The 2011 Tohoku-Oki Earthquake:
Displacement Reaching the Trench Axis
Toshiya Fujiwara,1* Shuichi Kodaira,2 Tetsuo No,2 Yuka Kaiho,2
Narumi Takahashi,3 Yoshiyuki Kaneda3
axis. A comparison of the bathymetry before and
after the earthquake shows a sharp contrast in seafloor elevation at the trench axis, and the sea floor
is shallower throughout the landward side. Notably, on the outermost landward slope, the 40-kmwide area between the slope break and the trench
axis, the difference between the 1999 and 2011
data shows that the sea floor is 16 T 9 (±SD) m
shallower on average (Fig. 1C). A comparison of
the 2004 and 2011 data (Fig. 1D) shows the same
trend, although the change was somewhat smaller
(11 T 8 m). Furthermore, upward and downward
changes in sea-floor elevation of T50 m are evident
at the axial sea floor (Fig. 1, C and D), which are
likely due to a submarine landslide (fig. S1E). A
comparison of the 1999 and 2004 data obtained
before the 2011 earthquake indicates no clear difference between the two sides of the trench axis [the
average sea-floor elevation is 0 T 7 m (Fig. 1E)].
The observed sea-floor elevation change on
the outermost landward slope corresponds to a
sum of vertical displacement and additional uplift
for the sloping sea floor due to horizontal displacement. We estimated the horizontal displacement
by calculating the offset distance to maximize the
he large tsunami that followed the 11 March
2011 Tohoku-Oki earthquake [moment magnitude (MW) 9.0] is believed to have been
caused by a fault rupture extending to a shallow
part of the subduction zone at the Japan Trench.
This is indicated by various seismic and geodetic
inversion procedures (1, 2); however, an accurate
up-dip limit of the coseismic displacement has not
yet been determined. We report repeated multibeam
bathymetric surveys across the trench in the rupture
zone before and after the earthquake to estimate its
up-dip limit and quantify sea-floor displacement.
In 1999 and 2004, multibeam bathymetric data
were acquired simultaneously during active-source
seismic surveys (3, 4). After the earthquake, from
22 to 23 March 2011, we carried out a bathymetric
survey along the same track (Fig. 1, A and B) (5).
The relative differences among these bathymetric
data are minimal on the seaward side of the trench
despite potential errors of several meters in vertical
displacement and ~20 m in horizontal displacement (5).
There were, however, large relative differences
landward extended up to the trench axis, suggesting the earthquake fault rupture reached the trench
T
50m Horizontal Displacement
'
143˚20
'
143˚10
'
143˚30
'
143˚40
'
143˚50
'
144˚00
'
'
144˚20
144˚10
'
144˚30
'
'
144˚50
'
144˚50
144˚40
38˚10'
B
10 km
-8000
-7000
'
143˚10
Landward Slope 38˚00'
Slope Break
-6000
'
143˚20
-4000
-3000
-2000 Depth (m)
'
'
'
'
'
144˚00
143˚50
144˚20
144˚10
-5000
'
143˚30
Seaward Slope
Trench Axis
143˚40
'
'
144˚40
144˚30
38˚10'
2011-1999
38˚00'
'
143˚50
'
144˚00
'
'
143˚20
43˚30'
1
'
143˚40
'
143˚50
39˚
'
144˚00
-50
10 km
-40
1
38˚
38˚10'
E
44˚10'
2004-1999
-30
-20
-10
38˚00'
0
10
20
30
Change in Seafloor Elevation (m)
40
'
144˚40
144˚
144˚50
146˚
A
44˚20'
1
Miyagi
'
144˚30
37˚
1
44˚40'
44˚50'
1
9cm
/ yr
Acknowledgments: We thank the crew of R/V Kairei and the
technicians of Nippon Marine Enterprises for their dedication.
