous, i.e. noisy slip distribution. As result, when we try to calculate data of a different kind (tsunami), misfit of these data can be large. Detailed comparison of tsunami waveforms for the first model (Fig. 8) shows that amplitude of direct tsunami wave is underestimated in gauge 807, slightly overestimated at gauges 802 and 803, and predominant period is too short at gauges 803 and 801. Stronger smoothing in the second model removes slip noise and improves tsunami fit at all gauges above, but reduces amplitudes of small slip patches (which are higher scale of slip heterogeneity in a multi-scale heterogeneous earthquake model, similar to model proposed by Aochi and Ide 2014). In result, amplitudes at gauges 804 and 802 become underestimated respectively, while amplitude at gauge 807 is still smaller than observed (Fig. 9). 9

10 In order to understand what details of tsunami source are critical for generation of the long-period waves at gauges 803 and 801, we should recall that tsunami waves propagate mainly perpendicular to the coast. In result, along strike variations of the fault slip are reflected in variations of amplitudes of tsunami along coast (Geist and Dmowska 1999, Lin et al. 2012). For this reason, we should compare details of sea surface uplift (tsunami source) east of the location of gauges 803 and 801 or slightly to East-North-East, because waveguide, 2nd from North (Fig. 6) is able to redirect waves slightly to South. In comparison to a heterogeneous sea surface uplift for the first model (Fig. 7, see area marked long-period source ) sea surface uplift for the second model (Fig. 12) is more homogeneous and wider. This resulted in increase of the long-period tsunami. 5. Tuning of the Source Model with the Tsunami Simulation Results To improve the fit of the short-period tsunami wave at the northern gauges to the observation, while keeping the fit of the long-period tsunami wave, we performed additional tuning of the second source model by taking advantage of the observation that onshore strong-motion data are less sensitive to slip near the trench, whereas tsunami data are very sensitive to this slip (e.g., Yokota et al. 2011, auxiliary materials). We applied a scaling mask to the second source model to increase slip near the trench in the northern part of the source area, that probably was smoothed out, and to make it more similar to that in the first source model. We estimated the mask parameters: location, scaling area, and scaling coefficient (Fig. 10, see also Fig. 12), by combining trial-and-error method and grid search method. First, we estimated suitable location of mask by a few trials and errors. Then, we applied grid search method. We used 3 cases for the mask width (1, 1.5 and 2 subfault sizes), 3 cases for the mask length (2, 3 and 4 subfault sizes), and 3 cases for the mask magnification (1.5, 2 and 3 times of slip amplitude). Finally, a two-dimensional smoothing square window with a width of half the width of the mask was applied. Totally 27 additional cases were simulated. Best fit model was selected by fit of amplitude and period of the short-period tsunami at northern gauges 802, 804 and 807. Masking procedure had almost no 10

11 effect on tsunamis at the southern gauges 801 and 803. Comparison of the observed and simulated seismic waveforms (Fig. 11) showed that the fit of the tuned model to the observed seismic waveforms was almost unchanged compared with the fit of the second source model (shown in Fig. 5). Fig. 12 shows distributions of the sea elevation in tsunami source and of the maximum amplitudes of propagating tsunami, similarly to Fig. 7. Although being smaller in amplitude, high uplift of the ocean surface at the edge of the seismic source near the trench extend to north and overlapped with the source of short-period tsunami inferred by the back projection analysis of tsunami crest arrival times performed by Tappin et al. (2014). We expect that in the tuned model, the northern-most waveguide become able to redirect wave energy southward and increased amplitude of the short-period tsunami in comparison to the second model. For the waveform details see Fig. 14 below. This waveguide effect also can be noticed clearly in the increase of maximum tsunami amplitude near the coast between gauges 804 and 807. Notice that width of tsunami source at latitude 39.0N (marked long-period source ) become larger than in Fig. 7, which resulted in increase of the long-period tsunami amplitude. Comparison of the observed and simulated tsunami waveforms (Fig. 13) showed that the fit of the tuned model to the short-period waves at the northern gauges was improved compared with the fit of both the first and the second source models (shown in Fig. 8 and Fig.9). Fig.14 demonstrate that in accordance with the observed waveforms, tsunami wavelength at southern gauge 801 become longer for the second source model and remain the same for the tuned source model. At the same time, amplitude of short-period tsunami at northern gauge 804 becomes larger for the tuned model than for the second model. 11

