Satake et al. Geosci. Lett. (2017) 4:33 https://doi.org/10.1186/s40562-017-0099-y

RESEARCH LETTER Open Access Diferent depths of near‑trench slips of the 1896 and 2011 Tohoku Kenji Satake1* , Yushiro Fujii2 and Shigeru Yamaki3

Abstract The 1896 Sanriku was a typical ‘ earthquake’ which caused large tsunami despite its weak ground shaking. It occurred along the 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 scientifc 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 from the northeastern part of the 2011 tsunami source model roughly repro- duced the 1896 tsunami heights on the , 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 shal- lower 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. Keywords: , , , 2011 Tohoku earthquake

Background Tis enigma was explained by a delayed tsunami genera- Te 11 March 2011 Tohoku earthquake (Mw 9.0) was the tion in the northern part of tsunami source through the largest instrumentally recorded earthquake in Japan and tsunami waveform analysis (Satake et al. 2013b; Tappin caused devastating tsunami damage including ~ 18,500 et al. 2014). However, the cause of the delayed tsunami casualties. Te ground shaking was felt throughout the generation is still controversial, either due to slip on shal- Japanese Islands with the maximum seismic intensity of low plate interface (Satake et al. 2013b) or submarine 7 on the Japan Meteorological Agency (JMA) scale, or landslide (Tappin et al. 2014). 11–12 on the Modifed Mercalli scale (Fig. 1a). Huge slip In the northern part of the 2011 tsunami source, the 15 (> 50 m) on the plate interface up to the Japan Trench June 1896 Sanriku earthquake occurred and caused the axis was estimated near the epicenter (~ 38.5°N) from worst tsunami disaster in Japan, with casualties of ~ 20, seismic waves (Ide et al. 2011), inland and submarine 000 (Shuto et al. 2007). Te 1896 Sanriku earthquake was geodetic data (Iinuma et al. 2012), and tsunami wave- a typical example of a ‘tsunami earthquake’ (Kanamori forms (Fujii et al. 2011; Satake et al. 2013b). On the con- 1972; Tanioka and Satake 1996b). Te origin time: 19 h trary, the largest tsunami heights on the Sanriku coast, 32 m (local time), the epicenter: 144°E, 39.5°N, and magni- ~ 40 m, were recorded ~ 100 km north (near 39.6°N). tude: M = 6.8 were estimated from Japanese seismological data (Utsu 1979). Te surface wave magnitude MS = 7.2 was assigned from global data (Abe 1994). Te moment *Correspondence: [email protected]‑tokyo.ac.jp magnitude Mw was estimated as 8.0–8.2, from a compari- 1 Earthquake Research Institute, The University of Tokyo, 1‑1‑1 Yayoi, Bunkyo‑ku, Tokyo 113‑0032, Japan son of aftershock activity with other large earthquakes Full list of author information is available at the end of the article (Utsu 1994). Te tsunami magnitude Mt was determined

© The Author(s) 2017. 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, and reproduction 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. Satake et al. Geosci. Lett. (2017) 4:33 Page 2 of 10

ab11 March 2011 Tohoku (M 9.0) 15 June 1896 Sanriku (M 8.2) JMA MM 45ºN JMA MM 7 11,12 Hanasaki 6+ 10 5 8 6- 9 4 6-7 5+ 8 3 4-5 5- 7 2 3 4 6 40º 3 4-5 1 2 2 3 1 2 Ayukawa

Choshi 35º

0 km 400 30º 130º 135º 140º 145ºE 130º 135º 140º 145ºE

cdHanasaki 1896 2011 40.5˚ 2 1896 Sanriku N 0 Kuji −2 2011 Tohoku 40˚ 8 Ayukawa 6 Miyako 39.5˚ 4 2011 Tohoku 2 1896 Sanriku 39˚ Ofunato 0

