#### Different depths of near-trench slips of the 1896 Sanriku and 2011 Tohoku earthquakes

Satake et al. Geosci. Lett.
Different depths of near-trench slips of the 1896 Sanriku and 2011 Tohoku earthquakes
Kenji Satake 0
Yushiro Fujii 2
Shigeru Yamaki 1
0 Earthquake Research Institute, The University of Tokyo , 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032 , Japan
1 Seamus Ltd , 2235 Kizaki, Kita-ku, Niigata 950-3304 , Japan
2 International Institute of Seismology and Earthquake Engineering, Building Research Institute , 1 Tachihara, Tsukuba, Ibaraki 305-0802 , Japan
The 1896 Sanriku earthquake was a typical 'tsunami earthquake' which caused large tsunami despite its weak ground shaking. It occurred along the Japan Trench in the northern tsunami source area of the 2011 Tohoku earthquake where a delayed tsunami generation has been proposed. Hence the relation between the 1896 and 2011 tsunami sources is an important scientific as well as societal issue. The tsunami heights along the northern and central Sanriku coasts from both earthquakes were similar, but the tsunami waveforms at regional distances in Japan were much larger in 2011. Computed tsunamis from the northeastern part of the 2011 tsunami source model roughly reproduced the 1896 tsunami heights on the Sanriku coast, but were much larger than the recorded tsunami waveforms. Both the Sanriku tsunami heights and the waveforms were reproduced by a 200-km × 50-km fault with an average slip of 8 m, with the large (20 m) slip on a 100-km × 25-km asperity. The moment magnitude Mw of this model is 8.1. During the 2011 Tohoku earthquake, slip on the 1896 asperity (at a depth of 3.5-7 km) was 3-14 m, while the shallower part (depth 0-3.5 km) slipped 20-36 m. Thus the large slips on the plate interface during the 1896 and 2011 earthquakes were complementary.
Background
The 11 March 2011 Tohoku earthquake (Mw 9.0) was the
largest instrumentally recorded earthquake in Japan and
caused devastating tsunami damage including ~ 18,500
casualties. The ground shaking was felt throughout the
Japanese Islands with the maximum seismic intensity of
7 on the Japan Meteorological Agency (JMA) scale, or
11–12 on the Modified Mercalli scale (Fig. 1a). Huge slip
(> 50 m) on the plate interface up to the Japan Trench
axis was estimated near the epicenter (~ 38.5°N) from
seismic waves
(Ide et al. 2011)
, inland and submarine
geodetic data
(Iinuma et al. 2012)
, and tsunami
waveforms
(Fujii et al. 2011; Satake et al. 2013b)
. On the
contrary, the largest tsunami heights on the Sanriku coast,
~ 40 m, were recorded ~ 100 km north (near 39.6°N).
This enigma was explained by a delayed tsunami
generation in the northern part of tsunami source through the
tsunami waveform analysis
(Satake et al. 2013b; Tappin
et al. 2014)
. However, the cause of the delayed tsunami
generation is still controversial, either due to slip on
shallow plate interface
(Satake et al. 2013b)
or submarine
landslide
(Tappin et al. 2014)
.
In the northern part of the 2011 tsunami source, the 15
June 1896 Sanriku earthquake occurred and caused the
worst tsunami disaster in Japan, with casualties of ~ 20,
000
(Shuto et al. 2007)
. The 1896 Sanriku earthquake was
a typical example of a ‘tsunami earthquake’
(Kanamori
1972; Tanioka and Satake 1996b)
. The origin time: 19 h
32 m (local time), the epicenter: 144°E, 39.5°N, and
magnitude: M = 6.8 were estimated from Japanese seismological
data
(Utsu 1979)
. The surface wave magnitude MS = 7.2
was assigned from global data
(Abe 1994)
. The moment
magnitude Mw was estimated as 8.0–8.2, from a
comparison of aftershock activity with other large earthquakes
(Utsu 1994)
. The tsunami magnitude Mt was determined
11 March 2011 Tohoku (M 9.0)
JMA
MM
b
15 June 1896 Sanriku (M 8.2)
Hanasaki
Ayukawa Choshi
1896 Sanriku
2011 Tohoku
8 Ayukawa
−2
2
0
6
4
2
0
−)2
m
(
e2
d
u
t
li 0
p
m
−A2
2011 Tohoku
1896 Sanriku
Choshi
2011 Tohoku
1896 Sanriku
0
30
60 90 120 150 180
Time (min)
as 8.6 from global data
(Abe 1979)
and 8.2 from Japanese
data
(Abe 1981)
. The ground shaking was weak (2–3 on
the JMA seismic intensity scale, corresponding to 4–5 on
the Modified Mercalli scale; Fig. 1b). However, the
tsunami heights on the Sanriku coast from the 2011 and 1896
earthquakes were roughly similar
(Fig. 1c, Tsuji et al. 2014)
as detailed in the “Tsunami data of the 1896 earthquake.”
