Progress in Earth andPlanetary Science

Masuda et al.
Progress in Earth and Planetary Science(2022) 9:65
https://doi.org/10.1186/s40645-022-00527-x

Open Access

RESEARCH ARTICLE

To what extent tsunami source information
can be extracted from tsunami deposits?
Implications from the 2011 Tohoku‑oki tsunami
deposits and sediment transport simulations
Hidetoshi Masuda1* , Daisuke Sugawara2, Tomoya Abe3 and Kazuhisa Goto4

Abstract
A quantitative understanding of paleotsunamis is a significant issue in tsunami sedimentology. Onshore tsunami
deposits, which are geological records of tsunami inundation, are used to reconstruct paleotsunami events. Numerical models of tsunami hydrodynamics and tsunami-induced sediment transport are utilized in such reconstructions
to connect tsunami deposit characteristics, flow conditions, and (paleo-) tsunami sources. Recent progress in tsunami
numerical modeling has increased the possibility of developing a methodology to estimate paleotsunami sourcesfrom tsunami deposits. Several previous studies have estimated paleotsunami sources using tsunami sediment transport simulations. However, the accuracy of paleotsunami source estimation has not yet been explored. Thus, to bridge
this research gap, in this study, we showed the potential and limitations of deposit-based tsunami source estimation
based on the 2011 Tohoku-oki tsunami deposit data on the southernmost part of the Sendai Plain, northeasternJapan. The tsunamigenic megathrust along the Japan Trench was divided into ten subfaults having similar lengths
and widths. The hypothetical source models with varying slips on each subfault were examined by comparing thedepositional volume and sediment source of onshore tsunami deposits. Due to limited information on the depositional area of the tsunami deposits used in the modeling, slips only in some parts of the entire tsunami source region
could be estimated. The fault slip was slightly overestimated but could be compared with previous well-constrained
source models. Thus, these results indicated that vast high-quality datasets of tsunami deposits can improve theaccuracy of paleotsunami source estimation. It is also suggested that the amplitude of the receding wave affects theerosion pattern from the shoreface to the nearshore area. Although sufficient data for paleotsunami source estimation are lacking, an effective combination of tsunami deposit data and sediment transport simulations potentially
improves the accuracy of the source estimation. The results will contribute to developing a framework of depositbased paleotsunami source modeling and assessing its accuracy.
Keywords: 2011 Tohoku-oki tsunami, Tsunami deposit, Paleotsunami, Tsunami source estimation, Tsunami sedimenttransport simulation*Correspondence: hidetoshi.masuda.s3@dc.tohoku.ac.jp
1
Department of Earth Science, Graduate School of Science, Tohoku
University, 6‑3 Aramaki Aza‑Aoba, Aoba‑ku, Sendai, Miyagi 980‑8578, Japan
Full list of author information is available at the end of the article

1 Introduction
A tsunami source is defined as a region in which thewater level is displaced from the still water level. In thecase of tsunamigenic earthquakes, tsunami sources areoften described by static focal parameters that determine
coseismic crustal deformation. Source modeling of modern tsunamis using instrumental observational data is a

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Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

major approach to understanding the focal region, size,
and rupture process of such tsunamigenic earthquakes.
Conversely, source modeling of earlier (or paleo-) tsunamis, such as those that occurred hundreds to thousandsof years ago, is crucial for the long-term assessment oftsunamigenic earthquakes.
Source modeling of modern and paleotsunamis
employs different approaches due to differences in theavailable data. Inverse modeling of instrumental records,
such as oceanographic (tsunami), seismic, and geodetic
data, is commonly used to determine the focal parameters of modern tsunamigenic earthquakes (Satake 1987;
Satake et al. 2013; Iinuma et al. 2012; Yamazaki et al.
2018). Contrastingly, paleotsunami source modeling utilizes historical records (e.g., documented run-up heights)
and geological records (e.g., tsunami deposits), whichrarely provide sufficient quantitative information for
inverse modeling as conducted for modern events.
Tsunami deposits provide geological information on
the inundation extents, flow conditions, and repeating
run-up and backwash flows (Fujiwara 2008). They havewidely been used for source modeling of paleotsunamis(Satake et al. 2008; Namegaya and Satake 2014; Butler
et al. 2014; Ioki and Tanioka 2016; Sugawara et al. 2019;
Dourado et al. 2021). Sandy tsunami deposits have been
extensively studied because they can be easily identified
as high-energy depositional events in stable environments, such as coastal lowlands (Minoura and Nakaya1991). Deposit-based tsunami source modeling typically
employs a trial-and-error approach (Aida 1977), which
exhaustively examines hypothetical source models using
forward tsunami simulation to assess which model best
explains the distribution of known tsunami deposits.
Most conventional reconstructions of deposit-based
paleotsunami sources have utilized only tsunami deposit
distribution as a constraint of minimum inundation
caused by tsunamis. These reconstructions compare
the observed characteristics of tsunami deposits withthe hydrodynamic simulations of tsunamis. However,recent post-tsunami field surveys (Srinivasalu et al. 2007;
Goto et al. 2011; Abe et al. 2012) have reported significant gaps between the tsunami inundation limits andthe maximum inland extent of sandy tsunami deposits;
furthermore, these gaps enlarge with increasing inundation distance (Abe et al. 2012). Thus, this increased concerns for the application of hydrodynamic simulations
in deposit-based tsunami source estimation because thegap between tsunami inundation and deposit extent can
result in possible underestimation of the tsunami size.
In the meanwhile, information associated with tsunami
deposits, such as thickness, volume, grain size, and sediment source, was not fully included in deposit-based
paleotsunami source modeling.

Page 2 of 20

Numerical modeling of tsunami-induced sedimenttransport has recently been applied in paleotsunami studies (Sugawara et al. 2014a; Sugawara 2021). Along withhydraulic data, information on deposit thickness and erosion depth can be obtained from tsunami sediment transport simulations and the results of the simulations can becompared directly with the sedimentary data of tsunami
deposits. As the application of tsunami sediment transport simulations in tsunami deposit research is still at its
nascent stage, examples of paleotsunami source modeling using sediment transport simulations are scarce(Sugawara et al. 2019; Dourado et al. 2021; Nakanishi and
Ashi 2022). Thus, the validity and limitations of the application of tsunami sediment transport simulations in tsunami source modeling have not yet been explored.
The possibility of tsunami source estimation using
sediment transport simulations on the 2011 Tohoku-oki
tsunami has been previously explored (Gusman et al.
2018; Hisamatsu et al. 2019). Gusman et al. (2018) conducted a sensitivity analysis with varying tsunami amplitudes and periods and found that the simulated deposit
thickness and grain-size distribution were controlled
by tsunami characteristics, such as wave amplitude andperiod. However, the relationship between the simulated
deposit distribution and tsunami source parameter was
not directly analyzed. Hisamatsu et al. (2019) estimatedthe source parameter of the 2011 Tohoku-oki tsunami
by utilizing tsunami sediment transport simulations andtsunami deposit data. Additionally, they used the conicalfault model proposed by Hisamatsu et al. (2017) and tsunami deposit data from three different sites on the Pacificcoast of Tohoku. Their deposit-based source modelingwell reproduced the moment magnitude of the earthquake; however, the maximum slip was underestimated.
Nevertheless, rectangular fault models are still dominantly used in source estimation of both modern andpaleotsunamis (Satake et al. 2013; Yamazaki et al. 2018;
Sugawara et al. 2019; Dourado et al. 2021; Nakanishi and
Ashi 2022). Thus, an examination of the framework using
the rectangular fault model can be useful to compare theresults with those of the rectangular model reported inprevious studies.
This study aimed to estimate tsunami sources basedon the 2011 Tohoku-oki tsunami deposit data from asmall area of ~ 0.8 ­km2 on the southernmost part of the
Sendai Plain. To acquire suggestions for paleotsunami
source estimation, we initiated the source modelingfrom the standpoint that has not been revealed regarding the slip distribution and paleotsunami research,even though vast knowledge on the earthquake has
been accumulated in the last decade. We explored thetsunami source based on the numerical simulation of
sediment transport that occurred due to the tsunami.

