Performance of uniform and heterogeneous slip distributions for the modeling of the November 2016 off Fukushima earthquake and tsunami, Japan
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Keywords2016 off Fukushima earthquake Tsunami Tsunami computation Uniform single-fault model Seismologically deduced finite fault slip model
finite fault slip model
the Global Centroid Moment Tensor Project
the Japan Meteorological Agency
the National Research Institute for Earth Science and Disaster Resilience
the US Geological Survey
VR for the first wave cycle
VR for the data period from the first wave arrival to 9:00 JST on 22 November 2016
After an earthquake of moment magnitude (Mw) 6.9 occurred beneath the Pacific Ocean off Fukushima Prefecture, Japan, on 22 November 2016 at 05:59 JST (UTC + 09:00), tsunamis were observed from Hokkaido in northern Japan to Wakayama Prefecture in western Japan. The maximum amplitude of the tsunami was 1.4 m at Sendai Port in Miyagi Prefecture (JMA 2016a). According to the Japan Meteorological Agency (JMA), this was a normal faulting event that occurred in the crust of the North American plate above its boundary with the Pacific plate (JMA 2016a). Its epicenter was about 50 km off the coast. Direct waves as well as reflected waves from the coast of Fukushima Prefecture were observed along the coast of Miyagi Prefecture (JMA 2017a). The distribution of aftershocks from this event defined an east-dipping fault plane (Headquarters for Earthquake Research Promotion 2016; Toda and Goto 2016).
Fujii and Satake (2016) and Gusman et al. (2017a) simulated the tsunami from this event using a single-fault model with a size of 20 × 10 km. Gusman et al. (2017a) and Adriano et al. (2018) estimated the tsunami source by inversion of the tsunami waveforms. Suppasri et al. (2017) conducted tsunami computations using 15-m-resolution topographic data and compared their results with data from field surveys. While the previous studies specified various wave source models, the question remains whether how the models obtained from the data limited to seismic waves could work, and how much performance a simple uniform single-fault model can have for a complicated model, which have heterogeneous slip distribution, in this event. It is important to discuss such models’ performances because it is sometimes desirable to obtain an earthquake source model to estimate tsunami waves with a simple process obtained with limited data from the viewpoint of tsunami prediction.
JMA utilizes an immediate centroid moment tensor (CMT) solution for an immediate tsunami forecast (Kamigaichi 2015). In that case, a uniform single-fault model is used since the slip distribution on the fault plane is unavailable in short duration soon after occurrence of the earthquake. Gusman et al. (2017a) pointed out that it was difficult to represent tsunami observation waveforms at all stations used for the tsunami source estimation with the single-fault model even if the size of the slip region of the model is adjusted. However, the optimum horizontal position of the model was not discussed in Gusman et al. (2017a). The distribution of slip on the fault plane, which is directly related to the area of tsunami generation, can be obtained as a finite fault slip model (FFM) estimated only with seismic waveforms (e.g., Yoshida et al. 2011; Iwakiri et al. 2014) as well as tsunami waveform inversion. Even though this event was relatively small, of magnitude 7 class, the FFM was obtained (JMA 2017b). So far, there have been studies on the use of FFM models for magnitude 8 class earthquakes to predict tsunami (e.g., Heidarzadeh et al. 2017; Gusman et al. 2017b). In those cases, the coastal grid intervals used for the tsunami computation were not so fine probably because of the long wavelength of tsunami waves considered. For the magnitude 7 class earthquakes, there have been few studies on the performance of the FFM by the comparison of tsunami waveforms.
In this study, we compared the performance of five models: the seismologically deduced single-fault model, the seismologically deduced FFM, the optimized single-fault model with tsunami waveform data, the FFM with horizontal shift, and the tsunami waveform inversion models of the previous studies. First, tsunami prediction by a single-fault model by CMT solution was compared with that by a seismologically deduced FFM. Next, an optimum single-fault model and the optimum FFM with horizontal shift were obtained using tsunami waveform data. Finally, the performances of models in this study were compared with that of the tsunami waveform inversion models of previous studies.
