1 Tsunami source of the 2011 off the Pacific coast of Tohoku, Japan 1 earthquake 2 3 Yushiro Fujii 1 , Kenji Satake 2 , Shin-ichi Sakai 2 , Masanao Shinohara 2 and 4 Toshihiko Kanazawa 2 5 6 7 1 International Institute of Seismology and Earthquake Engineering (IISEE), 8 Building Research Institute (BRI) 9 1-3 Tachihara, Tsukuba, Ibaraki 305-0802, Japan 10 11 2 Earthquake Research Institute (ERI), 12 University of Tokyo 13 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan 14 15 Submitted to EPS (Letter to the Editor) on April 9, 2011 16 Revised June 6, 2011 17 Accepted June 7, 2011 18 19
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Tsunami source of the 2011 off the Pacific coast of Tohoku, Japan 1
earthquake 2
3
Yushiro Fujii1, Kenji Satake2, Shin-ichi Sakai2, Masanao Shinohara2 and 4
Toshihiko Kanazawa2 5
6
7
1International Institute of Seismology and Earthquake Engineering (IISEE), 8
Building Research Institute (BRI) 9
1-3 Tachihara, Tsukuba, Ibaraki 305-0802, Japan 10
11
2 Earthquake Research Institute (ERI), 12
University of Tokyo 13
1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan 14
15
Submitted to EPS (Letter to the Editor) on April 9, 2011 16
Revised June 6, 2011 17
Accepted June 7, 2011 18
19
2
Abstract 20
Tsunami waveform inversion for the 11 March 2011 off Pacific coast of Tohoku 21
earthquake (M 9.0) indicates that source of the largest tsunami was located near 22
the axis of the Japan trench. Ocean bottom pressure and GPS wave gauges recorded 23
two-step tsunami waveforms, gradual increase of water level (~ 2 m) followed by an 24
impulsive tsunami wave (3 to 5 m). The slip distribution estimated from 33 coastal 25
tide gauges, offshore GPS wave gauges and bottom pressure gauges show that the 26
large slip, more than 40 m, was located along the trench axis. This offshore slip, 27
similar but much larger than the 1896 Sanriku “tsunami earthquake,” is 28
responsible to the recorded large impulsive peak. Large slip on the plate interface at 29
southern Sanriku-oki (~30 m) and Miyagi-oki (~17 m) around the epicenter, similar 30
location with larger slip than the previously proposed fault model of the 869 Jogan 31
earthquake, is responsible to the initial water rise and presumably large tsunami 32
inundation in Sendai plain. The interplate slip is ~ 10 m in Fukushima-oki, and less 33
than 3 m in Ibaraki-oki region. The total seismic moment is estimated as 3.8 × 1022 34
Nm (Mw = 9.0). 35
36
1. Introduction 37
3
A giant earthquake off the Pacific coast of Tohoku, Japan (38.1035°N, 38
142.861°E, M 9.0 at 14:46:18 JST according to Japan Meteorological Agency) on 39
March 11, 2011 generated a huge tsunami and caused 15,073 fatalities and 8,657 40
missing in Tohoku and Kanto regions (The National Police Agency, as of 26 May 41
2011). The USGS W phase moment tensor solution shows a shallow dipping thrust 42
mechanism with a strike parallel to the Japan trench, indicating an interplate 43
earthquake associated with the subduction of Pacific plate (Fig.1). Continuous GPS 44
data revealed coastal subsidence as large as one meter along the coast of Tohoku 45
area from GPS data (Geospatial Information Authority of Japan (GSI), 2011). 46
The Pacific coasts of Tohoku have suffered from large tsunamis in the past. 47
The 1896 Sanriku earthquake caused large (up to 38 m of runup height) tsunamis 48
on the Sanriku coast with 22,000 casualties, although the seismic shaking was not 49
very strong. Source of the tsunami of this “tsunami earthquake” (Kanamori, 1972) 50
was located near the trench axis (Tanioka and Satake, 1996b). The 1933 Sanriku 51
earthquake, a large normal fault earthquake (Kanamori, 1971) also caused large 52
(up to 29 m) tsunami with about 3,000 casualties. The tsunami heights from these 53
Sanriku earthquakes were less than a few meters in Sendai plain. However, the 869 54
Jogan earthquake produced large tsunami inundation up to a few kilometers 55
4
(Minoura and Nakaya, 1991), which was modeled by an interplate earthquake 56
(Satake et al., 2008). 57
On the basis of large historical earthquakes, The Earthquake Research 58
Committee (ERC) (2009) made long-term forecasts in northern, central, and 59
southern Sanriku-oki, Miyagi-oki, Fukushima-oki and Ibaraki-oki regions, as well 60
as tsunami earthquakes near trench axis. The estimated earthquake size was 61
M~7.7 for southern Sanriku-oki, M~7.5 for Miyagi-oki, M~7.4 for Fukushima-oki, 62
M~6.7-7.2 for Ibaraki-oki, and M~8.2 for offshore tsunami earthquakes. The ERC 63
also considered a multiple segment rupture of the Miyagi-oki and southern 64
Sanriku-oki regions with an estimated size of M~8.0. 65
In this paper, we estimate the tsunami source of the 2011 Tohoku 66
earthquake by inverting tsunami waveforms recorded at tide and wave gauges, GPS 67
wave gauges and ocean bottom tsunami sensors. 68
69
2. Tsunami Data 70
