Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanTSUNAMI SIMULATION FOR THE 2011 GREATTOHOKU EARTHQUAKE USING SEISMIC
INVERSION SOURCE MODEL AND FULLYNONLINEAR TSUNAMI MODEL
Anatoly PETUKHIN1, Kunikazu YOSHIDA2, Ken MIYAKOSHI3 andKojiro IRIKURA4
1

Senior researcher, earthquake engineering group, Geo-Research Institute,
Osaka, Japan, anatolyp@geor.or.jp
2
Senior researcher, earthquake engineering group, Geo-Research Institute,
Osaka, Japan, yoshida@geor.or.jp
3Group leader, earthquake engineering group, Geo-Research Institute,
Osaka, Japan, ken@geor.or.jp
4
Adjunct Professor, Aichi Institute of Technology, Professor Emeritus, Kyoto University,
Japan, irikura@geor.or.jp

ABSTRACT: The question we addressing here is the possibility of evenly good
simulation of observed ground motions and tsunami using the same source model. By
comparing simulated and observed tsunami waves we test source inversion andcharacterization technique for M9 class event on example of the 2011 Tohoku earthquake.
Simulation results fit observed tsunami waveforms in the off-shore area and reproduce
inundation data in most of target region.
Key Words: Great East Japan earthquake, source characterization, nonlinear tsunami
simulation

INTRODUCTIONOn March 11, 2001, M9.0 earthquake has occurred east off the Pacific coast of Tohoku, as a result of
thrust faulting on the interface of plate boundary between the Pacific and North American plates. This
earthquake generated tsunami of 30-40m high and strong ground motions up to 1000gal and more.
This is one of the best geophysically-recorded great earthquakes and due to this numerous source
models were generated 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. 2011).
The question we addressing here is the possibility of evenly good simulation of observed groundmotions and tsunami using the same source model. In this case we could use source modelingtechniques, which were developed for the strong-ground motion prediction (Irikura and Miyake 2010),
for the modeling of tsunami sources and prediction of possible tsunamis. A basement of the seismic612

Fig. 1 Final slip distribution of the source model (Yosida et al. 2011). The star and squares indicate therupture starting point and the strong-motion stations that are used for the inversion. Dotted line shows
plate boundaries (Bird, 2003)
source modeling is scaling relations between source parameters, e.g. fault area size, asperity area size,
slip value from one side, and seismic moment from another side (Somerville at al. 1999; Murotani etal., 2008). These scaling relations are estimated by generalization of the seismic source inversion
results. As the first step, by comparing simulated and observed tsunami waves we will test source
inversion technique on example of the 2011 Tohoku earthquake.

SOURCE MODEL
Here we used rupture process of the 2011 Tohoku earthquake inverted by the multi-time windowlinear waveform inversion method using the long-period (20-200s) strong-ground motion data
(Yoshida et al. 2011). Effects of complicated 3D velocity structure in subduction zone (effects ofaccretion prism and subducting plate) are negligible in this period range. For this reason accurate andcomputationally effective discrete wavenumber method of Bouchon (1981) combined with 1D
propagator matrix algorithm of Kennet and Kerry (1979) can be used for calculation of the Green’s
functions. From another side, signal-to-noise ratio of 20-200s long-period ground motions is large
enough for the Mw9.0 earthquake. Velocity records at very hard bedrock sites of the F-net, KiK-net
and Hokkaido University seismic networks were used for inversion. A single planar fault model of 475
km in strike and 240 km in dip is assumed. The rupture velocity inferred to be slower than 2.5 km/s atearly stage of the rupture process. The seismic moment of this earthquake was estimated to be 4.3e1022
Nm (Mw = 9.0).
The inverted slip distribution shows a large elongated asperity (large slip area) with a maximum slip of
47 m which is located on the shallower part of the fault plane, slightly north of epicenter (Fig. 1). Thisis consistent with other source models (e.g. Ide et al. 2011; Lay et al. 2011). Area of the moment rate
large amplitudes, which is responsible for generation of short period ground motions, is613

Fig. 2 Distribution of the sea surface elevation due to the source slip. Solid contours (1m interval)
indicate uplift, dashed contours (0.5m interval) – subsidence, thick contour – zero elevation, points –source model subfaults, star – epicenter location

Fig. 3 Bathimetry map of the target area. Arrows indicate seafloor ridges, which are potential
waveguides of tsunami waves. Red line and star mark indicates source plane and earthquake epicenter.
Bathymetry map on the right plot is scaled to 2000m for clarity614

shifted to deeper part of the source and have tendency to scatter in a few strong motion generation
areas. This is consistent with the empirical Green’s function simulation results of Kurahashi and
Irikura (2011). The rupture process is divided into three stages: first stage with moderate slip; second
stage with large and long-duration slip in the shallow part of the fault; and third stage with relatively
small and short-duration slip in the southern part of the fault. Rupture velocity is around 3–4 km/s inthe first and third stages, while rupture progression suspended for a while before the rupture of theasperity.

