Nakata et al.
Progress in Earth and Planetary Science(2024) 11:28
https://doi.org/10.1186/s40645-024-00631-0

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open Access

New source model for the 1771 Meiwa
tsunami along the southern Ryukyu Trench
inferred from high‑resolution tsunami
calculation
Koki Nakata1*, Kazuhisa Goto1 and Hideaki Yanagisawa2

Abstract
The 1771 Meiwa tsunami which struck the southern Ryukyu Islands (Sakishima Islands) had greater than 22 m run-up
height, leaving about 12,000 casualties in its wake. At many places, the tsunami inundation or lack of inundation
is well recorded in historical documents. Several tsunami source models have been proposed for this event using
historical records as constraints of tsunami calculations. Nevertheless, the source model remains under discussion.
This study re-evaluated the tsunami wave source model of the 1771 Meiwa tsunami using high-resolution (10 mmesh) bathymetric and topographical data for tsunami calculation, the latest historical record dataset, and seismological knowledge. Results demonstrated that a tsunami earthquake along the southern Ryukyu Trench was the likely
cause of the 1771 event. However, it is noteworthy that assumption of a large slip with 30 m is necessary for a shallow
and narrow region (fault depth = 5 km, fault width = 30 km, Mw = 8.49) of the plate boundary in the Ryukyu Trench,
which is far larger than previously thought. This requirement of very large initial water level change at the source
might involve not only the fault rupture along the plate boundary but also deformation by splay faults, inelastic
deformation of unconsolidated sediments near the trench axis, and/or giant submarine landslides. Results also showthat the effects of fault parameters on the run-up were quite different depending on the offshore coral reef width.
This phenomenon strongly constrained the fault width to 30 km. Our tsunami ray tracing analysis further revealed
the effects of bathymetry on tsunami propagation. It is noteworthy that meter-long huge tsunami boulders tend
to be distributed along the specific coasts at which the tsunami was concentrated by bathymetric effects. Thisfinding suggests that past tsunamis, including the 1771 event, might have affected the specific coral reefs on Sakishima Islands repeatedly, which is crucially important for understanding the heterogeneous distribution of tsunami boulders. This feature might also be useful to elucidate the effects of large tsunamis on the corals and reefs
because a direct comparison of coral reefs that are damaged and not damaged by tsunami waves is testable in narrow areas in the case of the Sakishima Islands.
Keywords 1771 Meiwa tsunami, Coral reef, Ryukyu Trench, Tsunami boulder, Tsunami earthquake, Tsunami modeling,
Tsunami ray tracing analysis*Correspondence:
Koki Nakata
nakata-koki864@g.ecc.u-tokyo.ac.jp
Full list of author information is available at the end of the article© The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

1 Introduction
On 24 April 1771, a huge tsunami, called the Meiwa (orYaeyama) tsunami, inflicted extensive damage mainly
to the Sakishima Islands of Japan (Fig. 1a, b). Causing
approximately 12,000 casualties (Goto et al. 2010a), it
was one of the most destructive historical tsunamis
ever to strike the Japanese archipelago.
Details of the damage caused by the Meiwa tsunami
are recorded in historical documents (Makino 1968;
Goto et al. 2010a). It is noteworthy for many sites

Page 2 of 27

that whether the tsunami inundated it or not is wellrecorded. In addition, the elevations and coordinatesof these points were resurveyed using high-precision
GNSS equipment, verifying the reliability of the historical descriptions (Goto et al. 2012). Using these data, themaximum runup height was estimated as greater than
22 m (most likely around 30 m) on Ishigaki Island, 15 m
on Tarama Island, and 18 m on Miyako Island (Gotoet al. 2012).

Fig. 1 a Map showing the study area location in the northwest Pacific. b Map showing the Sakishima Islands and Ryukyu Trench locations. c Closeup map of Sakishima Islands. Red, orange, and green areas respectively denote source models for the 1771 earthquake: IM, Imamura et al. (2001);
NK, Nakamura (2009); and MY, Miyazawa et al. (2012). The plate boundary was adopted from Iwasaki et al. (2015)

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

In addtion, geological evidence of past tsunamis havebeen reported for the Sakishima Islands. In general, theSakishima Islands are surrounded by well-developed
fringing reefs as much as 1.5 km wide (Hongo and Kayanne 2009), but the reefs are about 8 km around thesouthwestern coast of Ishigaki Island. Along the coast,
there are many meter-long coral boulders, so-calledtsunami boulders, that have been transported from thecoral reef by past tsunami events including the 1771
Meiwa tsunami (e.g., Goto et al. 2010a). The sizes andspatial distributions of tsunami boulders might reflect
the tsunami energy. For that reason, tsunami boulders
are expected to be a promising proxy to restrict estimates of the size of past tsunamis (e.g., Goto et al. 2014;
Hisamatsu et al. 2014; Watanabe et al. 2016). In addition, because many tsunami boulders at the SakishimaIslands consist of single Porites colonies, they are suitable to date the tsunami timing (Araoka et al. 2013).
Based on radiocarbon dating, Araoka et al. (2013)
reported that some tsunami boulders were depositedby the 1771 Meiwa tsunami. However, many other tsunami boulders were dated earlier than 1771 (Araoka
et al. 2013). Based on such results, they suggested thatpast tsunamis at the Sakishima Islands repeatedly cast
the boulders ashore with a 150–400 year recurrence
interval. It is also reported that distributions of tsunami boulders are not uniform: the boulders are patchily distributed at some specific coasts of the SakishimaIslands (Goto et al. 2010a), although it remains uncertain why tsunami boulders are concentrated at somecoasts.
Sandy tsunami deposits have also been reported in
the Sakishima Islands (Yamamoto 2008; Ando et al.
2018; Fujita et al. 2020). Not only the 1771 Meiwa tsunami sandy deposit, but two sandy tsunami deposits
and tsunami boulders by the earlier events have also
been identified (Ando et al. 2018; Fujita et al. 2020).
Results of tsunami deposit dating suggest that tsunamis of the same or greater size as the Meiwa tsunami
occurred repeatedly at approximately 600 year intervals
during the last 2000 year (Ando et al. 2018). The interpretation was supported by the reconstruction of coral
reef morphology based on the examination of molluscan assemblages in the tsunami deposits (Kitamura
et al. 2018). In addition, Yamamoto (2008) and Andoet al. (2018) found fissures beneath the Meiwa tsunami
deposit. Usami (2010) estimated the seismic intensity ofthe earthquake which generated the Meiwa tsunami as
4 on the scale of Japan Metrological Agency (JMA) in
the Sakishima Islands because there is no description ofdamage caused by seismic motion in historical records.
However, Ando et al. (2018) reported that the seismic intensity might have been greater than previously

Page 3 of 27

thought: it is expected to have been sufficient to produce fissures in the ground. If this were the case, theseismic intensity would be expected to be greater than
5 on the JMA scale according to Ando et al. (2018).
As reviewed in the next chapter, the source modelof the Meiwa tsunami is still under debate. Additionally, heterogeneous distribution of tsunami boulders
persists as an unresolved issue. Therefore, this study
was conducted to re-evaluate the tsunami wave source
model of the 1771 Meiwa tsunami using sufficiently
high-resolution bathymetric and topographic data
for tsunami calculation along with the latest historical record dataset (Goto et al. 2012) as the constraintof the source model. We further discuss the bathymetric effects of tsunami wave concentration toward somespecific coasts based on tsunami ray tracing analysis(Satake 1988).

2 Earlier studies of 1771 Meiwa tsunami source
models
Source models of the Meiwa tsunami have been proposed
based on several earlier studies (Imamura et al. 2001;
Nakamura 2009; Miyazawa et al. 2012; Okamura et al.
2018). These models are classifiable into three main models: (1) the intraplate earthquake plus submarine landslide (Imamura et al. 2001; Miyazawa et al. 2012); (2) theinterplate earthquake along the Ryukyu Trench (Nakamura 2009); and (3) the giant submarine landslide near
the Ryukyu Trench (Okamura et al. 2018). The locationsof the source models proposed by Imamura et al. (2001),
Miyazawa et al. (2012), and Nakamura (2009) are presented in Fig. 1c, with parameters presented in Table 1.
Among the previously proposed source models, themodel for the interplate earthquake along the Ryukyu
Trench is adopted in this study, because this model isbetter suited for the recent geological findings. The reasons to adopt this model together with issues of othermodels are summarized below.
2.1 Intraplate earthquake plus submarine landslide

Imamura et al. (2001) estimated an intraplate earthquake (moment magnitude (Mw) = 7.7) and submarine
landslide at the southeastern offshore of Ishigaki Islandas the Meiwa tsunami source model. They assumed thesubmarine landslide as the supplement tsunami source
to explain extremely high run-up height at the southerncoast of Ishigaki Island. This assumption is based on work
reported by Matsumoto and Kimura (1993) who proposed the presence of a submarine landslide near Kuroshima Island. However, the fault posited for this model
assumed a large slip of 20 m. In fact, this large slip is far
beyond the value which can be estimated from the typicalOkamura et al. (2018)

Submarine landslide

N/A

124.8000
N/A

124.2640

23.9100
24.1348

Fault 2

Submarine landslide

125.45125.3722

23.5

Fault

Fault 1

Nakamura (2009)

Miyazawa et al. (2012)124.486124.553

Longitude

24.2805

23.96624.088

Fault

Submarine landslide

Imamura et al. (2001)

Latitude

30

12

72

70

150

15

40

Length (km)Table 1 Parameters of the Meiwa tsunami source models proposed from earlier studies

80

5

36

35

30

10

20

Width (km)

N/A

76

259

240

255

260

270

Strike (°)

8

70

70

70

12

70

70

Dip (°)

N/A

90

90

90

90

90

90

Rake (°)

450

80

12

12

16

90

20

Slip (m)

