The southernmost portion of the Ryukyu Trench near the island of
Taiwan potentially generates tsunamigenic earthquakes with magnitudes from
7.5 to 8.7 through shallow rupture. The fault model for this potential region
dips 10
Almost all destructive tsunamis are generated by shallow earthquakes that
occur within subduction zones. Numerous destructive tsunami events, including
the
Probabilistic tsunami hazard analysis (PTHA) is a modification of probabilistic seismic hazard analysis (PSHA) (Cornell, 1968; SSHAC, 1997), and it is intended to forecast the probability of tsunami hazards for a given region as comprehensively as possible. The recurrence rates of earthquakes have typically been estimated using the Gutenberg–Richter relationship (Gutenberg and Richter, 1944) for a defined source region in consideration of tsunamis triggered by earthquakes. The assessment of the wave height is one of the primary differences between PTHA and PSHA. PSHA assesses the ground motion based on empirical attenuation relationships (Wang et al., 2016), while PTHA assesses tsunami wave heights using empirical approaches or tsunami simulations (Geist, 2002; Geist and Parsons, 2006, 2009). Geist and Parsons (2006) mentioned that the tsunami wave height follows a definable frequency–size distribution over a sufficiently long period of time within a given coastal region (Soloviev, 1969; Houston et al., 1977; Horikawa and Shuto, 1983; Burroughs and Tebbens, 2005). This method is of great use in establishing the tsunami probability for a region if there is an extensive catalog of observed tsunami wave heights. However, given the wide distribution of global tsunamigenic earthquakes within seafloor regions throughout subduction zones, the tsunami records obtained from coastal gauges or/and ocean buoys are too sparse to comprehensively assess the associated hazards and the recording time, since their deployment is too short to enable a study on the recurrence intervals of tsunamis and earthquakes. Consequently, because the existing tsunami catalog is limited, simulations represent an effective approach. Conventional tsunami simulation adopts a simple source approximation and applies elastic dislocation theory to calculate the deformation of the seafloor surface assuming a uniform slip over the entire fault surface (Okada, 1985; Okal, 1982). However, the complexities of earthquake rupture processes play a substantial role in the generation of tsunamis. Conventional approaches are therefore unable to capture various features of short-wavelength tsunamis in the near field (Geist, 2002; Geist and Parsons, 2009). The results of previous studies that simulated tsunamis originating from historical earthquakes around Taiwan (Ma and Lee, 1997; Wu et al., 2008) using uniform slip models agreed only with long-wavelength observations. For the purposes of hazard mitigation, it is critical to predict the amplitudes of tsunamis along various coastlines for a given earthquake as accurately as possible. To make such predictions, the effects of the rupture complexity must be taken into consideration. Recent developments in PTHA have included the adoption of stochastic slip distributions of earthquakes to determine the overall probability of particular tsunami heights (Geist and Parsons, 2006, 2009). The adoption of stochastic slip distributions is able to quantify the variations in reasonable evaluations of the probabilities of specified tsunami heights at individual locations resulting from a specific fault.
In this study, we assess the heights of tsunamis along the coastline of
Taiwan generated by the potential tsunamigenic zone at the southernmost end
of the Ryukyu subduction zone. This potential zone is located close to
Taiwan, and at least 10 earthquakes (
The estimated maximum magnitude of a possible earthquake scenario is
essential for establishing the fundamental seismic conditions of the tsunami
simulation. The scenario of a potential rupture fault extending to a depth of
13 km proposed by Hsu et al. (2012) occurs along the southernmost Ryukyu
trench with a rupture length of 120 km, a width of 70 km and a dip of
10
Moreover, the seismic moment is dependent on the rupture area (
Therefore, the maximum possible earthquake magnitude is
The rupture process of an earthquake is extremely complex. Seismic inversion
results reveal that the slip distribution of a rupture has a heterogeneous
spatio-temporal development. Consequently, using a simplified uniform slip
distribution to simulate a tsunami captures only the long-wavelength portion
of the tsunami field (Geist and Dmowska, 1999). In addition, the temporal
description of the seismic rupture process can be ignored because the
propagation velocity of the tsunami wave is substantially slower than the
seismic rupture velocity (Dean and Dalrymple, 1991; Ma et al., 1991; Wang and
Liu, 2006). Andrews (1980) showed that the static slip distribution is
directly related to stress changes and that the spectrum of the slip
distribution is proportional to
The heterogeneous slip distribution is proportional to
The parameter
The stochastic slip distribution is generated by a 2-D spatially random
distribution by imposing a self-similar characteristic beyond the corner
radial wave number, which is constrained by the rupture dimension, in the
wave number domain. In this study, the potential rupture fault is divided into
5
The map of Taiwan shows the fault model and recording stations used
in this study. The bathymetry is divided into two layers with different
resolutions. The resolution of the outer layer is 4 min, and the resolution
of the inner layer is 1 min. The red grid denotes the potential fault model
(
Figure 2 shows the computational domain, recording stations and fault model.