TSUNAMI SIMULATION
Numerical simulations of tsunami require three components: (1) source model, reflecting fault locationand slip distribution; (2) ocean bathymetry and coastal topography, and (3) tsunami propagation andinundation model.
Seafloor displacement modeled as a sum effect of all seismic subsources of the source model,
which are classical dislocation point sources, combining slip motions occurring on the oblique fault
plane embedded into semi-infinite elastic medium (Okada, 1985). Shear modulus equal 4.0x1010
kg/ms2 is assumed. Sea surface elevation (Fig. 2) is then calculated using curve fitting technique ofWatts et al. (2003). We used time dependent slip rate functions estimated by the multi-time window
source inversion on each subfault. We also consider time delay of subsources due to rupture
propagation. Although rupture velocity (~2000 m/s) is much higher than tsunami wave velocity (~500m/s for deep water around trench), weak effect of rupture propagation is possible.
Model of ocean bathymetry and coastal topography is combined from the 500m gridded
bathymetric data set J-EGG500 of the Japan Oceanographic Data Center (JDOC) and 250m gridded
inland topography of the Digital Elevation Model from the Geospatial Information Authority of Japan(GSI). Bathymetry map is shown in Fig. 3. 500m grid gives enough resolution for tsunami propagationand inundation in off-shore area and in simple coast-line environment of Sendai plain and Fukushima
prefecture in the southern part of the source region. However, in the northern part of source region, theRia environment on the Sanriku coast is composed from numerous small size bays, many of them have
only 1-3km size, which are just one-to-few grids of bathymetry model. Large simulation errors ofinundation and run-up are possible here. Another source of the tsunami wave amplification is the
propagation of wave along/above a submarine ridge. Wave velocity become smaller just above theridge and higher in neighboring valleys. This results in the geometrical focusing effect increasing
amplitude of tsunami wave, even in a flat coastal environment. In Fig. 3 potentially dangerous ridges
are shown by arrows.
For tsunami propagation and inundation we use a Boussinesq water wave model developed by
Wei and Kirby (1995) (program FUNWAVE). The model is fully nonlinear and dispersive, retaining
information to all orders in nonlinearity a/h (where a - wave amplitude, and h - water depth). Program
includes bottom dissipation and wave breaking, without which the wave would artificially amplify atthe coast, and allows simulation of the land inundation through a moving shoreline algorithm, which
has been fully validated for short-wave shoaling, breaking and run-up. Method has been calibrated toprovide a stable model for tsunami run-up, and has been successfully used to simulate various regional
earthquake tsunamis, including devastating 2004 Indian Ocean tsunami (e.g. Ioualalen et al., 2006).
Simulation area of the 2011 Tohoku tsunami is limited to 140°-145°E and 35°-41°N, for simulation
we used 500 m finite difference grid and 0.5 sec time step, number of steps is 11000.

TSUNAMI SIMULATION RESULTS
Results of tsunami simulation are compared with the off-shore gauge waveform data of the
Nationwide Ocean Wave Information network for Ports and HArbourS (NOWPHAS,
http://nowphas.mlit.go.jp/) and with on shore inundation data of the Tohoku Earthquake Tsunami

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Fig. 4 Distribution of maximum amplitudes of propagated tsunami waves. Location of the offshoregauges (triangles) and waveguide ridges from Fig. 3 (dashed arrows) are shown for reference. White
arrow points large run-up area in the Sendai plain

Fig. 5 Comparison of observed (upper) and simulated (lower) tsunami waveforms
Survey Group (release 20110601, http://www.coastal.jp/ttjt/). Many coastal tide gauges on the Tohoku
coast were broken by the first tsunami wave. Two offshore floating GPS wave gauges number 804 and802 at a 200m depth (see Fig. 4) and two cable pressure-gauges (TM-1 at 1600 m and TM-2 at 1000 m
depth) are recorded unusual two-stage tsunamis (Fig. 5). The water level gradually increased up to 2 mduring the first 10 minutes, and then impulsive tsunami wave having higher amplitude and shorter
period was observed. At southern GPS gauge number 806, similar two pulses were recorded, although616

Fig. 6 Right: Comparison of observed inundation heights (dots) and simulated peak values (line) for
the inverted source model of Yoshida et al. (2011). Left: Location of observation points
their periods were similar.
Simulation results fit observed tsunami waves in the off-shore area (Fig. 5), both direct wave andlater phases, which we interpret as the reflected waves, and reproduce inundation data on the coast of
the Sendai plain and in Fukushima (Fig. 6). Some variations of the inundation heights are possible
both due to effect of waveguides (e.g. Central Fukushima area) and effect of coastal bathymetry (e.g.
Northern Miyagi area). On the Sanriku coast, north of epicenter, simulated amplitudes are smaller thanobserved ones. Possible reason of the underestimated simulated amplitudes is a small resolution ofused bathymetry data for this area, mentioned above. Simulated waveforms in general reproduce
two-stage feature of the observed waveforms. We suppose that 1st stage is a result of tsunami
generation in a wide subsidence area just north of epicenter, while 2nd stage is result of high uplift ofthe ocean surface on the edge of seismic source near the trench, see Fig. 2. This is supported by backprojection analysis of tsunami arrival times of Hayashi et al. (2011), which show that primary crests oftsunami waves are generated in area centered at point 143.9E/38.5N.