Because of severity and wide extent of tsunami damage, tsunami field 71
surveys are still ongoing. Preliminary surveys reported the tsunami runup heights 72
> 30 m (The 2011 Tohoku Earthquake Tsunami Joint Survey Group, 2011). 73
5
The 2011 tsunami was also recorded instrumentally at various gauges. 74
Many coastal tide gauges on the Pacific coast stopped recording after the first 75
tsunami with > 9 m amplitude, because of power failure or the stations were washed 76
away by the tsunami. Three offshore gauges, one GPS wave gauge (Iwate S at ~200 77
m water depth) and two cabled pressure-gauges (TM-2 at ~1,000 m and TM-1 at 78
1,600 m depth), recorded the two-stage tsunamis (Fig. 2). The water level gradually 79
rose up to 2 m during the first 10 minutes, then impulsive tsunami wave with 3 - 5 80
m amplitude with a shorter period (~8 min) was recorded. At southern GPS 81
(Fukushima) and coastal (Onahama) gauges, similar two pulses were recorded, 82
although their periods were similar. 83
We use tsunami waveforms recorded at coastal tide and wave gauges, 84
offshore GPS wave gauges, deep-ocean bottom-pressure gauges (Fig. 1). While most 85
of coastal tide gauges stations went off-scale and did not record the tsunami peak, 86
the arrival time and the initial slope would provide information on the tsunami 87
source, hence we include them in the inversion. In order to retrieve a tsunami signal, 88
we first approximate a tidal component by fitting a polynomial function, and remove 89
it from the original record. 90
91
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3. Waveform Inversion 92
We divide the tsunami source into 40 subfaults (50 km x 50 km) to cover the 93
aftershock area (Fig. 3 and Table 1). Strike 193º, dip 14º, slip angle 81º are from the 94
USGS’s W phase moment tensor solution. Static deformation of seafloor is 95
calculated for a rectangular fault model (Okada, 1985). We also consider the effects 96
of coseismic horizontal displacement in regions of steep bathymetric slopes (Tanioka 97
and Satake, 1996a). Tsunami waveforms are calculated assuming a constant rise 98
time (or slip duration) of 30 s on each subfault, considering that the duration of the 99
first pulse of source time function was ~ 1 min (e.g., USGS). We assume an 100
instantaneous rupture. The slip distribution estimated from tsunami waveforms, 101
however, is not sensitive to the choice of rise time or rupture velocity (Fujii and 102
Satake, 2007). 103
To calculate tsunami propagation from each subfault to stations, the linear 104
shallow-water, or long-wave, equations are numerically solved by using a 105
finite-difference method (Fujii and Satake, 2007). While the nonlinearity becomes 106
important around coastal tide gauge stations, we confirmed by comparing the 107
nonlinear and linear computations that they produce similar arrival times and 108
initial slopes, while the peak amplitudes (not observed) are different. We use two 109
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sets of bathymetric data for calculating tsunami waveforms or Greens functions. 110
For the DART stations in the Pacific ocean, 2’ interval grid for 125°-175°E and 111
15°-55°N is resampled from GEBCO_08 30”grid data. For stations around Japan, 112
30” interval grid of JTOPO30, provided by Marine Information Research Center, is 113
used for 128°-150°E and 25°-45°N. Time steps of 3 s and 1 s are used to satisfy the 114
stability condition for the finite-difference method in the far-field and near-field 115
computations, respectively. 116
For the inversion, we use non-negative least square method (Lawson and 117
Hanson, 1974) and delete-half jackknife method (Tichelaar and Ruff, 1989) to 118
estimate slips and errors, respectively. The observed tsunami waveforms were 119
resampled at 1 min interval, hence synthetic waveforms are also computed at 1 min 120
interval. The total number of data points used for the inversion is 2818. Considering 121
the different amplitude and signal durations of tsunami waveforms recorded on 122
DART gauges, GPS gauges, and coastal tide gauge data, we use variable weights so 123
that the relative powers become similar. We weight nearby GPS gauge and bottom 124
pressure data 10, 20, or 30 times, and near-source tide gauge data 2 times or 10 125
times, because the duration of these data are shorter than the far-field stations. We 126
also weight the DART data ten times, because the amplitudes are much smaller. 127
8
128
4. The slip distribution 129
The inversion results are shown in Fig.3a and Table 1. The result shows a 130
tsunami source length (with >2 m slip) of about 350 km, extending from over 131
southern Sanriku-oki, Miyagi-oki, Fukushima-oki as well as near the trench axis. 132
The largest slips with more than 40 m are estimated along the Japan trench axis off 133
southern Sanriku-oki (subfaults 4 and 5). Around the epicenter, in southern 134