Tsunami waveform modeling of the 1896 Sanriku
earthquake has shown that slip occurred on a narrow
fault located near the trench axis
(Tanioka and Satake
1996b; Tanioka and Seno 2001)
. This is a common
feature of ‘tsunami earthquakes’ such as the 1992
Nicaragua or 2010 Mentawai earthquakes
(Satake and Tanioka
1999; Satake et al. 2013a)
.
Tanioka et al. (1997
) further
proposed that the 1896 Sanriku ‘tsunami earthquake’
occurred in a region where the ocean bottom topography
is rough, characterized by well-developed horst and
graben structures.
Polet and Kanamori (2000)
extended this
model to global subduction zones, based on the
examination of the source spectra of large (M > 7) earthquakes in
the 1990s. More recently,
Lay et al. (2012
) classified the
seismogenic zone of subduction zones into four domains
and assigned the shallowest domain (A: less than 15 km
depth) as a source region of ‘tsunami earthquakes.’
After the occurrence of the 2011 Tohoku
earthquake and tsunami, a question arose about the relation
between the 1896 and 2011 tsunami sources. Did both
earthquakes rupture the same shallow plate interface
or different parts? Why was the 1896 event a ‘tsunami
earthquake’ while the 2011 earthquake was not? These
are important issues both in science of tsunami
generation in subduction zones, particularly near the trench
axis, and also for tsunami hazard assessment.
In this study, we re-estimate the slip distribution,
particularly in depth direction, of the 1896 Sanriku ‘tsunami
earthquake’ based on both tsunami heights on the
Sanriku coast and the tsunami waveforms recorded on three
tide gage stations at regional distance in Japan. It should
be noted that tsunami height data on the Sanriku coast
have not been used in the previous studies of the 1896
earthquake. In order to find the best 1896 tsunami source
model, we start from the northern part of the 2011
source model, compute the tsunami heights on the
Sanriku coast and tsunami waveforms at tide gage stations,
and compare them with the 1896 observations. We also
compare the tsunami source models, or obtained slip
distributions, of the 1896 and 2011 earthquakes, and discuss
why the 2011 earthquake was not a ‘tsunami earthquake.’
Tsunami data of the 1896 earthquake
The 1896 tsunami was instrumentally recorded on three
tide gage stations at regional distances in Japan:
Hanasaki (440 km from the epicenter), Ayukawa (250 km), and
Choshi (500 km)
(Fig. 1b, Honda et al. 1908; Imamura
and Moriya 1939)
. Tanioka and Satake (1996b)
examined these waveforms, estimated the clock timing errors
as large as 5 min, and modeled the waveforms without
timing information. The 2011 tsunami was also recorded
at these tide gage stations, although the Ayukawa record
went off-scale immediately following the first tsunami
arrival at ~ 30 min from the earthquake
(Satake et al.
2013b)
. Comparison of the 1896 and 2011 tsunami
waveforms indicates that both periods and amplitudes of the
2011 waveforms are larger than those of the 1896
tsunami (Fig. 1d), probably due to the different sizes of
tsunami source.
For the 1896 tsunami heights along the Sanriku coasts,
at distances ranging from 170 to 250 km from the
epicenter, field surveys were made by three groups (Fig. 1c).
Yamana
(reproduced by Unohana and Ota 1988)
made
a post-tsunami survey from July through September of
1896 in all of the 37 villages along the Sanriku coast. The
largest heights of 55 m were reported at two locations.
While his report contains 168 diagrams, the reliability
of his measurements has been questioned
(Shuto et al.
2007)
.
Iki (1897)
made a survey in June and July of 1896
along the Sanriku coast. He measured tsunami heights
based on various kinds of traces and eyewitness accounts,
and assigned different reliabilities depending on the
kind of data. The maximum tsunami height was 24 m
at Yoshihama. In 1933, another devastating tsunami,
with maximum height of 29 m and approximately 3000
fatalities, was caused by the 1933 Sanriku earthquake
(Ms 8.5).
