Proceedings of the International Symposium on Engineering Lessons Learned fromthe 2011 Great East Japan Earthquake, March 1-4, 2012, Tokyo, JapanTHE 2011 OFF THE PACIFIC COAST OFTOHOKU-OKI EARTHQUAKE AND TSUNAMI:
INFLUENCE OF THE SOURCE CHARACTERISTICS
ON THE MAXIMUM TSUNAMI HEIGHTS
Ergin ULUTAS1
1

Department of Geophysical Engineering, Engineering Faculty, Kocaeli University, Kocaeli, Turkey,
ergin@kocaeli.edu.tr

ABSTRACT: This study was undertaken with reference to the Japan earthquake of 11 March
2011. The aim of the study is to simulate the wave propagation of the tsunami of this earthquake, bycomparing with the available deep ocean pressure sensors (DART) and tide gauge records. Nonlinear
shallow water equations are solved with a finite difference scheme, using a computational grid withdifferent cell sizes over GEBCO30 bathymetry data. Co-seismic source models proposed by different
organizations and researchers were carried out to explain the tsunami propagation. The source models
were used to model the deformation on sea bottom which is translated directly to the water surface.
The approach is based on the dislocation algorithm for a finite rectangular fault and empirical scalinglaws for earthquake sources. Based on the various source models, arrival times and maximum wave
heights are presented here followed by the analysis of the results. The assumption of the average
uniform slip models may be a good approach for the tsunami simulations offshore and far from thesource area. However, the heterogeneities of the slip distribution within the fault plane are significant
for the wave amplitude in the near field. For this purpose, a finite fault model was chosen as the finite
fault solution giving us the slip distribution along the fault. The chosen finite fault model was used as
an input for the simulation of the tsunami propagation in the region. The rupture process of the large
finite fault, including multiple fault segments, can profoundly influence the amplitudes, periods andarrival times of the tsunami waves. Thus, the tsunami at an observation point might be obtained bysumming the contributions over all multiple fault segments.
The modeled waves compared with the recorded waves at DART and tide gauge stations in respect
to travel times and maximum amplitudes. The source parameters established from the slip distribution
is efficient to fit the observations, confirming that the tsunami is much more sensitive to the seismic
moment and slip of the source. The results, compared to the observations on DART and tide gauge
records based on the proposed source models, enable the identification of the regions of highest
tsunami waves in the same region.

Key Words: Great East Japan earthquake, tsunami, shallow water theory, tsunami
simulation, fault model602