N/A

N/A

5

5

5

N/A

5

Depth (km)Nakata et al. Progress in Earth and Planetary Science(2024) 11:28
Page 4 of 27

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

scaling law (9.4 m; Wells and Coppersmith 1994). Similarly, Miyazawa et al. (2012) updated the model of Imamura et al. (2001): they assumed an intraplate earthquake(Mw = 8.2) plus a submarine landslide. However, the faultof this model is that it retained the assumption of a large
slip of 14 m compared to that estimated from the scalinglaw (6.7 m; Wells and Coppersmith 1994).
Moreover, subsequent works argued the occurrenceof a landslide offshore of Ishigaki Island in historictime. Ujiie et al. (1997) investigated a sediment coreobtained from the area at which Imamura et al. (2001)
and Miyazawa et al. (2012) had assumed a submarine
landslide. This core included many benthic foraminifera, which inhabit shallow coral reefs. Therefore, thecoral reef sediments were carried and deposited as turbidites. In addition, the latest turbidites were dated toabout 2000 years ago (Ujiie et al. 1997). No turbidite ofyounger origin was discovered. Based on results of thatstudy, Nakamura (2009) pointed out that no evidence
exists of a submarine landslide that occurred at 1771.
Recently, based on magnetic fabric measurements anddating of marine sediments, Kanamatsu et al. (2021) also
concluded that no landslide had occurred at the target
area during historical times. However, it is noteworthy
that not all turbidites are preserved in the core (Ikehara
et al. 2022). Therefore, the occurrence of a landslide in
1771 cannot be ruled out solely based on the absence of
1771 turbidite.
In summary, the occurrence of a submarine landslide
has been questioned. Moreover, a remaining issue is that
unusually large slip must be assumed. Therefore, othersource models, if there are better ones, are worth due
consideration.
2.2 Interplate earthquake along the Ryukyu Trench

Nakamura (2009) reported a tsunami earthquake(slip = 16 m, Mw = 8.0), which is an earthquake that generates a large tsunami relative to the intensity of its seismic motion (Kanamori 1972), along the southern Ryukyu
Trench. The Ryukyu Trench extends from Kyusyu to Taiwan (Fig. 1b). The Philippine Sea plate subducts beneaththe Eurasian plate on the Ryukyu Trench (Ando et al.
2009). Nakamura (2009) hypothesized that the Meiwa
tsunami originated from a tsunami earthquake because
historical documents describe no damage related toseismic motion. Tsunami earthquakes are believed tooccur in shallow and narrow regions at plate boundaries (e.g., Satake and Tanioka 1999). Nakamura (2009)
also assumed such an area along the Ryukyu Trench to
explain the historical traces of the Meiwa tsunami. Andoet al. (2018) subsequently estimated that the seismic
motion during the Meiwa event was strong because theyfound fissures beneath the Meiwa tsunami sandy deposit

Page 5 of 27

and pointed out that the earthquake might have been atypical interplate earthquake rather than the tsunami
earthquake.
The seismic activity of the Ryukyu Trench is under
debate. During the past 300 years, no clear evidence has
been reported of large interplate earthquakes (Mw > 8).
Peterson and Seno (1984) reported that interplate coupling of the Ryukyu Trench is weak. Consequently, thepossibility of the occurrence of large tsunamigenic earthquakes has been questioned (Peterson and Seno 1984).
Recent studies have also indicated that no typical seismogenic locked zone exists below 15 km depth in thesouthern Ryukyu Trench because both slow slip eventsand low-frequency earthquakes are predominant, respectively, at depths greater than 25 km and 15–25 km (Araiet al. 2016; Nakamura 2017). However, they also pointed
out that tsunami earthquakes can be generated at theshallowest part (< 15 km) of the trench (Arai et al. 2016;
Nakamura 2017). Some reports have described that thelocked zone exists in the southern Ryukyu Trench andthat interplate earthquakes can occur. For instance, Kano
et al. (2021) estimated that the coupling ratio is 13–36%
in the southern Ryukyu Trench based on GNSS observations. Debaecker et al. (2023) also reported the coupling
ratio as 10–100% in the southern Ryukyu Trench fromcrustal deformation during the most recent 200 years, asestimated from coral microatolls. In addition, Doo et al.
(2018) pointed out that the Ryukyu Trench has strong
coupling from gravity measurements.
Furthermore, seafloor seismic surveys have confirmed
the existence of splay faults extending from the interplate boundary in the southern Ryukyu Trench. In fact,
it was pointed out that not only earthquakes at the plateboundary but also earthquakes on splay faults might be
the Meiwa tsunami wave source (Hsu et al. 2013; Araiet al. 2016). However, the lack of topographic changes
caused by these faults in the seafloor indicates a low levelof activity. The splay fault earthquakes relation with the
Meiwa tsunami remains controversial (Izumi et al. 2016;
Nakamura 2017; Nishizawa et al. 2017).
In this way, although seismic activity of the southern Ryukyu Trench remains poorly understood, recent
research has indicated the possibility that earthquakes,
including tsunami earthquakes, might occur along thesouthern Ryukyu Trench. Therefore, the hypothesis of
the tsunami wave source of the 1771 Meiwa tsunami at
the Ryukyu Trench must be considered conscientiously.
2.3 Giant submarine landslide

Okamura et al. (2018) investigated bathymetry near the
Ryukyu Trench and inferred that the Meiwa tsunami
was triggered by a giant submarine landslide on a steep
slope that had formed by a strike-slip fault near theNakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 6 of 27

trench axis. According to numerical calculations, thissubmarine landslide could have reproduced the Meiwa
tsunami run-up (Okamura et al. 2018). However, it isuncertain whether the submarine landslide was indeed
generated in 1771. In addition, this model has difficulty
explaining the periodicity of tsunamis that might haveoccurred at several hundred year intervals at the Sakishima Islands (Araoka et al. 2013; Ando et al. 2018).
Because of this issue, we do not examine this model forthis study.
2.4 Points of improvement over earlier studies

As described above, various source models of the Meiwa
tsunami have been proposed but the model remains
unconfirmed. Other than the accumulation of seismological and geological knowledge, there is room for
improvement of earlier tsunami modeling. For example, the bathymetric and topographic data used for earlier studies have low resolution: 50 m by Imamura et al.
(2001) and Miyazawa et al. (2012), and 225 m by Nakamura (2009). Imamura et al. (2001) and Nakamura (2009)
did not perform inundation modeling but assumed
complete reflection near the coast. Therefore, tsunami
calculations might not be sufficiently accurate to assess
the tsunami wave source model properly. In fact, theSakishima Islands are surrounded by up to 1.5 km wide
fringing reefs of approximately 4 m depth. This wideand shallow bathymetry might affect tsunami inundation (e.g., Le Gal and Mitarai 2020). To assess the influence of reef bathymetry on the tsunami calculations,detailed bathymetry data should be used, especially forcoastal areas. The Headquarters for Earthquake Research
Promotion (2017) recommends about 10 m for detailed
tsunami inundation calculation. Moreover, after reportsof those earlier studies were published, Goto et al. (2012)
presented the most recent dataset of historical records.
Therefore, reappraisal of the source model using the latest dataset is necessary.

3 Methods
3.1 Tsunami numerical calculation

The TUNAMI-N2 code (Goto et al. 1997; Imamura et al.
2006) is applied for this study as a tsunami calculation
model. This model can do continuous calculation fromtsunami propagation to inundation. The nonlinear longwave theory, also known as the shallow water theory, isthe basis of this model. The governing equations are presented below.
∂η∂M∂N∂t + ∂x + ∂y = 0

(1)

∂M
∂
∂t + ∂x∂N∂∂t + ∂x

M2
D



MN
D

∂
+ ∂y

MN
D





∂
+ ∂y

N2
D

2

√

2

2

gn M M +N=0+ gD ∂η
∂x +
D7/3



+ gD ∂η
∂y +

gn2 M

√

(2)

M 2 +N 2

D7/3

=0

(3)
In these equations, η denotes the water level variation.
Also, M and N are the flow fluxes respectively in the x
and y directions. Regarding other variables, t represents
time, g (= 9.81 m/s2) expresses gravitational acceleration, n is Manning’s coefficient, and D (= h + η) denotes
the total water depth. Following The Japan Society of
Civil Engineers (2002), Manning’s coefficient was set as
0.025 ­m−1/3/s. Using the staggered leap-frog method,these governing equations were solved numerically (Imamura et al. 2006). The calculation time was up to 1 h
after the earthquake occurrence. The time step was set as
0.05 s. The seafloor deformation by the fault models wascomputed using equations presented by Okada (1985).
Here, both vertical and horizontal crustal deformation
was considered (Tanioka and Satake 1996). For the bathymetric and topographic data, the nesting grid system isused for tsunami calculation. The spatial grid sizes are
810 m in Region 1, 270 m in Regions 2a and 2b, 90 m in
Regions 3a and 3b, 30 m in Regions 4a to 4c, and 10 m in
Regions 5a to 5i (Fig. 2). The original bathymetry/topography data are the present data. To reproduce the likely
bathymetry/topography prevailing in 1771, some artificial landfills that have been created in recent years weredeleted. To identify the landfill areas, aerial photographs
taken in 1963 were used as a reference. ArcGIS Pro wasused to delete the landfill areas. These photographs wereobtained from the Geospatial Information Authority ofJapan. They were taken before the recent landfill creation.
In some areas, coral reefs have been artificially excavatedfor harbor construction. These areas were modified using
ArcGIS Pro to reproduce the pre-excavation topography (Additional file 1: Fig. S1). In addition, it is important to consider the possibility that the present coral reefbathymetry might differ from that in 1771, although thispossibility can be ruled out based on the following reasons. First, approximately 250 years since the 1771 event
is a short time for the coral reef development so that thebathymetric change due to the development of the coral
reef after the 1771 event should be negligible. Also, it isunlikely that tsunami largely destroy the coral reef itself.
Indeed, although there are some reports that individual
corals were destroyed by recent large tsunamis such as
the 2004 Indian Ocean tsunami (e.g., Kumaraguru et al.
2005), there are no reports that the coral reef itself has
been largely destroyed. Although coral reef fragments