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

High-density tsunami deposit data acquired from thesouthernmost part of the Sendai Plain (Abe et al. 2020)
along with pre- and post-tsunami topographic data
were used for benchmark and model inputs. Further,
the slip distribution of the estimated tsunami source
was discussed by comparing it with the results of othertsunami source models reported in previous studies.

2 Study area and sedimentary data
Deposits of tsunamis in the Sendai Plain, such as the869 Jogan, 1454 Kyotoku, 1611 Keicho, and 2011
Tohoku-oki, have been previously examined in detail(Sawai et al. 2008, 2012, 2015; Abe et al. 2012, 2020;
Shinozaki et al. 2015). The 2011 Tohoku-oki tsunami
caused extensive inundation throughout the Sendai
Plain (Mori et al. 2012; Haraguchi and Iwamatsu 2013).
The present study examined the 2011 Tohoku-oki tsunami and its deposits on the southernmost part of the
Sendai Plain in Yamamoto town, Miyagi Prefecture,northeastern Japan (Fig. 1). In the study area, tsunami
inundation reached 3 km from the coastline, with amaximum flow depth of 10 m (Suppasri et al. 2012).
Before the 2011 Tohoku-oki tsunami, a sandy beach(width of 0–80 m) was developed along the coastline.
The beach ridge (elevation of 2–3 m from Tokyo Peil[TP]) behind the sandy beach was covered by a coastal
forest, which was devastated by the 2011 Tohoku-oki
tsunami. Subsequently, a coastal dike (6.2 m from TP)
was built between the beach ridge and the backshore(Abe et al. 2020). The elevation of the lowland, which
is used mainly for rice paddies, is 2–3 m. The drowned
valley and the surrounding Pliocene sandstone hills(30 m from TP) are developed in the west of the lowland (Fujita et al. 1988). A small coastal pond, Suijinnuma, partially covers the entrance of the drowned
valley.
Sedimentary features, such as thickness, grain size, andsedimentary structures, of sandy and muddy tsunami
deposits were collected from 172 sites in the drowned
valley and the Suijin-numa pond to examine their spatial
distribution and sediment source and budget (Abe et al.
2020; Fig. 1c). The tsunami deposits on the study area, asreported by Abe et al. (2020), are summarized as follows:
The maximum thickness of the sandy tsunami deposit
was 40 cm at ~ 270 m inland from the coastline. These
deposits showed landward thinning and fining trends. In
addition, the sandy deposits near the coastline and on thebottom of the Suijin-numa pond comprised one to four
subunits associated with repeating run-up and backwash
flows. Based on the eroded area and the grain-size distribution, the main sources of the sandy tsunami deposits
were estimated as sandy beach and dunes.

Page 3 of 20

3 Methods
3.1 Numerical model and inputs

A two-dimensional horizontal (2DH) tsunami sedimenttransport model (TUNAMI-STM; Sugawara et al. 2014b;
Yamashita et al. 2016) was employed in this study. In thismodel, a depth-averaged tsunami hydrodynamic model,
TUNAMI-N2 (Goto et al. 1997), which is based on the
nonlinear long wave theory, was coupled with the sediment transport model (STM) proposed by Takahashi
et al. (2000). The STM considers sediment exchange
between the bed and suspended loads assuming a single
grain-size class of the sediments. Previous studies haveextensively utilized TUNAMI-STM and its derivatives toinvestigate tsunami-induced sediment transport due tothe 2011 Tohoku-oki earthquake (Sugawara et al. 2014b;
Yamashita et al. 2016, 2018; Arimitsu et al. 2017; Kusumoto et al. 2020) and to model the paleotsunami sourceof the 1867 Keelung earthquake (Sugawara et al. 2019).
Sugawara et al. (2014b) demonstrated that the generaltrend of deposit thickness along orthogonal transects tothe shoreline can be reproduced using STM. Yamashita
et al. (2016) showed that the simulated sediment volumesof erosion and deposition caused by the Tohoku-oki tsunami in Hirota Bay on the Sanriku Coast were roughly
consistent with observed volumes. The model has been
comprehensively described by Sugawara et al. (2014b)
and Yamashita et al. (2016).
A nesting grid system was used to optimize the computational efficiency and resolution of numerical modeling.
The computational domain was divided into six-layered
domains (R1–R6), with varying spatial resolutions andextents. Domain R1 has a spatial resolution of 1215 m
and covers the entire interplate tsunami source region
along the Japan Trench, whereas Domains R2–R6 havespatial resolutions ranging from 405 to 5 m with a constant ratio of 1/3. TUNAMI-N2 simulated tsunami propagation and inundation in all domains, while sedimenttransport simulations were performed only in Domain
R6 (Fig. 1a). The numerical analyses were conducted for
3 h after the earthquake occurred. A temporal resolutionof 0.1 s was selected to maintain numerical stability (i.e.,
Courant–Friedrichs–Lewy condition).
Bathymetric data were acquired from the public dataset provided by the Central Disaster Management Council, Cabinet Office, Government of Japan (http://​www.​bousai. ​ g o. ​ j p/ ​ k aigi​ rep/ ​ chuob ​ o u/ ​ s enmon/​ n ihon ​ k aiko_​chisi​majis​hin/​index.​html) and the M7005 bathymetricchart published by the Japan Hydrographic Association.
Topography data, which were based on the 5-m meshdigital elevation model (DEM) acquired using the lightdetection and ranging (LiDAR) technique, were provided
by the Geospatial Authority of Japan (https://​www.​gsi.​go.​jp/​kiban/). Both datasets were collected before the 2011

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

Page 4 of 20

Fig. 1 Study area and fault models. a Topography and bathymetry map of the calculated Domain R6. White rectangles and red polygons indicate
the survey point of tsunami trace height (Mori et al. 2012) and fixed bed, respectively. The blue line represents the inundation limit (Haraguchi
and Iwamatsu 2013). b Fault models. Bold solid and thin dashed rectangles indicate the geometry of the fault model proposed by Hayashi andKoshimura (2012) and Satake et al. (2013), respectively. c Enlarged view around the Suijin-numa pond. Yellow circles represent the survey points oftsunami deposits (Abe et al. 2020)

Tohoku-oki earthquake, and a Cartesian coordinate system based on the transverse Mercator Projection (Japan
Geodetic Datum 2000, Zone 10) was used.
Manning’s roughness coefficient (0.025 s/m1/3), which
represents the friction on bare ground and the ocean
floor (Kotani et al. 1998; Sugawara et al. 2014b), wasassumed in all computational domains to evaluate bottom friction in the modeling of tsunami propagationand inundation. The initial tide level was set at − 0.5 m

based on the tidal level at the Soma Port, which is located~ 7 km south of the study area, when the earthquake
occurred. Part of the engineered headlands, coastal dikes,
and roads that were not damaged by the 2011 tsunami
were assumed non-erodible in the tsunami sedimenttransport simulations (Sugawara et al. 2014b).
According to the results of the grain-size analysis
described by Abe et al. (2020), the average median grain
size of the tsunami deposits is ~ 1.9 φ (i.e., ~ 0.268 mm).