) −2 Choshi 38.5˚ 2 2011 Tohoku Ayukawa 0 Iki Runup 0 10 20 30 40 50 60 Amplitude (m 1896 Sanriku Matsuo Inundation Tsunami height (m) −2 Yamana 0306090 120 150 180 Time (min) Fig. 1 a Epicenter (black star) and seismic intensity distribution of the 2011 Tohoku earthquake, according to Japan Meteorological Agency. b Epi- center and seismic intensity distribution of the 1896 Sanriku earthquake. Locations of tide gage stations (open triangles) are also shown. c Tsunami heights on the Sanriku coast from the 1896 Sanriku tsunami (blue symbols with diferent shapes for the data source) and the 2011 Tohoku earth- quake (red symbols with diferent shapes for runup and inundation heights) from Tsuji et al. (2014). d Tsunami waveforms from the 1896 Sanriku (blue curves) and 2011 Tohoku (red curves) earthquakes recorded at the three tide gage stations Satake et al. Geosci. Lett. (2017) 4:33 Page 3 of 10

as 8.6 from global data (Abe 1979) and 8.2 from Japanese Choshi (500 km) (Fig. 1b, Honda et al. 1908; Imamura data (Abe 1981). Te ground shaking was weak (2–3 on and Moriya 1939). Tanioka and Satake (1996b) exam- the JMA seismic intensity scale, corresponding to 4–5 on ined these waveforms, estimated the clock timing errors the Modifed Mercalli scale; Fig. 1b). However, the tsu- as large as 5 min, and modeled the waveforms without nami heights on the Sanriku coast from the 2011 and 1896 timing information. Te 2011 tsunami was also recorded earthquakes were roughly similar (Fig. 1c, Tsuji et al. 2014) at these tide gage stations, although the Ayukawa record as detailed in the “Tsunami data of the 1896 earthquake.” went of-scale immediately following the frst tsunami Tsunami waveform modeling of the 1896 Sanriku arrival at ~ 30 min from the earthquake (Satake et al. earthquake has shown that slip occurred on a narrow 2013b). Comparison of the 1896 and 2011 tsunami wave- fault located near the trench axis (Tanioka and Satake forms indicates that both periods and amplitudes of the 1996b; Tanioka and Seno 2001). Tis is a common fea- 2011 waveforms are larger than those of the 1896 tsu- ture of ‘tsunami earthquakes’ such as the 1992 Nicara- nami (Fig. 1d), probably due to the diferent sizes of tsu- gua or 2010 Mentawai earthquakes (Satake and Tanioka nami source. 1999; Satake et al. 2013a). Tanioka et al. (1997) further For the 1896 tsunami heights along the Sanriku coasts, proposed that the 1896 Sanriku ‘tsunami earthquake’ at distances ranging from 170 to 250 km from the epi- occurred in a region where the ocean bottom topography center, feld surveys were made by three groups (Fig. 1c). is rough, characterized by well-developed horst and gra- Yamana (reproduced by Unohana and Ota 1988) made ben structures. Polet and Kanamori (2000) extended this a post-tsunami survey from July through September of model to global zones, based on the examina- 1896 in all of the 37 villages along the Sanriku coast. Te tion of the source spectra of large (M > 7) earthquakes in largest heights of 55 m were reported at two locations. the 1990s. More recently, Lay et al. (2012) classifed the While his report contains 168 diagrams, the reliability seismogenic zone of subduction zones into four domains of his measurements has been questioned (Shuto et al. and assigned the shallowest domain (A: less than 15 km 2007). Iki (1897) made a survey in June and July of 1896 depth) as a source region of ‘tsunami earthquakes.’ along the Sanriku coast. He measured tsunami heights After the occurrence of the 2011 Tohoku earth- based on various kinds of traces and eyewitness accounts, quake and tsunami, a question arose about the relation and assigned diferent reliabilities depending on the between the 1896 and 2011 tsunami sources. Did both kind of data. Te maximum tsunami height was 24 m earthquakes rupture the same shallow plate interface at Yoshihama. In 1933, another devastating tsunami, or diferent parts? Why was the 1896 event a ‘tsunami with maximum height of 29 m and approximately 3000 earthquake’ while the 2011 earthquake was not? Tese fatalities, was caused by the are important issues both in science of tsunami genera- (Ms 8.5). Matsuo (1933) made feld survey to measure the tion in subduction zones, particularly near the trench heights of both 1896 and 1933 tsunamis. Although the axis, and also for tsunami hazard assessment. 1896 tsunami heights were measured 37 years after the In this study, we re-estimate the slip distribution, par- occurrence based on the eyewitness accounts, the survey ticularly in depth direction, of the 1896 Sanriku ‘tsunami points were plotted on 1:50,000 maps and provided valu- earthquake’ based on both tsunami heights on the San- able information. Te often-quoted maximum height of riku coast and the tsunami waveforms recorded on three 38 m at Shirahama from the 1896 Sanriku tsunami was tide gage stations at regional distance in Japan. It should based on his report. In this study, we adopt the reported be noted that tsunami height data on the Sanriku coast tsunami heights by Iki (1897) and Matsuo (1933) and have not been used in the previous studies of the 1896 compare them with the calculated heights. Because of earthquake. In order to fnd the best 1896 tsunami source the sawtooth-shaped topography of the Sanriku coast, model, we start from the northern part of the 2011 often called a ria-type coast in Japan, both the 1896 and source model, compute the tsunami heights on the San- 2011 tsunami heights signifcantly change at short dis- riku coast and tsunami waveforms at tide gage stations, tance (Fig. 1c). Tsuji et al. (2014) compared the 1896 and and compare them with the 1896 observations. We also 2011 tsunami heights on the Sanriku coast and found the compare the tsunami source models, or obtained slip dis- median ratios (1896/2011) are 1.01, 0.85, and 0.29 on the tributions, of the 1896 and 2011 earthquakes, and discuss northern, central, and southern Sanriku coasts, respec- why the 2011 earthquake was not a ‘tsunami earthquake.’ tively, and 0.69 for the entire Sanriku coast. Tese indi- cate that the 1896 tsunami heights were similar to the Tsunami data of the 1896 earthquake 2011 tsunami heights on the northern and central San- Te 1896 tsunami was instrumentally recorded on three riku coasts. tide gage stations at regional distances in Japan: Hana- A careful manual observation of the tsunami was saki (440 km from the epicenter), Ayukawa (250 km), and conducted at the Miyako meteorological observatory Satake et al. Geosci. Lett. (2017) 4:33 Page 4 of 10

