Tsunami Hazard Assessment for the Hokuriku Region, Japan: Toward Disaster Mitigation for Future Earthquakes Tsunami Hazard Assessment for the Hokuriku Region, Japan: Toward Disaster Mitigation for Future Earthquakes

In Japan, compared with the Pacific coast, the Japan Sea coast has low seismicity and has experienced very few occurrences of historical tsunami damage. These characteristics lead to some difficulties in the promotion of disaster prevention education, because the Japan Sea coast has not often been threatened by earthquakes and tsunamis. In our study, focusing on the Hokuriku region in Japan, we conducted a tsunami simulation and examined the resulting tsunami hazard map. Three potential faults of Mw7.6 earthquake were selected to generate the tsunami. In addition, we calculated these three events with Mw7.8, given the inherent uncertainty in source parameters. Aside from tsunami height, arrival time, inundation height, and inundation area, we calculated the seismic intensity and the liquefaction occurrence rate by simplified methods. Our results indicated that Suzu City in Ishikawa Prefecture, located in the northeastern part of the Noto Peninsula, has a relatively high potential risk of tsunami as well as strong motion and liquefaction. Thus, Suzu City would represent a highly appropriate area in which to promote disaster prevention education in the Hokuriku region.


Introduction
The 2011 Tohoku earthquake (Mw9) generated a giant tsunami and caused the death of more than 18,000 inhabitants (including missing persons). Surprisingly, a considerable number of people did not evacuate due to a misunderstanding regarding the early-stage warning of a 3 m-high tsunami and/or too much trust in the protection afforded by high tidal banks, despite having sufficient evacuation time after the strong ground shaking. The Pacific coast of the Tohoku region has been repeatedly threatened by tsunamis, and thus appropriate disaster prevention education and evacuation drills have been conducted. However, it was nevertheless surprising that there were such a high number of victims even in regions with high disaster prevention awareness.
Compared with the Pacific coast, the Japan Sea coast has experienced few tsunami disasters, especially in the Hokuriku region, where the seismicity is low; however, disaster prevention awareness is also low. To promote practical disaster prevention education by making full use of lessons learned from the tsunami disaster following the 2011 Tohoku earthquake, it is crucial to deepen our understanding of a devastating tsunami following strong ground shaking and relevant damage from an earthquake.
In this study, the focus of interest is the Hokuriku region (Fukui, Ishikawa, and Toyama Prefectures). To date, each prefecture has conducted its own tsunami simulation and published hazard maps in which the region is limited to its own prefecture [1][2][3]. When the same seismic fault is examined, source parameters differ between prefectures. Therefore, it is difficult to use hazard maps as teaching materials to gain an understanding of the whole picture of a tsunami disaster, as a tsunami obviously takes no account of administrative boundaries. In addition, cooperation between adjacent prefectures in the matter of preparedness for future tsunami disasters is not without problems.
The 2011 Tohoku earthquake (Mw9) prompted investigation on the possible occurrence of a tsunami on the Japan Sea coast in two different research projects: one by the Ministry of Land, Infrastructure and Transport [4] and the other by the Ministry of Education, Culture, Sports, Science and Technology [5]. However, since the coverage of these studies is very broad, and they do not specifically focus on the Hokuriku region, it may be difficult to make use of the project results in local disaster prevention education in our region of interest.
Here, we carried out hazard assessment of a tsunami following an earthquake in the Hokuriku region. After considering the whole region, we extracted a model district to be prioritized in future disaster education. Using a simplified method, ground shaking and liquefaction rates were evaluated to gain insight into tsunami hazard in relation to strong ground motion.

Tsunami simulation
In the present study, we used TSUNAMI-K software, which was originally developed and published by a research group at Tohoku University as the analytical Fortran code of TUNAMI [6][7][8] and later incorporated with the GUI (graphical user interface) environment by Kozo Keikaku Engineering Inc. Details of the theory commentary are given in literatures [6][7][8]. The computer program TUNAMI developed by Tohoku University has been distributed worldwide as part of the Tsunami Inundation Modeling Extension (TIME) project promoted by collaboration of the International Union of Geodesy and Geophysics (IUGG) and the Intergovernmental Oceanographic Commission (IOC) of the United Nations Educational, Scientific and Cultural Organization (UNESCO) during the International Decade for Natural Disaster Reduction (IDNDR). Currently it has been recognized as the UNESCO's standard evaluation method for tsunami and used by 36 institutions of 19 countries, which suffered or will suffer tsunami hazards. So, the accuracy and reliability of the code have been verified by many studies (e.g., [9][10][11]). Here, the outline of numerical calculations and the analytical conditions, implemented into the analytical codes, are briefly summarized.