12 6. Discussion The combination of tsunami data with geodetic data (instead of strong-motion data) can also be successfully used for source inversion, because tsunami data are sensitive to slip near the trench, whereas geodetic data are sensitive to slip in nearshore parts of the source area. Both these kinds of data are essentially long-period phenomena, however, so such source models cannot be used to simulate strong, destructive short-period ground motion. To define the fault plane we used the 24-hour aftershock distribution for the first model and the 6-month aftershock distribution for the second model. In general, aftershocks over a period longer than 24 h are not used for seismic source inversion, but the amplitude of the tsunami wave at the northernmost offshore gauge (807), which was underestimated by a factor of 1.5 in the first model, was appropriately simulated by the tuned second model. The area of the 6-month aftershocks extended far to the north, but not to the south. Other observations support asymmetry of the source: for instrumentally recorded earthquakes off Tohoku, areas in which high-frequency (1 10 Hz) strong ground motion is generated, are located in the southern part of the source area (Kurahashi and Irikura 2013), while areas of long-period ground motion generation (slip asperities) are located both in the southern and in the northern parts of source area (Earthquake Research Committee, 2009). The short-period tsunami wave was well reproduced by using a single planar source model because the tsunami source was localized near the eastern shallow edge of the fault plane. This localization in our model may mimic the effect of a backstop fault in the actual fault system in the Japan Trench (Tsuji et al. 2011) or the effect of additional uplift of sediments near the toe of the inner trench slope caused by a large horizontal slip (Tanioka and Seno 2001; Gusman et al. 2012). A 3D curved fault model may be necessary for accurate source modeling and tsunami simulation. For example, large inconsistency of the long-period tsunami wave at the southernmost gauge 806 may reflect inaccuracy of the fault surface modeling, because in models using a 3D curved fault (e.g., Yokota et al. 2011) location of the large slip area is somewhat west of the location in models assuming a single planar fault (e.g., Suzuki et al. 2011). 12

13 For calculation of the sea surface elevation (tsunami source) near the trench, we didn t consider vertical effect of horizontal motion of the inclined landward slope of the trench (e.g. Hooper et al. 2012). The width of moved landward slope is around 50 km (Fujiwara et al. 2011) and for this reason vertical effect of horizontal motion can increase long-period (15-25 min) component of tsunami and improve tsunami waveform fit, because in our modelling this component is underestimated (see Fig 13). An alternative model of short-period tsunami generation is a landslide source near the trench (e.g. Tappin et al. 2014, Pararas-Carayannis 2014). Evidences for a possible landslide near trench were found in the seafloor displacement (Fujiwara et al. 2011). However, in case of landslide, due to downward movement of slide body first motion of tsunami wave is negative. We do not see this negative motion in observed tsunami. While this paper was under reviewing, Fujiwara et al. (2017) presented their most recent results on the seafloor displacement on the survey tracks crossing the trench axis at latitudes 39.2N and 39.5N. Within the accuracy limits they didn t find any prominent seafloor displacement. Result of Fujiwara et al. (2017) indicates that very large 100-m submarine landslide of Tappin et al. (2014), as well as very large 36-m fault slips of Satake et al. (2013) is unlikely. Our smaller realistic 25-m slip values also exceed 20 m accuracy limit of analysis of Fujiwara et al (2017). With new constraint of Fujiwara et al. (2017), new tsunami source models, e.g. the combination of a minor landslide with a minor slip near the trench, so as to suppress the first negative tsunami wave movement, may be required to explain the short-period tsunami wave. Traces of such landslides are evident in the results of Fujiwara et al (2017) for latitudes 39.2N and 39.5N. 7. Conclusions We simulated the tsunami generated by the 2011 Tohoku earthquake by using a source model estimated by inversion of long-period strong-motion waveform data. We obtained two inverted models 13

