Tanioka et al. Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-019-0278-x(2019) 6:30

Progress in Earth andPlanetary Science

RESEARCH ARTICLE

Open Access

Generation mechanism of large later
phases of the 2011 Tohoku-oki tsunami
causing damages in Hakodate,
Hokkaido, Japan
Yuichiro Tanioka1*, Mizuho Shibata2, Yusuke Yamanaka3, Aditya Riadi Gusman4 and Kei Ioki5

Abstract
The 2011 Tohoku-oki earthquake generated a large tsunami that caused catastrophic damage along the Pacificcoast of Japan. The major portion of the damage along the Pacific coast of Tohoku in Japan was mainly caused by
the first few cycles of tsunami waves. However, the largest phase of the tsunami arriving surprisingly late in
Hakodate in Hokkaido, Japan; that is, approximately 9 h after the origin time of the earthquake. It is important tounderstand the generation mechanism of this large later phase. The tsunami was numerically computed by solving
both linear shallow water equations and non-linear shallow water equations with moving boundary conditions
throughout the computational area. The later tsunami phases observed on southern Hokkaido can be much better
explained by tsunami waveforms computed by solving the non-linear equations than by those computed bysolving the linear equations. This suggests that the later tsunami waves arrived at the Hokkaido coast after
propagating along the Pacific coast of the Tohoku region with repeated inundations far inland or reflecting fromthe coast of Tohoku after the inundation. The spectral analysis of the observed waveform at Hakodate tide gaugeshows that the later tsunami that arrived between 7.5 and 9.5 h after the earthquake mainly contains a period of
45–50 min. The normal modes of Hakodate Bay were also computed to obtain the eigen periods, eigenfunctions,and spatial distribution of water heights. The computed tsunami height distributions near Hakodate and thefundamental mode of Hakodate Bay indicate that the large later phases are mainly caused by the resonance of thebay, which has a period of approximately 50 min. The results also indicate that the tsunami wave heights near the
Hakodate port area, the most populated area in Hakodate, are the largest in the bay because of the resonance ofthe fundamental mode of the bay. The results of this study suggest that large future tsunamis might excite thefundamental mode of Hakodate Bay and cause large later phases near the Hakodate port.
Keywords: Tsunami numerical simulation, Resonance of Hakodate Bay, Large late phase, 2011 Tohoku-oki earthquake

Introduction
The 2011 Tohoku-oki earthquake (Mw9.1) generated alarge tsunami, more than 20 m in height, which caused
catastrophic damage along the Pacific coast of the Tohoku region in Japan (Mori and Takahashi 2012). The
earthquake occurred at 14:46 on 11 March 2011. The
first destructive tsunami arrived along the Sanriku Coast
approximately 30 min after the origin time of the* Correspondence: tanioka@sci.hokudai.ac.jp1
Institute of Seismology and Volcanology, Faculty of Science, Hokkaido
University, N10W8 Kita-ku, Sapporo, Hokkaido 060-0810, Japan
Full list of author information is available at the end of the article

earthquake, and it arrived at the Sendai Plain approximately 70 min after the origin time (Japan Meteorological
Agency 2012) (Fig. 1). Although tsunamis repeatedly arrived along the Pacific coast of the Tohoku region, destructive tsunamis typically occurred during the first few cyclesof waves. Along the Pacific coast of Hokkaido in the northern part of Japan, the first tsunami wave arrived approximately 50 to 100 min after the earthquake. However, thelargest tsunami wave in this region was typically a later
phase of the tsunami. The largest tsunami, with a height of
2.4 m, arrived at mid-night in Hakodate when most people
slept. Surprisingly, it arrived approximately 9 h after the© The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to
the Creative Commons license, and indicate if changes were made.