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 7 of 27

Fig. 2 Spatial extents of grid layers of numerical modeling used for this study. Spatial grid sizes of the domains are 810 m (Region 1), 270 m(Regions 2a, 2b), 90 m (Regions 3a, 3b), 30 m (Regions 4a–4c), and 10 m (Regions 5a–5i)

were emplaced on the reef and the beach by the tsunami
as tsunami boulders at Sakishima Islands (e.g., Goto et al.
2010a), their total volume is far smaller than that of thecoral reef. Moreover, molluscan assemblages in tsunami
deposits reported by Ando et al. (2018) suggested thatthe reef topography has not been changed at least during
the last 1250 years (Kitamura et al. 2018). Based on theselines of evidence, we judged the reef bathymetry in 1771
would have been similar to that of today.
3.2 Fault parameters

For this study, a interplate earthquake along the southern
Ryukyu Trench was assumed as the tsunami wave source,
as described in Chapters 1 and 2. By changing the relevant parameters, 27 scenarios were calculated (Table 2
and Fig. 3). These include the original model proposed
by Nakamura (2009). We assumed a single rectangle
fault along the southern Ryukyu Trench. The parameters

we changed are the fault location, width, length, depth,and slip. A scaling law exists to ascertain the parametersof the interplate earthquake (e.g., Murotani et al. 2013).
However, in the case of the Meiwa tsunami, Nakamura(2009) estimated a much larger slip (16 m) than that
estimated using the scaling law (2.2 m; Murotani et al.
2013). For that reason, the fault parameter of the Meiwa
tsunami might not follow the scaling law. Therefore, thescaling law was not adopted for this study. For the RYa10
to RYc40 scenarios, the fault depth was set as 5 km andthe fault length as 225 km extending from off Ishigaki
Island to off Miyako Island, with the fault width varied
from 30 to 100 km, and the slip from 10 to 40 m. For the
RYad10 to RYcd40 scenarios, the fault depth was set as
15 km. The fault length, width, and slip were set as in
RYa10 to RYc40. For the RYae30 and RYaw30 scenarios,
the fault length was set as 150 km. The fault is set off Ishigaki Island for RYae30 and off Miyako Island for RYaw30.

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 8 of 27

Table 2 Fault parameters used for this study (Moment magnitude was calculated while assuming rigidity of 30 GPa)
LatitudeLongitude

Length (km)Width (km)Strike (°)

Dip (°)

Rake (°)

Slip (m)Depth (km)Mw

Nakamura (2009)23.5

125.45

150

30

255

12

90

16

5

8.0

RYa10

23.667126.162

225

30

255

12

90

10

5

8.14

RYa20

23.667126.162

225

30

255

12

90

20

5

8.37

RYa30

23.667126.162

225

30

255

12

90

30

5

8.49

RYa40

23.667126.162

225

30

255

12

90

40

5

8.58

RYb10

23.667126.162

225

50

255

12

90

10

5

8.29

RYb20

23.667126.162

225

50

255

12

90

20

5

8.52

RYb30

23.667126.162

225

50

255

12

90

30

5

8.64

RYb40

23.667126.162

225

50

255

12

90

40

5

8.72

RYc10

23.667126.162

225

100

255

12

90

10

5

8.49

RYc20

23.667126.162

225

100

255

12

90

20

5

8.72

RYc30

23.667126.162

225

100

255

12

90

30

5

8.84

RYc40

23.667126.162

225

100

255

12

90

40

5

8.92

RYad1024.095126.044

225

30

255

12

90

10

15

8.14

RYad2024.095126.044

225

30

255

12

90

20

15

8.37

RYad3024.095126.044

225

30

255

12

90

30

15

8.49

RYad4024.095126.044

225

30

255

12

90

40

15

8.58

RYbd1024.095126.044

225

50

255

12

90

10

15

8.29

RYbd2024.095126.044

225

50

255

12

90

20

15

8.52

RYbd3024.095126.044

225

50

255

12

90

30

15

8.64

RYbd4024.095126.044

225

50

255

12

90

40

15

8.72

RYcd1024.095126.044

225

100

255

12

90

10

15

8.49

RYcd2024.095126.044

225

100

255

12

90

20

15

8.72

RYcd3024.095126.044

225

100

255

12

90

30

15

8.84

RYcd4024.095126.044

225

100

255

12

90

40

15

8.92

RYae3023.667126.162

150

30

130

12

90

30

5

8.34

RYaw3023.444125.213

150

30

130

12

90

30

5

8.34

The fault dip angle was set to 12° in all scenarios to matchthe subduction angle of the plate boundary, as describedby Nakamura (2009). Recently, Arai et al. (2016) notedfrom a seismic reflection survey of the southern Ryukyu
Trench that the dip angle varies between 5 and 15° withincrease in depth. In addition, we calculated the average
dip angle as 12° from the survey results between depthsof 5 and 25 km by Arai et al. (2016). Therefore, ourassumption of the dip angle to be 12° is also consistent
with the results by Arai et al. (2016).
3.3 Fault model evaluation methods

We used the tsunami trace data presented by Goto
et al. (2012) to evaluate the fault models. Goto et al.
(2012) surveyed the coordinates and elevation of thetsunami trace points where historical records and folklore had indicated tsunami inundation or no inundation. For this study, 60 points with confidence levels A
or A′, which are regarded as the most reliable according
to the confidence criteria defined by Goto et al. (2012),
were used (Fig. 4).

For fault model evaluation, the method reported
by Aida (1978) is often used (e.g., Nakamura 2009;
Miyazawa et al. 2012). As indicators for the evaluationof fault models, Aida (1978) proposed K, which indicatesthe geometric mean of the ratio between the observedand calculated tsunami height, and κ, which denotes thegeometric standard deviation of the ratio.
In the case of the Meiwa tsunami, although many historical documents indicate the presence or absence ofinundation, there are no points at which the tsunami
height is known because the flow depth is not statedin the historical documents. Therefore, the reproducibility cannot be assessed adequately using K/κ. A different assessment method must be adopted. Then, for thisstudy, we evaluated the tsunami source model by checking whether each tsunami trace point could be reproduced in the tsunami run-up calculation.
In the case of wide plain terrain, a risk exists of underestimating the slip from the inundation area only, notincluding the tsunami height because the inundation area
is affected not only by the slip but also by the fault widthNakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 9 of 27

Fig. 3 a Fault positions at 5 km depth (Rya10–Ryc40). b Fault positions at 15 km depth (Ryad10–Rycd40). c Fault positions of Ryae30 and Ryaw30.
The contour lines represent the depth distribution of the plate boundary every 10 km. Data for plate boundary depth profiles are from Slab 2.0(Hayes et al. 2018). Trench axis data are from Iwasaki et al. (2015)(e.g., Satake et al. 2013). However, the Sakishima Islands
are islands of raised coral reefs with narrow flat terrain
near the coast (Goto 2016). Because of such topography(i.e. relatively simple slope setting), tsunami heights areeasily reflected in the inundation area. Therefore, with
sufficient assessment points, the risk of underestimating

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 10 of 27

Fig. 4 Locations of tsunami trace points based on Goto et al. (2012). Red circles represent points with inundation. Blue circles represent points
with no inundation. Distribution of tsunami trace points on a Taketomi Island and Ishigaki Island and b Tarama Island, Ikema Island, and Irabu
Island. In this figure, (1)–(8) respectively stand for the regional divisions used for the model evaluation: (1) western part of Ishigaki Island (Area 1),(2) Taketomi Island to the southwestern part of Ishigaki Island (Area 2), (3) southeastern part of Ishigaki Island (Area 3), (4) eastern part of Ishigaki
Island (Area 4), (5) northern part of Ishigaki Island (Area 5), (6) Tarama Island (Area 6), (7) western Miyako Island, Irabu Island and Ikema Island (Area 7),
and (8) southern part of Miyako Island (Area 8). The topography and bathymetry in (1)-(8) are based on 10 mesh topography and bathymetry data.
Grey areas in (2) and (7) are areas without 10 m mesh bathymetry data. The contour level is 10 m

the slip is regarded as low. The methodology of this study
is consequently regarded as effective for assessing thevalidity of the fault model of the Meiwa tsunami.
Based on the consideration presented above, the fault
models were evaluated for this study by the percentageof the number of tsunami trace points that were reproduced by the tsunami run-up calculations. A higher
reproducibility is associated with a more suitable tsunami wave source model. We inferred that the tsunami
trace points were inundated if the mesh containing thetrace point was inundated by tsunami calculation in 10 m

mesh topography data. To elucidate the reproducibilityof tsunami run-up for each region, we divided the Sakishima Islands into eight regions (Fig. 4): (1) western Ishigaki Island (Area 1), (2) Taketomi Island to southwestern
Ishigaki Island (Area 2), (3) southeastern Ishigaki Island(Area 3), (4) eastern Ishigaki Island (Area 4), (5) northern
Ishigaki Island (Area 5), (6) Tarama Island (Area 6), (7)western Miyako Island, Irabu Island, Ikema Island (Area7), and (8) southern Miyako Island (Area 8). This division differs from the regions of 10 m mesh topography/
bathymetry data in Fig. 2.