14 by using strong-motion data only and by strong-motion data plus additional constrains from long-term aftershock distribution (fault plane extended to North), tsunami and the sea-bottom GPS. The forward tsunami simulation, performed with the first model having large slip near the trench, but heterogeneous (and probably noisy) overall slip distribution, reproduced short-period (4-5 min) tsunami, although overall tsunami fitting is poor. Due to removing noise by the constrained smoothing (in order to adjust seafloor GPS data), tsunami simulation performed using the second model reproduced both the short period tsunami wave (4-5 min) and the long-period tsunami wave (15-25 min). In this way we demonstrate that with appropriate constraining, seismic inversion models can be helpful for tsunami forecast too. Smoothing is an effective tool to remove short-wavelength noise, but at the same time it removes probable short-wavelength sources of tsunami. By the grid search method, we estimated a model that restore short-wavelength source near trench in northern part of the fault, and reproduced both short- and long-period tsunami waves by a single model. Thus, we confirmed one more time that by proper constraining of the seismic source inversion (by GPS and tsunami data in our case), the uncertainties inherent in the source inversion method can be reduced. Acknowledgments We used the tsunami waveform data of the Nationwide Ocean Wave Information network for Ports and HArbourS. Bathymetry and topography models were provided by the Japan Oceanographic Data Center and the Geospatial Information Authority of Japan, respectively. We thank the National Research Institute for Earth Science Disaster Prevention and Hokkaido University for providing the strong-motion data. Discussions with Prof. Tanioka inspired this study. Also, we are indebted to James Kirby for providing the tsunami simulation program. The clarity and completeness of the paper was improved by two anonymous reviewers. Co-author s contributions A.P. made tsunami simulations and wrote draft text, K.Y. performed seismic source inversions, K.M. take 14

15 leading role in discussions and proofreading of manuscript, K.I. was responsible for general guidance, and all co-authors were working on text and figures. 15

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21 Figures Fig. 1 Locations of floating GPS gauges (numbered triangles) and tsunami waveforms of the direct waves observed at them. Long-period waves (see text) are highlighted by a thick green line; short-period waves are highlighted by a thick red line 21

22 Fig. 2 Final slip distribution of the first source model (Yoshida et al. 2011). The star indicates the rupture starting point, and the squares indicate the strong-motion stations used for the inversion. Dotted lines show tectonic plate boundaries 22

23 Fig. 3 Comparison of observed velocity waveforms (upper lines) with synthetic velocity waveforms (lower lines) of the first source model for strong-motion sites in Fig. 2. The origin of time axis is the arrival time of the P-wave. Note that the order of the records is from north to south 23

24 Fig. 4 Comparison of the final slip distribution between the first source model (a) and the second source model (b) 24

25 Fig. 5 Comparison of observed velocity waveforms (upper lines) with synthetic velocity waveforms (lower lines) of the second model 25

26 Fig. 6 Bathymetry in the target area. Arrows indicate locations of seafloor ridges, which are potential waveguides of tsunami waves. The dashed red rectangles indicate source plane of the first and second source models, and the red star indicates the earthquake epicenter 26

27 Fig. 7 a: Distribution of the sea surface elevation anomalies caused by the source slip of the first model. Solid contours (interval, 1 m) indicate uplift and dashed contours (interval, 0.5 m) indicate subsidence relative to the zero contour (thick line). Short-period and long-period sources are indicated by arrows. b: Distribution of maximum amplitudes of propagated tsunami waves. Triangles indicate offshore gauges, and arrows indicate waveguide ridges (see Fig. 6). The star indicates the earthquake epicenter. Semi-circled pattern east of epicenter is a visualization artefact due to stroboscopic effect of rupture propagation 27

28 Fig. 8 Comparison of observed tsunami waveforms (upper lines) with those simulated (lower lines) by the first source model. Peak amplitudes of observed waves are shown for reference Fig. 9 Comparison of observed tsunami waveforms (upper lines) with those simulated (lower lines) by the second source model 28

29 Fig. 10 Slip distribution simulated by the second source model (a), scaling mask (b), and the tuned and scaled model (c) 29

30 Fig. 11 Comparison of observed velocity waveforms (upper lines) with synthetic velocity waveforms (lower lines) of the final tuned model 30

31 Fig. 12 a: Distribution of the sea surface elevation anomalies caused by the source slip of the tuned model. Solid contours (interval, 1 m) indicate uplift and dashed contours (interval, 0.5 m) indicate subsidence relative to the zero contour (thick line). Short-period and long-period sources are indicated by arrows. b: Distribution of maximum amplitudes of propagated tsunami waves for the tuned model. Triangles indicate offshore gauges, and arrows indicate waveguide ridges (see Fig. 6). The star indicates the earthquake epicenter. White half-ellipse indicate location of the scaling mask. Yellow lines are the back-projection isochrones from (Tappin et al., 2014) 31

32 Fig. 13 Comparison of observed tsunami waveforms (upper lines) with the simulated tsunami waveforms (lower lines) of the tuned (final) source model Fig. 14 Comparison of observed tsunami waveforms (black lines) with the simulated tsunami waveforms of the first source model (blue), second source model (green) and tuned final source model (red). Arrows indicate improvements of the second model (M2) vs. first model (M1), and the tuned model (TM) vs. second model 32