Tanioka et al. Progress in Earth and Planetary Science(2019) 6:30

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Fig. 1 The slip distribution of the 2011 Tohoku-oki earthquake (Fujii et al. 2011) used to compute tsunamis in this study. The diamonds show thelocations of the four tide gauges, that is, Hakodate, Tomakomai, Tomakomai-nishi, and Urakawa, to compare the observed and computed
tsunami waveforms. The original tsunami waveform (without tide removal) observed in Hakodate (Japan Meteorological Agency 2012) isdisplayed in the middle

Tanioka et al. Progress in Earth and Planetary Science(2019) 6:30

earthquake (Fig. 1). We found several pictures of the tsunami inundation on the internet; they were taken during
the night in Hakodate. Photographs of the tsunamis werealso taken from the top of the building near the Hakodate
harbor by NHK, the Japan Broadcasting Corporation. Figure 1 shows that the tide in Hakodate was much smaller
than the tsunami waves and thus could not have caused
the largest tsunami that occurred during the night. To support the importance of a long-time tsunami evacuations, it
is important to understand the generation mechanism of
the large later phases, particularly in Hakodate.
Previously, the 2004 Kushiro earthquake in Hokkaido also resulted in a relatively large later tsunami,
which arrived approximately 1 h after the first, one in
Urakawa. This later tsunami was generated by anedge wave that propagated across the large shallow
water area off Cape Erimo, Hokkaido (Tanioka and
Katsumata 2007). As far-field tsunamis, the 2006
earthquake caused large later tsunami waves, approximately 3 to 6 h after the first tsunami wave, along the
Pacific coast of Japan. These later tsunamis were generated by the scattering of tsunami waves in the shallow region near the Emperor Seamounts in the
Pacific Ocean (Koshimura et al. 2008; Tanioka et al.
2008). The 2006 Kurile earthquake also caused a large
destructive later tsunami at Crescent City along theWest Coast of the USA. This large later tsunami was
generated by the combination of the shallow bathymetry near the Mendocino Escarpment off Crescent
City, amplification of the tsunami heights by the oscillation at the continental shelf, and resonance of the
Crescent City harbor (Horrillo et al. 2008; Kowalik
et al. 2008). The 2011 Tohoku-oki tsunami also
propagated across the Pacific Ocean and caused
strong currents around the Hawaiian Islands that led
to the closure of harbors for up to 38 h. The long
duration of the strong currents was caused by themultiscale resonance of the shallow water surrounding the island chain, an island with interconnectedshelves, and reefs and harbors (Cheung et al. 2013).
Borrero et al. (2013) also reported tsunami waves arriving late in New Zealand, which were caused by
the 2011 Tohoku-oki earthquake.
In this study, we computed 10 h of the 2011 Tohoku
tsunami after the origin time of the earthquake. The observed tsunami waveforms recorded at several tidegauges along the Pacific coast on southern Hokkaido
were compared with the computed ones to check thatthe later phases were well simulated. Subsequently, thegeneration mechanism of the large later tsunami wave in
Hakodate was identified using the spectral analysis of
the observed waveform, computed tsunami propagation
snapshots off the Hakodate area, and resonance modes
computed for Hakodate Bay.

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Methods/Experimental
Waveform data

Original waveforms observed at two tide gauges in Hakodate and Urakawa (Fig. 1) were digitized from the report ofthe 2011 Tohoku-oki earthquake by the Japan Meteorological Agency (JMA 2012). The observed digital tsunami
waveform data, from which the ocean tides at a tide gaugein Tomakomai-nishi and a coastal wavemeter in Tomakomai were removed, were provided by the Nationwide Ocean
Wave Information Network for Ports and Harbors (NOWPHAS); the data were obtained from the NOWPHAS website (https://nowphas.mlit.go.jp/prg/pastdata). The observed
waveform data were compared with the computed tsunami
waveforms to check that the observed later phases of thetsunami were well reproduced by those computed.
Tsunami simulation

Several source models for the 2011 Tohoku-oki earthquake have been suggested to explain the observed tsunami (e.g., Fujii et al. 2011; Gusman et al. 2012; Satake
et al. 2013; Tappin et al. 2014; Yamazaki et al. 2018). In
this study, the slip distribution estimated from the tsunami waveforms observed at tide gauges, offshore GPS
wave gauges, and bottom pressure gauges near Japan(Fujii et al. 2011) (Fig. 1) was chosen as source model tonumerically compute the tsunami.
The large later phases of the tsunami observed onsouthern Hokkaido, such as in Hakodate, did not directly propagate from the source but propagated along
the Pacific coast of the Tohoku region as edge waves
with repeated inundations far-inland or were reflectedfrom the coast of Tohoku after the inundation. This indicates that the tsunami inundation computations along
the Tohoku and Hokkaido coasts are necessary to reproduce the later phases of the observed tsunami in Hakodate on Hokkaido. In this study, first, the tsunami wasnumerically computed by solving the linear shallow
water equation using a totally reflected boundary condition
along the coast. Next, a tsunami numerical inundation
computation was carried out by solving the non-linear shallow water equations using a moving boundary condition(Imamura 1996; Goto et al. 1997) throughout the entire
computational area (Fig. 1). A homogeneous Manning’s
roughness coefficient of 0.025 m−1/3s was assumed for thebottom surface. A grid system of 30 arc-seconds was used
for these simulations. The time step was set to 0.5 s by satisfying the stability condition.
Spectral analysis of observed tsunami waveform