Governing equations
For the tsunami analyses, the shallow-water long-wave theory is used. The governing equations are expressed in Eqs. (1)- (3).
Here, η is the water level, h is still water depth, D is the total water depth (h +η), g is the gravitational acceleration, n is Manning's roughness coefficient (described later), and M and N are the flow flux (flow rate per unit width) in the x-and y-direction, respectively. Eq. (1) represents a continuous equation, which corresponds to the law of conservation of mass. Eqs. (2) and (3) represent equations of motion for the x-and y-direction, respectively.
Eqs. (2) and (3) are derived from the Navier-Stokes equation, taking into account the characteristics of the tsunami: (a) the viscosity can be ignored since it is targeted for seawater, (b) the wavelength is long relative to the water depth, and (c) the seawater from the water surface to the sea bottom flows together at a uniform horizontal flow velocity. See Refs. [6][7][8] for detailed derivation.
Eqs. (2) and (3) are used when the tsunami height cannot be ignored with respect to the water depth in a shallow sea, usually at a water depth of 50 m (sometimes 100 m or 200 m). In the case of deep water, the second, third, and fifth terms of Eqs. (2) and (3) become small, and their solutions approach those from the linear long-wave equations. In the present study, Eqs. (2) and (3) are used as they are to calculate the tsunami inundation to the land.  . Each of these three earthquake faults consists of two or three small faults with different strike angles.

Initial conditions
For the evaluation of crustal deformation of the seafloor accompanying the earthquake, we use the static deformation [12] of the sea bottom surface, which corresponds to the initial water level of the tsunami simulation. The fault parameters that specify the seismic fault model are set as shown in Table 1, referring to the report on the Ministry of Land, Infrastructure and Transport [4]. For each of the three seismic faults, two cases are calculated: Case 1 with Mw7.6 and Case 2 with Mw7.8 (in which slip displacement of the fault in Case 1 is doubled). Case 2 is intended to give inherent uncertainty in source parameters as a lesson from the 2011 Tohoku earthquake. In addition, it is assumed that the slip distribution on the fault plane is uniform and the propagation of rupture is not taken into account (the velocity of rupture propagation is assumed to be infinite). The method in Ref. [6] is used for the amount of outflow from the calculation area on the offshore side, in which free transmission is made and reflection to the calculation area is suppressed. It is assumed that the amount of water η (g Â h) 1/2 flows out at a progressive long-wave velocity of (g Â h) 1/2 , where η is the wave level just inside the boundary.

Run-up condition to the land
To calculate the tsunami's run-up to land according to shallow-water long-wave theory, the method in Ref. [13] is used. In this method, the topography at the run-up fronts is treated as steplike grids, and the flow is evaluated using Eqs. (1)-(3). When the water level η of the seaside grid is higher than the ground height z of the landside grid, the difference is defined as the actual water depth D, and the water level and the flow rate are calculated. D > 10 À5 (m) is often used as a criterion for considering a tsunami's run-up to land (e.g., [14]). This kind of boundary to treat tsunami's run-up is called the moving boundary [8]. After comparison of several methods to treat the moving boundary, the method in Ref. [13] is selected and implemented into the computational code TUNAMI because of its accuracy [8].

Tide level conditions
The average sea level in the Japan Sea is 0.2 m higher than T. B. (mean sea level in Tokyo Bay).
In the present study, the tide level is set to AE0 m.

Submarine topography data and land altitude data
For tsunami simulation, the seafloor depth data and land altitude data are required. For the offshore, we use the 1 km grid water depth data of the Japan Sea area from JTOPO30 (30-s grid water depth data in Japan's coastal waters) [15] published by the Marine Information Research Center of the Japan Hydrographic Association. For the nearshore, we use the coastal 500 m grid water depth data [16] published by the Japan Coast Guard. Furthermore, for the land data necessary for the run-up analysis, we use the 50 m grid land altitude data [17] published by the Geospatial Information Authority of Japan.