(Miyako is shown in Fig. 1c), and published in the timing. In addition, the tsunami arrival times were meas- annual report of the Central Meteorological Observa- ured relative to the earthquake. Terefore the timing of tory (1902). It describes as follows. “At 19 h 32 m 30 s tsunami arrival at Miyako provides additional important (local time), a weak shock of earthquake was felt, last- information. ing for about 5 min. Its direction was ENE–WSW and the nature was extremely slow. At about 19 h 50 m, the Tsunami computations sea began to recede. At about 20 h, the water rose, but We use the subfault confguration of the 2011 Tohoku fell somewhat in a few minutes. At 20 h 07 m, the biggest earthquake of Satake et al. (2013b). Only eight subfaults wave of about 4.5 m high came in with a fearful boom- (0A to 1D: Fig. 2a, Table 1) in the northern and shallow ing sound, and instantly swept away all houses or living part of the source are adopted. Each subfault is 50 km things that were in its path. Subsequently, six waves of long and 25 km wide. Te strike, dip, and slip angles are more or less heights came until the noon of the follow- 193°, 8°, and 81°, respectively. Te subfaults are placed on ing day.” At the Miyako observatory, seismograph obser- the Pacifc plate (Nakajima and Hasegawa 2006), and the vation already started in those days (Omori and Hirata top depths beneath seafoor are 0 and 3.5 km for shallow- 1899), hence the observer must be sensitive to accurate est (row 0) and next (row 1) subfaults (Table 1). Seafoor

a 2011 (L 200 km) b 2011 (L 150 km) c 1896 Inversion d 1896 Final e Uniform at 3.5-7 km f Uniform at 0-3.5 km Water height (m) Slip (m) 141˚E 142˚E 143˚E 144˚E 0 1 2 3 4 5 6 7 8 9 10 0481216202428323640 41˚N km 0 10000

1A 40˚N 0A 1B 0B 1C 39˚N 0C 1D 0D y 38˚N 41˚N

40˚N

39˚N

Iki Matsuo Cal. (Iki) Cal. (Matsuo) 38˚N 0210 0430 0 0210 0430 0 0210 0430 0 0210 0430 0 0210 0430 0 0210 0430 0 Tsunami height (m) Tsunami height (m) Tsunami height (m) Tsunami height (m) Tsunami height (m) Tsunami height (m) 2 2 2 2 2 2 Hanasaki Hanasaki Hanasaki Hanasaki Hanasaki Hanasaki