Temporal variations in the frequency or period of thetsunami waveform observed in Hakodate were computed using the method proposed by Rabinovich et al.
(2006) and Rabinovich and Thomson (2007). Thismethod is based on narrow-band filters, with a Gaussian

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window, Hn(ω), that isolates a specific center frequency,
ωn = 2πfn:

cannot be explained by the computed ones and aremostly overestimated. These later tsunamis arriving at
the tide gauge stations on southern Hokkaido propagated along the Pacific coast of the Tohoku region withrepeated inundations far inland or were reflected fromthe coast of Tohoku after the inundation. When large
tsunamis propagate far inland, their energy is dissipatedby the bottom friction. Therefore, the amplitude of thereflected tsunami is reduced. Thus, the tsunami numerical simulation based on the totally reflected boundary
condition at the coast cannot reproduce the later phasesof the observed tsunamis on southern Hokkaido. Hence,the computed results cannot be used to discuss the generation mechanism of the largest later tsunami phases
observed in Hakodate.
Next, the tsunami waveforms computed by solving thenon-linear shallow water equations using a moving
boundary condition were compared with the observations, as shown in Fig. 3. In this case, not only the firstwave but also the later phases of the observed tsunami
waveforms at the four tide gauges were well explainedby the computations. We therefore used the results ofthis simulation to analyze the largest later phase observed at the tide gauge in Hakodate.
To investigate the generation mechanism of the large
sinusoidal waves that were observed between 7.5 h (450min) and 9.5 h (570 min) after the earthquake, as shownin Fig. 3a, four snapshots of the tsunami height distribution taken near Hakodate 460, 480, 505, and 535 minafter the earthquake occurrence were used (Fig. 4). The
sinusoidal waves have a period of approximately 50 min.
The snapshots are taken 460 and 505 min after theearthquake correspond to the bottom of two troughs inthe time series of the tsunami waveform arriving in
Hakodate between 450 and 570 min after the earthquake, as shown in Fig. 3a. Both snapshots of the tsunami height distributions show that the entire sea at
Hakodate Bay subsided. However, the snapshots aretaken 480 and 535 min after the earthquake correspondto the top of two peaks in the same time series of thetsunami waveform (Fig. 3a). Both snapshots of these tsunami height distributions show that the entire sea in
Hakodate Bay rose in those cases. These results suggestthat the resonance of the fundamental mode of Hakodate Bay is responsible for the generation of the large
later phases at the tide gauge in Hakodate.

Tanioka et al. Progress in Earth and Planetary ScienceH n ðωÞ ¼ e−αð ω Þ

ω−ωn 2

ð1Þ

The frequency resolution is controlled by the parameter α. The higher the value of α is, the better is theresolution in the frequency domain, but the poorer isthe resolution in the time domain. In this study, we
chose the same value as that used in Rabinovich et al.
(2006), that is, α = 80. The demodulation of the observed
tsunami time series produces a matrix of amplitudes ofwave motions with columns representing times and rows
representing periods.
Computation of the resonance modes for Hakodate Bay

The normal mode solution of the linear shallow waterequation for an irregular bay has been numerically obtained by several researchers (Loomis 1975; Satake andShimazaki 1987; Satake and Shimazaki 1988; Horrillo et
al. 2008). Wu and Satake (2018) also computed normal
mode solutions for the Sea of Japan. The wave equation
for the linear shallow water approximation is as follows:∂2 h¼ g∇∙ðd∇hÞ
∂t 2

ð2Þ

where h is the wave height, g is the gravitational acceleration, and d is the water depth. By assuming that thewave height periodically changes over time, h can be
expressed as follows:hðx; y; t Þ ¼ Φðx; yÞ expðiωt Þ

ð3Þwhere Φ(x, y) is the spatial distribution of the wave
height and ω is the angular frequency. Substituting (3)into (2), we obtain:∇∙ðd∇ΦÞ ¼ λΦwhere λ ¼ −ω2 =g:ð4ÞThis is an eigenvalue problem with the eigenvalue λand eigenfunction Φ(x, y). The symmetrical numericalform of Eq. (4), as shown by Loomis (1975), is solved toobtain the eigen period and eigenfunction Φ(x, y), thatis, the spatial distribution of the water height.