Numerical scheme
For numerical calculations, Eqs. (1)-(3) are discretized and solved by using the finite difference method. An orthogonal coordinate grid is used in the spatial domain, and a staggered grid is used in the variable placement. The leapfrog method is used in the time domain, which provides neutral stability with no dissipation error. In the discretization of the spatial domain, three grid sizes are used: 450 m for the whole region, 150 m for the intermediate region, and 50 m for the nearshore and the land. The whole region for analysis is shown in Figure 1, in which the yellow frame is the region discretized into 50 m grids. We analyze the calculations performed in the time domain with a time step of 0.1 s and tsunami propagation for 180 min after an earthquake fault ruptures.

Manning's roughness
The fifth term in Eqs. (2) and (3) represents the friction effect against the sea bottom during tsunami propagation, which varies rapidly when Manning's roughness n changes. In the present study, n is fixed at 0.025, with a reference to [10].

Evaluation of strong motion
To provide an overview of a disaster not only from the perspective of tsunami inundation but also from the damage occurrence of strong ground shaking and liquefaction, simplified methods based on the attenuation formula of the maximum velocity are used to calculate the seismic intensity and the liquefaction occurrence rate in the whole region. Here, the methodologies are briefly summarized.

Seismic intensity
The seismic intensity (The Japan Meteorological Agency seismic intensity scale) is evaluated through three steps: (1) the evaluation of the maximum velocity on the engineering bedrock, (2) the evaluation of the amplification factor of the maximum velocity from the engineering bedrock to the ground surface, and (3) the evaluation of the seismic intensity from the maximum velocity at the surface.
In the first step, the maximum velocity on the engineering bedrock (a layer with the S-wave velocity of 600 (m/s)) is evaluated using Eq. (4) by the empirical formula [18][19]: log 10 PGV 600 ¼ 0:58 M w þ 0:0038D þ d À 1:29 À log 10 X þ 0:0028 Â 10 0:50Mw À Á À 0:002X (4) where PGV is abbreviation of "peak ground velocity", PGV 600 is the maximum velocity (cm/s) on the engineering bedrock with S-wave velocity of 600 m/s, Mw is the moment magnitude, D is the depth of the source (km), d is the coefficient depending on the earthquake type (d = 0 for a crustal earthquake, d = À0.02 for an interplate earthquake, and d = 0.12 for an in-plate earthquake), and X is the fault's shortest distance between the fault plane and the target site (km). In the present study, the maximum velocity is estimated for a crustal earthquake. Eq. (4) is obtained by the regression analysis based on 543 data of the maximum velocity from 21 earthquakes that occurred in Japan (Mw5.8-8.2). Its validity and usefulness have been confirmed by many researchers in many earthquakes (e.g., [20][21][22][23][24]).
In the second step, the amplification factor of the maximum velocity from the engineering bedrock to the surface is calculated by the following relationship [25]: where ARV (m/s) represents the amplification rate factor of the maximum velocity from the engineering bedrock to the surface and AVS30 (m/s) represents the average S-wave velocity from the surface to a depth of 30 m, ranging between 100 and 1500 m/s. According to Eq. (5), the ground motion becomes larger when AVS30 is lower than 600 m/s, whereas it becomes smaller when AVS30 is higher than 600 m/s. The maximum velocity at the ground surface, PGV, can be obtained by multiplying the maximum velocity at the engineering velocity, PGV 600 , in Eq. (4) by the amplification factor ARV in Eq. (5): log 10 PGVs ¼ log 10 PGV 600 Â ARV ð Þ ¼log 10 PGV 600 þ log 10 ARV ¼ log 10 PGV 600 À 0:852 log 10 AVS30=600 ð Þ In the third step, according to Refs. [26,27], the seismic intensity on the ground surface can be calculated using the following formula: I ¼ 2:286 þ 2:088 Â log 10 PGVs Using the above three-step procedure, it is possible to calculate the seismic intensity at an arbitrary point from a given seismic fault. In the present study, using the AVS30 of a 250 m grid based on the geomorphologic classification published by NIED's Japan Seismic Hazard Information Station (J-SHIS) [28,29], the seismic intensity of the targeted area is evaluated.