0 0 0 0 0 0

−2 −2 −2 −2 −2 −2 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 4 4 4 4 4 4 Ayukawa Ayukawa Ayukawa Ayukawa Ayukawa Ayukawa

2 2 2 2 2 2

0 0 0 0 0 0

−2 −2 −2 −2 −2 −2

−4 −4 −4 −4 −4 −4 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 2 2 2 2 2 2 Choshi Choshi Choshi Choshi Choshi Choshi

0 0 0 0 0 0 Amplitude (m) −2 −2 −2 −2 −2 −2 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 30 60 90 120 Time (min) Time (min) Time (min) Time (min) Time (min) Time (min) Fig. 2 Comparison of 6 models a 2011 model with 8 subfaults and 200 km long, b 2011 model with 6 subfaults and 150 km long, c 1896 inversion model, d 1896 fnal model, e uniform (20 m) slip at 3.5–7 km depth, f uniform (20 m) slip at 0–3.5 km depth. (top) Slip distribution on subfaults (color bar scale in the right) and computed maximum tsunami height (color bar scale in the left) for 6 models. (middle) Observed and computed tsunami heights on the Sanriku coast. Red and yellow circles show observed heights by Iki (1897) and Matsuo (1933), respectively. Blue and green circles with bars are computed heights on 6″ grid. (bottom) Tsunami waveforms at three tide gage stations at regional distances. Red curves are observed waveforms and blue curves are computed ones Satake et al. Geosci. Lett. (2017) 4:33 Page 5 of 10

Table 1 Subfault locations and the slip amounts for four source models No. Lat.(°N)* Lon.(°E)* 2011 8 subfaults 2011 6 subfaults 1896 inversion 1896 fnal (m) Sum 1896 2011 Ratio 2011/1896 (m) (m) (m) (m) +

0A 40.198 144.35 11 11 6 6 16 1.9 1A 40.24809 144.06599 1 1 3 3 4 0.3 0B 39.738 144.331 21 21 3 3 23 7.6 1B 39.78808 144.04,888 3 3 20 20 23 0.2 0C 39.3 144.2 36 36 7 3 39 13.4 1C 39.35008 143.91966 14 14 5 20 33 0.7 0D 38.862 144.069 31 0 0 7 37 4.5 1D 38.91208 143.7904 22 0 0 5 28 4.4

* 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 seafoor, for subfaults 0* and 1*, respectively