The potential rupture fault is divided into 5
The maximum, minimum and average wave heights with their standard deviations for the PTA probability distributions (in meters) with the maximum wave heights from the uniform slip model. The water depths at the stations in the computational mesh are also included.
The stochastic slip model produces different slip distributions with the same
fault geometry in addition to a constant average slip and a constant seismic
moment. The model is used to describe the heterogeneous slip pattern of an
earthquake and to further examine its effect on the tsunamis originating from
the southernmost end of the Ryukyu subduction zone adjacent to Taiwan.
According to the previous sections, the maximum possible earthquake magnitude
is determined to be
The static vertical displacement of the ocean floor is modeled using elastic dislocation theory (Okada, 1985) with a static slip distribution. The vertical seafloor displacement is modeled as the initial water level, and the horizontal component of the seabed displacement is not included in the simulation. Figure 3a shows the initial water elevations produced by a uniform slip distribution, and Fig. 3b exhibits the maximum free-surface elevation during the propagation. Figure 3c and e demonstrate the initial water elevations produced by the stochastic slip distributions (Fig. 1b and d). The initial water elevation with a uniform slip distribution is simple and smooth, but those with stochastic slip models are more complex and relatively heterogeneous. Nonuniform slip causes an apparent change in the wavelength distribution of the initial free-surface elevation (i.e., the potential energy distribution), which affects the path of energy propagation. In the uniform slip scenario, the maximum free-surface elevation pattern is straightforward and clearly controlled by the topography. However, many strong and seemingly chaotic paths of wave energy appear in the nonuniform slip scenarios, and the free-surface field exhibits additional uncertainties in terms of the flow. In Fig. 3b, the maximum free-surface elevation mainly propagates toward two places where the seafloor bathymetry becomes shallow relative to the deep areas northeast of Taiwan, as shown in Fig. 2. Although the propagation paths due to the nonuniform slip distributions (Fig. 3d and f) also have the same characteristics, it is notable that the paths followed by the wave energy differ depending on the rupture pattern. To the northeast of Taiwan in Fig. 3f, there is a strong wave path connecting the two higher-elevation areas of bathymetry. However, this behavior is not observed in Fig. 3b and d. In addition, the maximum elevation on the footwall in Fig. 3d is higher than that in Fig. 3f. In Fig. 3b, the high elevation appears only along the coast on the footwall side. These results indicate that the wave energy variation depends on the rupture pattern, thereby causing differences in the wave paths and leading to completely different tsunami amplitudes.
Panels
Thirty stations located along the coastlines are available for recording the amplitude of the tsunami wave height. Relative to the other stations, stations 25 (Shihti), 26 (Hualien) and 27 (Suao) are situated near the potential rupture fault, and they have high wave amplitudes and enormous variations in the tsunami simulations of 100 different slip distributions; consequently, the time series of the wave heights at these stations are shown as an example (Fig. 4). The time series of the wave heights at the other stations are shown in the Supplement. The variability in the distribution of the initial free-surface elevation results in substantial phase changes and different wave heights. It is worth noting that the average of the disordered and chaotic time series produced by the 100 different slip distributions is almost identical to the results of the time series produced by the uniform case. This implies that the uniform slip distribution simply represents an average result and that it cannot represent all of the possible situations.
According to the statistical results from 100 different slip patterns (Table 1) for 30 stations, Hualien station has a maximum wave amplitude of 7.32 m, and its maximum wave amplitude interval ranges from 1.87 to 7.32 m, which constitutes the widest interval for any recording site, and the standard deviation of this distribution is 1.024 m. These findings indicate that Hualien station has a high uncertainty in this scenario. However, the maximum wave amplitudes from the uniform slip distribution are relatively lower than those from the stochastic results. Following the above findings, we need to consider whether the estimations from the uniform slip case are appropriate for hazard analysis by focusing on the maximum wave amplitude issue.
The time series of the wave heights recorded at stations 25 (Shihti), 26 (Hualien) and 27 (Suao). Gray lines represent the time series of 100 different slip distributions, black lines represent the averages of the gray lines, blue lines represent the 95 % confidence intervals, and red lines are the time series produced using uniform slip distribution. Parts of the wave heights at station 27 are lower than the water depths, and thus, these curves have been truncated.
According to the results of our simulations, we calculate the probability of the peak tsunami amplitude (PTA) at each recording station as shown in the histogram of Fig. 5. To verify the representativeness of the PTA probability distributions, another 100 sets of different slip distributions are produced and simulated under the same seismic conditions. In Fig. 5, the shapes of the PTA distributions from another 100 sets (black lines) are similar to the shapes of the histograms from the first 100 sets. These results verify the representativeness of the PTA probability distributions produced from 100 sets of slip distributions. This test also reinforces the reproducibility of our simulations and demonstrates that the number of simulations is roughly satisfactory for statistical analysis. Of course, the more slip distributions we use, the more comprehensive and stable the range we obtain.