Liquefaction occurrence rate
The relationship between the seismic intensity and the liquefaction occurrence rate [30,31] is expressed as: where P Iiq (I) represents the liquefaction occurrence rate at the seismic intensity I, Φ is the cumulative normal distribution function, μ is the mean value, and σ is the standard deviation; μ and σ are determined by classifying 15 types of geomorphologic classification-representing the potential to liquefy-into 4 groups according to liquefaction risk and by performing a regression analysis for each group with the least squares method based on the data of seismic intensity and liquefaction occurrence rate (see Refs. [30,31] for details). Parameters to evaluate the liquefaction occurrence rate, μ and σ, are summarized in Table 2. For example, liquefaction begins to occur near seismic intensity 5.0. in group 1, which is the most liable to liquefy (natural levees, abandoned river channels, lower slopes of dunes, lowland between coastal dunes and bars, reclaimed land, and filled land). Note that parameters μ and σ in Table 2 are determined based on the liquefaction data over 1400 from the recent 9 damaging earthquakes in Japan [30,31] and applied to successfully reproduce the liquefaction occurrence locations due to the 2011 Tohoku earthquake [32].

Overview of tsunami propagation
For each of the three earthquake faults, we conducted a tsunami simulation on two cases with different magnitudes: Case 1 Mw7.6 and Case 2 Mw7.8. The maximum tsunami height is shown in Figures 2-7. The displayed range of these figures corresponds to the yellow frame inside Figure 1, with the southwestern end as the origin, the distance in the east-west and north-south direction (km) is taken in the horizontal direction, and the maximum tsunami  height is taken in the vertical direction (m). Similar plots have been done for the inundation depth and tsunami arrival time but omitted because of space. The general features from these results are discussed below.

North off the Noto Peninsula fault
The maximum height of the tsunami in Case 1 (Mw7.6) ( Figure 4)

Other findings
In Case 2, the slip displacement on the fault is double that of Case 1, meaning that the tsunami height is nearly double in the vicinity of the fault, although in the coastal area away from the fault the height is $1.5 times. In this analysis, the nonlinear long-wave equations are solved for the whole area, and in the coastal area near the land, the water becomes shallow and the effect of the submarine friction term increases.
The overall distribution characteristics of tsunami height change significantly for each of the three faults; except in the vicinity of the fault, the tsunami height at the Noto Peninsula tends to be high. In particular, it is predicted that Suzu City, Ishikawa Prefecture, located at the tip of the Noto Peninsula, has a high tsunami and broad inundation areas compared with other areas.

From the perspective of strong ground motion
For a better understanding of a tsunami in a series of disasters triggered by an earthquake, the ground shaking and liquefaction occurrence rates were calculated for each fault. The seismic intensity and the liquefaction occurrence rate depend on the maximum velocity evaluated by Eq. (4). As can be seen from this equation, the difference of 0.2 in Mw between Cases 1 and 2 leads to a difference of 5-25% in the maximum velocity, depending on the fault distance. It also leads to a difference of 0.04-0.2 in the seismic intensity. These differences become smaller when the site is closer to the epicenter. Therefore, for the seismic intensity and liquefaction occurrence rate, here the results only for Case 1 are shown and discussed.
The maximum seismic intensity across the whole range is 5+ for the Wakasa Sea Knoll Chain fault (Figure 8(a)), 6+ for north off the Noto Peninsula fault (Figure 9(a)), and 6+ for east off the Noto Peninsula fault (Figure 10(a)). The maximum liquefaction occurrence rate across the whole range is 0.45% for the Wakasa Sea Knoll Chain fault (Figure 8(b)), 21% for north off the Noto Peninsula fault (Figure 9(b)), and 16% for east off the Noto Peninsula fault (Figure 10(b)).