displacement is calculated for a rectangular fault model the axis (row 0, depth of 0–3.5 km) are 11–36 m, whereas in an elastic half-space (Okada, 1985). We also consider those on row 1 at the depth of 3.5–7 km range from 1 the efects of horizontal displacement on a steep bathym- to 22 m. Te average slip for the eight subfaults is 17 m, 21 etric slope (Tanioka and Satake 1996a). yielding the seismic moment of 3.5 × 10 Nm and the Te non-linear shallow-water equations including corresponding moment magnitude Mw of 8.3, assuming 10 2 advection and bottom friction terms and the equation of the rigidity of 2 × 10 N/m . Te computed tsunami continuity on the spherical coordinate system are numer- heights are similar to the observed heights on the north- ically solved (Satake 1995). We adopt the fnite-diference ern Sanriku coast, but larger than those on the southern method with the grid interval of 6″ (140 to 190 m). Te coast (Figs. 2a, 3). Te geometric mean K is 0.70 and bathymetry data are sampled from J-EGG500 (mesh data the geometric standard deviation κ is 1.56 for a total of with 500 m interval provided by Japan Oceanographic 403 tsunami heights reported by Iki (1897) and Matsuo Data Center) and M-7000 series digital bathymetry (1933) (Additional fle 1: Table S1, Additional fle 2: Table chart (provided by Japan Hydrographic Association), but S2). newer coastal topography such as breakwater around tide Because the eight subfaults of the 2011 model pro- gage stations are removed to reproduce the situation in duced larger tsunami heights than the observed values 1896. Te tide gage station at Choshi was located at 35° on the southern Sanriku coast, we drop the southern- 44.0′N, 140° 50.4′E, diferent from the current location. most subfaults (0D and 1D), and adopt the six subfaults. Te computations are made for 3 h after the origin time Te average slip becomes 14 m, the seismic moment is 21 with a time step of 0.3 s. 2.1 × 10 Nm, and Mw = 8.2. Te computed tsunami For the Sanriku coast, additional computations includ- heights on the southern Sanriku coast become smaller ing inundation on land with the fnest grid size of 75 m and similar to the observed (Figs. 2b, 3). Te geomet- are also made, and the computed tsunami heights are ric mean K becomes 0.93, indicating that observed and compared with the 143 heights reported by Iki (1897) computed heights are almost the same, and the geomet- and the 260 heights reported by Matsuo (1933) (Fig. 3, ric standard deviation κ is 1.50. However, the computed Additional fle 1: Table S1, Additional fle 2: Table S2). To tsunami waveforms at regional distances are much larger quantify the comparison, the geometric mean K and geo- than the recorded ones, particularly at Hanasaki and metric standard deviation κ of observed and computed Ayukawa (Fig. 2b). Tus the slip distribution of the 2011 heights (Aida 1978) are computed. If K is larger than one, Tohoku tsunami model, either six or eight subfaults, can the observed heights are larger than the computed ones. reproduce the tsunami heights on the Sanriku coast but Te geometric standard deviation can be considered as overestimates the tsunami waveforms at the tide gage sta- an error factor. Te smaller κ means the smaller scatter tions located at regional distances. Tis is expected from hence the better model. the comparison of the 1896 and 2011 data; the tsunami heights are similar on the Sanriku coast, but the ampli- The 1896 tsunami source models tude and period of tsunami waveforms are very diferent We frst adopt the northeastern eight subfaults of the (Fig. 1c, d). 2011 Tohoku earthquake tsunami source model (Satake In order to fnd a model that explains the tsunami et al. 2013b). Te slips on the shallowest subfaults along waveforms, we conduct inversion of the 1896 tsunami Satake et al. Geosci. Lett. (2017) 4:33 Page 6 of 10

a 40 Iki 35 2011 (L200 km) 30 2011 (L150 km) 25 1896 Inversion 20 1896 Final 15 10 sunami height (m) 5 0 Loc. # 1 10 20 30 40 50 60 70 80 90 1001110 20 130140 Lat. 40.5°340.0°39.5° 9.3° 38.7°338.5° 8.3°N b 40 Matsuo 35

)T 2011 (L200 km) 30 2011 (L150 km) 25 1896 Inversion 20 1896 Final 15 10 Tsunami height (m 5 0 Loc. # 120406080100 120140 160180 200220 240260 Lat. 40.3°340.0°39.0° 8.9° 38.8°338.7° 8.5° Fig. 3 Tsunami heights on the Sanriku coast reported by (a) Iki (1897) and (b) Matsuo (1933) are shown by black circles. Computed tsunami heights on 75 m grids for the four diferent models are shown by colored lines. Note that the scale for horizontal axis is location numbers (Additional fle 1: Table S1, Additional fle 2: Table S2), not distance. The latitudes for the locations are also shown

waveforms recorded at three tide gage stations. Because of eight subfaults is 8 m, yielding the seismic moment of 21 poor timing accuracy, the observed waveforms are shifted 1.6 × 10 Nm and the moment magnitude of Mw = 8.1. so that the initial motion of observed and computed waves Te computed tsunami heights on the Sanriku coast is aligned. Te inversion method is similar to Satake et al. become larger, particularly on the southern Sanriku (2013b), but only the spatial slip distribution is estimated. coast, and the geometric mean K becomes 1.11 with the Te inversion model (Fig. 2c) shows large (20 m) slip on geometric standard deviation of κ = 1.39 (Fig. 3, Addi- subfault 1B, deeper and second northernmost subfault. tional fle 1: Tables S1, Additional fle 2: Table S2). Te Te slip on other fve subfaults ranges 3–7 m, and the aver- computed tsunami waveform at Ayukawa, located at the 21 age slip is 7 m, which yields seismic moment of 1.1 × 10 southern Sanriku coast, also becomes larger than the pre- Nm and the moment magnitude of Mw = 8.0. Tis model vious model. However, the computed tsunami waveforms is basically similar to that of Tanioka and Satake (1996b), at regional distances (Hanasaki and Choshi) are very although their average slip is smaller (5.7 m) and the dip similar to the previous model and the observed ones. angle is larger (20°). Te tsunami heights on the Sanriku Tis model explains both tsunami heights on the Sanriku coast computed from this model are smaller than the coast and the recorded tsunami waveforms, and yields observations (Figs. 2c, 3). Te geometric mean K is 1.87, the smallest κ, hence considered as the best model of the and the geometric standard deviation κ is 1.46. Tis model 1896 Sanriku earthquake. reproduces tsunami waveforms at regional distances but As mentioned in “Tsunami data of the 1896 earth- underestimates the Sanriku tsunami heights, particularly quake,” there is an additional observation of the 1896 on the southern Sanriku coast. Sanriku tsunami: tsunami arrival times at Miyako obser- We fnally extend the large (20 m) slip to the south- vatory. Tey reported that sea water started to recede at ern subfault (1C) (Fig. 2d). Te average slip on the 18 min, and the maximum tsunami of 4.5 m was observed Satake et al. Geosci. Lett. (2017) 4:33 Page 7 of 10