Matsuo (1933)
made field survey to measure the
heights of both 1896 and 1933 tsunamis. Although the
1896 tsunami heights were measured 37 years after the
occurrence based on the eyewitness accounts, the survey
points were plotted on 1:50,000 maps and provided
valuable information. The often-quoted maximum height of
38 m at Shirahama from the 1896 Sanriku tsunami was
based on his report. In this study, we adopt the reported
tsunami heights by
Iki (1897)
and
Matsuo (1933)
and
compare them with the calculated heights. Because of
the sawtooth-shaped topography of the Sanriku coast,
often called a ria-type coast in Japan, both the 1896 and
2011 tsunami heights significantly change at short
distance (Fig. 1c). Tsuji et al. (2014) compared the 1896 and
2011 tsunami heights on the Sanriku coast and found the
median ratios (1896/2011) are 1.01, 0.85, and 0.29 on the
northern, central, and southern Sanriku coasts,
respectively, and 0.69 for the entire Sanriku coast. These
indicate that the 1896 tsunami heights were similar to the
2011 tsunami heights on the northern and central
Sanriku coasts.
A careful manual observation of the tsunami was
conducted at the Miyako meteorological observatory
(Miyako is shown in Fig. 1c), and published in the
annual report of the
Central Meteorological
Observatory (1902
). It describes as follows. “At 19 h 32 m 30 s
(local time), a weak shock of earthquake was felt,
lasting for about 5 min. Its direction was ENE–WSW and
the nature was extremely slow. At about 19 h 50 m, the
sea began to recede. At about 20 h, the water rose, but
fell somewhat in a few minutes. At 20 h 07 m, the biggest
wave of about 4.5 m high came in with a fearful
booming sound, and instantly swept away all houses or living
things that were in its path. Subsequently, six waves of
more or less heights came until the noon of the
following day.” At the Miyako observatory, seismograph
observation already started in those days
(Omori and Hirata
1899)
, hence the observer must be sensitive to accurate
timing. In addition, the tsunami arrival times were
measured relative to the earthquake. Therefore the timing of
tsunami arrival at Miyako provides additional important
information.
Tsunami computations
We use the subfault configuration of the 2011 Tohoku
earthquake of Satake et al. (2013b). Only eight subfaults
(0A to 1D: Fig. 2a, Table 1) in the northern and shallow
part of the source are adopted. Each subfault is 50 km
long and 25 km wide. The strike, dip, and slip angles are
193°, 8°, and 81°, respectively. The subfaults are placed on
the Pacific plate
(Nakajima and Hasegawa 2006)
, and the
top depths beneath seafloor are 0 and 3.5 km for
shallowest (row 0) and next (row 1) subfaults (Table 1). Seafloor
a 2011 (L 200 km)
41˚1N41˚E 142˚E 143˚E 144˚E
km
0 100
1A
1B
1C
1D
0A
0B
0C
0D
Iki
Matsuo
Cal. (Iki)
Cal. (Matsuo)
38˚N 0 T10sunam2i0heig3h0t (m)40
2 Hanasaki
40˚N
39˚N
y
38˚N
41˚N
40˚N
39˚N
0
2
0
−2
b 2011 (L 150 km) c 1896 Inversion
Water height (m) 0 1 2 3 4 5 6 7 8 9 10
* Location (latitude [Lat.] and longitude [Lon.]) indicates the northeast corner of each subfault. The fault length: 50 km, the fault width: 25 km, the strike: 193°, the dip
angle: 8°, and the slip angle: 81° are common to all the subfaults. The top depths are 0 km and 3.5 km beneath seafloor, for subfaults 0* and 1*, respectively
displacement is calculated for a rectangular fault model
in an elastic half-space
(Okada, 1985)
. We also consider
the effects of horizontal displacement on a steep
bathymetric slope
(Tanioka and Satake 1996a)
.