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

Thus, in the simulations conducted in the present study,
we assumed the single grain size as 0.267 mm, which has
been used in the flume experiment by Takahashi et al.
(2011). The settling velocity of sand in still water was
firstly calculated by Rubey’s (1933) formula and thendynamically corrected considering hindered settlingin the concentrated suspended sediments (Richardson
and Zaki 1954; van Rijn 2007). Critical friction velocity,which is a function of grain size, was evaluated according to Iwagaki (1956). Grain-size-dependent parameters
α and β, for bedload and exchange rates, determined by
Takahashi et al. (2011) were used. Manning’s roughness
coefficient for STM is independent of that for TUNAMIN2 (Yamashita et al. 2016). As the Manning’s roughness
coefficient for sand beds is difficult to constrain empirically, a value of 0.015 s/m1/3 for STM was employed to
calculate the friction velocity for the sediment transport
simulations by optimizing the resulting deposition of thereference simulation (see Sects. 3.2.2 and 4.1).
3.2 Procedures
3.2.1 Metrics for comparing simulations and observations

Although STM can reproduce the overall trend of deposit
thickness, the simulated deposit thickness at a given
point is generally scattered around the observed value(Sugawara et al. 2014b, 2015). This can be associated withlocal variations in deposit thickness due to the effects of
microtopographies on tsunami flow and sediment transport process (Hori et al. 2007; Fujiwara and Tanigawa
2014). The sparsely observed data cannot resolve thelocal variability of the deposit thickness comprehensively,
while the simulated deposit thickness exhaustively covers
all computational grids. Thus, simulations can reproduce
the details of the local variability in the deposit thickness
if the spatial grid size and precision of the topographic
data are sufficiently high to resolve the microtopographies. In the present study, we adopted the LiDAR-based
DEM with a spatial grid spacing of 5 m to numerically
express such microtopographies. To avoid direct comparison at the scattered data points, we used observed andsimulated deposit volumes in the study area based on theapproach employed by Dourado et al. (2021), who compared the core-based depositional volume and calculated
volume in several scenarios to select the most suitablesource model for the 1755 Lisbon tsunami. The depositional volume was precisely estimated using sufficient
sedimentary data and was potentially available as a constraint of deposit-based source modeling.
The thickness data of 162 points from 174 samples
obtained by Abe et al. (2020) were used to estimate theobserved deposit volume. In this study, we used thethickness of the sandy tsunami deposits because the STM
cannot analyze muddy sediment transport.

Page 5 of 20

Gridded data of the observed deposit thickness in the
study area (Fig. 2b) were generated using the adjustable tension continuous curvature spline interpolation(surface module in the Generic Mapping Tools version
6; Smith and Wessel 1990; Wessel et al. 2019). The gridded thickness data (> 0 m) were then used to calculate
the deposit volume after clipping data through a polygon, which included the inundation limit of the reference
simulation (see Sects. 3.2.2 and 4.1) on the valley floor
and coastward limit of the observed thickness data on the
coastal plain. As a result, it is estimated that 85,336 ­m3 oftsunami deposits was lying on 823,204 ­m2 of the inundation area, based on the observed deposit thickness. Thisestimated deposition volume was used as a constraint of
the source modeling. To reduce the difference in spatial
density of the observed and simulated data and for better comparison, simulated deposit thicknesses extracted
from the survey points of Abe et al. (2020) were interpolated in the same way as the observed data, considering the difference in the spatial characteristics of theobserved and simulated data. Note that the inundation
limits used for clipping varied in each scenario.
3.2.2 Model calibration

The 2011 Tohoku-oki tsunami was initially numericallysimulated using a published source model to validate thesimulation with the given parameter settings. The tsunami source model by Satake et al. (2013) that resolves
the spatiotemporal evolution of the slip distribution wasused to calculate seafloor deformation and the resulting initial tsunami waveform. Okada’s (1985) formula
was used to calculate the seafloor deformation considering the effect of horizontal motion of a sloping seafloor(Tanioka and Satake 1996).
The boundary condition (flux) between domains R4
and R5 was calibrated based on the geometric mean
K and geometric standard deviation κ of the ratio ofobserved tsunami height to simulated height (Aida 1978),following Sugawara et al. (2014b). The tsunami traceheight datasets reported by the 2011 Tohoku Earthquake
Tsunami Joint Survey Group (Mori et al. 2012) within
Domain R6 were employed regardless of the reliability
index of each datum.
The preliminary tsunami hydrodynamic simulationand sediment transport simulation using the original
source parameters given by Satake et al. (2013) underestimated the tsunami measurements in the study
area. Aida’s (1978) criteria for model validation, whichassesses the ratio of observed tsunami heights to simulated heights, was found to be K = 1.22 for the geometricmean and κ = 1.22 for the geometric standard deviationfor 59 trace heights within the computational Domain
R6 (Additional file 1: Fig. S1). Moreover, the thicknesses

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Page 6 of 20

0.2

0.3

0.4

0.5

Deposition (m)Thickness (m)

0.5

0.3
0.2
0.1
0.0
0.5

Thickness (m)Simulation

(c)

0.4

0

500

1000

1500

Abe et al. (2020)

(d)

0.4

2000

0.3
0.2
0.1
0.0

0

500

1000

1500

2000

Distance from shoreline (m)Fig. 2 Observed deposition and results of the sediment transport simulation for model and parameter validation (i.e., the reference simulation). a
Thickness of the resampled and interpolated thickness based on the simulation. b Interpolated sand thickness distribution around the Suijin-numa
pond. Thickness data were collected by Abe et al. (2020). c Shore-normal distribution of the simulated deposit thickness on the survey sites of Abeet al. (2020). d Shore-normal distribution of the observed deposit thickness (modified after Abe et al. 2020)of tsunami deposits were underestimated (Additional
file 1: Fig. S2), suggesting that a positive calibration of
the boundary condition was necessary to fit the simulations to the observations. A calibrated simulation, in
which the flux was increased to 115%, was performed,
considering the K value of the preliminary result; consequently, an improved result with K = 0.99 and κ = 1.24
was acquired after comparing 77 trace height sites that
met the reproducibility criteria (0.95 < K < 1.05 andκ < 1.45; Japan Society of Civil Engineers 2002). The
calibrated simulation results were used for the reference
simulation in the source modeling.
3.2.3 Fault model and sensitivity to subfault location