INTRODUCTION
The March 3, 2011 Tohoku-Oki earthquake generated a tsunami that was observed all over the Pacificregion and caused enormous demolition in coastal Japan. This is is the fourth largest earthquake in theworld and the largest in Japan since instrumental recordings began in 1900. The tsunami is also mostdeadly and destructive event caused by an earthquake after the 2004 Sumatra earthquake. Thisdevastating tsunami mostly affected coastal districts of Iwate, Miyagi, Fukushima, Ibaraki and Chiba
Prefectures with maximum heights greater than 10 m. The official death tall from the earthquake wasconfirmed as 15216 and injured as 5719 (JRCS, 2011). Epicentral parameters from USGS (UnitedStates Geological Survey) are 38.297°N, 142.372°E, origin time 05:46:24 UTC (14:46:24 JST). The
moment magnitude determined by JMA (Japan Meteorological Agency) and USGS was 9.0 with adepth of 23.7 and 30 km respectively. There had been hundreds of aftershocks, many greater thanmagnitude 6 (Fig.1). The largest of the aftershocks was Mw: 7.7. The main shock is much larger thanthe expected earthquakes on the asperities of the Off-Miyagi Prefecture (Yamanaka and Kikuchi 2004).
Although few events greater than magnitude 8.0 have occurred in the last several hundred years in theregion, none of them triggered abnormous high wave tsunami heights as this earthquake. This situation
is an indication of the re-evaluation of tsunami simulations to understand the rupture processing andmechanism of tsunamis consideering the future earthquakes in the same area. Furthermore, it is much
more important than past, as a result of increasing population due to the economic development of thecoastal provinces of Japan.
Tsunamis are very large ocean or sea wave triggered by various large scale disturbances of theocean floor such as submarine earthquakes, volcanic activities or landslides (Yolsal et al., 2007). The
lenghts of tsunami waves may be up to a two hundred kilometers from one wave crest toanother. The length and period of tsunami waves are a function of the sudden vertical changes in thesea floor. The sudden vertical changes cause a large volume of the water to be displaced from its
equilibrium position to new position. The displacement of large bodies of water due to seismic
disturbances results in a change in the body of water rise called tsunami. Although they haverelatively small heights off shore, they may become enormous as they approach shallow coastal areas.
Tectonically active regions like the Japan are adversely and repeatedly hit by tsunamis. The
Pacific coast of Japan has experienced tsunamis from the earthquakes around the Pacific Ocean
several times in this century (Watanabe, 1985; Tanioka et al., 1997). The subduction of Pacific Platealong the Japanese Trench is responsible for many large underthrusting earthquakes and giant tsunamis
in that region. The 2011 off the Pacific coast of Tohoku-Oki Earthquake occurred off the Pacific coastof the northeastern part of Honshu. The occurrence of this earthquake and gigantic tsunami willquantify to examine the different aspects of researchers for the evaluation and assessment ofearthquakes and tsunamis in the region. Hence, it was aimed to consantrate on tsunami simulation of
the 2011 off the Pacific coast of Tohoku-Oki Earthquake by using different orientations of the tsunami
sources and to compare the numerical results with the available data observations.

TSUNAMI SOURCE MODELSThe accurate prediction of maximum heights and tsunami arrival times rely mainly on the estimationof earthquake parameters and fault plane models. The impulsive fault plane models assume that theseafloor deforms instantaneously and the entire fault line ruptures simultaneously (Wang and Liu,
2006). The initial condition for the expected tsunami in the region may be taken to coincide with thevertical coseismic displacement of the sea floor induced by the earthquake. To determine thepropagation time and the final amplitude of tsunamis at a site due to submarine earthquakes, it isnecessary to identify the magnitude, location of epicentre and source parameters of tsunamigenic
earthquakes. The source parameters for tsunami simulations are faulting geometry (source depth,
strike, dip, rake angles), seismic moment, fault surface, fault area, amount of slip, location (distancefrom shore) and beach geometry (water depth and beach slope) (Yolsal, et al., 2007). The verticalco-seismic displacement of the sea floor, assumed to be responsible for the initial water surface603

deformation giving rise to the tsunami, was computed using the dislocation algoritm provided by
Okada (1985) in this study. For this purpose, it was collected the earthquake parameters and source
characterizations issued by different researchers and organizations that would be an input for thetsunami simulations of the earthquake (Table 1).
The size of the source area for this event was given by different researches. The width and lengthof the fault plane (LFP) was suggested from the 150 km to 240 wide km and from 450 to 640 km long.
The aftershock sequence included 3 aftershocks with magnitudes of 7.0 or larger, nearly 40 withmagnitudes between 6.0 and 7.0, and over 350 events in the magnitude range from 5.0 to 6.0 in the
200 km wide, 500 km long aftershock region (Ammon et al., 2011). The aftershocks occurred at anedge of the relatively large slip area of the mainshock (Yoshida et al., 2011). The 200 km wide, 500
km long aftershock region was assumed for the fault area except for the rupture area constructed
through inversion of teleseismic studies referenced in Table 1. The width of the fault plane (WFP) for
this event was estimated as in the following equations due to the measured width yielded by aftershock
distribution:

WFP =

MS
cos(δ )

(1)

where WFP is width of fault plane, MS is measured width, and δ is dip angle. The top of the fault
was calculated as follows:

TOF = h − ((Sinδ )d )(2)

where TOF is top of the fault in km, h is the depth of earthquake (hypocenter), δ is dip angle and dis the half of fault WFP. It was adopted the hypocentral depth estimates for the initiation of theearthquake is 24 km (JMA, 2011) and 30 km (Ammon et al., 2011) respectively. The hypocenter was
assumed at the center of the fault. It should be note that a centroid location, which is a release point ofseismic energy mainly, is not always the same as the hypocenter. Therefore, the hypocentral depths
were used instead of centroid depths to define the size of rupture area. Then, the remained parameters
as it was pointed out before were examined and compiled to provide inputs for the Okada (1985)
vertical dislocation model. In order to make numerical simulations, the different source and rupture
parameters employed. Numerical simulations were performed in 7 stages by considering the different
source parameters as CS (Candidate Sources) (Table 1): 1) the manually determined rCMT (research
CMT) solution 23 minutes after origin time (Polet and Tihio, 2011), (2) the gCMT solution of a CMTs
using long period surface waves issued by National Earthquake Information Center (NEIC) of theUnited States Geological Survey ( USGS, 2011), (3) Moment tensor inversion of 123 W-phaserecordings (Ammon et al., 2011), (4) the rupture process of the earthquake using teleseismic bodywaves located in the 480×150 km2 fault area (Koketsu et al., 2011; Yagi, 2011), (5) Multiple double
couples (MDC) analysis conducted using 1-hour long period seismic waves (Shao et al., 2011), (6)USGS finite fault model (Hayes, 2011), (7) the fault parameters adapted to match the reasonabletsunami simulation waveforms.

604

Fig. 1. Locations of main and aftershocks of Tohoku-Oki Earthquake (Data from NEIC, 2011)

The candidate source (CS) models except CS6 specify the focal geometry and the scalar moment, but
not the slip distribution along the fault; consequently an average uniform slip over the entire fault area
was assumed. If it is assumed an earthquake with magnitude Mw, the amount of slip motions can becomputed using the following equations:

M 0 = µDLW2
M w = log10 M 0 − 10.7
3

(3)
(4)

where µ is the rigidity of earth mantle, D is the amount of average slip motion (slip) and L is thelength of the fault plane and W is the width of the fault plane, Mo is the scalar moment of anearthquake and Mw is the moment magnitude of an earthquake (Aki, 1966; Hanks and Kanamori,1979). The earthquake source parameters, their units, calculated average slip and vertical dislocations
were given in Table 1. The displacements of sea floor calculated for every candidate sources were
given in Fig. 2. On the other hand, the calculation of average slip via equation (3) has limitations dueto the correct estimation of fault width and fault length for up-dip fault motions. However, joint source
inversion results show that the rupture behavior of the earthquake resulted in >50 m slips and therupture occurred on a large triangular shaped slip zone with the average slip over the entire fault model
was about 15-20 m (Lay et al., 2011; Lee et al., 2011). Thus, it was also used 20 m uniform averageslip for the comparisons of the simulations with the DART (Deep-Ocean Assesment and Repoting ofTsunamis) and tide gauge records..

605

Table 1. Source parameters used in this study
Source parameters
Mw
Seismic Moment
Depth (km)
LFP(km)WFP (km)
Strike, Dip, RakeTOF (km)Average Slip (m)Max-Min
Vert.dislocation (m)

CS-1
8.9

CS-2

CS-3

CS-4

CS-5

CS-6

CS-7
(This study)
9.0

24
500

9.1
5.31
30
500

9.0
3.9
30
500

9.0
5.6
23
500

9
3.4
26
480

9.0
4.90
30
550

205

203

205

200

150

260

200

186/12/76
2.74

203/10/88
12.36

202/13/92
7.09

199/10/92
5200/12/83
8.4

7.75

199/10/92
7.5

6.1
2.62
-0,97

13.08
5.35
-2,38

9.47
4.16
-1,42

14.0
5.82
-2,37

11.81
5.00
-2,37

8.57
8.76
-1,95

20
8.27
-3.33

24
500

WFP and Average slip was calculated from Eq .(1) and Equation 3 except for the CS-5 and CS-6
Seismic moment scale: 10**22 Nm