TSUNAMI SIMULATION USING CHARACTERIZED SOURCE MODEL
For prediction of future tsunamis we could try to use source modeling techniques, which weredeveloped for the strong-ground motion prediction (Irikura and Miyake 2010). A basement of theseismic source modeling is scaling relations between the characterized source parameters and seismic
moment, which are result of generalization of the seismic source inversion results. Here we test source
characterization technique for M9 class event on example of the 2011 Tohoku earthquake.
Fig. 7 shows result of characterization of the slip distribution from Fig. 1 using trimming
technique of Somerville et al. (1999). Bold line indicates asperity. Parameters of the characterized
source are shown in Table 1. On Fig. 8 these parameters are compared with the average relationships
for subduction zone earthquakes of Murotani et al. (2008); good agreement is found.
At the next step we simulated tsunami using 500m grid similarly to the first case above. It isnatural that pulse width becomes wider in case of characterized source model. For this reason
waveform agreement become worth in the northern part (gauges 807, 804 and 802), but much better in617

the southern part (gauges 803, 801 and 806). Contrary, maximum inundation heights distribution
didn’t change very much (compare Fig. 9 and Fig. 6). Maximum difference is around 40%, which isnatural payment to the uncertainty of the source model. We conclude that characterized source
approach is promising for tsunami prediction.

Fig. 7 Result of the source model characterization. Thick line indicates characterized asperity.

Fig. 8 Comparison of parameters of the characterized source model (star) with average relationships(line) for subduction zone earthquakes (circle)

Table 1 Parameters of the characterized source model
Source parameter
Total rupture area
Combined area ofasperities
Number of asperities
Average slip
Asperity slip
Background slip

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Value
1.1281x1012 m2
3.1250x1010 m2
1
10.5 m
22 m
6m

Fig. 9 Right: Comparison of observed inundation heights (dots) and simulated peak values (line) forthe characterized source model. Left: Location of observation points
DISCUSSION AND CONCLUSIONS
Tsunami of the 2011 Tohoku earthquake was simulated using source model estimated by inversion of
the long-period strong-motion waveform data. Forward tsunami simulation results demonstrate good
agreement with observation data, namely tsunami waveforms for off-shore gauges and on-shore
inundation heights. We also verified the characterized source model approach, which is widely used
for prediction of the strong ground motions. This indicates that source models developed forprediction of strong ground motions can be used for prediction of tsunami too.
In spite of good fit of tsunami waveforms at off-shore gauges, inundation heights on the Sanriku
coast are underestimated with a factor of 2. Due to effect of source, first tsunami wave at the off-shoregauge 807 in this area is underestimated with a factor of 1.5. Inundation heights underestimation,corrected for this underestimation due to source, can be reduced to a factor of 1.3. There is a tendency
that accurate simulation of the tsunami inundation employing detailed bathymetry data and small
finite-difference grid (20-30 m instead of 500 m used in this study) could improve fit with observation
data. In another case, an additional tsunami source, north of existing source, maybe necessary to
explain high inundation in the North Sanriku Coast. We should notice that existing source is traced by
the aftershock distribution and can not be extended to the north. Additional tsunami source may havedifferent nature, submarine landslide for example.
The two-stage tsunami waveforms, having gradual rise and impulsive high amplitude wave were
well reproduced with a single plane source model due to localization of tsunami source near theeastern shallow edge of fault plane. This effect of our single plane model may mimic similar effect of
the back-stop fault of the real fault model in Japan Trench (Tsuji et al. 2011), or effect of an additional
uplift of sediments near a toe of an inner trench slope due to a large horizontal slip (Tanioka and Seno,
2011, Tanioka et al. 2011). 3D curved fault model may be necessary for accurate source modeling andtsunami simulation. For example, inconsistency of simulated narrow peaks with observed wide peaksin the southern part of the model (gauges 801, 803) may be result of this inaccuracy of the fault
surface modeling.

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ACKNOWLEDGMENTS
We used the tsunami waveform data of the Nationwide Ocean Wave Information network for Portsand Harbours (NOWPHAS), and tsunami field observations of the Joint Tohoku Earthquake Tsunami
Survey Group. Bathymetry models are provided by JODC, JAMSTEC and JHA. We are indebt toJames Kirby, Philip Watts and Stéphan Grilli, provided tsunami simulation program.

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