We used a set of subfaults (S1–S10) to consider slip
heterogeneity (Fig. 1b). The geometries of the subfaults

of a simple multi-segment fault model (Hayashi andKoshimura 2012) were adopted as an interplate fault
plane along the Japan Trench because the subfault segmentation of Satake et al. (2013) is extremely fine anddeposit-based source estimation could not accurately
estimate the source location and slip distribution. The
fault model of Hayashi and Koshimura (2012) was
modified from the model originally proposed by Imamura et al. (2011) based on the aftershock distributionof the 2011 Tohoku earthquake (Nettles et al. 2011;
Asano et al. 2011). The fault plane was divided into 10
subfaults having both lengths and widths of 100 km.
Hereinafter, all source models were assumed to have apure reverse faulting mechanism and a rise time of 30 s.
Crustal deformation was calculated according to Okada

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

(1985) without considering the effects of the horizontal
motion of the trench slope (Tanioka and Satake 1996).
The modeled rupture area extended 500 km and200 km in the N–S and E–W directions, respectively. The
slip distribution of the entire tsunami generation region
could not be potentially recovered based on the tsunami
deposit data acquired only from the study area. Thus, toclarify the contribution of each subfault to the study area,tsunami propagation, inundation, and sediment transport due to each subfault were simulated individually. A
unit slip of 10 m was assigned to a subfault, and the slips
for the remaining subfaults were set to zero. Simulations
by each subfault were compared to identify major contributing subfaults, which were then used for estimating
fault slip based on the comparison of the simulated andobserved volumes of the tsunami deposits. We evaluatedthe sensitivity of each subfault based on the total deposition volume within Domain R6 (including the seafloor),
since the inundation and onshore deposition are often
minor in this sensitivity analysis.
Simulated deposit volume was sensitive to the distance to subfaults that acted as tsunami sources (Fig. 3).
Deposit volumes by the shallower subfaults near the
trench axis (S1–S5; Fig. 1b) were 44–388% more thanthose by the deeper subfaults near the shore (S6–S10) on
the same latitude. The maximum deposition (317,433 ­m3)
was calculated using the shallower S4 subfault, whereas
the minimum deposition (3753 ­m3) was calculated using
the deeper S6 subfault. Deposit volumes by the shallower S3 and S5 subfaults (85,837 ­m3 and 87,833 ­m3,
respectively) were less than one-third of the adjacent S4;Page 7 of 20

similarly, the deposit volumes by S8 and S10 (33,764 ­m3
and 30,772 ­m3, respectively) were nearly one-seventh of
S9 (221,114 ­m3). These results suggested that the volumesof the tsunami deposits could be explained primarily
according to the slips on S4 and/or S9, which are locatedsoutheast, offshore of the study area.
3.2.4 Sediment transport simulations with varying slips

Changes in the deposit volume with varying fault slips
were further examined for subfaults S4 and S9 in a totalof 14 different rupture patterns. Since S4 has the largest
sensitivity, estimation of the S4 slip was prioritized. The
minimum fault slip for S4 and S9 was set to 10 m and 5 m,
respectively, while a < 5 m slip indicated that the slip wasabsent on the subfault. Maximum fault slips for S4 andS9 were set to 40 m and 10 m, respectively, considering
the slip distribution in Hayashi and Koshimura (2012).
This assumption was generally consistent with otherfault models of the 2011 Tohoku-oki earthquake (Satake
et al. 2013; Yamazaki et al. 2018). Although the large slips(> 40 m) in previous models occurred on several narrowsubfaults, in this study, such slips will be expressed as anaveraged smaller slip within a large subfault instead of theimpulsive slip distribution.
3.2.5 Sensitivity analysis on grain size

The TUNAMI-STM code approximates a single grainsize class of sediments. However, real tsunami deposits
consist of different grain-size distributions. In the present
study area, the median grain size of the tsunami deposits ranges from 1.3 φ to 2.6 φ (Abe et al. 2020). This can

Fig. 3 Deposition associated with the individual subfault models. Uniform slip of 10 m is assumed for each subfault. Whole deposition volume in
Domain R6 is displayed

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

result in uncertainty in tsunami sediment transport simulations. Ultimately, the uncertainty could propagate to theestimated fault slip because its estimation was based on thecomparison between the simulated and observed deposit
volumes.
Thus, a sensitivity analysis of grain size was conducted toevaluate the uncertainty in source modeling. The grain size
was set from 70 to 130% of the reference value (0.267 mm)with a 10% interval. Grain-size-dependent parameters,such as settling velocity in still water, critical friction velocity, and empirical grain-size-dependent parameters, α andβ for transport formulas, were recalculated using the grain
size in each case. The parameters, α and β, were calculatedby the following approximations (Masaya et al. 2020):

α = 9.8044 e−3.366d
β = 0.0002 e−6.5362d

Page 8 of 20

where d indicates the grain size. Moreover, the source
model proposed by Satake et al. (2013) with the calibration was employed for the sensitivity analysis.

4 Results
4.1 Tsunami inundation and deposition from calibrated
simulation

Calibrated numerical results on tsunami height andmorphological changes are shown in Fig. 4. The tsunami height exceeded 8 m at the center of the study area
(Fig. 4a). Additionally, the tsunami extensively inundated the valley floor where the Suijin-numa pond was
located. The simulated inundation limit was consistent
with the observed limit reported by Haraguchi and Iwamatsu (2013). Erosion due to the tsunami inundation wasconcentrated near the coastline (Fig. 4b); additionally,
alongshore and cross-shore erosion types were identified. Alongshore erosion, which occurred near coastal
dikes, showed a width of ~ 100 m and a depth of ~ 1 m,
whereas cross-shore erosion was observed on the beach

8
6
4
2
0

Tsunami height (m)

10

−0.5

−0.4

−0.3

−0.2

−0.1

0.0

0.4

0.5

Erosion (m)

0.0

0.1

0.2

0.3

Deposition (m)Fig. 4 Results of the reference simulation. a Distribution of the maximum tsunami height in Domain R6. Blue and white lines represent simulated
and observed inundation limits, respectively. Black frame shows the spatial range of Fig. 2b and c. b Distribution of erosion depth near the
Suijin-numa pond. Black line indicates the 0 m contour after the simulation. c Distribution of deposition thickness

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

and shallow sea floor near the breached coastal dikes.
Further, on the backland, several erosion lines were recognized along road embankments. Simulated deposits
were relatively thin on the shore and thick on the shallow
sea bottom (Fig. 4c). Similar to erosion, abrupt changes indeposit thickness along the embankments were identified(Fig. 4c).
The simulated deposit volume (Vsim; Fig. 2a) was
86,645 ­m3, which was consistent withthe observeddeposit volume Vobs = 85, 336 m3 . The simulated
deposit was distributed approximately 1900 m from thecoastline with a maximum value of ~ 0.4 m at 434 mfrom the coastline (Fig. 2c). Simulated deposit distribution (Fig. 2a and c) indicated that the deposit was thicker
on the seaward of the Suijin-numa pond. The thicknessof simulated deposits was generally thin inside the valley
and increased locally. The observed thickness distribution was generally comparable with the simulated result(Fig. 2b). However, the locations of the thick deposits
on the seaward of the Suijin-numa pond differed in thesimulations and observations. In particular, the deposit
thickness in the Suijin-numa pond in the observations
was almost zero, whereas it was relatively more in thesimulations. Although a significant scatter was observed,
the simulated deposit thickness decreased with increasing distance from the coast (Fig. 2c). Generally, the shorenormal distribution of the simulated deposit thickness iscomparable with the observed thickness (Abe et al. 2020;
Fig. 2d).
4.2 Sediment transport simulations with varying fault slips

