- Research Letter
- Open Access

# Tsunami source and inundation features around Sendai Coast, Japan, due to the November 22, 2016 *M*_{w} 6.9 Fukushima earthquake

- Bruno Adriano
^{1}Email authorView ORCID ID profile, - Yushiro Fujii
^{2}and - Shunichi Koshimura
^{1}

**5**:2

https://doi.org/10.1186/s40562-017-0100-9

© The Author(s) 2018

**Received:**12 September 2017**Accepted:**29 December 2017**Published:**12 January 2018

## Abstract

The tsunami source of the 2016 Fukushima Earthquake, which was generated by a normal faulting earthquake mechanism, is estimated by inverting the tsunami waveforms that were recorded by seven tide gauge stations and two wave gauge stations along the north Pacific coast of Japan. Two fault models based on different available moment tensor solutions were employed, and their locations were constrained by using the reverse tsunami travel time from the stations to the epicenter. The comparison of the two fault slip models showed that the fault model with a strike = 49°, dip = 35°, and rake = −89° more accurately simulated the observed tsunami data. This fault model estimated a fault area of 40 km \(\times\) 32 km. The largest slip was estimated as 4.66 m at a 6.09 km depth, larger slips also concentrated between depths of 6.06 and 10.68 km, and located southwest of the epicenter. Assuming a rigidity of \(2.7\times 10^{10}\) N/m\(^2\), the estimated moment magnitude was \(3.35\times 10^{19}\) Nm (equivalent to *M*_{w} = 6.95). In addition, a comparison of nonlinear tsunami simulations using finer bathymetry around Sendai Coast verified that the above fault slip model could better reproduce the tsunami features observed at Sendai Port and its surroundings. Finally, we analyzed the nonlinear tsunami computed from our best fault slip model. Our simulations also corroborated the height of the secondary wave amplitude observed at Sendai Port, which was caused by the reflected tsunami waves from the Fukushima coast, as described in previous studies. Furthermore, we found that the initial positive wave recorded inside Sendai Bay resulted from the addition of the initial incoming wave and the tsunami wave reflected off Sendai Coast, between Natori River and Sendai Port.

## Keywords

- The 2016 Fukushima earthquake
- Tsunami source inversion
- Tsunami numerical modeling

## Background

Considering that before the 2011 Tohoku Earthquake, the seismic activity on the northern Pacific coast of Japan was relatively low, and since the 2011 event the seismic activity has not also reduced to pre-quake levels, this earthquake was considered an aftershock of the 2011 Tohoku-Oki Earthquake (Rathi 2016; Aoki and Kikuchi 2016). The moment tensor solution was estimated by several agencies, including the Global CMT Catalog project, the USGS, and the National Research Institute of Earth Science and Disaster Resilience (NIED). All solutions proposed a normal faulting mechanism for this earthquake. The associated moment magnitude, however, differed for each solution. For instance, the GCMT solution estimated a moment magnitude of \(3.18\times 10^{19}\) Nm (*M*_{w} = 6.9), with a focal depth at 12.0 km; the USGS’s solution estimated a moment magnitude of \(2.48\times 10^{19}\) Nm (*M*_{w} = 6.90), with a focal depth at 9.0 km; and the NIED’s solution estimated a moment magnitude of \(3.47\times 10^{19}\) Nm (*M*_{w} = 7.0; *M*\(_\text{JMA}\) = 7.4), with a focal depth at 11.0 km. The relative differences of the estimated solutions indicates that further studies are needed to better constrain its value. The NIED also evaluated the ground shaking recorded in the strong-motion seismographs network KiK-net and reported a maximum ground pick acceleration (PGA) of 256 cm/s^{2} in Iwaki station, Fukushima Prefecture.

The tsunami generated after the 2016 Fukushima earthquake was recorded at several coastal tide gauges and offshore buoys located along the Pacific coast of Japan (Fig. 1a). At stations located south from the epicenter (Onahama, Oarai, and Choshi stations), the maximum tsunami amplitude was recorded during the first cycle of the tsunami waveform; in contrast, the maximum recorded amplitude at almost all stations located north from the epicenter (Miyagi Central, Sendai Offshore, Sendai Port, Ayukawa, and Ofunato) was recorded during the second cycle of the tsunami waveform. The maximum amplitude of the southern stations was 0.6 m (Onahama stations), belonging to the first wave cycle. At the Sendai New Port station, the maximum amplitude was approximately 1.68 m, belonging to the second wave cycle, and the amplitude of the second wave cycle was 0.6 m (Fig. 6). The water level changes due to the intrusion of the generated tsunami into Sunaoshi River was also measured by the river basin monitoring station located close to Yawata bridge (Fig. 1e) (Suppasri et al. 2017).