The 2011 survey, part of the program launched following the
earthquake, was supported by a Grant-in-Aid for Special Purposes
of the Ministry of Education, Culture, Sports, Science, and
Technology (MEXT) and a contribution from JAMSTEC.
www.sciencemag.org/cgi/content/full/334/6060/1240/DC1
Materials and Methods
Fig. S1
Table S1
Reference (9)
22 July 2011; accepted 4 November 2011
10.1126/science.1211554
50
36˚
Fig. 1. Changes in sea-floor elevation between bathymetric data before and after the 2011 Tohoku-Oki
earthquake. (A) Location map with bathymetric survey track shown as yellow line. Coseismic horizontal
displacement is estimated over the landward slope indicated by solid portion of yellow line. Cross shows
the epicenter. (B) Multibeam bathymetry collected in 2011. Red triangles mark the trench axis; the blue
triangle marks the landward slope break. Change in sea-floor elevation by subtracting the 1999
bathymetric data from the 2011 data (C), the 2004 data from the 2011 data (D), and the 1999 data from
the 2004 data (E). The yellow star marks location of probable submarine landslide.
1240
References and Notes
1. S. Ide, A. Baltay, G. C. Beroza, Science 332, 1426
(2011); 10.1126/science.1207020.
2. T. Maeda, T. Furumura, S. Sakai, M. Shinohara,
Earth Planets Space 63, 803 (2011).
3. T. Tsuru et al., J. Geophys. Res. 107, 2357 (2002).
4. A. Ito et al., Geophys. Res. Lett. 32, L05310 (2005).
5. Material and methods are available as supporting
material on Science Online.
6. M. Sato et al., Science 332, 1395 (2011); 10.1126/
science.1207401.
7. M. Kido et al., paper no. MIS036-P10 presented at Japan
Geoscience Union Meeting 2011, 22 to 27 May 2011,
Chiba, Japan.
8. Y. Ito et al., Geophys. Res. Lett. 38, L00G05 (2011).
Supporting Online Material
Pacific Plate
JA
1
2011-2004
38˚00'
'
'
144˚30
142˚
KU
10 km
43˚10'
144˚20
140˚
40˚
38˚10'
D
'
144˚10
H
'
143˚40
TRENC
'
143˚30
N
143˚20
+
'
'
PA
10 km
TOHO
C
143˚10
cross correlation of bathymetry (5). The estimated
displacement is 56 m relative to the 1999 data, and
50 m relative to the 2004 data, toward the eastsoutheast. After restoring the horizontal displacement, the average elevation change became 10 T
7 m in comparison between the 1999 and 2011
data (7 T 7 m between 2004 and 2011). We interpret these to represent vertical displacement from
the fault motion along the subducting plate and
uplift from other unknown processes such as inelastic deformation. Overall, the sea floor on the
outermost landward slope moved ~50 m eastsoutheast toward the trench and ~7 to 10 m upward between 1999 and 2011.
Our results are consistent with results of coseismic displacements determined at Global Positioning System (GPS)/acoustic sea-floor geodetic
stations (6, 7) and other ocean-bottom instruments
(8). Although our estimate of the average vertical
displacement may be larger because of coseismic
displacement, the earthquake probably caused little
change on the seaward side. Combined with these
geodetic studies, our study demonstrates the coseismic displacement increased toward the trench
and reached the trench axis. This large coseismic
horizontal displacement and the steeply sloping sea
floor produced large additional uplift by ~4 to 6 m
in addition to the vertical displacement (5). This
uplift was likely an important factor contributing to
the generation of the massive pulsating pattern of
tsunami waves (2).
2 DECEMBER 2011
VOL 334
SCIENCE
1
Institute for Research on Earth Evolution (IFREE), Japan Agency for
Marine-Earth Science and Technology (JAMSTEC), Natsushima-cho
2-15, Yokosuka 237-0061, Japan. 2IFREE, JAMSTEC, Showa-machi
3173-25, Kanazawa-ku, Yokohama 236-0001, Japan. 3Earthquake
and Tsunami Research Project for Disaster Prevention, JAMSTEC,
Showa-machi 3173-25, Kanazawa-ku, Yokohama 236-0001, Japan.