Figure 5 compares the deposit volumes estimated basedon the field data and the results of the sediment transport simulations. Owing to large slips on both S4 andS9, the volume of deposition in the study area was also
large. To explain the observed deposition (85,336 ­m3),
slip amounts of over 35 m and 5 m were required forS4 (se3510) and S9 (se4005), respectively (Fig. 5). Even
if an exclusive slip of 40 m is assumed on S4, without aslip on S9, the simulated deposit volume was 78% of theobserved volume, indicating that large slip is requiredon the deeper subfault S9. Results of the source models, se1010 and se1005, suggested that a combinationof ~ 10 m slip near the trench axis and 5–10 m near
the shore could not facilitate the formation of tsunami
deposits in the study area (Fig. 5).
4.3 Sensitivity analysis of grain size

Figure 6 compares the shore-normal distribution of thesimulated tsunami deposit thickness across varying grain
sizes. At ~ 780 m from the shoreline, the maximum andaverage deposit thicknesses of fine grain size (0.187 mm,
which is 70% of the reference size; Fig. 6a) were 0.36 m

Page 9 of 20

and 0.13 m, respectively, while those of coarse grain size
(0.347 mm, which is 130% of the reference size; Fig. 6b)
were 0.30 m and 0.07 m, respectively. Comparing Fig. 6aand b, the landward thinning trend is more notable withthe coarser grain size. The sensitivity analysis results also
showed a significant change in the depositional volume
corresponding to the different grain sizes (Table 1). At agrain size of 0.187 mm, the deposition volume increased
to 131% of the reference simulation, whereas as the grain
size increased to 0.347 mm, the deposit volume reduced
to 72% of the reference simulation.

5 Discussion
5.1 Validation of the tsunami sediment transport
simulation

To better simulate tsunami-induced sediment erosion, transport, and resulting morphological changes,
an accurate reproduction of tsunami hydrodynamics(e.g., tsunami height, waveform, and flow velocity) is
necessary. The tsunami source model used in this study(Satake et al. 2013) could reproduce the observed tsunami waveforms at offshore stations and coastal tidegauges. However, these tsunami records were sparsely
distributed spatially; additionally, coastal inundation was
highly dependent on the resolution of the DEM used forthe simulation. Thus, the validity of the tsunami source
model does not necessarily guarantee a successful prediction of coastal inundation by a high-resolution simulation. Therefore, the simulation was calibrated with aflux factor of 115% based on the comparison results ofthe simulated and measured tsunami heights (Mori et al.
2012). Consequently, the simulated tsunami heights wereclose to the observations (see Sect. 3.2.2 and Additional
file 1: Fig. S1). Additionally, the calibrated simulation well
reproduced the observed inundation limit (white line in
Fig. 4a; Haraguchi and Iwamatsu 2013).
Nevertheless, a better hydrodynamic simulation does
not necessarily indicate a successful reproduction of sediment transport and sediment transport simulations must
be validated through comparisons with field measurements. However, a point-by-point comparison is not feasible considering the local variability of deposit thickness,
which cannot fully be addressed during the field observations. Thus, we compared the simulated and observed
depositional volumes that could serve as a robust metricfor validating the simulations.
The simulated deposition volume Vsim = 86, 645 m3
was almost
consistent with the observed deposition volume Vobs = 85, 336 m3 , indicating that the magnitudeof sediment transport was correctly simulated in thereference simulation. The overall deposition trend inboth simulations and observations was similar, except
in the Suijin-numa pond (Fig. 2). Qualitatively, theMasuda et al. Progress in Earth and Planetary Science(2022) 9:65

Page 10 of 20

Fig. 5 Calculated deposition volumes from 14 models with varying fault slips on subfaults S4 and S9. Hypothetical models se3510 and se4005 well
reproduced the depositional volume estimated based on the observation; black line (Abe et al. 2020)

observed (Abe et al. 2020; Fig. 2d) and simulated (Fig. 2c)shore-normal thickness distributions were similar. Further, the simulation demonstrated that the erosion due
to the tsunami devastated the beach (Fig. 4b), and thecross-shore erosion changed the coastline significantly.
Previous studies deduced that the concentrated backwash eroded the beach deposits, and the scour, similar
to a small bay (so-called tsunami bay), remained evenafter the tsunami (Yoshikawa et al. 2015, 2017, 2018; Abeet al. 2020). Specifically, the simulation results indicatedthat the concentrated erosion on the beach was qualitatively consistent with such a deduction. Based on thesequantitative and qualitative comparisons of the deposition volumes, the calibrated tsunami sediment transport
simulation successfully reproduced the general characteristics of the tsunami inundation and sediment deposition, thus suggesting the possibility of investigating thetsunami source based on the simulated deposit volume.
Despite the successful reproduction of the onshore deposition, the simulated volume of the beach erosion was
6.85 × 104 m3, whereas the observed erosion volume was
1.34 × 105 m3 (Abe et al. 2020). Considering the consistency in onshore deposition, this difference in erosion may
influence the offshore rather than the onshore deposition

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

Page 11 of 20

Fig. 6 Grain-size-dependent changes of the shore-normal distribution of simulated tsunami deposits. a Results of the finest (d = 0.187 mm) and bcoarsest grain size (d = 0.347 mm)Table 1 Summary of the sensitivity analysis of the grain sized (mm)

w0 (m)

uc (m)αβVsim ­(m3)

Rd (%)

0.187

0.021360.01463

5.22

0.214

0.025760.01498

4.77

5.89 × ­10−5

0.240

0.02983

0.01528

4.37

0.267

0.03386

0.01556

4.0

0.294

0.03768

0.01582

3.64

0.320

0.041160.01605

3.34

0.347

0.04458

0.01628

3.05

113,591131

4.94 × ­10−5

99,161114

4.17 × ­10−5

92,180106

4.4 × ­10−5

86,645100

2.93 × ­10−5

78,49391

2.47 × ­10−5

70,57381

2.07 × ­10−5

62,68772

d , Grain size; w0, Settling velocity in the static water column; uc, Critical shear velocity; α, Empirical parameter for the bedload formula; β, Empirical parameter for theexchange rate formula; Vsim, Volume of resampled and interpolated deposit around Suijin-numa; Rd, Ratio of deposition volume to the reference (d = 0.267 mm)
resultprocess. Thus, the results of the calibrated tsunami sediment transport simulation can be regarded as valid aslong as it is focused on the onshore deposition.
5.2 Tsunami source model inferred from the tsunami
deposit and its source

Among the models se3510 and se4005, it is difficult
to judge based solely on the deposit volume whichis the better one because both models well reproduce the deposition volume (Fig. 5). Even if measured tsunami heights are available, the judgment isstill uneasy because the difference in the K (1.15 for
se3510 and 1.13 for se4050) and κ (1.21 for se3510 and
1.22 for se4050) metrics is quite small. Similarly, thecomparison of the inundation limit is not promising tofind their difference (Fig. 7). Therefore, another metricother than those is necessary to further constrain thetsunami source.
Masaya et al. (2021) highlighted that simulated sediment source provides additional information to estimate paleotsunami sources. They proposed the ratioof marine-origin deposits to whole deposits, Psea , asdefined:Psea =Vsea
Vall