Tsunami waveform records have been proven to contain reliable information for retrieving the slip distribution of the earthquake source, especially for earthquakes generated along the subduction zones (Satake and Tanioka 1999; Fujii and Satake 2006, 2013; Fujii et al. 2011; Gusman et al. 2015; Heidarzadeh and Satake 2015; Adriano et al. 2016; Yoshimoto et al. 2016). Furthermore, detailed tsunami simulations using high-resolution bathymetry and topography data provide valuable information to specifically analyze tsunami inundation features and thereby validate the estimated tsunami sources (Kakinuma et al. 2012; Fukutani et al. 2016; Adriano et al. 2016; Heidarzadeh et al. 2017). Here, to improve the tsunami source estimate and further analyze the observed tsunami features around Sendai Coast, we first estimate the fault slip distribution of the tsunami source using the moment tensor solution proposed by GCMT and USGS as a reference. We conducted a tsunami waveform inversion analysis of the tsunami signal recorded at seven tide gauges and two wave gauge stations. Finally, the nonlinear tsunami simulation, which uses a finer bathymetry around Sendai Bay, computed from the best fault slip distribution is analyzed to further understand the observed tsunami features around Sendai Coast.

## Data

### Tsunami waveform data

List of stations used for tsunami waveform inversion

Station | Longitude | Latitude | Source | A.T. (min.) |
---|---|---|---|---|

(°E) | (°N) | |||

Ofunato | 141.75 | 39.02 | JMA | 49 |

Ayukawa | 141.51 | 38.30 | JMA | 35 |

Sendai Port | 141.02 | 38.27 | JMA | 63 |

Sendai Offshore | 141.07 | 38.25 | NOWPHAS | 57 |

Miyagi Central | 141.68 | 38.23 | NOWPHAS | 30 |

Soma | 140.96 | 37.83 | GSI | 46 |

Onahama | 140.89 | 36.93 | JMA | 29 |

Oarai | 140.57 | 36.31 | JMA | 50 |

Choshi | 140.86 | 35.74 | JMA | 45 |

### Bathymetry data

All computational domains for nonlinear tsunami modeling are shown in Fig. 1. The grid size varies from 10 to 810 m of spatial resolution. The bathymetry data used in the largest domain (Fig. 1a) are constructed from the 12 arc-s grid interval J-EGG500 (JODC-Expert Grid data for Geography—500 m) published by the Japan Oceanographic Data Center. These data were resampled to construct an 810 m grid size domain. We also combined the local bathymetry data provided by the Miyagi Prefecture office to create the other domains. The grid sizes for domains (b), (c), and (d) are 270, 90, and 30 m, respectively. Finally, the bathymetry data around Sendai Port and Sendai Plain, domain (e) in Fig. 1, were based on 5-m spatial resolution topography and a bathymetry dataset for the period after the 2011 Tohoku tsunami and before the 2016 Fukushima earthquake that was developed by Tohoku University. This dataset also includes two breakwaters located offshore of Sendai Port (Fig. 1e). The final grid size for the last domain is 10 m. For the linear tsunami simulation, an additional computation domain was prepared by merging and resampling all previous five domains into 3 arc-s of the grid size domain. In this last domain, for proper tsunami modeling at coastal points, the current coastal morphology around Choshi, Oarai, Onahama, Soma, Ayukawa, and Ofunato stations were manually drawn. Here, using the latest satellite images available in Google Earth, we include offshore breakwaters and seawalls that were damaged or destroyed during the 2011 Tohoku tsunami.

## Methods

### Tsunami numerical modeling

There are two tsunami models used in this study. The first is Tohoku University’s numerical analysis model, which was developed to investigate far-field tsunamis and is based on a spherical coordinate system and constant grid (TUNAMI-F1) model (Imamura et al. 1996), and the linear shallow water equations. This model was used to calculate the Green’s function in the tsunami waveform inversion analysis. These simulations were computed using the largest domain (Fig. 1a) with a 3 arc-s grid size. The computational time step was set to 0.2 s to satisfy the stability condition, and the total computation time of tsunami propagation was 3 h.

The second tsunami numerical model used is the TUNAMI-N2 version for near-field modeling, which is based on the nonlinear shallow water equations and a Cartesian coordinate system (Imamura et al. 1996). Here, to reduce the computational cost we constructed a nested-grid system, as shown in Fig. 1a–e, of five domains with grid size varying from 10 up to 810 m (Adriano et al. 2016), as described in the previous section. The roughness coefficient was set equal to 0.025 (Kotani et al. 1998) for all computational domains. The computational time step was set to 0.3 s, with a total computation time of tsunami propagation of 6 h. Details of the scheme for nonlinear tsunami modeling are described in Adriano et al. (2013, 2016).