Sanriku region (subfaults 14 and 15), the estimated slip is 28-34 m. On the deeper 135
subfault in Miyagi-oki region (subfaults 24, 25, 34 and 35), the slip is 9-23 m. To the 136
north of the epicenter, 5-11 m slip is estimated in a part of central Sanriku region 137
(subfault 13 and 23). To the south, the slip is ~ 10m in Fukushina-oki region 138
(subfaults 27 and 28), and < 3 m in Ibaraki-oki region (subfaults 29 and 30). The 139
total seismic moment is calculated from these slip distributions as 3.8 × 1021 Nm 140
(Mw = 9.0) by assuming the rigidity of 5.0 × 1010 N/m2 for all the subfaults. The slip 141
distribution and the size clearly indicate that multiple segments of the ERC’s 142
long-term forecast ruptured simultaneously. 143
The synthetic waveforms generally agree with the observed ones at most 144
stations (Fig. 3). The two-stage tsunami observed at offshore gauges (TM-1, TM-2, 145
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Iwate M, and Iwate S) is well reproduced. The initial part of tsunami, small 146
negative wave followed by gradual increase at coastal tide gauge stations (Miyako, 147
Kamaishi, Ofunato and Soma) is also reproduced. 148
Seafloor deformation calculated from the estimated slip distribution (Fig. 149
3b) shows very large uplift (> 10 m) near the trench axis and about 5 m uplift near 150
epicenter. Near the coast, subsidence up to 2 m, as observed by the GPS data (GSI, 151
2011) is predicted. 152
153
4. Discussions and Conclusions 154
The large slip estimated near the trench axis is similar to the 1896 Sanriku 155
earthquake (Tanioka and Satake, 1996b), although the 2011 slip was much larger. 156
Large offshore slip is responsible to the very large and destructive tsunami on the 157
Sanriku coast. To confirm this, we computed tsunami waveforms from the large slip 158
near the trench axis, and compared it with the tsunami waveforms at selected 159
offshore stations (Fig.2). The computed tsunami waveforms show later arrivals than 160
the observed initial tsunami arrivals, but reproduce the large impulsive tsunamis. 161
Unlike the 1896 earthquake, large slip was also estimated on the plate 162
interface at deeper depth in southern Sanriku-oki and Miyagi-oki regions. The 163
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initial gradual rise of sea level observed at some stations is due to the interplate slip 164
(Fig.2). Large tsunami inundation (> 5 km ) in Sendai plain may be due to such a 165
nearshore, deeper slip on the plate interface. For the 869 Jogan tsunami, similar 166
large inundation (a few km) estimated from the tsunami deposits was reproduced 167
only by an interplate model. Narrow fault near trench axis (“tsunami earthquake” 168
model) or outer-rise normal fault model could not produce large inundation, because 169
of shorter wavelength of seafloor deformation (Satake et al., 2008). 170
The inversion of available tsunami waveforms showed that the large 171
tsunami from the 2011 off the Pacific coast of Tohoku earthquake was produced by 172
both very large displacement near the trench axis and deeper interplate slip in the 173
southern Sanriku-oki, Miyagi-oki, and Fukushima-oki regions. The former explains 174
the largest and impulsive tsunami waveforms, while the latter reproduces the 175
initial part of the tsunami waveforms, as well as large inundation on the Sendai 176
plain. The survey results of coastal tsunami run-up, for example > 30 m near 177
central Sanriku-oki region, may require additional tsunami source(s), not revealed 178
by available tsunami waveform data. 179
180
Acknowledgments. 181
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JCG and JMA provided tide gauge data. Ports and Harbors Bureau (PHB) 182
under the Ministry of Land, Infrastructure, Transport and Tourism (MLIT) and 183
Port and Airport Research Institute (PARI) provided tide gauge, wave gauge and 184
GPS wave gauge data. The data of ocean bottom tsunami sensors of JAMSTEC and 185
DART of NOAA were downloaded from their web sites. Most of the figures were 186
generated using the Generic Mapping Tools (Wessel and Smith, 1998). This 187
research was partially supported by Grants-in-Aid for Scientific Research (B) (No. 188
21310113), Ministry of Education, Culture, Sports, Science and Technology (MEXT). 189
190
References 191
Earthquake Research Committee, Long-term forecast of earthquakes from 192
Sanriku-oki to Boso-oki (revised) (in Japanese), Headquarters for 193
Earthquake Research Promotion, 80pp, 2009. 194
Fujii, Y., and K. Satake, Tsunami Source of the 2004 Sumatra-Andaman 195
Earthquake inferred from Tide Gauge and Satellite Data, Bull. Seism. Soc. 196
Am., 97, S192-S207, 2007. 197
Geospatial Information Authority of Japan, The 2011 off the Pacific coast of Tohoku 198
Earthquake: Crustal Deformation and Fault Model (Preliminary), 199