Discussion
Calculation of the inundation area in the target area using a geographic information system (GIS) showed that the largest inundation area was estimated to be about 38 km 2 in Case 2 east off the Noto Peninsula fault, followed by $17 km 2 in Case 2 north off the Noto Peninsula fault. In Case 2 of the Wakasa Sea Knoll Chain fault, the inundation area was $7.6 km 2 , which is slightly smaller than the area of $9.0 km 2 in Case 1 east off the Noto Peninsula fault. Comparing Case 2 with Case 1, the inundation area increased 2.2 times in the Wakasa Sea Knoll Chain fault and 2.9 times north off the Noto Peninsula fault, 4.2 times east off the Noto Peninsula fault. In Case 2, the slip displacement on the fault is double that of Case 1, but the inundation area of the tsunami is much greater than that.
After observing the inundation area using the GIS, we decided to focus on Suzu City, Ishikawa Prefecture, which is expected to have the largest inundation area from both north off the Noto Peninsula fault and east off the Noto Peninsula fault. As an example, the inundation area of the city from the east off the Noto Peninsula fault is illustrated in Figures 11 and 12, which highlight the area around Misaki Town, Suzu City. In Case 2 (Figure 12), the tsunami runs up $1.9 km from the mouth of the Kino River, which is 1.5 times further than in Case 1 ( Figure 11).
In other inundation areas of the city, the tsunami runs up 1.5-1.7 km further from the coast in Case 2, which is two to four times the distance in Case Next, for the tip of the Noto Peninsula including Suzu City in Ishikawa Prefecture, an enlarged map of the seismic intensity and the liquefaction occurrence rate for north off the Noto Peninsula fault and east off the Noto Peninsula fault is shown in Figures 13 and 14. The lowland along the coast of Suzu City is subjected to strong shaking, with the seismic intensity   The inundation area of a tsunami is likely to occur in the coastal lowland, where strong ground motion may induce building damage and soil liquefaction. Therefore, it is important to examine the impact of damage caused by ground shaking on evacuation route and evacuation time. This is not limited to Suzu City but is common to the entire area where there is flooding caused by the tsunami and provides an important perspective for future damage estimation.
As noted, in the Hokuriku region, relatively few earthquakes are felt, and disaster prevention awareness is low. The resources (people, time, budget, etc.) that can be input for the promotion of disaster education are always limited. Under these circumstances, to obtain the maximum effect from limited resources, it is preferable to introduce intensive resources in a specific area with a high disaster risk, rather than treating the whole area equally. In this respect, Suzu City may be a model district, and if the promotion of disaster prevention is successful in the city, it could be fruitfully expanded to other areas.

Conclusions
In our study, focusing on the Hokuriku region in Japan, we conducted a tsunami simulation and examined the resulting tsunami hazard map. Three potential faults of Mw7.6 earthquake were selected to generate the tsunami: the Wakasa Sea Knoll Chain fault, north off the Noto Peninsula fault, and east off the Noto Peninsula fault. In addition, we calculated these three events with Mw7.8, given the inherent uncertainty in source parameters. Aside from tsunami height, arrival time, inundation height, and inundation area, we calculated the seismic intensity and the liquefaction occurrence rate by simplified methods. Our findings in the present study are summarized as follows.
• In Case 2 (Mw7.8), the slip displacement on the fault is double that of Case 1 (Mw7.6), meaning that the tsunami height is nearly double in the vicinity of the fault, although in the coastal area away from the fault the tsunami height is $1.5 times. In this analysis, the nonlinear long-wave equations are solved for the whole region, and in the coastal area near the land, the water becomes shallow and the effect of the submarine friction term increases.
• Comparing Case 2 with Case 1, the inundation area increased 2.2 times in the Wakasa Sea Knoll Chain fault and 2.9 times north off the Noto Peninsula fault, 4.2 times east off the Noto Peninsula fault. In Case 2, the slip displacement on the fault is double that of Case 1, but the inundation area of the tsunami is much greater than that.
• The overall distribution characteristics of tsunami height change significantly for each of the three faults; except in the vicinity of the fault, the tsunami height at the Noto Peninsula tends to be high. In particular, it is predicted that Suzu City, Ishikawa Prefecture, located at the tip of the Noto Peninsula, has a high tsunami and broad inundation areas compared with other areas.
• Our results indicated that Suzu City in Ishikawa Prefecture, located in the northeastern part of the Noto Peninsula, has a relatively high potential risk of tsunami as well as strong motion and liquefaction. Thus, Suzu City would represent a highly appropriate area in which to promote disaster prevention education in the Hokuriku region.
• The inundation area of a tsunami is likely to occur in the coastal lowland, where strong ground motion may induce building damage and soil liquefaction. Therefore, it is important to examine the impact of damage caused by ground shaking on evacuation route and evacuation time. This is not limited to Suzu City but is common to the entire area where there is flooding caused by the tsunami and provides an important perspective for future damage estimation.