Results
Tsunami numerical simulation

First, the tsunami waveforms computed by solving thelinear shallow water equations were compared with theobservations, as shown in Fig. 2. The first arrival wavesof the observed tsunami waveforms occurring at fourtide gauge stations, that is, Hakodate, Tomakomai,
Tomakomai-nishi, and Urakawa, are relatively well explained by the computations. However, the later phasesof the observed tsunami waveforms at these stations

Spectral analysis of observed tsunami waveform in Hakodate

Figure 5 shows the result of the spectral analysis of thetsunami waveform in Hakodate; the period of theobserved tsunami exhibits a temporal variation. The
observed tsunami has a main period of 45–50 min
throughout the record after its arrival, that is, about 90
min after the earthquake. The initial part of the tsunami

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Fig. 2 Comparison of observed (blue) and computed (orange) tsunami waveforms by solving the linear shallow water equations at four tidegauges, in a Hakodate, b Tomakomai, c Tomakomai-nishi, and d Urakawa, shown in Fig. 1

during 3 h after the tsunami arrival has a shorter periodof 25–28 min. However, this shorter period disappears in
the later part of the tsunami. This indicates that the energy of the tsunami with a shorter period was dissipatedmore by the bottom friction during the inundation thanthat of the tsunami with a longer period. The large latertsunami that was observed between 7.5 h (450 min) and9.5 h (570 min) after the earthquake contains a strong

with a period of 45–50 min within a broader period of
45–58 min and a weak peak with a period of 32–38 min.
Normal mode calculation for Hakodate Bay

Figure 6 shows the results of the normal mode calculation for Hakodate Bay. In this calculation, a node wasset at the mouth of Hakodate Bay as shown in Fig. 6.
The fundamental mode has an eigen period of 49.60

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Fig. 3 Comparison of observed (blue) and computed (orange) tsunami waveforms by solving the non-linear shallow water equations with amoving boundary condition at the four tide gauges, in a Hakodate, b Tomakomai, c Tomakomai-nishi, and d Urakawa. The sinusoidal latertsunami phases that arrived in Hakodate between 7.5 and 9.5 h after the earthquake were investigated. Snapshots of the tsunami height
distribution were taken 460, 480, 505, and 534 min after the earthquake (red lines) and were analyzed (Fig. 4)

min. The observed later tsunami had a main period near
the eigen period (approximately 50 min), which indicatesthat the fundamental mode was excited by the 2011
Tohoku-oki tsunami (Fig. 3a and Fig. 5). The eigenfunction, that is, the spatial distribution of the water height,of the first mode in Fig. 6a is large near the Hakodate
port area, which is the most populated region of Hakodate.
The eigenfunction is also similar to the tsunami height distribution computed for Hakodate Bay (four snapshots in
Fig. 4). This confirms that the first mode was excited by theTanioka et al. Progress in Earth and Planetary Science(2019) 6:30

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Fig. 4 Snapshots of the tsunami height distribution around Hakodate taken 460, 480, 505, and 535 min after the earthquake, as shownin Fig. 3a2011 Tohoku-oki tsunami and is the main cause of thelarge later tsunami phases observed in Hakodate. The second mode has an eigen period of 38.69 min (Fig. 5b). The
eigenfunction of the second mode has another node off the
Hakodate port at Hakodate Bay. The eigenfunction of thesecond mode in Fig. 5b is also large near the Hakodate port
area. The eigen period of the second mode is similar to a
weak peak with a period of about 32–38 min between 7.5 h
and 9.5 h after the earthquake occurrence (Fig. 5). The second mode may therefore be slightly excited. The eigen periods of the other modes are much shorter and not
responsible for the large later phase.