The non-linear shallow-water equations including
advection and bottom friction terms and the equation of
continuity on the spherical coordinate system are
numerically solved
(Satake 1995)
. We adopt the finite-difference
method with the grid interval of 6″ (140 to 190 m). The
bathymetry data are sampled from J-EGG500 (mesh data
with 500 m interval provided by Japan Oceanographic
Data Center) and M-7000 series digital bathymetry
chart (provided by Japan Hydrographic Association), but
newer coastal topography such as breakwater around tide
gage stations are removed to reproduce the situation in
1896. The tide gage station at Choshi was located at 35°
44.0′N, 140° 50.4′E, different from the current location.
The computations are made for 3 h after the origin time
with a time step of 0.3 s.
For the Sanriku coast, additional computations
including inundation on land with the finest grid size of 75 m
are also made, and the computed tsunami heights are
compared with the 143 heights reported by
Iki (1897)
and the 260 heights reported by
Matsuo (1933)
(Fig. 3,
Additional file 1: Table S1, Additional file 2: Table S2). To
quantify the comparison, the geometric mean K and
geometric standard deviation κ of observed and computed
heights
(Aida 1978)
are computed. If K is larger than one,
the observed heights are larger than the computed ones.
The geometric standard deviation can be considered as
an error factor. The smaller κ means the smaller scatter
hence the better model.
The 1896 tsunami source models
We first adopt the northeastern eight subfaults of the
2011 Tohoku earthquake tsunami source model
(Satake
et al. 2013b)
. The slips on the shallowest subfaults along
the axis (row 0, depth of 0–3.5 km) are 11–36 m, whereas
those on row 1 at the depth of 3.5–7 km range from 1
to 22 m. The average slip for the eight subfaults is 17 m,
yielding the seismic moment of 3.5 × 1021 Nm and the
corresponding moment magnitude Mw of 8.3, assuming
the rigidity of 2 × 1010 N/m2. The computed tsunami
heights are similar to the observed heights on the
northern Sanriku coast, but larger than those on the southern
coast (Figs. 2a, 3). The geometric mean K is 0.70 and
the geometric standard deviation κ is 1.56 for a total of
403 tsunami heights reported by Iki (1897) and
Matsuo
(1933)
(Additional file 1: Table S1, Additional file 2: Table
S2).
Because the eight subfaults of the 2011 model
produced larger tsunami heights than the observed values
on the southern Sanriku coast, we drop the
southernmost subfaults (0D and 1D), and adopt the six subfaults.
The average slip becomes 14 m, the seismic moment is
2.1 × 1021 Nm, and Mw = 8.2. The computed tsunami
heights on the southern Sanriku coast become smaller
and similar to the observed (Figs. 2b, 3). The
geometric mean K becomes 0.93, indicating that observed and
computed heights are almost the same, and the
geometric standard deviation κ is 1.50. However, the computed
tsunami waveforms at regional distances are much larger
than the recorded ones, particularly at Hanasaki and
Ayukawa (Fig. 2b). Thus the slip distribution of the 2011
Tohoku tsunami model, either six or eight subfaults, can
reproduce the tsunami heights on the Sanriku coast but
overestimates the tsunami waveforms at the tide gage
stations located at regional distances. This is expected from
the comparison of the 1896 and 2011 data; the tsunami
heights are similar on the Sanriku coast, but the
amplitude and period of tsunami waveforms are very different
(Fig. 1c, d).
In order to find a model that explains the tsunami
waveforms, we conduct inversion of the 1896 tsunami
20
40.0°
waveforms recorded at three tide gage stations. Because of
poor timing accuracy, the observed waveforms are shifted
so that the initial motion of observed and computed waves
is aligned. The inversion method is similar to Satake et al.
(2013b), but only the spatial slip distribution is estimated.
The inversion model (Fig. 2c) shows large (20 m) slip on
subfault 1B, deeper and second northernmost subfault.
The slip on other five subfaults ranges 3–7 m, and the
average slip is 7 m, which yields seismic moment of 1.1 × 1021
Nm and the moment magnitude of Mw = 8.0. This model
is basically similar to that of Tanioka and Satake (1996b),
although their average slip is smaller (5.7 m) and the dip
angle is larger (20°). The tsunami heights on the Sanriku
coast computed from this model are smaller than the
observations (Figs. 2c, 3). The geometric mean K is 1.87,
and the geometric standard deviation κ is 1.46. This model
reproduces tsunami waveforms at regional distances but
underestimates the Sanriku tsunami heights, particularly
on the southern Sanriku coast.
We finally extend the large (20 m) slip to the
southern subfault (1C) (Fig. 2d). The average slip on the
eight subfaults is 8 m, yielding the seismic moment of
1.6 × 1021 Nm and the moment magnitude of Mw = 8.1.