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

Page 12 of 20

Fig. 8 Volumes of the whole deposits (Vall) and marine-origin
deposits (Vsea) around the Suijin-numa pond (simulated according
to the method by Masaya et al. 2021). Ratios Psea = Vsea /Vall for eachcase are shown
0

2

4

6

8

10

Maximum tsunami height (m)Fig. 7 Distributions of the maximum tsunami height attributed to a
se3510 and b se4005. White and blue lines indicate the observed andsimulated inundation limits

where Vsea and Vall denote the volumes of marine-origin
deposits and whole tsunami deposits in the area of comparison, respectively. A numerical experiment shows that
the Psea ratio varies depending on the tsunami waveformand can be a constraint of deposit-based tsunami source
modeling (Masaya et al. 2021). In the present approach of
Eulerian simulations, exact value of Vsea cannot be calculated directly. Thus, Vsea was approximated based on thedeposit volume calculated assuming that the entire land
is non-erodible.
Although an exact Psea may not be obtained from real
tsunami deposits, contributions of different sedimentsources can be elucidated by detailed analyses. The sandy
tsunami deposits in the Sendai Plain formed by the 2011
Tohoku-oki tsunami have been estimated to originate
onshore (Szczuciński et al. 2012; Takashimizu et al. 2012;
Putra et al. 2013). For example, marine diatom species
occupy only ~ 2% of the entire diatom assemblage in the
sandy fraction of the tsunami deposits in the northern
Sendai Plain (Takashimizu et al. 2012). Existing tsunami
sediment transport simulations support such micropaleontological findings (Sugawara et al. 2014b). In the present study area, Abe et al. (2020) elucidated the onshore
source of the tsunami deposits by comparing pre- andpost-tsunami DEMs and grain-size distributions of

the deposits. Psea in the reference simulation is only 3%(Fig. 8), which fits the estimation by Abe et al (2020).
Deposit distributions are in general similar among themodels se4005 and se3510 (Fig. 9). However, seafloor
erosion near the coastline differs significantly. In the caseof se4005 (Fig. 9c), a shore-parallel band of seafloor erosion was found ~ 200 m offshore of the coastline, whereas
such a band was located much closer to the land and was
relatively narrow in se3510 (Fig. 9a). The difference in offshore erosion can affect the contribution of the marine
sediment (i.e., Psea ). Figure 8 shows that se4005 shows agreater contribution (Psea = 37%) comparing with se3510(Psea = 23%).
Figure 10 compares the tsunami waveforms by threedifferent source models (Satake et al. 2013, se3510, andse4005) at a virtual tide station SJN1 (Fig. 1). The waveforms by the models se3510 and se4005 are in generalsimilar, except for a period between 45 and 63 min.
Among a whole range of waveforms, se3510 and se45005
have different features compared to Satake et al. (2013).
Major differences are the duration of the main wave
and its precedent sea-level drop. With hypotheticalsource models, an abrupt sea level drop (receding wave
45–63 min) occurred prior to the arrival of the main
wave. The simulation by model se4005 yielded a larger
receding wave compared with that by se3510. In the reference model (Satake et al. 2013), a gradual and moderate decrease in the sea level appeared prior to the main
wave. Masaya et al. (2021) pointed out that the periodof the main wave and the amplitude of the precedent
receding wave control the erosion of the shallow seafloor.

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

Page 13 of 20

Seafloor erosion

−0.5

−0.4

−0.3

−0.2

−0.1

0.0

0.0

Deposition (m)Erosion (m)

0.1

0.2

0.3

0.4

0.5

Deposition (m)2(e)

Shoreline
se3510se4005(f)

Shoreline
se3510se400510Erosion (m)

0
−1
−2
−3

Onshore−4−0.70

Offshore
−0.35

0.00

0.35

0.70

Shore-normal distance (km)Fig. 9 Results of the sediment transport simulation using the source models, se3510 (a and b) and se4005 (c and d). Morphological changes(negative and positive values indicate erosion and deposition, respectively) around the Suijin-numa pond are displayed. Black lines represent
post-tsunami 0 m contours for each scenario. (e) Deposition trend of these scenarios along the transect are shown in (a–d) as a white line. (f)Erosion trends along the same transect as (e)With a larger precedent receding wave, nearshore seafloor is exposed extensively and the main wave with alonger period exerts a persisting bottom shear stress on

the seabed, resulting in greater sediment erosion andentrainment into the flow.

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

Page 14 of 20

Fig. 10 Waveforms recorded on a virtual tide station, SJN1. Along with scenarios se3510 and se4005, a waveform associated with the source modelof Satake et al. (2013) is shown as a reference. Black and gray arrows indicate the duration of the main wave associated with hypothetical models(se3510 and se4005) and the reference simulation, respectively

Considering the minor contribution of seafloor sediments (Abe et al. 2020), simulations with a lower Psea
value are preferable. Thus, the model se3510 better
explains the sediment source of the 2011 Tohoku-oki
tsunami deposits in the study area. Note that Psea of the
hypothetical models is much higher than that of the reference simulation (Psea = 3%). The hypothetical models
may have a limitation on the reproducibility of the waveforms and resulting Psea due to their insufficient spatial
and temporal resolution of the slip distribution.
The above approach to constrain the tsunami source
model based on Psea relies on the assumption that differences between beach and shoreface deposits can be
identified and fractions of respective deposits can bequantified. Distinguishing the deposits based on geological proxies is difficult because the differences may not be
evident in general cases as the littoral drift system mixes
and homogenizes these deposits. Therefore, to apply Psea
for general cases, a new methodology to quantify fractions of beach and shoreface deposits is required.
5.3 Comparison with existing source models

Figure 11 compares the slip models inferred from thisstudy and previous studies. Iinuma et al. (2012), Satake
et al. (2013), and Yamazaki et al. (2018) estimated theslip distribution based on geodetic inversion, tsunami
inversion, and a combination of iterative forward modeling of tsunamis and inversion of teleseismic P-waves,respectively. The fault model of Yamazaki et al. (2018)
represents a self-consistent slip that can explain seismic

and tsunami waveforms and tsunami inundation. In thisstudy, the slip distribution estimated based on the tsunami deposits (se3510; Fig. 11a) showed a larger slip on
S4 near the trench axis than in other models. Conversely,
the slip amount on the landward S9 was consistent withthat in the other models. Although the slip amount issmaller than that near the trench axis, a “deep large slip”(Satake et al. 2013), shown as subfaults surrounded by athick frame in Fig. 11, is necessary to explain the deposit
volume in the study area. This was consistent with theresults of Satake et al. (2013), who indicated the significant contribution of the “deep large slip” to the extended
inundation in the Sendai Plain.
Satake et al. (2013) also reported that the “shallowhuge slip” near the trench axis does not influence theinundation in the Sendai Plain. In fact, the tsunami
sediment transport simulation based on the source
model proposed by Satake et al. (2013) without the“shallow huge slip” can explain not only the observed
inundation but also deposit volume (Additional file 1:
Fig. S3). Here, the question that arises is whether thedeposit-based fault model se3510 was inconsistent
with the findings of Satake et al. (2013). In this study,
the assumption of different ranges of slips on deep
(0–10 m) and shallow (0–40 m) subfaults was used forslip estimation, based on the slip distributions of the2011 Tohoku-oki earthquake determined by Hayashi
and Koshimura (2012), which attributed larger slips
to the shallow subfaults. If the ranges of the slip to betested are not constrained based on the existing fault