(See figure on next page.)
Fig. 5 Computed results of maximum water level for the model proposed in Nakamura (2009). a Calculation result with 810 m mesh for the entire
Ryukyu Trench to the Sakishima Islands. b Calculation result for Ishigaki and Taketomi islands. The upper left panel is the result with 30 m meshand the contour level in this panel is 50 m. The others are the result with 10 m mesh and the contour level in these panels is 10 m. c Calculation
result for Tarama to Miyako islands. The upper left panel is the result with 270 m mesh and the contour level in this panel is 200 m. The others are
the result with 10 m mesh and the contour level in these panels is 10 m. Numbers (1)–(8) in (b) and (c) correspond to the regional classification(Areas 1–8) in Fig. 4

Nakata et al. Progress in Earth and Planetary ScienceFig. 5 (See legend on previous page.)(2024) 11:28

Page 11 of 27

100

100

2/4

2/4

4/4

RYc10

RYc20

RYc30

50

100

4/4

2/4

3/4

4/4

4/4

1/4

RYbd40

RYcd10

RYcd20

RYcd30

RYcd40

RYae302/4

4/4

RYbd20

RYbd304/4

2/4

RYad40

4/4

RYad30

RYbd10100

3/4

RYad20

25

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

1/4

4/4

4/4

3/4

2/4

4/4

4/4

2/4

2/4

4/4

4/4

3/4

1/4

4/4

4/4

2/4

2/4

3/4

2/4

1/4

1/4

3/4

3/4

1/4

1/4

1/4

Numberofpoints

Total

25

100

100

75

50

100

100

50

50

100

100

75

25

100

100

50

50

75

50

25

25

75

75

25

25

25

Rate
(%)

− 3.8 mNaN

NaN

− 3.2 m− 6.0 mNaN

NaN

− 2.8 m− 9.4 mNaN

NaN

− 3.2 m− 9.4 mNaN

NaN

− 3.9 m− 9.4 m− 1.0 m− 3.8 m− 3.8 m− 9.4 m− 3.8 m− 3.8 m− 3.8 m− 5.0 m− 3.8 mMaximum
differenceofinundatedheight

2/15

15/15

12/15

11/15

4/15

15/15

15/15

15/15

10/15

15/15

12/15

12/15

6/15

15/15

15/15

15/15

9/15

15/15

15/15

12/15

5/15

15/15

12/15

8/15

2/15

6/15

Numberofpoints

13

100

80

73

27

100

100

100

67

100

80

80

40

100

100

100

60

100

100

80

33

100

80

53

13

40

Rate
(%)

Inundated sites

16/16

8/16

13/16

15/16

16/16

0/16

2/16

10/16

14/16

2/16

13/16

15/16

16/16

0/16

10/16

12/16

14/16

2/16

8/16

14/16

16/16

8/16

15/16

16/16

16/16

16/16

Numberofpoints

100

50

81

94

100

0

13

63

88

13

81

94

100

0

63

75

88

13

50

88

100

50

94

100

100

100

Rate
(%)

Non-inundated
sites

18/31

23/31

25/31

26/31

20/31

15/31

17/31

25/31

24/31

17/31

22/31

26/31

22/31

15/31

25/31

27/31

23/31

17/31

23/31

26/31

21/31

23/31

27/31

24/31

18/31

22/31

Numberofpoints

Total

58

74

81

84

65

48

55

81

77

55

71

84

71

48

81

87

74

55

74

84

68

74

87

77

58

71

Rate
(%)

− 9.3 m+ 8.4 m− 2.0 m,+ 6.8 m− 4.8 m,+ 1.7 m− 7.9 m+ 17.5 m+ 12.9 m+ 9.9 m− 5.3 m,+ 3.2 m+ 11.9 m− 2.0 m,+ 6.8 m− 4.8 m,+ 1.7 m− 6.1 m+ 16.5 m+ 11.2 m+ 7.7 m− 5.7 m,+ 2.2 m+ 11.2 m+ 8.1 m− 2.7 m,+ 1.5 m− 7.0 m+ 7.9 m− 2.8 m,+ 2.9 m− 5.0 m− 9.4 m− 6.4 mMaximum
differenceofinundatedheightArea 2 (Taketomi Island to southwestern Ishigaki Island)

0/4

3/4

2/4

2/4

0/4

4/4

3/4

2/4

1/4

3/4

2/4

2/4

1/4

3/4

3/4

2/4

1/4

3/4

2/4

2/4

1/4

4/4

3/4

2/4

1/4

2/4

Numberofpoints

0

75

50

50

0

100

75

50

25

75

50

50

25

75

75

50

25

75

50

50

25

100

75

50

25

50

Rate
(%)

Inundated sites

5/5

5/5

5/5

5/5

5/5

1/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

5/5

2/5

5/5

5/5

5/5

5/5

Numberofpoints

100

100

100

100

100

25

100

100

100

100

100

100

100

100

100

100

100

100

100

100

100

40

100

100

100

100

Rate
(%)

Non-inundated
sites

5/9

7/9

7/9

7/9

5/9

5/9

8/9

7/9

6/9

8/9

7/9

7/9

6/9

8/9

8/9

7/9

6/9

8/9

7/9

7/9

6/9

6/9

8/9

7/9

6/9

7/9

Numberofpoints

Total

Area 3 (Southeastern Ishigaki Island)

56

78

78

78

56

56

89

78

67

89

78

78

67

89

89

78

67

89

78

78

67

67

89

78

67

78

Rate
(%)

− 16.6 m− 6.9 m− 12.1 m− 17.7 m− 19.8 m+ 3.6 m− 4.1 m− 11.1 m− 19.0 m− 0.5 m− 12.1 m− 17.7 m− 17.2 m− 4.5 m− 8.8 m− 14.4 m− 19.0 m− 5.1 m− 10.4 m− 14.5 m− 18.6 m+ 5.7 m− 2.4 m− 11.4 m− 18.6 m− 14.5 m

Maximum
differenceofinundatedheight(2024) 11:28

100

100

75

50

100

100

50

50

75

25

4/4

1/4

RYc40

RYad10

50

50

75

2/4

3/4

RYb30

25

25

25

RYb40

1/4

RYb20

75

3/4

1/4

RYa40

RYb10

75

1/4

3/4

RYa20

RYa30

25

25

1/4

1/4

NK

Rate
(%)

NumberofpointsNumberofpointsRate(%)

Non-inundated
sites

Inundated sites

Area 1 (Western Ishigaki Island)

Reproducibility

RYa10

Model

Table 3 The tsunami trace point recurrence rate in Ishigaki and Taketomi Islands and the difference in the maximum run-up height in each region (Areas 1 to 5)

Nakata et al. Progress in Earth and Planetary Science
Page 12 of 27

3/4

Numberofpoints

Total

75

Rate
(%)
− 3.8 mMaximum
differenceofinundatedheight
93

Rate
(%)
14/16

Numberofpoints
88

Rate
(%)

Non-inundated
sites

28/31

Numberofpoints

Total

Area 5 (Northern Ishigaki Island)

14/15

NumberofpointsInundated sites

90

Rate
(%)
− 1.5 m,+ 3.7 mMaximum
differenceofinundatedheightArea 2 (Taketomi Island to southwestern Ishigaki Island)

3/4

75

Rate
(%)
5/5

Numberofpoints
100

Rate
(%)

Non-inundated
sites

Ishigaki, Taketomi total

NumberofpointsInundated sites

8/9

Numberofpoints

Total

Area 3 (Southeastern Ishigaki Island)

89

Rate
(%)

− 1.1 mMaximum
differenceofinundatedheight

100

100

100

100

100

100

100

100

100

100

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

RYa40

RYb10

RYb20

RYb30

RYb40

RYc10

RYc20

RYc30

RYc40

RYad10 2/2

RYad20 2/2

RYad30 2/2

RYad40 2/2

RYbd10 2/2

RYbd20 2/2

RYbd30 2/2

RYbd40 2/2

RYcd10 2/2

100

100

100

100

100

100

100

100

100

100

2/2

2/2

RYa20

RYa30

100

100

2/2

100

100

50

50

100

100

100

100

100

100

50

100

100

100

100

100

100

100

100

100

100

100

4/4

4/4

3/4

3/4

4/4

4/4

4/4

4/4

4/4

4/4

3/4

4/4

4/4

4/4

4/4

4/4

4/4

4/4

4/4

4/4

4/4

4/4

100

100

75

75

100

100

100

100

100

100

75

100

100

100

100

100

100

100

100

100

100

100

NaN

NaN

+ 6.1 m+ 4.7 m

NaN

NaN

NaN

NaN

NaN

NaN

+ 2.1 m

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

1/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

1/2

100

100

100

100

100

100

100

100

100

100

100

100

50

100

100

100

100

100

100

100

50

100

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

1/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

1/2

100

100

100

100

100

100

100

100

100

100

100

100

50

100

100

100

100

100

100

100

50

100

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

− 0.7 m

NaN

NaN

NaN

NaN

NaN

NaN

NaN

− 0.7 m

13/27

10/27

26/27

26/27

23/27

17/27

26/27

22/27

21/27

12/27

26/27

26/27

23/27

15/27

25/27

23/27

19/27

11/27

26/27

22/27

15/27

7/27

48

37

96

96

85

63

96

81

78

44

96

96

86

56

93

85

70

41

96

81

56

26

23/23

23/23

3/23

8/23

17/23

21/23

9/23

15/23

20/23

23/23

6/23

17/23

19/23

21/23

9/23

15/23

21/23

23/23

12/23

22/23

23/23

23/23

100

100

13

35

74

91

39

65

87

100

26

74

83

91

39

65

91

100

52

96

100

100

36/50

33/50

29/50

34/50

40/50

38/50

35/50

37/50

41/50

35/50

32/50

43/50

42/50

36/50

34/50

38/50

40/50

34/50

38/50

44/50

38/50

30/50

72

66

58

68

80

76

70

74

82

64

66

86

84

72

68

76

80

68

76

88

76

60

(2024) 11:28

1/2

1/2

2/2

2/2

2/2

2/2

2/2

2/2

1/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

2/2

NK

RYa10

Non-inundated sitesTotal

Inundated sites

Maximum Inundated sites
Maximum Inundated sites
Non-inundated
Total
Non-inundated
Total
difference
difference
sites
sites
of
of
Number Rate (%) Number Rate (%) Number Rate (%) inundated Number Rate (%) Number Rate (%) Number Rate (%) inundated Number Rate (%) Number Rate (%) Number Rate (%)
of pointsof pointsof pointsofpointsofpointsofpointsof pointsof pointsof points
heightheightNaN