The computed tsunami heights on the Sanriku coast
become larger, particularly on the southern Sanriku
coast, and the geometric mean K becomes 1.11 with the
geometric standard deviation of κ = 1.39 (Fig. 3,
Additional file 1: Tables S1, Additional file 2: Table S2). The
computed tsunami waveform at Ayukawa, located at the
southern Sanriku coast, also becomes larger than the
previous model. However, the computed tsunami waveforms
at regional distances (Hanasaki and Choshi) are very
similar to the previous model and the observed ones.
This model explains both tsunami heights on the Sanriku
coast and the recorded tsunami waveforms, and yields
the smallest κ, hence considered as the best model of the
1896 Sanriku earthquake.
As mentioned in “Tsunami data of the 1896
earthquake,” there is an additional observation of the 1896
Sanriku tsunami: tsunami arrival times at Miyako
observatory. They reported that sea water started to recede at
18 min, and the maximum tsunami of 4.5 m was observed
at 35 min after the earthquake. To compare with these
reports, we compute the tsunami waveforms at Miyako
(Fig. 4). The tsunami waveform from the 1896 final model
shows initial negative wave followed by the positive wave
with an amplitude of ~ 3.4 m at around 35 min. While
this is slightly smaller than the observed value, the timing
is similar to the reported. The timing of the peak
amplitude from the 2011 model is later (Fig. 4).
Effect of fault depth on tsunami heights
The final model of the 1896 Sanriku earthquake consists
of large (20 m) slip with smaller (3–7 m) slips around it.
In order to examine the effects of the small slips around
the largest one, we trim these smaller slips and compute
tsunamis from a uniform 20 m slip model on a
100km × 25-km fault at a depth of 3.5–7 km (Fig. 2e). The
tsunami heights on the Sanriku coast are similar to the
above final model (K = 1.32), while the computed
tsunami waveforms are slightly different; the periods of the
first wave become shorter and the amplitude at Ayukawa
is slightly larger.
For comparison, we also test another model of uniform
20 m slip, with the same size, at shallowest (0–3.5 km)
part (Fig. 2f ). The tsunami heights on the Sanriku coast
Miyako
2011
(L200 km)
4
)
m
(
e
litu2
d
p
m
A
0
1896
Final
0
from this model are smaller (K = 1.63), while the tsunami
waveforms at regional distances are similar to those from
the previous uniform-slip model at 3.5–7 km depth.
These models indicate that the tsunami heights on the
Sanriku coast are larger from slip on the deeper subfaults
(3.5–7 km depth) than that on the shallowest subfaults
(0–3.5 km depth). Two factors may contribute to this
difference: distance from the source to the coast and the
seafloor displacement due to faulting at different depths.
The deeper subfaults are located closer to the coast than
shallowest subfaults, thus the tsunami heights are larger
on the coast. In addition, the deeper (3.5–7 km) subfaults
produce larger seafloor displacements than surface
rupture (top depth of 0 km), hence the tsunami heights are
also larger. The water depth at these subfaults are also
different: the water is deeper for the shallower subfaults
near the trench axis. However, additional tests indicate
that the water depth difference makes an insignificant
effect for the tsunami heights on the Sanriku coast.
Comparison of 1896 and 2011 sources
During the 1896 Sanriku earthquake, the large (20 m)
slip occurred on subfaults (1B and 1C: Table 1) at a depth
of 3.5–7 km. The slips on surrounding subfaults range
3–7 m, including the shallowest subfaults (0–3.5 km).
During the 2011 Tohoku earthquake, large slips (> 10 m)
occurred at the shallowest subfaults. On the subfaults
where the 1896 slip was large (1B and 1C), the 2011
slips were 3 and 14 m (Fig. 5). The slip ratio (2011/1896)
is smaller than one in the deeper (3.5–7 km) subfaults
except for the southern one (1D), while the ratio ranges
1.9–13 on the shallowest subfaults (Table 1).
This indicates that the 2011 northern slip near the
trench axis, delayed ~ 3 min of the main slip near the
epicenter, occurred on parts where the 1896 slip was not very
large. The sum of subfault slip ranges from 20 to 40 m on
shallowest subfaults (rows 0). The plate convergence rate
is about 8 m per century
(e.g., Sella G et al. 2002)
, hence
these may correspond to 250–500 years of slip deficit.