*To whom correspondence should be addressed. E-mail:
[email protected]
www.sciencemag.org
Downloaded from www.sciencemag.org on February 4, 2013
BREVIA
www.sciencemag.org/cgi/content/full/334/6060/1240/DC1
Supporting Online Material for
The 2011 Tohoku-Oki Earthquake: Displacement Reaching the Trench
Axis
Toshiya Fujiwara,* Shuichi Kodaira, Tetsuo No, Yuka Kaiho, Narumi Takahashi,
Yoshiyuki Kaneda
*To whom correspondence should be addressed. E-mail: [email protected]
Published 2 December 2011, Science 334, 1240 (2011)
DOI: 10.1126/science.1211554
This PDF file includes:
Materials and Methods
Fig. S1
Table S1
References
Materials and Methods
Analysis Method
The bathymetric data in 1999, 2004, and 2011 were collected using a SeaBeam 2112
with a 12 kHz frequency and a 2°×2° beam width. For analysis, we used only the data
obtained by beams within a 45° swath width (Figs. 1C-E) among 120° swath width
available (Fig. 1B) because these inner beam soundings have higher accuracy and less
effects of errors in water column sound velocity. The RMS depth accuracy of the inner
beam sounding is 0.2 % of water depth, and thus is 6-15 m in the 3000-7600 m depth in
the study area. The sea surface height variation due to ocean tide, that is a possible error
of the depth sounding, is estimated to be within ±50 cm (8). The beam footprint sizes,
which affect the spatial resolutions along- and across-track directions, are ~100-250 m at
these depths. However, the sounding sampling interval was rather short, ~40 m along
track, at a survey speed of 4 knots. To compare different surveys with random sounding
locations, the bathymetric data were gridded by using the Generic Mapping Tools (GMT)
software (9). Continuous curvature surface gridding algorithm 'surface' and pre-processor
filter 'blockmedian' were operated for the gridding. The data were gridded at a spacing of
0.025 arc-minute (finer than the mean spacing of the raw soundings) to avoid aliasing.
Direct comparisons of absolute values of soundings were hampered by the
differences of sound velocities in seawater used to calculate the water depths and by the
uncertainty of ship position. To avoid the apparent offsets of locations from different
surveys, a set of the gridded bathymetry data was horizontally shifted relative to the
others so as to minimize the variance of depth differences (maximize the crosscorrelation of the bathymetry). Offsets were examined separately for the seaward and
landward sides of the trench, because the seaward slope is thought to have suffered little
change from the 2011 earthquake, whereas large displacements are likely in the
outermost landward slope (143°34'E-143°57'E) after the earthquake (Fig. 1). The area
near the trench axis was excluded from this analysis because the bathymetric change is
clearly affected by probable landsliding (Figs. 1 and S1E). The offsets estimated on the
seaward side are considered to be systematic errors for the entire area. Consequently,
after subtraction of these systematic errors, the mean values of the change of seafloor
elevation on the seaward side become zero, and the mean values of elevation change on
the landward side should represent the average uplifts caused by the coseismic
displacement of the 2011 earthquake (Fig. 1 and Table S1).
The coseismic horizontal displacements on the landward slope were estimated by
the amounts of horizontal shift relative to those on the seaward slope (Figs. S1A-S1C and
Table S1). Note that there is 20 m dislocation in the northeast direction between the two
datasets prior to the earthquake, although coseismic displacement is presumed to be
absent (Fig. S1C). The offset may suggest uncertainty in our estimation of the amount of
shift. The mean values of the elevation changes calculated after horizontal dislocations
are interpreted as the coseismic vertical displacement of the landward plate. The
difference between the vertical displacement and the observed seafloor elevation change
is considered to be an additional uplift for a sloping seafloor (Fig. S1D).
2
Fig. S1.
Contour maps showing standard deviations (~variances) of depth differences between
different surveys for given shifted locations. (A) Comparison between 1999 and 2011
data, (B) comparison between 2004 and 2011 data, and (C) comparison between 2004
and 1999 data, respectively. Red and blue contours show standard deviations of the
landward slope and the seaward slopes, respectively. Crosses indicate the minimum
peaks of the standard deviations. Arrows show vectors of horizontal shifts from landward
to seaward. (D) Schematic cross-section showing coseismic displacement. A sum of a
vertical displacement and an additional uplift for a sloping seafloor correspond the
observed seafloor elevation changes shown in Fig. 1. The inset is for illustrative purposes
(not to scale). (E) Bathymetric cross section at the trench. Red and black indicate 2011
and 1999 data.
3
Table S1.
Estimated coseismic displacements caused by the 11 March 2011 Tohoku-Oki
Earthquake in the outermost landward slope area, off Miyagi in the Tohoku district.