at 35 min after the earthquake. To compare with these from this model are smaller (K = 1.63), while the tsunami reports, we compute the tsunami waveforms at Miyako waveforms at regional distances are similar to those from (Fig. 4). Te tsunami waveform from the 1896 fnal model the previous uniform-slip model at 3.5–7 km depth. shows initial negative wave followed by the positive wave Tese models indicate that the tsunami heights on the with an amplitude of ~ 3.4 m at around 35 min. While Sanriku coast are larger from slip on the deeper subfaults this is slightly smaller than the observed value, the timing (3.5–7 km depth) than that on the shallowest subfaults is similar to the reported. Te timing of the peak ampli- (0–3.5 km depth). Two factors may contribute to this tude from the 2011 model is later (Fig. 4). diference: distance from the source to the coast and the seafoor displacement due to faulting at diferent depths. Efect of fault depth on tsunami heights Te deeper subfaults are located closer to the coast than Te fnal model of the 1896 Sanriku earthquake consists shallowest subfaults, thus the tsunami heights are larger of large (20 m) slip with smaller (3–7 m) slips around it. on the coast. In addition, the deeper (3.5–7 km) subfaults In order to examine the efects of the small slips around produce larger seafoor displacements than surface rup- the largest one, we trim these smaller slips and compute ture (top depth of 0 km), hence the tsunami heights are tsunamis from a uniform 20 m slip model on a 100- also larger. Te water depth at these subfaults are also km × 25-km fault at a depth of 3.5–7 km (Fig. 2e). Te diferent: the water is deeper for the shallower subfaults tsunami heights on the Sanriku coast are similar to the near the trench axis. However, additional tests indicate above fnal model (K = 1.32), while the computed tsu- that the water depth diference makes an insignifcant nami waveforms are slightly diferent; the periods of the efect for the tsunami heights on the Sanriku coast. frst wave become shorter and the amplitude at Ayukawa is slightly larger. Comparison of 1896 and 2011 sources For comparison, we also test another model of uniform During the 1896 Sanriku earthquake, the large (20 m) 20 m slip, with the same size, at shallowest (0–3.5 km) slip occurred on subfaults (1B and 1C: Table 1) at a depth part (Fig. 2f). Te tsunami heights on the Sanriku coast of 3.5–7 km. Te 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) Miyako 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). Te slip ratio (2011/1896) 2011 is smaller than one in the deeper (3.5–7 km) subfaults (L200 km) except for the southern one (1D), while the ratio ranges 1.9–13 on the shallowest subfaults (Table 1). 4 Tis indicates that the 2011 northern slip near the trench axis, delayed ~ 3 min of the main slip near the epi- center, occurred on parts where the 1896 slip was not very 2 large. Te sum of subfault slip ranges from 20 to 40 m on shallowest subfaults (rows 0). Te plate convergence rate