Although the depths of largest slip of the 1896 and 2011
earthquakes were different, the frictional properties on
these shallowest subfaults may be similar.
Takahashi et al.
(2004
) estimated the seismic velocity structure along the
northern Japan Trench by using the wide-angle airgun
and ocean bottom seismogram data. The closest profile
to the 1896 Sanriku earthquake source (Fig. 6) indicates
that both faults are located at the contact zone between
deformed area (Vp = 3.2–2.6 km/s) and oceanic crust
(Vp = 5.3–5.6 km/s), suggesting similarities of fault zone
properties. Hence the complimentary slips of the 1896 and
2011 earthquakes indicate slip partitioning of these events.
If the 2011 northern slip occurred at shallower part
than the 1896 source, a question might arise why the
18 min
35 min
30
Time (min)
60
38˚
144˚
2011 earthquake was not a ‘tsunami earthquake.’ As
indicated in Fig. 1a, the ground shaking was felt in most part
of Japan in 2011. However, a careful inspection of Fig. 1a
shows that the strong ground shaking was recorded
to the south of the epicenter, where large (> 10 m) slip
occurred at deeper (> 7 km) subfaults. While the 2011
earthquake has a feature of ‘tsunami earthquake’ in the
northern part of the source, deeper slip in the southern
part of the source caused strong ground shaking, hence
the 2011 was not a ‘tsunami earthquake.’
The delayed rupture along the northern Japan Trench
during the 2011 Tohoku earthquake was estimated by
tsunami data
(Satake et al. 2013a; Tappin et al. 2014)
,
but not recorded on other types (seismographs or
highrate GPS) of data. It was thus attributed as submarine
landslide by Tappin et al. (2014). However, comparative
multibeam surveys before and after the 2011 Tohoku
earthquake in the northern Japan Trench did not detect
large bathymetry change indicating large submarine
landslide
(Fujiwara et al. 2017)
. The current study
clarifies that the 2011 tsunami source was on shallower fault
further from the coast than the 1896 Sanriku ‘tsunami
earthquake’ which caused weak ground shaking.
Therefore, it is possible that the fault motion was too slow and
weak to be detected on seismic or high-rate GPS data.
Conclusions
The 1896 Sanriku ‘tsunami earthquake’ occurred along
Japan Trench north of the 2011 Tohoku earthquake.
While the tsunami heights on the northern and central
Sanriku coasts were similar for the two tsunamis, the
tsunami heights on the southern Sanriku coast and the
tsunami waveforms at regional distances were smaller
for the 1896 earthquake. To model the 1896 tsunami
source, we started from the northern subfaults of the
2011 Tohoku earthquake model, and modified them to
obtain the final fault model. The final model is 200 km
long, 50 km wide, with the average slip of 8 m, but large
(20 m) slips on deeper subfaults. This is contrary to the
2011 Tohoku earthquake model, which had large slips at
shallowest subfaults. Thus the slip distributions on
shallow parts of plate interface were different for the 1896
Sanriku and 2011 Tohoku earthquakes.
Additional files
Additional file 1: Table S1. Tsunami heights on the Sanriku coast
measured by
Iki (1897)
and computed from six models: 2011 (L 200 km), 2011
(L 150 km), 1896 inversion, 1896 final, uniform slip at 3.5–7 km depth and
uniform slip at 0–3.5 km depth.
Additional file 2: Table S2. Tsunami heights on the Sanriku coast
measured by
Matsuo (1933)
and computed from six models: 2011 (L 200 km),
2011 (L 150 km), 1896 inversion, 1896 final, uniform slip at 3.5–7 km depth
and uniform slip at 0–3.5 km depth.
Authors’ contributions
KS made overall design of the study and drafted the manuscript. YF made
tsunami simulation and inversion using the coarse grid. SY made detailed
computations on the Sanriku coast with the fine grid for various fault models.
All the authors discussed on the manuscript. All authors read and approved
the final manuscript.
Acknowledgements
We thank Dr. David Tappin and an anonymous reviewer for their critical
comments on the original manuscript, which helped us to improve the paper. This
work was partially supported by JSPS KAKENHI Grant Number JP16H01838.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The data used in this study are from published literature.
Ethics approval and consent to participate
Not applicable.
Funding
JSPS KAKENHI Grant Number JP16H01838.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.
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