4
References and Notes
1. S. Ide, A. Baltay, G. C. Beroza, Shallow dynamic overshoot and energetic deep rupture
in the 2011 Mw 9.0 Tohoku-Oki earthquake. Science 332, 1426 (2011);
10.1126/science.1207020. doi:10.1126/science.1207020 Medline
2. T. Maeda, T. Furumura, S. Sakai, M. Shinohara, Significant tsunami observed at
ocean-bottom pressure gauges during the 2011 off the Pacific coast of Tohoku
Earthquake. Earth Planets Space 63, 803 (2011). doi:10.5047/eps.2011.06.005
3. T. Tsuru et al., Along-arc structural variation of the plate boundary at the Japan Trench
margin: Implication of interplate coupling. J. Geophys. Res. 107, 2357 (2002).
doi:10.1029/2001JB001664
4. A. Ito et al., Bending of the subducting oceanic plate and its implication for rupture
propagation of large interplate earthquakes off Miyagi, Japan, in the Japan Trench
subduction zone. Geophys. Res. Lett. 32, L05310 (2005).
doi:10.1029/2004GL022307
5. Material and methods are available as supporting material on Science Online.
6. M. Sato et al., Displacement above the hypocenter of the 2011 Tohoku-Oki
earthquake. Science 332, 1395 (2011); 10.1126/science.1207401.
doi:10.1126/science.1207401 Medline
7. M. Kido et al., paper no. MIS036-P10 presented at Japan Geoscience Union Meeting
2011, 22 to 27 May 2011, Chiba, Japan.
8. Y. Ito et al., Frontal wedge deformation near the source region of the 2011 TohokuOki earthquake. Geophys. Res. Lett. 38, L00G05 (2011).
doi:10.1029/2011GL048355
9. P. Wessel, W. H. F. Smith, Free software helps map and display data. Eos Trans. AGU
72, 441 (1991). doi:10.1029/90EO00319
Displacement Above the Hypocenter
of the 2011 Tohoku-Oki Earthquake
Mariko Sato,1* Tadashi Ishikawa,1 Naoto Ujihara,1 Shigeru Yoshida,1 Masayuki Fujita,1
Masashi Mochizuki,2 Akira Asada2
n 11 March 2011, a large interplate earthquake [moment magnitude (Mw) = 9.0]
occurred at the plate boundary off Miyagi
Prefecture, northeastern Japan. The focal region
inferred from the distribution of aftershocks
stretches about 500 km long and 200 km wide
offshore (1).
Various studies have been under way to understand the mechanism of occurrence of this
earthquake. For example, the Geospatial Information Authority of Japan (GSI) has reported coseismic displacements on land, on the basis of
the dense Global Positioning System (GPS) network (2). The largest displacement has been detected at the Oshika peninsula (Fig. 1), amounting
to about 5 m toward east-southeast (ESE) and
about 1 m downward. The GSI also estimated
slip distribution on the plate boundary from the
observed displacements, and the maximum slip
was about 24 m near the hypocenter (2). Because the Oshika peninsula is located about 130
km away from the epicenter of the earthquake,
it is preferable to measure crustal movements
closer to the focal regions, that is, on the sea floor,
to better constrain the focal mechanism of the
event.
In order to monitor crustal movements offshore, we have been carrying out sea-floor geodetic
observations by using the GPS/acoustic combination technique (3–5) (fig. S1). Five sea-floor reference points were installed off the Tohoku region
between 2000 and 2004 (Fig. 1) with campaign
O
observations carried out three times a year on
average.
The latest observations before the event were
conducted in November 2010 at KAMS and
KAMN and in February 2011 at MYGI, MYGW,
and FUKU. After the event, we conducted observations at these sites for the period from 28 March
to 5 April (6).
Comparison between before and after the
event yielded coseismic displacements of 5 to
24 m toward ESE and – 0.8 to 3 m upward (Fig.
1, table S1). In particular, at MYGI near the epicenter, we detected a huge coseismic displacement of about 24 m toward ESE and about 3 m
upward. Observation errors after the event are
somewhat large (up to 50 to 60 cm) compared
with those in regular campaigns (up to several
centimeters) (6). The observed displacements
include any postseismic movements for about
20 days after the mainshock. They would also include coseismic displacements by foreshocks
and aftershocks (1), some of which are large
enough to affect these sites. However, a displacement caused by each of them is estimated to be
a few tens of centimeters at most, and the total
amount other than that of the coseismic signal by
the mainshock is not larger than 1 m. Therefore,
these data illustrate huge coseismic movements
and its spatial variance by the mainshock just
above the focal region.