Discussion and conclusions
This study shows that the later tsunami phases along
the Pacific coast of the Hokkaido region, which werecomputed by solving the non-linear shallow waterequations with a moving boundary condition, explain
the observed tsunamis much better than those computed by solving the linear shallow water equations.
This indicates that the later tsunami waves arrived at
the tide gauge in Hakodate after propagating along
the Pacific coast of the Tohoku region as edge waves
with repeated inundations far inland or reflectingfrom the coast of Tohoku after the inundation. The

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Fig. 5 A period-time plot for the 2011 Tohoku-oki tsunami observed at a tide gauge in Hakodate. The time axis is based on the origin time ofthe earthquake. Amplitudes are given in decibels based on the maximum amplitude

spectral analysis of the waveform shows that the tsunami observed in Hakodate has a period of 45–50
min throughout the record after its arrival. This indicates that the tsunami waves that arrived at themouth of Hakodate Bay excited the first mode of

Hakodate Bay. The later tsunami waves mainly excited the first mode of the bay after propagating
along the Pacific coast of the Tohoku region.
The eigenfunction of the first mode, that is, the spatial
water height distribution, is the largest near the

Fig. 6 Eigenfunctions, that is, the spatial distributions of the water heights, and eigen periods of the first mode (a), fundamental mode, andsecond mode (b) computed from actual bathymetry for Hakodate Bay. The red ellipse shows the Hakodate port area which is the mostpopulated and famous tourist area in Hakodate

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Hakodate port area, which is the most populated andfamous tourist area in Hakodate. Large future tsunamis
might excite the first mode of Hakodate Bay and cause
large later phases near the Hakodate port. The residents
and local disaster management office of Hakodate
should be aware that there is a high possibility of large
later tsunamis near the Hakodate port area when a tsunami warning is issued from the JMA. Citizens need tobe evacuated from tsunami-affected areas for a much
longer time than expected.

Horrillo J, Knight W, Kowalik Z (2008) Kuril Islands tsunami of November 2006: 2.
Impact at Crescent City by local enhancement. J Geophys Res 113:C01021.
https://doi.org/10.1029/2007JC004404
Imamura F (1996) Review of tsunami simulation with a finite difference method.
In: Yeh H, Liu P, Synolakis C (eds) Long-Wave run-up models. World Scientific,
Singapore, pp 231–241
Japan Meteorological Agency (2012) Report on the 2011 off the Pacific coast of
Tohoku earthquake, Technical Report of the Japan Meteorological Agency,
133, 479 pp. (in Japanese)
Koshimura S, Hayashi Y, Munemoto K, Imamura F (2008) Effect of the emperor
seamounts on trans-oceanic propagation of the 2006 Kuril Island earthquake
tsunami. Geophys Res Let 35:L02611. https://doi.org/10.1029/2007GL032129
Kowalik Z, Horrillo J, Knight W, Logan T (2008) Kuril Islands tsunami of November
2006: 1. Impact at Crescent City by distant scattering. J Geophys Res 113:
C01020. https://doi.org/10.1029/2007JC004402
Loomis H. G. (1975) Normal modes of oscillation of Honolulu harbor, Hawaii,
Hawaii Inst. Geophys. Rep., HIG-75-20, 20 pp.
Mori N, Takahashi T (2012) The 2011 Tohoku earthquake tsunami joint survey
group, 2012, Nationwide post event survey and analysis of the 2011 Tohoku
earthquake tsunami. Coastal Eng J 54(1):1250001. https://doi.org/10.1142/
S0578563412500015
Rabinovich AB, Thomson RE (2007) The 26 December 2004 Sumatra tsunami:
analysis of tide gauge data from the world ocean part 1. Indian Ocean andSouth Africa. Pure Appl Geophys 164:261–308
Rabinovich AB, Thomson RE, Stephenson FE (2006) The Sumatra tsunami of 26
December 2004 as observed in the North Pacific and North Atlantic oceans.
Surv Geophys 27:647–677. https://doi.org/10.1007/s10712-006-9000-9
Satake K, Fujii Y, Harada T, Namegaya Y (2013) Time and space distribution of
coseismic slip of the 2011 Tohoku earthquake as inferred from tsunami
waveform data. Bull Seis Soc Am 103(2B):1473–1492. https://doi.org/10.1785/
0120120122
Satake K, Shimazaki K (1987) Computation of tsunami waveforms by a superposition of
normal modes, J. Phys. Earth, 35:409–414.
Satake K, Shimazaki K (1988) Free oscillation of the Japan Sea excited byearthquakes – II. Model approach and synthetic tsunamis. Geophys J
93:457–463
Tanioka Y, Hasegawa Y, Kuwayama T (2008) Tsunami waveform analyses of the 2006
underthrust and 2007 outer-rise Kurile earthquakes. Adv Geosci 14:129–134
Tanioka Y, Katsumata K (2007) Tsunami generated by the 2004 Kushiro-oki
earthquake. Earth Planets Space 59:e1–e3
Tappin DR, Grilli ST, Harris JC, Geller RJ, Masterlark T, Kirby JT, Shi F, Ma G,
Thingbaijam KKS, Mai PM (2014) Did a submarine landslide contribute to the2011 Tohoku tsunami? Marine Geology 357:344–361. https://doi.org/10.1016/
j.margeo.2014.09.043
Wu Y, Satake K (2018) Synthesis and source characteristics of tsunamis in the sea
of Japan based on normal-mode method. J Geophys Res 123:5760–5773.
https://doi.org/10.1029/2018JB01570
Yamazaki Y, Cheung KF, Lay T (2018) A self-consistent fault slip model for the2011 Tohoku earthquake and tsunami. J Geophys Res SE 123:1435–1458.
https://doi.org/10.1002/2017JB014749