Area 4 (Eastern Ishigaki Island)

NaN

Model

75

3/4

Rate
(%)

NumberofpointsNumberofpointsRate(%)

Non-inundated
sites

Inundated sites

Area 1 (Western Ishigaki Island)

Reproducibility

RYaw30Model

Table 3 (continued)

Nakata et al. Progress in Earth and Planetary Science
Page 13 of 27

Area 5 (Northern Ishigaki Island)

Ishigaki, Taketomi total

100

100

100

100

RYcd40 2/2

2/2

RYae30

RYaw30 2/2

2/2

2/2

1/2

1/2

2/2

100

100

50

50

100

4/4

4/4

3/4

3/4

4/4

Non-inundated sitesTotal

100

100

75

75

100

NaN

NaN

+ 7.8 m+ 2.0 m

NaN

2/2

2/2

2/2

2/2

2/2

100

100

100

100

100

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

2/2

2/2

2/2

2/2

2/2

100

100

100

100

100

NaN

NaN

NaN

NaN

NaN

24/27

7/27

26/27

22/27

20/27

89

26

96

81

74

21/23

23/23

13/23

19/23

22/23

91

100

57

83

96

45/50

30/50

39/50

41/50

42/50

90

60

78

81

84

For the maximum difference of the inundated height, negative values indicate underestimation and positive values indicate overestimation. When both negative and positive values are written, both underestimated andoverestimated tsunami trace points exist and the maximum value of each is indicated100

RYcd30 2/2

Inundated sites

Maximum Inundated sites
Maximum Inundated sites
Non-inundated
Total
Non-inundated
Total
difference
difference
sites
sites
of
of
Number Rate (%) Number Rate (%) Number Rate (%) inundated Number Rate (%) Number Rate (%) Number Rate (%) inundated Number Rate (%) Number Rate (%) Number Rate (%)
of pointsof pointsof pointsof pointsof pointsof pointsof pointsof pointsof points
heightheightArea 4 (Eastern Ishigaki Island)

RYcd20 2/2

Model

Table 3 (continued)

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28
Page 14 of 27

0/6

0/6

0/6

0/6

3/6

0/6

2/6

5/6

6/6

0/6

6/6

6/6

6/6

1/6

4/6

6/6

6/6

2/6

6/6

6/6

6/6

0/6

6/6

6/6

6/6

1/6

0/6

RYa20

RYa30

RYa40

RYb10

RYb20

RYb30

RYb40

RYc10

RYc20

RYc30

RYc40

RYad10

RYad20

RYad30

RYad40

RYbd10

RYbd20

RYbd30

RYbd40

RYcd10

RYcd20

RYcd30

RYcd40

RYae30

RYaw30

0

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

0/6

1/6

6/6

6/6

6/6

0/6

6/6

6/6

6/6

2/6

6/6

6/6

4/6

1/6

6/6

6/6

6/6

0/6

6/6

5/6

2/6

0/6

3/6

0/6

0/6

0/6

0/6

0

17

100

100

100

0

100

100

100

33

100

100

67

17

100

100

100

0

100

83

33

0

50

0

0

0

0

Number Rate (%)
of points

Total− 2.3 m− 2.9 m

NaN

NaN

NaN

− 3.3 m

NaN

NaN

NaN

− 1.2 mNaN

NaN

− 0.1 m− 2.7 m

NaN

NaN

NaN

− 3.0 mNaN

− 0.2 m− 1.9 m− 3.1 m− 0.3 m− 2.5 m− 3.5 m− 6.1 m− 4.2 m

0/4

0/4

4/4

4/4

4/4

1/4

4/4

4/4

3/4

1/4

4/4

4/4

4/4

1/4

4/4

4/4

4/4

1/4

4/4

4/4

2/4

0/4

2/4

1/4

0/4

0/4

0/4

0

0

100

100

100

25

100

100

75

25

100

100

100

25

100

100

100

25

100

100

50

0

50

0

0

0

0

Number Rate (%)
of points

Maximum difference Inundated sites
of inundated height

1/1

1/1

0/1

0/1

1/1

1/1

0/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

0/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

100

100

0

0

100

100

0

100

100

100

100

100

100

100

0

100

100

100

100

100

100

100

100

100

100

100

100

Number Rate (%)
of points

Non-inundated
sites

1/5

1/5

4/5

4/5

5/5

2/5

4/5

5/5

4/5

2/5

5/5

5/5

5/5

2/5

4/5

5/5

5/5

2/5

5/5

5/5

3/5

1/5

3/5

2/5

1/5

1/5

1/5

20

20

80

80

100

40

80

100

80

40

100

100

100

40

80

100

100

40

100

100

60

20

60

40

20

20

20

Number Rate (%)
of points

Total

Area 7 (Western Miyako Island, Irabu Island, Ikema Island)− 5.3 m− 1.9 m+ 5.8 m+ 1.0 mNaN

− 2.0 m+ 1.0 mNaN

− 0.4 m− 2.8 m

NaN

NaN

NaN

− 3.4 m+ 1.0 mNaN

NaN

− 3.4 mNaN

NaN

− 0.6 m− 3.7 m− 1.7 m− 2.5 m− 3.6 m− 6.0 m− 5.1 mMaximum differenceof inundated height(2024) 11:28

17

100

100

100

0

100

100

100

33

100

100

67

17

100

100

100

0

100

83

33

0

50

0

0

0

0

Number Rate (%)
of points

Number Rate (%)
of points

RYa10

Non-inundated
sites

Inundated sites

Area 6 (Tarama Island)

Reproducibility

NK

Model

Table 4 The tsunami trace point recurrence rate in Tarama, Miyako, Irabu, and Ikema islands, and the difference between the maximum run-up height of tsunami trace points ineach region (Areas 6 to 8)

Nakata et al. Progress in Earth and Planetary Science
Page 15 of 27

2/3

3/3

3/3

3/3

2/3

2/3

3/3

3/3

2/3

2/3

3/3

3/3

2/3

3/3

3/3

3/3

2/3

2/3

3/3

3/3

0/3

2/3

2/3

3/3

3/3

2/3

RYa20

RYa30

RYa40

RYb10

RYb20

RYb30

RYb40

RYc10

RYc20

RYc30

RYc40

RYad10

RYad20

RYad30

RYad40

RYbd10

RYbd20

RYbd30

RYbd40

RYcd10

RYcd20

RYcd30

RYcd40

RYae30

RYaw30

67

100

100

67

67

0

100

100

67

67

100

100

100

67

100

100

67

67

100

100

67

67

100

100

100

67

67

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

NaN

2/3

3/3

3/3

2/3

2/3

0/3

3/3

3/3

2/3

2/3

3/3

3/3

3/3

2/3

3/3

3/3

2/3

2/3

3/3

3/3

2/3

2/3

3/3

3/3

3/3

2/3

2/3

67

100

100

67

67

0

100

100

67

67

100

100

100

67

100

100

67

67

100

100

67

67

100

100

100

67

67

− 7.4 mNaN

NaN

− 3.7 m− 8.3 m− 12.9 m

NaN

NaN− 1.0 m− 9.5 m

NaN

NaN

NaN

− 8.0 mNaN

NaN

− 5.5 m− 8.7 mNaN

NaN

− 1.0 m− 10 m

NaN

NaN

NaN

− 5.5 m− 8.0 m

2/13

4/13

13/13

12/13

12/13

1/13

13/13

13/13

11/13

5/13

13/13

13/13

11/13

4/13

13/13

13/13

12/13

3/13

13/13

12/13

6/13

2/13

8/13

4/13

3/13

2/13

2/13

15

31

100

92

92

8

100

100

85

38

100

100

85

31

100

100

92

23

100

92

46

15

62

31

23

15

15

Number of Rate (%)
points

1/1

1/1

0/1

0/1

1/1

1/1

0/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

0/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

1/1

100

100

0

0

100

100

0

100

100

100

100

100

100

100

0

100

100

100

100

100

100

100

100

100

100

100

100

Number of Rate (%)
points

3/14

5/14

13/14

12/14

13/14

2/14

13/14

14/14

12/14

6/14

14/14

14/14

12/14

5/14

13/14

14/14

13/14

4/14

14/14

13/14

7/14

3/14

9/14

5/14

4/14

3/14

3/14

21

36

93

86

93

14

93

100

86

43

100

100

86

36

93

100

93

29

100

93

50

21

64

36

29

21

21

Number of Rate (%)
pointsTotal(2024) 11:28

The method of description is the same as in Table 3

2/3

RYa10

Number of Rate (%)
pointsNumber of Rate (%)
pointsNumber of Rate (%)
pointsNon-inundated sites

Inundated sites

Maximum differenceof inundated height

Non-inundated sites

Inundated sites

Total

Tarama, Miyako, Ikema, Irabu total

Area 8 (Southern Miyako Island)

Reproducibility

NK

Model

Table 4 (continued)

Nakata et al. Progress in Earth and Planetary Science
Page 16 of 27

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 17 of 27

Moreover, it is important to understand not only
whether tsunami inundation was reproduced, but also, if
not reproduced, the extent to which inundation is overestimated or underestimated. The difference in run-up
heights was calculated as the difference in elevation fromthe inundated (not inundated) trace points to the nearest
grid where inundation was (not) calculated in the 10 m
mesh bathymetry data.

propagation, tsunami ray tracing analysis (Satake 1988)
was performed. With this analytical method, tsunami
propagation can be represented by a tsunami ray perpendicular to the wave front of the tsunami. Concentrated tsunami rays indicate that tsunami energy isconcentrated because of the bathymetry (Satake 1988).