TSUNAMI MODELLING, BATHYMETY DATA, ANALYSIS AND COMPARISONS
Shallow water wave equations that are applicable to cases where the horizontal scale of the flow ismuch bigger than the depth of the fluid are used in tsunami modeling (Liu et al., 2009). Numericalsimulations of tsunami propagation for 7 candidate sources were performed using a model called
TUNAMI-N2 (Imamura et al., 2006). The model was originally authored by Professor Fumihiko
Imamura in Disaster Control Research Center in Tohoku University (Japan) through the Tsunami
Inundation Modeling Exchange (TIME) program (Goto et al., 1997). TUNAMI-N2 is one of the key
tools for developing studies for propagation and coastal amplification of tsunamis in relation to different
initial conditions. GEBCO (General Bathymetric Chart of the Ocean) with a 30 arc-second global
bathymetry data were used in simulations. It was used two levels of computation grids for proper
amplification. The grids consist of a 4’ grid describing the open ocean (Computation area A) and 1’
grid (Computation area B) describing the Coasts of Honshu. The maps of maximum tsunami heights
are shown in Fig. 3. Four deep ocean pressure sensors named DART and tide gauge stations wereused as the comparison points of tsunamis. The locations of DART and tide gauge stations were shownin Figure 3h. 4’ grid was choosen to compare the simulated and observed results in the open ocean. 1’
grid was choosen for the comparison of tide gauges and DART 21418 which is the nearest DART to
Japan. The total calculation time was set to three hours for the computation area of A, and the total
calculation time was set to one hour for the computation area B. Tsunami Analysis Tool (TAT)developed by Annunziato (2007) were used to visualize tsunami travel time, tsunami propagation,
maximum heights and comparison of the results with DART and tide gauge records. For each of thetsunami sources defined in Table 1, time series of sea level were extracted from the model outputs atthe closest grid point to the several observation locations. These time series and simulated tsunami
heigts were shown in Fig. 4. The figures consist of arbitrary chosen observation locations showing theobserved and simulated tsunami heights.

606a) CS-1b) CS-2c) CS-3d) CS-4e) CS-5f) CS-6g) CS-7

Fig. 2. Vertical dislocation of the sea floor due to different source models.

607a) CS-1b) CS-2c) CS-3d) CS-4a) CS-5b) CS-6c) CS-7d) CS-7 (4’ calculation grid)Fig. 3. Maximum computed heights for computation area A and B (CS-7, 4’calculation grid).

608

a) DART 21418 (Red: CS-7, Green: CS-1)b) DART 21418 (Orange CS-2, Purple: CS-3c) DART 21418 (Pink:: CS-6)d) DART 21418 (Brawn:CS-4, Blue: CS-5)e) Ofunato (Red:CS-6, Green: CS-7)e) Choshigyogo (Red: CS-6, Green: CS-7)

Fig. 4. Comparison of the observed (blue) and simulated tsunami heights in several location