### Fault models

*M*

_{w}6.9 earthquake according to Papazachos et al. (2004)s' scaling law. Thus, we set a tsunami source of 40 km \(\times\) 32 km (Fig. 2). The assumed fault area is also consistent with the fault area of 1347.8 km\(^2\) given by Murotani et al. (2013).

At the time of writing this paper, the 2016 Fukushima Earthquake has been investigated by different agencies; as a result, several moment tensor solutions have been associated with this event, including those of the USGS (WCMT), Global CMT project, NIED (based on F-net system), and JMA (CMT and WCMT). Gusman et al. (2017) conducted a sensitivity analysis of some of the previous solutions by computing synthetic tsunami waveforms based on single-fault models of different dimensions and depths. They found that faults with a 12-km depth better fit the observed tsunami waveform. Furthermore, fault models with southeast deepening direction of the moment solution can reproduce the observed tsunami waveform relatively well. The latest finding can be verified by the post-event survey conducted by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) around the fault area (available at http://www.jamstec.go.jp/j/about/press_release/20170301/), where 1–2 m recent surface cracks were observed, indicating a northeast–southwest fault orientation.

Fault models and estimated slip for each model

No. | GCMT (NP1) | USGS (NP2) | ||||||
---|---|---|---|---|---|---|---|---|

Lon. | Lat. | Depth | Slip | Lon. | Lat. | Depth | Slip | |

(°E) | (°N) | (km) | (m) | (°E) | (°N) | (km) | (m) | |

1 | 141.24 | 37.26 | 1.50 | 0.00 | 141.27 | 37.22 | 1.50 | 0.00 |

2 | 141.31 | 37.30 | 1.50 | 1.92 | 141.33 | 37.27 | 1.50 | 2.06 |

3 | 141.38 | 37.35 | 1.50 | 1.59 | 141.39 | 37.33 | 1.50 | 1.66 |

4 | 141.44 | 37.40 | 1.50 | 0.70 | 141.45 | 37.38 | 1.50 | 0.57 |

5 | 141.51 | 37.44 | 1.50 | 0.00 | 141.51 | 37.43 | 1.50 | 0.00 |

6 | 141.29 | 37.21 | 6.09 | 0.00 | 141.31 | 37.19 | 7.54 | 0.22 |

7 | 141.36 | 37.26 | 6.09 | 4.66 | 141.37 | 37.24 | 7.54 | 3.38 |

8 | 141.42 | 37.30 | 6.09 | 4.29 | 141.43 | 37.30 | 7.54 | 5.18 |

9 | 141.49 | 37.35 | 6.09 | 0.00 | 141.50 | 37.35 | 7.54 | 0.00 |

10 | 141.56 | 37.40 | 6.09 | 0.38 | 141.56 | 37.40 | 7.54 | 1.32 |

11 | 141.34 | 37.17 | 10.68 | 3.70 | 141.36 | 37.16 | 13.58 | 4.07 |

12 | 141.41 | 37.21 | 10.68 | 0.54 | 141.42 | 37.21 | 13.58 | 0.00 |

13 | 141.47 | 37.26 | 10.68 | 1.39 | 141.48 | 37.26 | 13.58 | 0.00 |

14 | 141.54 | 37.31 | 10.68 | 0.00 | 141.54 | 37.32 | 13.58 | 0.00 |

15 | 141.61 | 37.35 | 10.68 | 0.00 | 141.60 | 37.37 | 13.58 | 0.00 |

16 | 141.39 | 37.12 | 15.27 | 0.21 | 141.40 | 37.13 | 19.61 | 0.00 |

17 | 141.45 | 37.17 | 15.27 | 0.00 | 141.46 | 37.18 | 19.61 | 0.00 |

18 | 141.52 | 37.22 | 15.27 | 0.00 | 141.52 | 37.23 | 19.61 | 0.00 |

19 | 141.59 | 37.26 | 15.27 | 0.00 | 141.58 | 37.29 | 19.61 | 0.00 |

20 | 141.66 | 37.31 | 15.27 | 0.00 | 141.64 | 37.34 | 19.61 | 0.00 |

### Tsunami source inversion

The tsunami waveform inversion analysis is based on the methodology proposed by Satake (1987). This methodology has been proven to be sufficiently powerful to estimate the fault slip distribution of a tsunamigenic earthquake, considering that most of the earthquake source occurs beneath the ocean bottom, particularly in subduction zones (Satake and Tanioka 1999; Fujii and Satake 2006; Adriano et al. 2016; Gusman et al. 2017). We construct the Green’s functions using the linear tsunami propagation from each sub-fault, assuming 1 unit slip. The initial seafloor deformation is calculated using a static deformation of a rectangular dislocation model (Okada 1992). In addition, the effect of the co-seismic horizontal displacement, in the region of steep bathymetric slopes (Tanioka and Satake 1996), is included. The tsunami amplitudes recorded at the offshore stations are approximately ten times smaller than those recorded at coastal gauges. To ensure equality on the tsunami amplitudes between the coastal tide gauge stations and the offshore wave gauge stations, a weight factor of 10 was applied to the offshore stations (Fujii et al. 2011). Furthermore, to avoid incorporating nonlinear components from the waveforms at coastal stations, we utilize only the first wave cycle of the synthetic and observed tsunami waveforms. The number of sub-faults satisfies the known–unknown variables condition in the inversion methodology described by Satake (1987). The slip of each sub-fault is estimated using the non-negative least square method, and its corresponding error is calculated using the jackknife method (Fujii and Satake 2006, 2007).