3.4 Assessing bathymetry effects on tsunami propagation

To verify the reproducibility of our calculations, we first
calculated the model proposed by Nakamura (2009)(Fig. 5). The reproductivity rates of tsunami trace points
by this model in each region are presented in Table 3(Ishigaki Island and Taketomi Island in Areas 1–5) andTable 4 (Tarama, Miyako, Ikema, and Irabu islands
in Areas 6–8). This model can reproduce all tsunami
trace points in Areas 4 and 5. However, the reproducibility rates of inundated trace points in Area 2 are only
40%, 50% in Area 3, and 25% in Area 1. The largest

In the case of the Meiwa tsunami, tsunami heights andcasualties were inferred as extraordinarily high at somespecific sites (e.g., Goto et al. 2012). In addition, tsunami boulders are patchily distributed along the coastof the Sakishima Islands (Goto et al. 2010a). Nevertheless, the widths and shapes of coral reefs seem generally
similar (Goto et al. 2010a). It remains uncertain why
such tsunami focusing occurred at some specific coasts.
To investigate the effects of bathymetry on tsunami

4 Results
4.1 Tsunami inundation by the Nakamura (2009) modelFig. 6 Graphs showing a the reproducibility rate of tsunami trace points (%), b the maximum underestimation, and c the maximum overestimationof the run-up height for each model and area. NK denotes the model proposed by Nakamura (2009). RYa30, which is the best model for the Meiwa
tsunami, is highlighted in yellow. The left panel presents results for Areas 1–5 (Ishigaki and Taketomi islands) and the right panel for Areas 6–8(Tarama, Ikema, Irabu, and Miyako islands). In (b) and (c), the maximum underestimated (overestimated) value is shown as 0 if no tsunami trace
points are underestimated (overestimated)Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

underestimations of calculated run-up heights are 6.4 m
for Area 2, 18.6 m for Area 3, and 5.0 m for Area 1.
Moreover, in Area 6, the model cannot reproduce allinundated trace points. The greatest underestimation of
run-up height is 4.2 m. In Area 8, one of the three inundated points cannot be explained. The calculated run-up
height is underestimated by as much as 8 m. In Area 7,
not all inundated trace points can be reproduced. The
calculated run-up height is underestimated by as muchas 5.1 m. In this way, the model proposed by Nakamura(2009) underestimates the run-up of the 1771 Meiwa tsunami in most regions of the Sakishima Islands.
4.2 Parameter study of tsunami inundation

The reproducibility of tsunami trace points by the models tested for this study (RYa30–RYaw30) is presented inTables 3 and 4. Figure 6 graphically displays the reproducibility rates of tsunami trace points and the maximum
values of underestimation/overestimation of the run-up
for each model.
For RYa10–RYcd40, in Area 1, RYc30, RYc40, RYad40,
RYbd30, and RYbd40 reproduced all tsunami trace
points. Although RYa30 is unable to reproduce one trace
point, the underestimation of this tsunami trace point in
run-up height is only 3.8 m. In Area 2, RYa30 and RYc20
have the greatest reproducibility with 87%. Both models
partly overestimate and underestimate run-up heights atsome tsunami trace points, with the maximum underestimate of 2.8 m and the maximum overestimate of 2.9 m
for RYa30, and the maximum overestimate of 7.7 m for
RYc20. Therefore, RYa30 is the best-fit model for Area
2. In Area 3, the models with the highest reproducibility(89%) were RYa30, RYb40, RYc30, RYc40, RYad30, andRYad40. For these models, RYad40 was found to have thesmallest difference in run-up height, with 0.5 m, followed
by RYa30 with 2.4 m. Therefore, the RYa30 model reproduced the run-up well in the second. In Area 4, models
other than RYc40, RYbd30, and RYbd4, including RYa30,
can reproduce all five tsunami trace points. In Area 5, allmodels except RYa10 and RYc10, including RYa30, wereable to explain the tsunami trace points. In this way, for
the RYa10–RYcd40 models, RYa30 had the highest reproducibility rate (88%, 44/50 points) for Taketomi Island to
Ishigaki Island in Areas 1–5 (Fig. 7).

Page 18 of 27

In Areas 6–8 (Tarama Island, Miyako Island, Irabu
Island, and Ikema Island), RYb40, RYc30, RYad40, andRYbd30 reproduce all tsunami trace points (14 points).
However, these models are unable to reproduce run-up
on Ishigaki Island. For example, RYad40 overestimates
the run-up height up to 11.2 m in Area 2 and 5.1 m in
Area 3. RYa30, which is the best-fit model for the run-up
on Ishigaki Island and Taketomi Island (Areas 1–5), cannot reproduce all tsunami trace points in Area 6, or someinundated points in Area 7. However, the underestimation of run-up height in these areas by RYa30 is only lessthan 2.5 m. Therefore, although RYa30 cannot reproduce
some points in Areas 6 and 7, this model can reproduce
the run-up distribution for the entire study region.
Based on the consideration presented above, we inferthat the best model for the 1771 Meiwa tsunami in
RYa10–RYcd40 is RYa30 (depth = 5 km, width = 30 km,
slip = 30 m, Mw = 8.49). The RYa30 model is graphicallyshown in Fig. 8.
4.3 Sensitivity of fault depth, width, and length on local
tsunami inundation

Through the parameter study, we realized that inundation at the southern part of Ishigaki Island (Areas 2 and
3) is affected sensitively by fault parameters. First, we
specifically examined the fault model depth. When we set
the fault model depth as 15 km, RYad20 (width = 30 km,
slip = 20 m) was the best model for Area 2, but this model
underestimated the run-up height with 17.7 m in Area 3.
However, RYad40 (width = 30 km, slip = 40 m) or RYbd40(width = 50 km, slip = 20 m) can explain all tsunami trace
points in Area 3 but overestimates the run-up heightof more than 10 m in Area 2. Consequently, if the fault
depth is set as 15 km, then no fault model can explain thetsunami run-up height in Areas 2 and 3 simultaneously.
Next, we specifically examined the fault model width.
If the fault depth is set as 5 km, then a longer fault
width is associated with a wider inundation area, as in
Area 2 (Fig. 9a). For example, when the slip is 30 m, thetsunami inundated the narrowest area when the fault
width was 30 km (RYa30) compared to the inundation
limit lines for different fault widths (50 km and 100 km)
in Area 2 (Fig. 9a). In Area 3, when the fault width was
30 km, a tsunami inundated the widest area (Fig. 9b).

(See figure on next page.)
Fig. 7 Calculation results of maximum water level for RYa30. a Calculation result with 810 m mesh for the entire Ryukyu Trench to the SakishimaIslands. b Calculation result for Ishigaki and Taketomi islands. The upper left panel is the result with 30 m mesh and the contour level in thispanel is 50 m. The others are the result with 10 m mesh and the contour level in these panels is 10 m. c Calculation result for Tarama to Miyako
islands. The upper left panel is the result with 270 m mesh and the contour level in this panel is 200 m. The others are the result with 10 m meshand the contour level in these panels is 10 m. Numbers (1)–(8) in (b) and (c) correspond to the regional classification (Areas 1–8) in Fig. 4

Nakata et al. Progress in Earth and Planetary ScienceFig. 7 (See legend on previous page.)(2024) 11:28

Page 19 of 27

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 20 of 27

Fig. 8 Map view of the RYa30 model, which is the best-fit model for the Meiwa tsunami. Data for plate boundary depth profiles are from Slab 2.0(Hayes et al. 2018). Trench axis data are from Iwasaki et al. (2015)

Fig. 9 Images showing the inundation limit lines at southern coast of Ishigaki Island for each fault length when the fault depth is 5 km and the slip
is 30 m. a Area 2 (southwest part of Ishigaki Island), and b Area 3 (southeast part of Ishigaki Island). Red, blue, and green lines respectively represent
the inundation limits for the RYa30 model (fault width = 30 km), the RYb30 model (fault width = 30 km), and the RYc30 model (fault width = 100 km).
The black line shows the shoreline. The grey line shows the 5 m contour of the topography and the bathymetry

Consequently, the sensitivity in run-up against thefault width is opposite between the southwestern (Area2) and southeastern (Area 3) parts of Ishigaki Island.
Therefore, to explain the run-up in southwest (Area 2)
and southeast (Area 3) Ishigaki Island simultaneously,
the fault depth must be as shallow as 5 km. Moreover,the fault width must be as narrow as 30 km.
Finally, we specifically examined the fault length.
In the case of RYaw30, in which the fault length was
shortened from RYa30 to 150 km and set as off ofIshigaki Island, the run-up was well reproduced on
Ishigaki Island (reproducibility rate of tsunami trace
points = 90%), but not all the inundated trace points
were able to be reproduced from Tarama Island to
Miyako Island (Areas 6–8). The run-up height wasunderestimated by as much as 7.4 m. RYae30, which
is set off of Miyako Island with a short fault length(150 km), can only reproduce 27% of the inundated
trace points, and the run-up height was underestimatedby as much as 16.6 m on Ishigaki Island. Consequently,
the fault should be extended from off of Ishigaki Island
to Miyako Island to explain the distribution of tsunami
traces. However, this study is inadequate for determining the extension of fault length, especially further
toward the northeast, because there are no islands.
Therefore, no constraint information related to fault
length is available.
4.4 Bathymetry effects on coastal tsunami heightand velocity

Figure 10 shows the maximum tsunami height by
RYa30 and tsunami rays calculated using tsunami ray
tracing analysis. Tsunami rays are concentrated inNakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 21 of 27

Fig. 10 Figures depicting the results of wave ray tracing and the maximum water level distribution of the tsunami based on the RYa30 model. a
Entire Ryukyu Trench to the Sakishima Islands, b around Ishigaki Island, and c around Miyako Island. Thick pink lines in (b) and (c) show the tsunami
boulder distribution (Goto et al. 2010a). The contour level is 500 m in (a) and 100 m in (b), (c)areas with high tsunami wave heights, indicating thatwaves are concentrated because of the bathymetry. For
example, Shiraho-oki Sea Hill, with diameter of about
3 km, is southeast off of Ishigaki Island (Goto 2016). It
refracts and focuses the tsunami on the Ibaruma coastof Ishigaki Island (Fig. 10b). In addition, when comparing the distribution of tsunami boulders (Goto et al.
2010a) with tsunami height and ray tracing, tsunami
boulders are basically in the area where tsunami rays
are concentrated offshore, and where tsunami waves
are high (Fig. 10b, c). One notable exception is Miyara
Bay, where tsunami boulders of up to 700 t are present (Goto et al. 2010b). However, because of offshore
bathymetry, no significantly greater tsunami wave
height was found (Fig. 10b).