Tanioka et al. Progress in Earth and Planetary Science

Acknowledgements
We would like to thank Editage (www.editage.jp) for English language
editing. We thank two anonymous reviewers for helpful comments toimprove the manuscript.
Funding
This study was supported by the Ministry of Education, Culture, Sports,
Science and Technology (MEXT) of Japan, under its Earthquake and Volcano
Hazards Observation and Research Program.
Availability of data and materials
Data sharing not applicable to this article. Please contact author for data requests.
Authors’ contributions
YT proposed the topic, conceived and designed the study, and computed
the normal mode. MS carried out the tsunami simulation and analyzed thecomputed data. YY helped the interpretation of the results. AG helped in theconstruction of the tsunami simulation program. KI helped in the installationof the tsunami simulation program and the interpretation of the result. All
authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.
Author details
1
Institute of Seismology and Volcanology, Faculty of Science, Hokkaido
University, N10W8 Kita-ku, Sapporo, Hokkaido 060-0810, Japan. 2JR Central
Japan Railway Company, Nagoya, Aichi 450-6101, Japan. 3Department of Civil
Engineering, The University of Tokyo, Tokyo 113-8656, Japan. 4GNS Science, 1
Fairway Drive, Avalon, Lower Hutt 5010, New Zealand. 5National Institute ofAdvanced Industrial Science and Technology, Tsukuba 305-8560, Japan.
Received: 17 October 2018 Accepted: 12 March 2019

References
Borrero JC, Bell R, Csato C, DeLange W, Goring D, Greer SD et al (2013)
Observations, effects and real time assessment of the March 11, 2011
Tohoku-oki tsunami in New Zealand. Pure Appl Geophys 170:1229–1248
Cheung KF, Bai Y, Yamazaki Y (2013) Surges around the Hawaiian islands fromthe 2011 Tohoku tsunami. J Geophys Res: Oceans 118:5703–5719. https://doi.
org/10.1002/jgrc.20413
Fujii Y, Satake K, Sakai S, Shinohara M, Kanazawa T (2011) Tsunami source of the2011 off the Pacific coast of Tohoku earthquake. Earth Planets Space 63:55.
https://doi.org/10.5047/eps.2011.06.010
Goto C, Ogawa Y, Shuto N, Imamura F (1997) Numerical method of tsunami
simulation with the leap-flog scheme, IUGG/IOC TIME project, IOC manualand guides, vol 35, Paris, pp 1–126. https://www.jodc.go.jp/info/ioc_doc/
Manual/122367eb.pdf
Gusman AR, Tanioka Y, Sakai S, Tsushima H (2012) Source model of the great
2011 Tohoku earthquake estimated from tsunami waveforms and crustal
deformation data. Earth Planet Sci Lett 341:234–242. https://doi.org/10.1016/j.
epsl.2012.06.006