Methodology and data
East-dipping CMT solutions for the 22 November 2016 event from various institutions
Seismologically deduced FFM (finite fault slip model)
The seismologically deduced FFM models an earthquake fault as a set of small sub-faults, each with its own slip amount and slip history. The FFM used in this study is based on analysis of teleseismic body waves. The analysis starts by assuming a fault plane (often specified from the CMT solution) and an initial rupture starting point (typically the hypocenter). The parameters are estimated from the time-series waveform at seismic observation stations at teleseismic distances of 30°–100°. In this study, which assumed that a high-quality FFM is obtained in real time, we used the FFM released by the JMA (JMA 2017b) about 1 month after the earthquake. (The FFM gave Mw 7.2, which was larger than the Mw 6.9–7.0 given by CMT analyses.) The horizontal location of the FFM was not adjusted in use for the tsunami computation.
Tsunami observation data
Tsunami computation and bathymetry data
The tsunami computation relies on solving nonlinear long-wave equations with a staggered leapfrog finite-difference scheme. The TUNAMI code (e.g., Imamura 1995; Goto et al. 1997) was used, with input/output modifications by the Meteorological Research Institute. Crustal deformation at the seafloor is calculated by the method of Mansinha and Smylie (1971) on the basis of fault parameters set by a single-fault model or an FFM. The tsunami computation assumes that the seafloor deformation instantaneously displaces the sea surface to the same extent.
Measurement of amplitude and period
The amplitude and period of the first wave cycle were used to compare the computed and observed waveforms. Because the main effect of this normal faulting event was subsidence of the seafloor, we measured the pulling wave as the first wave cycle, ignoring the weak push wave that preceded it.
Waveform coincidence score
We determined VR on the basis of two different data lengths. In one (VR1), only the first wave cycle was compared, and in the other (VR2), the full waveform from the first wave cycle to 9:00 JST on 22 November 2016 was compared.
Tsunami computation by seismologically deduced single-fault model and FFM
Model fault parameters
Multiple faults (JMA 2017b)
C (optimized single-fault)
D (optimized FFM)
Model B shifted horizontally
Model B contains a region of strong local subsidence that does not appear in model A, which reflects a region of large slip on the fault plane (Fig. 3). A comparison of computed and observed waveforms shows that model B more closely approximated the observed amplitudes than model A (Fig. 4).
Optimization of single-fault model based on tsunami data
FFM with horizontal shift
We improved the horizontal fault location produced by the FFM to fit the observed tsunami waveforms through a grid search that first shifted model B horizontally at intervals of 0.05° and then refined the grid search at 0.01° intervals while keeping the slip distribution unchanged. The number of computations was 30 (6 × 5) for 0.05° and 80 (8 × 10) for 0.01°.
Comparison of single-fault models and FFMs
In the comparison with the single-fault model by scaling law (model A), the FFM (model B) is advantageous because it has the information of the slip distribution of the fault plane. In fact, the model B better represented the amplitude than model A (Fig. 5b). Tsunami amplitude is the most important factor for tsunami forecast. When only with seismic data, the FFM could narrow the range of forecast of the tsunami amplitude.
In the comparison between the optimum single-fault model (model C) and the FFM with horizontal shift (model D), the model C was superior to the model D with the smaller amplitude differences (Fig. 5b) and the VR values (Fig. 5d). The first reason for this is that the main slip region was concentrated in one place that the single-fault model could express. The second reason is that the slip distribution and slip amount of the FFM may have not been strictly represented due to estimation errors in the seismological analysis, while there was no limitation on fault parameters of the optimum single-fault model to fit the observed tsunami waveforms.