5 Discussion
5.1 The 1771 Meiwa tsunami model revisited

For this study, we examined the tsunami wave sourceof the 1771 Meiwa tsunami using the latest historical records as constraints. Consequently, we demonstrated that the RYa30 model (depth = 5 km, fault
width = 30 km, fault length = 225 km, slip = 30 m,
Mw = 8.49) (Fig. 8) is the best model to reproduce tsunami historical records.

Comparing our fault model to that reported by Nakamura (2009) (depth = 5 km, fault width = 30 km, fault
length = 150 km, slip = 16 m) shows that both models
set the slip area in a shallow and narrow part of theplate boundary, but the slip amount estimated in thisstudy (= 30 m) is far larger than that proposed by Nakamura (2009). This large size is attributable to the difference in tsunami calculation methods used for eachstudy. Nakamura (2009) calculated the tsunami heightby assuming reflection at 10 m water depth, whichmight lead to neglect of the effects of coral reef bathymetry in shallow waters. Wide coral reef bathymetry basically attenuates tsunami wave energy (e.g., Kunkel et al.
2006; Gelfenbaum et al. 2011; Le Gal and Mitarai 2020).
In this study, the tsunami attenuation effects by thecoral reef topography were better incorporated because
we conducted tsunami calculation including inundation, and high-resolution (10 m mesh) topographic data
were adopted. Consequently, a larger slip was required
for this study to reproduce the tsunami run-up height.
Regarding the fault length, Nakamura (2009) set thelength as 150 km, with the fault not extending to off ofMiyako Island. Our model set the fault length as 225 km
to cover the entire area off Ishigaki Island to Miyako
Island. Nakamura (2009) assumed the maximum run-upNakata et al. Progress in Earth and Planetary Science(2024) 11:28

height at Miyako Island as 10 m based on a report by
Kawana (2000). However, Goto et al. (2012), which wasused as a constraint for this study, reported the tsunami
inundation on Miyako Island as much larger (18 m). For
this reason, our fault model became generally larger thanthat proposed by Nakamura (2009).
Our model incorporates the assumption of a very large
slip in a shallow and narrow region of the plate boundary along the Ryukyu Trench. This feature of a very large
slip in a shallow and narrow region of the plate boundary is consistent with the features of tsunami earthquakes(e.g., Satake and Tanioka 1999). Additionally, in termsof seismology, one can infer that the Ryukyu Trench has
no typical locked zone but that tsunami earthquakes canoccur in shallow areas (Arai et al. 2016; Nakamura 2017).
Therefore, our proposed model is classifiable as a tsunami earthquake, as pointed out by Nakamura (2009).
However, Ando et al. (2018) recognized fissuresbeneath the Meiwa tsunami deposits and estimated thatthe seismic motion during the Meiwa event was sufficiently strong to form fissures in the ground. In addition, contrary to assertions of Arai et al. (2016) and of
Nakamura (2017), it has also been pointed out that somelocked areas exist in the southern Ryukyu Trench, whichmight be subject to large subduction zone type earthquakes (Doo et al. 2018; Kano et al. 2021; Debaecker
et al. 2023). Therefore, the fault rupture might extend not
only to the shallow part of the plate boundary but also to
deeper parts such as that of the 2011 Tohoku-oki earthquake (e.g., Satake et al. 2013). In any case, our results
imply that a large slip in the shallow and narrow part ofthe plate boundary is decisive for reproducing the run-up
distribution of the 1771 Meiwa tsunami.
Why could such a large slip have occurred at the shallow plate boundary? Lessons learned from the 2011
Tohoku-oki earthquake and tsunami provide useful insights. To explain the run-up heights of the 2011
Tohoku-oki tsunami, a large slip must be assumed near
the trench axis at Miyagi-oki (central part of the Japan
Trench, slip = 69 m) and at Sanriku-oki (northern partof the Japan Trench, slip = 36 m), according to Satake
et al. (2013). For the Miyagi-oki region, fault rupture isestimated as having extended up to the trench axis, causing a horizontal displacement of 50 m and a verticaldisplacement of 10 m, based on exploration of the seafloor bathymetry (Fujiwara et al. 2011). Decreased shear
stress because of high pore-fluid pressure in the décollement (the shallow region of the plate-boundary fault) has
been proposed as a reason for the fault rupture extending
nearly to the trench axis (e.g., Ujiie et al. 2013). In fact,reflection surveys have indicated that pore water pressure at the décollement in Miyagi-oki is very high (Hondori and Park 2022).

Page 22 of 27

By contrast, for Sanriku offshore, bathymetry surveys
indicate displacement of less than 20 m horizontally andseveral meters vertically by the 2011 event, and indicatethat fault rupture does not extend to the trench axis
(Fujiwara et al. 2017). Therefore, the seafloor displacement caused by the fault motion is necessary to explaina large slip (36 m) near the trench axis, but so are otherprocesses. Regarding other processes, inelastic deformation of unconsolidated sediments near the trench axis
(Tanioka and Seno 2001) has been implicated as involvedin this large slip of the 2011 event (e.g., Ma and Nie 2019;
Du et al. 2021). In the southern Ryukyu Trench, highpore-fluid water pressure has also been reported in the
décollement of the southern Ryukyu Trench (Arai et al.
2016). Therefore, it can be inferred that the decrease in
shear stress attributable to high pore-fluid pressure in
the décollement might also have occurred in the southern Ryukyu Trench. In addition, unconsolidated sediments with 70 km width and 15 km depth are estimatedas existing near the Ryukyu Trench axis. The sedimentshape is similar to that of the Japan Trench at off Sanriku (Arai et al. 2016). Therefore, the inelastic deformation of unconsolidated sediments near the trench axis in
the southern Ryukyu Trench might be a reason for theoccurrence of a large slip in the shallow part of the plateboundary.
However, even for the well-measured 2011 Tohokuoki tsunami, the involvement of other factors enhancing
the tsunami such as splay faults (e.g., Sugino et al. 2013)
and submarine landslides (e.g., Tappin et al. 2014) havealso been proposed, and the source mechanisms havenot been clarified well (Sugawara 2021). Therefore, for
the Meiwa tsunami, which is far less-documented thanthe 2011 Tohoku-oki tsunami, it is difficult to determine the cause(s) of the large slip near the trench axis.
Thus, the slip of the tsunami wave source model estimated in this study may encompass various causes of
the tsunami including slip along the plate boundary,
splay faults, and submarine landslides. It is noteworthy
that the slip amount estimated here is determined tosatisfy the requirement of a very large initial water levelchange at the source. We cannot fully exclude the possibility that splay faults or a non-seismic source(s) suchas submarine landslides contributed to enhance the tsunami. Indeed, the existence of the splay faults along the
Ryukyu Trench was reported by Hsu et al. (2013) andArai et al. (2016) and there is the possibility that theyenhanced the Meiwa tsunami. Similarly, submarine landslides may have been involved in the tsunami (Okamura
et al. 2018). If these were the cases, then the slip amountof the interplate earthquake itself estimated in this study
could be decreased. Therefore, our estimated slip amountof the interplate earthquake should be regarded as theNakata et al. Progress in Earth and Planetary Science(2024) 11:28

Page 23 of 27

Fig. 11 a Aerial photograph of southern Ishigaki Island. The eastern side has about 1 km wide coral reefs, whereas the western side is surroundedby an approximately 8 km wide coral reef (Sekisei Lagoon). The aerial photograph was provided by ESRI. b Cross-sections of maximum waterlevels (upper panel), maximum current velocities (middle panel), and bathymetry (lower panel) off the southwestern coast of Ishigaki Island.
Cross-sectional lines are shown as A–C–B in (a). For both the maximum water level and maximum flow velocity, the red line shows RYa30 (fault
width = 30 km), the blue line shows RYb30 (fault width = 50 km), and the green line shows the RYc30 (fault width = 100 km). c Cross-sectionsof maximum water levels (upper panel), maximum flow velocities (middle panel), and the bathymetry (lower panel) offshore southeast of Ishigaki
Island. Cross-sectional lines are shown as A′–B′ in (a). For both maximum water level and maximum flow velocity, the red line represents RYa30 (fault
width = 30 km), the blue line represents RYb30 (fault width = 50 km), and the green line represents RYc30 (fault width = 100 km)

maximum possible value of the single rectangular fault
model. At this moment, we do not have sufficient evidence to judge whether the Meiwa tsunami was generated only by the interplate earthquake or not. Therefore,
additional seismological and sedimentological researches
along the southern Ryukyu Trench must be conducted
to ascertain whether the Meiwa tsunami was indeed
enhanced by additional sources such as splay faults andsubmarine landslides.
5.2 Unique identification of the fault width using
differences of run‑up processes as a constraint