The horizontal movement at MYGI is more
than four times larger than that detected on land
and almost equal to the maximum slip on the
plate boundary inferred from terrestrial measurements (2). Additionally, the horizontal displacement at KAMS, located about 70 km northeast
of the epicenter, is as large as that at MYGI. Therefore, it is reasonable to interpret that the area where
coseismic displacement is greater than 20 m spans
at least 70 km. These results suggest that slip on
the plate boundary near the trench exceeded the
20- to 30-m level estimated as a maximum by the
terrestrial data (2), because slip on the plate boundary should be much larger than displacement of
the sea floor.
It is also evident that the up-down components of displacement at MYGI and MYGW
show opposite polarity. Because the terrestrial
data exhibit subsidence (2), the polar reversal
of the vertical displacement from downward to
upward expected from the upper plate rebound
at the event occurred offshore. Thus, the hinge
line corresponding to null displacement is located on the east side of MYGW.
With only five observation sites, we may not
be able to constrain the detailed feature of focal
mechanism, but we believe that the coseismic
displacements obtained offshore in this study
will provide far better constraints than only the
terrestrial data in inferring a fault model for this
event.
References and Notes
1. Japan Meteorological Agency, www.jma.go.jp/jma/en/
2011_Earthquake.html (2011).
2. Geospatial Information Authority of Japan, www.gsi.go.jp/
cais/topic110421-index-e.html (2011).
3. A. Asada, T. Yabuki, Proc. Jpn. Acad. Ser. B 77, 7
(2001).
4. M. Fujita et al., Earth Planets Space 58, 265
(2006).
5. M. Sato et al., Geophys. Res. Lett. 38, L01312
(2011).
6. Materials and methods are available as supporting
material on Science Online.
Acknowledgments: We thank Y. Honkura for valuable
comments and suggestions, O. L. Colombo for assistance
with GPS software, and the GSI for providing us with
the GPS data. The installation of MYGW was funded by
the Ministry of Education, Culture, Sports, Science and
Technology of Japan. Averaged position data for the
five stations are available in the supporting online
material.
Downloaded from www.sciencemag.org on February 4, 2013
BREVIA
Supporting Online Material
www.sciencemag.org/cgi/content/full/science.1207401/DC1
Materials and Methods
Fig. S1
Table S1
References
22 April 2011; accepted 11 May 2011
Published online 19 May 2011;
10.1126/science.1207401
Fig. 1. Horizontal (A) and vertical (B) coseismic displacements at the sea-floor reference points, associated with the 2011 Tohoku-Oki earthquake. Red squares and a yellow star show locations of sea-floor
reference points and the epicenter, respectively. The position reference is Shimosato (an open triangle).
www.sciencemag.org
SCIENCE
VOL 332
1
Hydrographic and Oceanographic Department, Japan Coast
Guard, 5-3-1 Tsukiji, Chuo-ku, Tokyo 104-0045, Japan. 2Institute
of Industrial Science, University of Tokyo, 4-6-1 Komaba,
Meguro-ku, Tokyo 153-8505, Japan.
*To whom correspondence should be addressed. E-mail:
[email protected]
17 JUNE 2011
1395
www.sciencemag.org/cgi/content/full/science.1207401/DC1
Supporting Online Material for
Displacement Above the Hypocenter of the 2011 Tohoku-Oki
Earthquake
Mariko Sato,* Tadashi Ishikawa, Naoto Ujihara, Shigeru Yoshida, Masayuki Fujita,
Masashi Mochizuki, Akira Asada
*To whom correspondence should be addressed. E-mail: [email protected]
Published 19 May 2011 on Science Express
DOI: 10.1126/science.1207401
This PDF file includes:
Materials and Methods
Fig. S1
Table S1
References
Materials and Methods
Seafloor geodetic observation
A schematic picture of the seafloor geodetic observation system that we have
developed is shown in Fig. S1. The system measures the ranges from the on-board
transducer to the seafloor acoustic transponders through round-trip acoustic travel times,
while simultaneously gathering kinematic GPS data. The vessel’s attitude is also
measured on board by the dynamic motion sensor, which are used to determine the
coordinates of the on-board transducer relative to those of the GPS antenna.