CONCLUSIONS AND DISCUSSIONS
Numerical tsunami simulations were conducted with the proposed fault models and assumptions of thefault parameters of March 11, 2011 Mw:9.0 Tohoku-Oki earthquake. Variations in the tsunami wave
field are examined in relation to uniform and non-uniform slip models that are characterized by fault
parameters of the earthquake. The six different candidate sources assuming the uniform slip werecompared with the slip distribution model issued by USGS. After employing the different source
models and assumed fault parameters, the maximum vertical dislocations of the sea floor were
calculated 2.62, 5.35, 4.16, 5.82, 5.00, 8.76 and 8.27 for CS-1, CS-2, CS-3, CS-4, CS-5, CS-6 andCS-7 candidate sources respectively. The results show that an assumption of uniform slip
underestimates the maximum height of tsunami amplitude by using the Eq. (3) in this earthquake dueto the various predicted seismic moments. Thus, it should be noted that it is often difficult to validate
the average slip due to the predicted length and width of the fault plane. Tests of assuming different
average slip values indicate that the lower values of average slip calculated from Eq. (3) due to the fault
area may not qualify the correct tsunami predictions in comparison to non-uniform slip distributions. It
is still a challenge to use non-uniform slip distributions so-called finite fault models immediately after
the earthquake in tsunami predictions. Because the calculation techniques are based on static andseismic data inversion selected based upon data quality and azimuthal distribution. Thus, the finite
fault models may not be performed in a reasonable time that provides us multiple fault segments ofvariable local slip, rake angle, depth, rupture time and several other parameters.
The results also show that the most critical parameter affecting the tsunami heights is theprediction of seismic moment, dip of the fault, average slip and determination of the depth of top of
the fault. The results show that the depth of top of the fault affects the tsunami heights due to thelarge width and large length of the fault. Hence, it should be note that the estimation of the hypocenter
is important especially large mega thrust earthquakes. Near real time determination of seismic
moments were issued lower immediately after the earthquake. Thus, the tsunami wave heights were
simulated lower due to the rapid prediction of seismic moments issued by seismological organizations
than those of post-event analysis. In summary, the findings of this study could be use to understand theeffect of different source parameters on tsunami simulations. The goal of the study was not based onmodeling the inundation area. However, the findings may be used by decision-makers that address the
maximum heights of waves for the Honshu Island coasts.

609

ACKNOWLEDGMENTS
I would like to thank A. Annunziato for sharing Tsunami Analysis Tool (TAT) program visualizing
tsunami simulations and comparing the simulations with DART and tide gauge records. I am also
grateful to Japan Meteorology Agency for providing tide gauge data.

REFERENCES
Aki, K. (1966). “Generation and propagation of G waves from the Niigata earthquake of June 14,
1964. Part 2. Estimation of earthquake moment, released energy and stress-strain drop from G
wave spectrum”, Bull. Earth. Res. Inst., Vol. 44, 73-88.
Ammon, C.J., Lay, T., Kanamori, H. and Cleveland, M. (2011). “A rupture model of the 2011 off the
Pacific coast of Tohoku-Oki Earthquake.” Earth Planets Space, Vol. 63, 693–696.
Annunziato, A. (2007). “The Tsunamı Assesment Modellıng System by the Joint Research Center”
Science of Tsunami Hazards, Vol, 26, 70-92.
Goto C, Ogawa Y, Shuto N, Imamura F. (1997). “Numerical Method of Tsunami Simulation with theLeap-Frog Scheme (IUGG/IOC Time Project)” IOC Manual, UNESCO, No. 35.
Hanks, T.C., and Kanamori, H. (1979). “A moment magnitude scale” Journal of Geophysical Research,
Vol.84, 2348-2350.
Hayes, G. (2011). “ Finite Fault Model,Updated Result of the Mar 11, 2011 Mw 9.0 Earthquake
Offshore Honshu, Japan”
http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/finite_fault.php
Imamura, F., Yalciner, A.C. and Ozyurt, G. (2006). “Tsunami Modelling Manual” available from:http://ioc3.unesco.org/TsunamiTeacher/data/Resource/PDF/PubPriv_109_TMM.pdf,(accessed
on 25 Novamber 2011).
JMA: Japan Meoerological Agency. (2011). “The 2011 off the Pacific coast of Tohoku Earthquake–Portal”, available from: http://www.jma.go.jp/jma/en/2011_Earthquake.html.
JRCS: Japanese Red Cross Society. (2011). 6 Month Report Glide no. EQ-2011-000028-JPN August
31.
Kazuki Koketsu, K.,Yokota, Y.,Nishimura, N.,Yagi, Y.,Miyazaki, S., Satake, K.,Fujii, Y., Miyake H.,
Sakai, S.,Yamanaka, Y., and Okada, T. (2011) “ A unified source model for the 2011 Tohoku
earthquake.” Earth and Planetary Science Letters, Vol. 310, 480–487.
Lay, T., Ammon, C.J., Kanamori, H., Xue, L., and Marina J.K Kim. (2011). “Possible large near-trenchslip during the 2011 Mw 9.0 off the Pacific coast of Tohoku Earthquake.” Earth Planets Space, 63,
687–692.
Lee, S-J., Huang, B-S., Ando, M., Chiu, H-C., and Wang, J-H. (2011). “Evidence of large scale
repeating slip during the 2011 Tohoku-Oki earthquake” Geophysical Research Letters, Vol. 38,
L19306, doi:10.1029/2011GL049580.
Liu, Y., Shi, Y., David, A.y., Serve, E.O.D., Yuan, X., and Xing, H.L. (2009) “Comparison of linear andnonlinear shallow wave water equations applied to tsunami waves over the China Sea.” Acta
Geotechnica, Vol. 4, 129–137.
NEIC: National Earthquake Information Center. (2011). “Earthquake Search Results” available from:http://neic.usgs.gov
Okada, Y. (1985). “Surface deformation due to shear and tensile faults in a half-space.” Bulletin of the
Seismological Society of America.” Bulletin of the Seismological Society of America, Vol. 75,
1135-1154.
Polet, J. and Thio, H.K. (2011). “Rapid calculation of a Centroid Moment Tensor and waveheight
predictions around the north Pacific for the 2011 off the Pacific coast of Tohoku Earthquake.”610