Based on our high-resolution modeling, we showedthat tsunami inundations at Area 2 and Area 3 are sensitively variable by fault widths (Fig. 9). When the fault
depth is 5 km, a longer fault width is associated with awider the inundation area, as in Area 2, and with a narrower inundation area as in Area 3 (Fig. 9). Consequently,
the response of inundation against fault width differed
between the two areas.
There are several reasons for this difference. First, thefault width is well known as mainly affecting the tsunami
wavelength. A shorter fault width generates a shorter
wavelength of the tsunami and vice versa (e.g., Satake
et al. 2008). In addition, the coral reef widths differ in twoareas. In Area 3, the coral reef is about 1 km wide, but
in Area 2 the island is surrounded by a coral reef withmore than 8 km width, which is called the Sekisei Lagoon(Fig. 11a). The relation between tsunami wavelength,

which is mainly controlled by fault width, and the coral
reef width might cause large variations in inundation areas. Figure 11b and c shows the maximum wave
heights and velocities along the transect on the coral reefin the two areas. In Area 2, wave heights and velocities
become the highest outside the reef and around the reefedge when the fault width is 30 km, but as they propagate
over the greater than 8 km wide Sekisei Lagoon, wave
heights decrease more with shorter fault widths. Moreover, velocities become almost constant at the shoreline,
irrespective of the fault width. Fundamentally, tsunamis
with shorter wavelengths (= shorter fault widths) havehigher velocities (e.g., Gusman et al. 2012). Wave heights
are also higher for shorter wavelengths because of thestronger effects of wave shoaling and breaking offshoreof the coral reef. Therefore, outside the reef and aroundthe reef edge, the shorter the fault width is, the higher thetsunami height is and the faster the tsunami is. Also, thetsunami energy was attenuated by wave separation andwave breaking when the tsunami inundated the coral reef
(Mohandie and Teng 2009). When the wave is high relative to the coral reef depth, as was the case of the Meiwa
event, tsunami energy attenuation is more pronounced
when the ratio of coral reef width to wavelength is large(Lynett 2007). Therefore, when the reef width is wide, as
is true in Sekisei Lagoon, the longer wavelength (= fault
width) caused higher wave height near the shore. The
velocity is almost identical irrespective of the fault width.
Therefore, in Area 2, longer tsunami wavelengths (= fault

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

widths) produce a wider inundation area. By contrast,
Area 3 is characterized by the shorter width of the coral
reefs relative to Area 2. Therefore, the attenuation effectof the reef is insufficiently effective: waves with shorter
wavelengths and higher velocities reach the shore as theyare. Therefore, in Area 3, shorter tsunami wavelengths(= shorter fault widths) caused a wider inundation area.
This difference in the fault width effects on the inundation area between the southwest (Area 2) and southeast(Area 3) of Ishigaki Island strongly constrains the 30 km
fault width.
5.3 Bathymetry controlled the tsunami run‑up,
distributions of tsunami boulders, and effects on coralecosystems

The previous study suggests that the distribution oftsunami boulders is not constant, but they are concentrated on some specific coasts (Goto et al. 2010a). Tsunami boulders at the Sakishima Islands are composed
mainly of reef and coral rocks. The Sakishima Islands
coasts are surrounded constantly by coral reefs of similar sizes. Therefore, the distribution of tsunami boulders might not be controlled by ecological phenomena(i.e., the presence/absence of the boulder source (= corals and coral reefs)). Actually, it is noteworthy that wave
heights were typically high where tsunami boulders
were distributed (Fig. 10). Tsunami ray tracing analysis
further revealed that the rays were fundamentally concentrated in the places where the tsunami waves werehigh and boulders were concentrated. These results
imply that tsunami boulders are present in areas where
the tsunami energy is concentrated because of thebathymetric effects, even though a single rectangle fault
model is assumed. One remarkable exception is the distribution of numerous large boulders on the Miyara Bay
coral reef and its hinterland (Goto et al. 2010b; Hisamatsu et al. 2014; Nakata et al. 2023). This exception
might be explained by the multiple reflections or thepresence of large channels that penetrated through thecoral reefs of Miyara Bay and which are formed by theriver inflow. In these narrow channels, a jetting effectmight have amplified tsunami energy locally (Gelfenbaum et al. 2011) and could have enhanced the force
necessary to launch large boulders from the reef slope
to the reef flat (Hisamatsu et al. 2014). Indeed, the maximum velocity by RYa30 is higher in the channel partof Miyara Bay than in the surroundings, with velocities
greater than 20 m/s (Additional file 1: Fig. S2).
The tsunami boulders on the Sakishima Islands weretransported not only by the 1771 Meiwa tsunami but also
by earlier tsunami waves. They are distributed in similar areas (Goto et al. 2010a; Araoka et al. 2013). Therefore, it is likely that not only the Meiwa tsunami, but also

Page 24 of 27

earlier tsunami waves were influenced by the bathymetry
and were concentrated to the same coasts as the Meiwa
tsunami. At such coasts, the tsunami wave height andvelocity around the reef edge reached approx. 20 m andapprox. 22 m/s, respectively, according to our calculations. These values are extraordinarily high compared tothose of other recent historical tsunami events that haveaffected the coral reefs, such as the 2004 Indian Ocean
tsunami and the 2009 Samoan tsunami (Goto et al. 2007;
Dilmen et al. 2015). Goto et al. (2019) reported that coralecosystems around the Sakishima Islands might havebeen reset repeatedly by large tsunamis. Our results further imply that the extent of coral damage could be nonuniform, even on the coasts of the Sakishima Islands.
Specifically, coral damage might be outstanding at specific coasts, where tsunami boulders are now concentrated because the area can always be characterized byhigh tsunami wave heights and velocities as a result of
the bathymetric effects, irrespective of the fault size andposition.

6 Conclusions
For this study, we re-evaluated the tsunami wave sourceof the 1771 Meiwa tsunami numerically using detailed
topography and bathymetry data as well as the latest historical record dataset. The results indicate that a large slipof 30 m in a shallow and narrow region of the plate boundary in the southern Ryukyu Trench (fault depth = 5 km,
fault width = 30 km) is necessary to reproduce the historical record. This finding in turn indicates that the Meiwa
event should be categorized as the typical tsunami earthquake, although a 30 m slip is extraordinarily large and it
demands seismological explanation. Our results pose astriking contrast to the results of Minamidate et al. (2022)
who suggested no occurrence of large tsunamigenic earthquake along the central Ryukyu Trench. Therefore, different seismological settings should be considered between
the southern and central Ryukyu Trench. The large slip
in this shallow and narrow region of the plate boundary
along the southern Ryukyu Trench might not necessarily be explainable solely by fault rupture. Other potential
causes for enhancement of tsunami waves are deformationby splay faults, inelastic deformation of unconsolidated
sediments near the trench axis and/or submarine landslides. Furthermore, we investigated bathymetry effects on
tsunami propagation. Our findings demonstrated that tsunami boulders were distributed in areas where tsunamis
were focused because of bathymetric effects. This result
implies that tsunami damage to corals and reefs might not
be uniform along the coast of the Sakishima Islands, butdamage might be concentrated at some specific reefs: consequently post-tsunami recovery processes of coral reefs
might differ even at reefs with close mutual proximity.

Nakata et al. Progress in Earth and Planetary Science(2024) 11:28

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​024-​00631-0.
Additional file 1: Figure S1. (a) Topography and bathymetry map ofsouthern Ishigaki Island. The upper panel is the current topography andbathymetry data. The area circled in red is the landfill area. The lower
panel is topography and bathymetry data from which the landfill area isremoved, and the topography and bathymetry are closer to what it was
in 1771. (b) Topography and bathymetry map of Tarama Island. The upper
panel is the current topography and bathymetry data. The area circled in
red is where the coral reefs have been excavated. The lower panel shows
the bathymetry and topography data, which is re-filled in the excavatedarea. Figure S2. (a) Aerial photograph of the Miyara Bay. This is provided
by the Geospatial Information Authority of Japan. The inflow of rivers
has created channels in the coral reef. Contour lines represent elevations
every 10 m. (b) Calculated results of maximum velocity in Miyara Bay using
RYa30 model. The flow velocity is greater than the surroundings in thechannel area and is more than 20 m/s. Contour lines represent elevations
every 10 m.
Acknowledgements
We appreciate Okinawa Prefecture for providing topography and bathymetry
data used for tsunami calculations. We also thank T. Maeda and three anonymous reviewers for their constructive comments. We used the plate boundarymodel proposed by Iwasaki et al. (2015), which was constructed from
topography and bathymetry data by the Geospatial Information Authority ofJapan (250 m digital map), Japan Oceanographic Data Center (500 m meshbathymetry data, J-EGG500, http://​www.​jodc.​go.​jp/​jodcw​eb/​JDOSS/​infoJ​
EGG_j.​html), and the Geographic Information Network of Alaska, University of
Alaska (Lindquist et al. 2004). We also used the GMT (Generic Mapping Tools)
Versions 6.1.1 (Wessel et al. 2019) for data handling and plotting Figures 1 to 5,
7, and 8. Figures 9 and 11a were created using ArcGIS Pro.
Author contributions
KG proposed the topic and designed the research. KN and HY conductednumerical calculations. KN and KG prepared an original draft. All authors
participated in discussions and approved the final manuscript.
Funding
This study was supported by the Ministry of Education, Culture, Sports,
Science and Technology (MEXT) of Japan, under its Second Earthquake andVolcano Hazards Observation and Research Program (Earthquake and Volcano
Hazard Reduction Research) and by JSPS KAKENHI Grant Number 21H04508.
Availability of data and materials
Please contact the author for data requests.

Declarations
Competing interests
The authors declare that they have no competing interest.
Author details
1
Department of Earth and Planetary Science, The University of Tokyo, 7‑3‑1
Hongo, Bunkyo‑ku, Tokyo 113‑0033, Japan. 2 Department of Regional Communication Studies, Faculty of Regional Studies, Tohoku Gakuin University, 3‑1
Shimizukoji, Wakabayashi‑ku, Sendai, Miyagi 980‑8511, Japan.
Received: 8 December 2023 Accepted: 25 April 2024

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