Uncertainty of horizontal location from seismic data
Comparison of models in this study and models from previous studies
We compared the results of the optimum single-fault model (model C) and the FFM with horizontal shift (model D) and the tsunami inversion models of previous studies (Gusman et al. 2017a; the GCMT model of Adriano et al. 2018). The Mw of the model C (Mw 6.95 [μ = 30 GPa]; Mw 6.92 [μ = 27 GPa]) almost agrees with Mw 7.0 (μ = 27 GPa) of Gusman et al. (2017a) and Mw 6.95 (μ = 27 GPa) of Adriano et al. (2018). It is also consistent with the Mw 6.9–7.0 from the CMT solutions. The normalized root-mean-square misfit (Heidarzadeh et al. 2016) for the model C was 0.75 for the same data period as the calculation of VR2, which is lower (better) than 0.85 in the prototype single-fault model (GCMT NP1) of Gusman et al. (2017a). The value only for Sendai Shinko was 0.47, which was also lower (better) than 0.686 in the tsunami inversion model of Adriano et al. (2018). From the comparison with the figures shown in the papers, the single-fault model in this study has almost equivalent performance with Gusman et al. (2017a) and Adriano et al. (2018). This means that a simple model has the almost same performance as a complicated model in this event. The first reason for this is that the main slip region on the fault plane was concentrated in one place in this event; therefore, the single-fault model could express it. The second reason may be that the horizontal position of small sub-faults is fixed beforehand in the tsunami waveform inversion, while the horizontal position of the single-fault model can be freely moved at 0.01° interval in this study.
Figure 9 shows the horizontal locations of the negative peak of the initial sea surface displacement for various models. The location of the model D in this study is close to that of Gusman et al. (2017a); and the location of the model C is close to that of Adriano et al. (2018). The location of the model C is located about 10 km south–southwest of that of the model D. The location of the model C would be more plausible since it can express the tsunami waveforms better than the model D (Fig. 5d). The location difference between the Gusman et al. (2017a) and the Adriano et al. (2018) may be due to the difference of the number of sub-faults and locations.
The seismologically deduced FFM has an advantage in terms of the information of slip regions of fault plane and was superior to the seismologically deduced single-fault model, especially in predicting amplitudes of tsunami. When only with seismic data, the FFM could narrow the range of forecast of tsunami amplitude.
The optimized single-fault model with tsunami data has performance to represent the observed tsunami waveforms at 13 stations well. It is better than the prototype single-fault model of Gusman et al. (2017a) and has the almost equivalent performance with the tsunami waveform inversion models of Adriano et al. (2018). The horizontal location of its negative peak of the initial sea surface displacement located close to that of Adriano et al. (2018) rather than that by the centroid location of CMT solution. In case the main generation region of the tsunami is concentrated in one place like this event, the tsunami wave can be expressed by a single-fault model by conducting the detailed grid search.
The centroid location of CMT solution and the absolute location of the FFM were not necessarily proper enough to get good agreement between observed and computed tsunami waves, while the Mw, the focal mechanism, the centroid depth of CMT solution, and the relative slip distribution of a seismologically deduced FFM were effective to represent tsunami wave reproduction. This may be due to difference in the propagation speeds between seismic wave and tsunami wave. Since this event occurred at the shallow depth, the speed of tsunami wave is particularly slow. To utilize the analysis of seismic waves in tsunami forecasting, careful attention should be paid to its horizontal uncertainty, especially when a tsunami occurs in shallow water.
KN proposed the initial idea of this study, conducted the analyses and drafted the manuscript. YH made suggestions about the organization and method of the article. HT supported the tsunami computation and the evaluation of the results. KF gave advice on using the FFM. YY gave advice on using the FFM and supported the manuscript preparation. AK made suggestions about the organization of the article and supported the manuscript preparation. All authors read and approved the final manuscript.
Records from tide gauge stations and GPS buoys were provided by the Port Authority of the Ministry of Land, Infrastructure, Transport and Tourism, the Geospatial Information Authority of Japan website (http://tide.gsi.go.jp/main.php?number=18), and the Japan Meteorological Agency. We used the TUNAMI code developed by Tohoku University as a tsunami computing simulation code, with input/output modifications by the Meteorological Research Institute. Topographical data were provided by the Cabinet Office Central Disaster Management Council, which are also available on the website (http://www.bousai.go.jp/kaigirep/chuobou/senmon/nihonkaiko_chisimajishin/index.html). Parts of the figures were created with Generic Mapping Tools (Wessel and Smith 1998). We thank Editor Stephen Bannister and two anonymous reviewers for their thorough reviews and valuable suggestions on improving the quality of this article.
The authors declare that they have no competing interests.
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