Masuda et al. Progress in Earth and Planetary Science

140°

142°

144° 140°142°(2022) 9:65

144°

40°

40°

38°

38°

36°

36°

40°

40°

38°

38°

36°

36°
100 km

0

10

20

30

40

50

Slip (m)Fig. 11 Slip distribution models of the 2011 Tohoku-oki earthquake.
Red frames represent the projected shapes of subfaults S4 and S9.
Plate boundary was retrieved by Iwasaki et al. (2015). a Source model
se3510. b TP-MOD based on iterative forward tsunami simulationand teleseismic inversion by Yamazaki et al. (2018). c Slip distribution
inferred by tsunami waveform inversion (Satake et al. 2013).
Thick-framed subfaults belong to the “deep slip”; other subfaults
belong to the “shallow slip.” d Slip distribution proposed according toan inversion of geodetic observation by Iinuma et al. (2012)

model, the balance of the estimated slip on the deepand shallow subfaults may differ. Thus, in this study,
the empirical assumption of the slip range may haveresulted in the selection of the slip distribution with alarger shallow slip. In addition to the assumption about
the maximum slip, the subfault size might explain
this conflict. Here, only a seaward half of subfault S4
belongs to the “shallow slip” domain defined by Satake
et al. (2013). A combination of narrow and wide subfault in shallow and deep parts, respectively (an example can be found in Ioki and Tanioka 2016), may be
more suitable for this kind of discussion.
Compared with se3510, se4005 had a slip distribution that was larger on S4 and smaller on S9. Thisimplies that the larger slip on the landward S9 (se3510)

Page 15 of 20

contributed to the smaller receding wave (Fig. 10). A
huge slip near the trench axis caused significant subsidence of the sea floor and the sea surface landwardof the rupture area (Satake and Tanioka 1999). However, with a larger slip on the deep portions of the plateinterface, such negative sea surface displacement isnegated due to larger crustal uplifting directly below.
Thus, the smaller amount of marine-origin materials
in the onshore tsunami deposit by the se3510 source
model can be associated with the larger slip on Subfault
S9 and the resulting smaller receding wave near thecoastline.
Ignoring the contribution of other subfaults might affectthe slip amounts on S4 and S9. In fact, S3, which is equivalent to the segment with the largest slip during the Tohokuoki earthquake, was located directly north of S4. Although
the sensitivity of the fault slip to the deposit volume in the
study area was low, a huge slip (over 30 m) on S3 similar toprevious models may affect the sediment erosion and deposition in the study area and reduce the slip amount on S4.
However, without any prior knowledge of the slip distribution, it may be difficult to assume such a distant large slip
in a paleoseismic event. The paleotsunami source model aswell as se3510 (Fig. 11a) can be incomplete if reconstruction relies on spatially limited tsunami deposit data.
It is noteworthy that se3510 is a solution based on several assumptions from the result of the sensitivity analysis and known general along-dip slip distribution. In thisstudy, the optimal solution seemed not to be determined
without any a priori assumptions because the geological data for tsunami source modeling are quite limited.
Two problems in this study, the incomplete spatial extent
of the reconstructed source and strong dependency
on the assumptions, may be conquered by using extensive geological data along the tsunami-prone coast. The
estimation of the slip on each subfault can also be moreaccurate by properly solving trade-off relationships
among all subfault slips in the source region. Thus, forbetter deposit-based tsunami source modeling, the availability of tsunami deposit data from a wide area along thetsunami-prone coast is essential.
5.4 Uncertainty in deposit‑based source estimation

Various factors, such as inputs and model setups, associated with tsunami sediment transport modeling canintroduce uncertainties in the numerical simulations(Jaffe et al. 2016; Sugawara 2019). The results of the simple sensitivity analysis (Table 1) showed the fluctuatedsimulated deposit volume with changes in grain size. In
general, the grain size of the sediment source is difficult
to constrain despite its importance in the simulations.

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

Figure 12 demonstrates that the uncertainty in grainsize setting propagated via the numerical simulation to
the estimated fault slip. With a fixed fault slip, the deposit
volume was ~ 15,000 ­m3 smaller for every 0.05 mmincrease in the grain size. Such a change was nearly
equivalent to the variations in the deposit volume, due
to a decrease in the fault slip on S4 by ~ 4.3 m with thefixed grain size. Although it is just an example, this comparison indicated that the uncertainty due to sedimentgrain size should be carefully considered in paleotsunami
source estimation.
5.5 Implications for paleotsunami studies

Deposit-based source modeling requires the accurate
simulation of tsunami deposit formation at surveyedsites. The bottom deposits of coastal ponds and lakes
are important candidate sites for field surveys in paleotsunami research due to the high preservation potentialof tsunami deposits (Sawai et al. 2008; Furumura et al.
2011; Kempf et al. 2017). Previously, the bottom sediments of the Suijin-numa pond have been surveyed toinvestigate the paleotsunami history (Sawai et al. 2008).
Thus, the successful simulation of lake-bottom tsunami
deposit formation will greatly contribute to the assessment of tsunami magnitude. Despite this importance,
the simulated thickness distribution in the Suijin-numa
pond was significantly different from the observed distribution even in the reference simulation (Fig. 2). This

Fig. 12 Comparison of changes in the deposition volume withvariations in slip on S4 (with fixed slip of 10 m on S9) and grain size.
Dashed lines indicate linear approximations of the data shown in thesame color

Page 16 of 20

could be caused by the limitation of 2DH hydrodynamic
simulation (TUNAMI-N2), which cannot simulate threedimensional flow and the resulting sedimentary process.
Thus, this limitation will hinder the application of such
numerical models in paleotsunami source estimation
based on lake-bottom tsunami deposits.
Regarding the paleotsunami source modeling, wehave more difficulties than in this study. Available datafor inputs, such as topography, land condition, and initial tide level, can be poorly constrained. Moreover,post-depositional processes can modify the thickness oftsunami deposits, leaving them unidentifiable near the
distribution limit (Szczuciński 2012; Spiske et al. 2020).
Even if deposits can be identified, the consolidation oftsunami deposits can decrease the deposit thickness andvolume and cause an underestimation of the slip. These
uncertain inputs, boundary conditions, and constraints
hinder the accurate estimation of a paleotsunami source.
Thus, the uncertainty in the estimated source should bedemonstrated even though the estimation appears to be
successful.
The combination of forward and inverse models (i.e.,hybrid modeling; Sugawara et al. 2014a; Jaffe et al. 2016)is a promising approach for deposit-based tsunami
source modeling. Inverse models of tsunami-induced
sediment transport (Jaffe and Gelfenbaum 2007; Tangand Weiss 2015; Naruse and Abe 2017) are useful to
extract tsunami flow conditions, such as flow velocity,
inundation depth, and concentration of suspended sediments, from sedimentary features of tsunami deposits.
Inverse modeling is mainly a contrasting approach to forward modeling of tsunami-induced sediment transport(e.g., TUNAMI-STM), whereas hybrid modeling utilizes
both models to complement each other; for example, forward simulation can be used to validate an assumption of
the inverse model and inverse calculations can be used toestimate the hydraulic constraint of the forward model.
Although the methodology is not yet established, thisapproach might be effective to mitigate the uncertainty ofthe tsunami source and the accurate estimation thereof.
Furthermore, considering the uncertainties of tsunami
deposit characteristics, using the deposit thickness orvolume as the only constraint of source estimation cancreate problems. Although difficult to implement, including constraints from various kinds of sedimentary data
is a possible solution. In addition to thickness, volume,and sediment source, grain-size distribution of tsunami
deposits may provide clues on the characteristics of thetsunami source (Gusman et al. 2018). Tsunami source
modeling with sediment transport simulations has thepotential to fully utilize such sedimentary data. Other
paleoseismological information, such as coseismic crustal deformation and historical records, can be consideredMasuda et al. Progress in Earth and Planetary Science(2022) 9:65