### Validation of tsunami source

To evaluate the accuracy of each fault model for reproducing the inundation features around Sendai Port, we conduct nonlinear tsunami simulations using finer bathymetry data with 10 m of spatial resolution. The tsunami waveform recorded at Sendai New Port station, located inside Sendai Bay (Fig. 1e), was used for validation. In addition, the monitoring system of the river basin administered by the Miyagi Prefecture Government recorded the water level at the Sunaoshi River stations (Miyagi Prefecture Government 2016). This station is located near Yawata bridge (Fig. 1e), and the water level was recorded with 1 h of sampling. The first 6 h of the time series of the water level was used to evaluate the accuracy of the fault models. The performance of each fault model on recreating the tsunami data was assessed using the normalized root mean square error (NRMSE) (Heidarzadeh et al. 2016).

## Result and discussion

### Fault slip distribution

#### Fault model based on GCMT solution

*M*

_{w}= 6.95), which is 5% larger than that proposed by GCMT (\(3.18\times 10^{19}\) Nm). The computed seafloor deformation from the slip model generates a maximum subsidence of approximately 1.22 m and uplift of 0.10 m (Fig. 3b). Because of the small dip angle, part of the uplift field is located to the east of the fault area. On the other hand, as described by Gusman et al. (2017), the location and dimension of the subsidence deformation are consistent with underwater 1–2 m surface cracks surveyed by JAMSTEC (Fig. 3c).

In general, the synthetic and observed tsunami waveforms are consistent at most of the stations (Fig. 3c), especially at those located less than 1 arc-degree away from the epicenter. For instance, in the case of Ofunato station (northernmost location) the modeled tsunami arrives slightly slower. The first cycle of the tsunami signal, however, is well reproduced by the slip model. At Ayukawa station, the arrival time, first cycle, and later phases of the tsunami waveform are also generally consistent with the observed data. Although nearly the entire phase of the tsunami signal is relatively well explained at the Sendai Port station, the amplitude of the first negative and positive waves are smaller than the observed ones. In contrast, at the Sendai Offshore and Miyagi Central offshore stations, the synthetic signals are consistent with their corresponding observations. For the Soma, Onahama, and Oarai stations, the first cycle also fits accordingly with the observed data, and the amplitudes are almost perfectly reproduced. The amplitudes in the second cycle, however, are relatively smaller than the recorded data. Finally, the waveform at Choshi station (southernmost location) is not accurately solved by the slip model. Nonetheless, the solutions at these stations are an improvement of previous inversion results (Adriano et al. 2017). The variance reduction obtained from the estimated slip model is approximately equal to 51.5%.

#### Fault model based on USGS solution

*M*

_{w}= 6.94), assuming a rigidity of \(2.7\times 10^{10}\) N/m

^{2}. This is 28% greater than the proposed USGS solution (\(2.48\times 10^{19}\)). The computed seafloor displacement also generates a larger subsidence of 1.12 m compared with the uplift displacement of 0.19 m (Fig. 4b). The magnitude of the subsidence area generated by this model are also consistent with the underwater surface cracks (1–2 m) found by JAMSTEC (Fig. 4c). Following the behavior of normal faulting events, the uplift region is located to the west of the fault area. This fact may indicate that the USGS model may perform better to reproduce the seafloor deformation due to the 2016 Fukushima tsunami.