Earth Planets Space, Vol.63, 541–545.
Shao, G., Liu, X., Ji, C. and Maeda, T. (2011). “Focal mechanism and slip history of the 2011 Mw
9.1 off the Pacific coast of Tohoku Earthquake, constrained with teleseismic body and surface
waves” Earth Planets Space, 63, 559–564, 2011
Tanioka, Y., Ruff, L., and Satake, K. (1997) “What controls the lateral variation of large earthquake
occurrence along the Japan Trench.” The Island Arc, 6, 261-266.
USGS: U.S. Geological Survey. (2011). “Global CMT Project Moment Tensor Solution,
http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/neic_c0001xgp_gcmt.php,
Wang, X.M., Liu, P.L.F. (2006) “An analysis of 2004 Sumatra earthquake fault plane mechanisms andIndian Ocean tsunami.” Journal of Hydraulic Research, Vol. 44, 147–154.
Watanabe, H. (1985). “Hazardous Tsunami Calatalogues in Japan.” Univ. Tokyo Press, 206 pp.
Yagi, Y. (2011). “The 2011 Tohoku-oki Earthquake (Ver. 3)”
http://www.geol.tsukuba.ac.jp/~yagi-y/EQ/Tohoku/index-e.html
Yamanaka, Y. and Kikuchi, M. (2004). “Asperity map along the subduction zone in northeastern Japan
inferred from regional seismic data.” Journal of Geophysical Research, Vol. 109, B07307,
doi:10.1029/2003JB002683.
Yolsal, S., Taymaz, T. and Yalciner, A.C. (2007). “Understanding tsunamis, potential source regions
and tsunami-prone mechanisms in the Eastern Mediterrenean.” Geological Society of London,
Special Publication, Vol. 291, 201-230.
Yoshida, Y., Ueno, H., Muto, D. and Aoki, S. (2011). “Source process of the 2011 Off the Pacific
Coast of Tohoku-Oki earthquake with the combination of teleseismic and strong motion data.”
Earth Planets Space, Vol. 58, 1–5.

.

611