as additional constraints (Sugawara et al. 2019; Dourado et al. 2021). Moreover, seismological scaling laws
(Murotani et al. 2013; Skarlatoudis et al. 2016), which
are empirical relationships between fault parameters, areuseful to construct hypothetical fault models (Minamidate et al. 2022). Such additional constraints should be
examined from the perspectives of both geology andnumerical modeling.

6 Conclusions
This study examined the potential and limitations of tsunami source estimation based on the 2011 Tohoku-oki
tsunami deposits collected from the southernmost part of
the Sendai Plain. The tsunami sediment transport model
was employed to fully utilize the observed sedimentarydata. The sensitivity analysis conducted using single subfault models revealed that coseismic slips on only twoout of ten subfaults could be reconstructed based on thetsunami deposits. We initially examined the hypothetical source model by comparing the tsunami deposit volumes. Two possible source models passed the selection
and were further investigated. Based on the sedimentsource information, the source model, se3510, with slipsof 35 m and 10 m on the shallow and deep parts of thefault, respectively, was preferred. Although the slip near
the trench axis was larger than that of the previously proposed models, the results of source modeling showed thatthe slip distribution of the triggering earthquake could be
estimated reasonably based on the tsunami deposits. Notethat the optimal model se3005 relies on several assumptions to compensate poor spatial extent of geological data.
The application of the sediment transport simulations
facilitated the direct comparison of the calculated sedimentary information (e.g., deposit thickness, volume,and source) with sedimentological observations andinterpretation. In particular, the tsunami deposit volume was utilized as the primary constraint of source
modeling, and the corresponding observation data
were suitable for comparison. We also used the sediment source information, which was obtained using thesediment transport model as an additional constraint.
Based on the trial-and-error approach and the additional constraint, an overestimated but comparable slipon the specific region of the megathrust was deduced.
This result suggested that, even with high-quality data,
the precise estimation of the slip based on tsunami
deposits was difficult because of the dependence on thedeposits in a limited area. Further, the entire depictionof a giant interplate earthquake from tsunami deposits
can be time-consuming because it requires the compilation of sedimentary data from a wide area of the devastated coast and trial-and-error simulation throughout

Page 17 of 20

the dizzying array of hypothetical scenarios. However,the uncertainties of sedimentary data and the simulated
result will make such attempts difficult. Thus, using
additional constraints other than the deposit thickness
or volume is one solution to improve the accuracy of
paleotsunami source modeling.
Abbreviations
2DH: Two-dimensional horizontal; DEM: Digital elevation model; LiDAR: Lightdetection and ranging; STM: Sediment transport model; TP: Tokyo Peil.

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​022-​00527-x.
Additional file 1: Fig. S1. Comparison of the scatter plot of the observed
and simulated tsunami heights with and without the calibration of theboundary condition for the computational Domain R6. The original (notcalibrated) tsunami source model is proposed by Sateke et al. (2013).
Observational data were retrieved from Mori et al. (2012). The black line
indicates a perfect agreement. Fig. S2. Characteristics of the sedimentary
results of the simulation using the source model of Satake et al. (2013)
without considering the calibration of the boundary condition to thecomputational Domain R6. a Distribution of deposition. The blue line
shows the limit of the simulated inundation area, which was narrower
than that after calibration (Fig. 2c). b Shore-normal distribution of deposit
thickness with and without calibration. The thickness on most sites
increased with the calibration. Fig. S3. Results of the sediment transport
simulation using the deep slip model (subfaults on 2–4 columns definedin Satake et al. 2013; thick-framed subfaults in Fig. 10). a Distributionof erosion depth. b Distribution of deposition. Blue line represents thesimulated inundation limit. Black dashed line represents the actual inundation limit reported by Haraguchi and Iwamatsu (2013). c Comparisonof deposition volume. Even though there is no positive calibration of flux,
the result from the deep slip model exceeds that from original model withthe calibration (composite of deep and shallow slips).
Acknowledgements
We would like to thank the two anonymous reviewers and the associate
editor Masaki Yamada for their constructive comments which improved thismanuscript. DEMs used for constructing bathymetric and topographic data
for numerical simulations were provided by the Geospatial Authority of Japan.
The plate models by Iwasaki et al. (2015) were constructed using topographic
and bathymetric data by the Geospatial Information Authority of Japan(250 m digital map), Japan Oceanographic Data Center (500-m mesh bathymetry data, J-EGG500, http://​www.​jodc.​go.​jp/​jodcw​eb/​JDOSS/​infoJ​EGG_j.​html),
and Geographic Information Network of Alaska, University of Alaska (Lindquist
et al. 2004). The Generic Mapping Tools version 6 (Wessel et al. 2019) was
employed for data handling and constructing figures.
Author contributions
HM conducted numerical analyses and interpreted the results. DS proposed
the topic, conceived, and designed the study and assisted in the resultinterpretation. TA and KG provided the observed sedimentary data and collaborated with the corresponding author in the writing of the manuscript. All
authors read and approved the final manuscript.
Funding
This research was supported partly by the collaborative research project by
the Shimizu Corporation and Tohoku University (FY2020–FY2022).
Availability of data and materials
The datasets used and/or analyzed during the current study are available fromthe corresponding author upon reasonable request.

Masuda et al. Progress in Earth and Planetary Science(2022) 9:65

Declarations
Competing interests
The authors declare that they have no competing interests.
Author details
1
Department of Earth Science, Graduate School of Science, Tohoku University,
6‑3 Aramaki Aza‑Aoba, Aoba‑ku, Sendai, Miyagi 980‑8578, Japan. 2 International Research Institute of Disaster Science, Tohoku University, 468‑1 Aramaki
Aza‑Aoba, Aoba‑ku, Sendai, Miyagi 980‑8572, Japan. 3 Geological Surveyof Japan, National Institute of Advanced Industrial Science and Technology, 1‑1‑1 Higashi, Tsukuba, Ibaraki 305‑8567, Japan. 4 Department of Earthand Planetary Science, The University of Tokyo, 7‑3‑1 Hongo, Bunkyo‑ku,
Tokyo 113‑0033, Japan.
Received: 12 July 2022 Accepted: 27 November 2022

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