Amplitude (m) is about 8 m per century (e.g., Sella G et al. 2002), hence 0 1896 these may correspond to 250–500 years of slip defcit. Final Although the depths of largest slip of the 1896 and 2011 earthquakes were diferent, 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. Te closest profle to the 1896 Sanriku earthquake source (Fig. 6) indicates 18 min 35 min that both faults are located at the contact zone between 03060 deformed area (Vp = 3.2–2.6 km/s) and oceanic crust Time (min) (Vp = 5.3–5.6 km/s), suggesting similarities of fault zone Fig. 4 Tsunami waveforms computed at Miyako from the 2011 properties. Hence the complimentary slips of the 1896 and model (8 subfaults) and the 1896 fnal model. Dashed lines (18 min 2011 earthquakes indicate slip partitioning of these events. and 35 min after the earthquake origin time) indicate the observed If the 2011 northern slip occurred at shallower part tsunami arrivals of frst and maximum waves (see text) than the 1896 source, a question might arise why the Satake et al. Geosci. Lett. (2017) 4:33 Page 8 of 10

40˚

40

30

20

Slip (m)

10

140˚

142˚ 38˚

144˚ Fig. 5 Cumulative slips on subfaults of the 2011 (red columns) and 1896 (blue) earthquakes. The main slip was on the shallowest subfaults in 2011 (Satake et al. 2013b), while it was on the deeper subfaults in 1896

Fig. 6 Velocity structure profle touched in Takahashi et al. (2004). Both 1896 and 2011 slips were on the shallowest part of the subduction zone near trench axis, below low velocity prism Satake et al. Geosci. Lett. (2017) 4:33 Page 9 of 10

2011 earthquake was not a ‘tsunami earthquake.’ As indi- Authors’ contributions KS made overall design of the study and drafted the manuscript. YF made cated in Fig. 1a, the ground shaking was felt in most part tsunami simulation and inversion using the coarse grid. SY made detailed of Japan in 2011. However, a careful inspection of Fig. 1a computations on the Sanriku coast with the fne grid for various fault models. shows that the strong ground shaking was recorded All the authors discussed on the manuscript. All authors read and approved the fnal manuscript. to the south of the epicenter, where large (> 10 m) slip occurred at deeper (> 7 km) subfaults. While the 2011 Author details 1 earthquake has a feature of ‘tsunami earthquake’ in the Earthquake Research Institute, The University of Tokyo, 1‑1‑1 Yayoi, Bunkyo‑ku, Tokyo 113‑0032, Japan. 2 International Institute of Seismology northern part of the source, deeper slip in the southern and Earthquake Engineering, Building Research Institute, 1 Tachihara, Tsukuba, part of the source caused strong ground shaking, hence Ibaraki 305‑0802, Japan. 3 Seamus Ltd, 2235 Kizaki, Kita‑ku, Niigata 950‑3304, the 2011 was not a ‘tsunami earthquake.’ Japan. Te delayed rupture along the northern Japan Trench Acknowledgements during the 2011 Tohoku earthquake was estimated by We thank Dr. David Tappin and an anonymous reviewer for their critical com- tsunami data (Satake et al. 2013a; Tappin et al. 2014), ments on the original manuscript, which helped us to improve the paper. This work was partially supported by JSPS KAKENHI Grant Number JP16H01838. but not recorded on other types (seismographs or high- rate GPS) of data. It was thus attributed as submarine Competing interests landslide by Tappin et al. (2014). However, comparative The authors declare that they have no competing interests. multibeam surveys before and after the 2011 Tohoku Availability of data and materials earthquake in the northern Japan Trench did not detect The data used in this study are from published literature. large bathymetry change indicating large submarine Ethics approval and consent to participate landslide (Fujiwara et al. 2017). Te current study clari- Not applicable. fes that the 2011 tsunami source was on shallower fault further from the coast than the 1896 Sanriku ‘tsunami Funding JSPS KAKENHI Grant Number JP16H01838. earthquake’ which caused weak ground shaking. Tere- fore, it is possible that the fault motion was too slow and Publisher’s Note weak to be detected on seismic or high-rate GPS data. Springer Nature remains neutral with regard to jurisdictional claims in pub- lished maps and institutional afliations. Conclusions Received: 9 September 2017 Accepted: 7 December 2017 Te 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 References tsunami heights on the southern Sanriku coast and the Abe K (1979) Size of great earthquakes of 1873–1974 inferred from tsunami data. J Geophys Res 84:1561–1568 tsunami waveforms at regional distances were smaller Abe K (1981) Physical size of tsunamigenic earthquakes of the northwestern for the 1896 earthquake. To model the 1896 tsunami Pacifc. 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