The synthetic and observed tsunami waveform are also consistent at most of the stations (Fig. 4c). The synthetic waveform at Ofunato (northernmost location), Ayukawa, Soma, Onahama, and Oarai are well reproduced both in the initial phase and in the later phases, where the first negative and positive amplitudes and the arrival time fit notably well with the observed data. Similarly, at both of the offshore stations (Sendai Offshore and Miyagi Central), the synthetic and observed records are similar. Similar to the previous slip model, the modeled tsunami signal at the Sendai Port and Choshi stations cannot be well reproduced by the USGS-based slip model. The variance reduction obtained from the estimated slip model is approximately equal to 43.8%.

### Comparison of both slip models

In general, the slip distribution from both models shows similar patterns (Figs. 3a, 4a). The largest slip is estimated in the second-shallow fault row, with depths of 6.09 and 7.54 km for the GCMT- and USGS-based fault models, respectively. The slip from the USGS model, however, is almost 1.0 m greater than that from the GMCT model. This is because the depth differs between the sub-faults; in general, deeper sub-faults are associated with greater slip. The former is also observed in the sub-fault at depths of 10.68 and 13.58 km. The associated seafloor deformation also shows similar characteristics in the subsidence regions, with maximum displacements of approximately 1.20 m for both models. The uplift region, however, is located at different sections of the fault area (Figs. 3b, 4b); i.e., east in the GCMT model and west in the USGS model. These conditions are related to the dip angle, as steep angles generate the highest vertical displacement and gradual faults lead to expanded deformation (Satake and Tanioka 1999; Tanioka and Satake 1996). The small dip angle of the GCMT slip model generates an uplift field on the hanging wall (east of the fault plane).

### Comparison of tsunami features at Sendai Bay

### Analysis of the tsunami propagation around Sendai Bay

## Conclusion

We estimated the tsunami source of the 2016 Fukushima Earthquake, adopting two fault geometries based on the GCMT and the USGS moment tensor solutions. The slip distribution from both models was estimated using the tsunami signal recorded at seven tide gauge stations and two offshore wave gauges located on the north Pacific coast of Japan. We found that although both slip models could solve the recorded tsunami waveforms relatively well, the GCMT-based slip model (strike = 49°, dip = 35°, and rake = −89°) better explained the observed data at most of the stations. This slip model also accurately solved the later wave phases of the tsunami waveform that were not used for the waveform inversion. The inversion result yielded a fault with an area of 40 km \(\times\) 332 km extending southwest from the epicenter. The largest slip was estimated as 4.66 m at 6.09 km depth, while larger slips also concentrated between 6.06 and 10.68 km depth, located southwest of the epicenter. Assuming a rigidity of \(2.7\times 10^{10}\) N/m^{2}, the moment magnitude computed from the GCMT slip model was \(3.35\times 10^{19}\) Nm (equivalent to *M*_{w} = 6.95), which is slightly larger than that proposed by GCMT (3.18\(\times 10^{19}\) Nm). Using both slip models, we conducted a nonlinear tsunami simulation using high-resolution bathymetry data to analyze the tsunami propagation around Sendai Coast. It was found that the GCMT slip model accurately reproduced the tsunami waveform recorded at Sendai New Port (NRMSE = 0.686). The nonlinear simulation using the GCMT slip model also precisely reproduced the arrival time and amplitude of the second positive wave recorded inside Sendai Bay (amplitude = 1.65 m). The simulation using finer bathymetry data also verified the previous findings, which stated that the secondary positive wave, as observed at the station located north of the epicenter, was due to the reflection of the initial tsunami wave (negative polarity) after impacting the coastal region of Soma city. Finally, our simulations also highlight that the initial positive wave recorded inside Sendai Bay was the result of the addition of the initial incoming wave and the reflected tsunami wave from Sendai Coast, between Natori River and Sendai Port.

## Declarations

### Authors' contributions

BA conducted the data analysis and solutions, and wrote the major portion of the manuscript. YF and SK supervised the proceeding of the analysis, and helped writing the manuscript. All have substantial contributions to the completion of the study. All authors read and approved the final manuscript.

### Acknowledgements

This research was supported by the Japan Society for the Promotion of Science (JSPS) under the Project: Fusion of Real-time Simulation and Remote Sensing for Tsunami Damage Estimation to Latin America (JSPS-Grant: P16055), the JST CREST (Grant number JPMJCR1411), and the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of JAPAN.

### Competing interests

The authors declare that they have no competing interests.

### Consent for publication

Not applicable.

### Ethical approval and consent to participate

Not applicable.

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## Authors’ Affiliations

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