By combining the round-trip travel time obtained by acoustic ranging and the
positions of the GPS antenna at the moment of acoustic wave emission and reception, we
determine the positions of the seafloor transponders. The positions of grouped
transponders are finally averaged to a virtual position of the seafloor reference point.
The methodology of our observation technique in detail was described in (4).
Using this system, we conducted seafloor geodetic observations at five reference
points (Fig. 1; Table S1) about 20 days after the mainshock. Although we acquire
acoustic ranging data of about 5,000 shots at a single reference point in a regular
campaign, only 1,200~4,000 shots were obtained in the observations after the event at
each reference point to cover all the relevant reference points within our limited ship time.
The position reference is Shimosato in central Japan (Fig. 1A), which is located
about 800 km southwest of the epicenter of the Tohoku-oki earthquake. We determined
positions of terrestrial GPS stations on the coast of Tohoku region, closer to the seafloor
reference points, which were actually used as references for kinematic GPS analyses,
from Shimosato’s reference coordinates. Although Shimosato was also affected by the
earthquake, the co-seismic displacement has been observed to be a few centimeters,
which is negligible in our present discussion.
Observation errors of this technique are up to several centimeters in regular
campaigns. However, for the observations after the earthquake, they are supposed to be
about 10~20 cm at MYGI, MYGW and FUKU, and about 50~60 cm at KAMS and
KAMN, which are inferred from determined relative positions between multiple
transponders at each reference point in comparison with those in regular campaigns
before the event. There are three possible causes for this deterioration. First, the number
of shots for acoustic ranging at each reference point was fewer than those in regular
campaigns as mentioned above. Second, some transponders could have slipped by the
strong impact exerted by the earthquake. And lastly, there could have been a local
deformation within an array of transponders at each reference point.
2
GPS Antenna
Survey
Vessel
Motion
Sensor
Acoustic
Transducer
XBT
XCTD
CTD
Seafloor Stations
(Mirror Transponders)
Fig. S1.
Schematic picture of the seafloor geodetic observation system consisting of four acoustic
mirror-type transponders at the seafloor and one GPS antenna/receiver, one undersea
acoustic transducer and one dynamic motion sensor on-board. A set of four acoustic
transponders has been placed on the seafloor at each reference point to form a square
whose corners are directed to the north, south, east and west, with a length of the
diagonal approximately equal to the mean water depth in the area.
3
Table S1.
Estimated coordinates of seafloor reference points before and after the 2011 Tohoku-oki
earthquake. The coordinates are the averaged positions of grouped transponders.
Site name
KAMN
KAMS
MYGI
MYGW
FUKU
Observation
date
11/16/2010
4/3/2011
11/19/2010
4/5/2011
2/21/2011
3/28/2011
2/21/2011
3/27/2011
2/23/2011
3/29/2011
°
38
38
38
38
38
38
38
38
37
37
Latitude
′
″
53
16.740
53
16.551
38
11.271
38
10.981
4
51.388
4
51.051
8
55.897
8
55.734
9
58.002
9
57.948
°
143
143
143
143
142
142
142
142
142
142
Longitude
′
″
21
43.869
21
44.443
15
48.021
15
48.893
54
59.881
55
0.788
25
59.327
25
59.919
4
51.233
4
51.412
Height
m
-2306.51
-2304.90
-2193.21
-2191.72
-1645.83
-1642.69
-1044.71
-1045.49
-1209.47
-1208.61
4
References
1. Japan Meteorological Agency, http://www.jma.go.jp/jma/en/2011_Earthquake.html (2011).
2. Geospatial Information Authority of Japan, http://www.gsi.go.jp/cais/topic110421-indexe.html (2011).
3. A. Asada. T. Yabuki, Proc. Jpn. Acad. Ser. B, 77, 7 (2001).
4. M. Fujita, T. Ishikawa, M. Mochizuki, M. Sato, S. Toyama, M. Katayama, K. Kawai, Y.
Matsumoto, T. Yabuki, A. Asada, O. L. Colombo, Earth Planets Space, 58, 265 (2006).
5. M. Sato, H. Saito, T. Ishikawa, Y. Matsumoto, M. Fujita, M. Mochizuki, A. Asada, Geophys.
Res. Lett., 38, L01312, doi:10.1029/2010GL045689 (2011).