The probabilities of the PTA along the coast of Taiwan (blue:
stations 1
In Fig. 5, the PTA distributions for the stations in eastern Taiwan (red
markers) have much higher values than those in western Taiwan (blue
markers) due to the specified location of the tsunami source. The shapes of
the PTA distributions in eastern Taiwan resemble lognormal distributions,
while those in western Taiwan resemble normal distributions. We suppose that
the attenuation of the wave propagation causes the lognormal distributions to
degenerate into normal distributions. The PTAs produced by a uniform slip
distribution are generally located in the middle of the PTA distributions.
Both PTA values (i.e., the value of the PTA from the uniform slip
distribution and those from the stochastic slip distribution models) decrease
with distance from the potential fault due to the attenuation of the wave
propagation (Fig. 5 shows the results for all stations, and Fig. 6 shows the
results for stations 20 through 30 in eastern Taiwan). However, some
stations, e.g., stations 17, 19 and 21, do not precisely follow this trend;
this could be the result of the coastal topography and the presence of an
energy channel. From Fig. 3d, in comparison with the adjacent coastline,
station 21 is located exactly where the wave energy gathers. In addition,
broad distributions are frequently observed at promontories along the
coastline and are caused by complex propagation path effects between the
source region and the recording locations (Geist, 2002). There are many
compound factors that affect the tsunami propagation and maximum wave height.
Figure 6 presents the relation between the distance and wave height and shows
the PTA distributions following Fig. 5. The
Although the seismic parameters have already been defined as constants in our experiment, there exists an uncertainty in the PTA, which is not a constant value. Hence, the uniform case cannot provide this uncertainty, and thus, the PTA could be underestimated. The results give specific PTA ranges, which represent the wave height uncertainties for the scenario of earthquakes originating from the Ryukyu Trench. It is therefore necessary to consider the effects of a heterogeneous slip distribution to comprehensively assess the tsunami hazard.
The relation between the distance and wave height for stations 20
to 30 in eastern Taiwan. Panel
Most coastlines threatened by near-field tsunamis, such as the coasts of
Chile, Japan and Indonesia, are parallel to the trench axis of the associated
subduction zones. Many tsunami events, including the
The effect of a heterogeneous slip distribution is important and necessary
for near-field estimations (Geist, 2002 and Ruiz et al., 2015).
Figure 5 shows that the PTA distributions in the near field are broad, and
they narrow with increasing distance from the potential fault. The
uncertainty in the near field is higher than in the far field. At most
of the eastern stations, the values of the average PTA approach uniform
results, but the uniform slip results at stations 25 and 26 are close to the
minimum PTA (Table 1). Geist (2002) presented the average and extreme
nearshore PTA calculated for 100 different slip distributions and compared
them with the uniform slip results (Fig. 6a in Geist, 2002). The range of the
PTA also becomes narrower with increasing distance. The values from the
uniform slip distribution and the average PTA are similar, but some of the
average values are close to the minimum PTA between approximately 19 and
19.5
Four nuclear power plants (NPPs) are located on the island of Taiwan.
According to the numerical results, we infer that the mean PTA in the coastal
area of NPP4 ranges from approximately 2 to 3 m. The distribution at this
plant may be wider than those at other nuclear power plants due to its
position relative to the tsunami source. Moreover, NPP4 is located on the
shore of a bay with a curved shape; the magnification effect from the
geometrical shape of the bay may serve to enhance the PTA therein. NPP3 also
exhibits this condition insomuch that the energy is concentrated at the
location of the plant (Fig. 3b, d and f). For the coastal areas around NPP1
and NPP2, the PTA distributions are between 1 and 2 m. The coastlines of
these two nuclear power plants slightly face the direction of tsunami
propagation, and thus, their PTAs should be higher than those along adjacent
coastlines (Fig. 3b, d and f). In general, under this scenario, the coastline
at NPP4 has the largest threat. Although NPP3 is far from the tsunami source,
it faces a wave height of approximately 1.5 m on average with a
The use of heterogeneous slip patterns clearly delineates the range of possible waveforms and provides more information on latent uncertainties in the wave height. The 95 % confidence intervals for the wave height from 100 sets in each time series provide us with a specific range for the amplitude of the tsunami wave (Fig. 4). According to these time series, we are aware of the periods of tsunami runup and runoff and can prepare supporting policies to reduce associated disasters. For example, a nuclear power plant uses a trench from the ocean to intake water to cool the reactor; thus, if the sea level is too low to take in water, the temperature of the reactor will rise excessively, causing a nuclear disaster. Based on the results of simulations, we can estimate how much water should be stored for tsunami runoff. This issue requires more attention in Taiwan because four nuclear power plants are located near the coast.
The results of the tsunami simulations illustrate that the effect of the slip
distribution on the rupture plane has significant effects on the wave
propagation and wave height. The correctness of this slip distribution
determines whether the wave height calculations represent a useful reference.
However, some parameters of the stochastic models could influence the
synthetic slip distributions. For instance, the exponent of the slip spectrum
is associated with the roughness of the slip distribution. Higher exponential
values inhibit the powers of high wave numbers, leading to smoother slip
distributions; conversely, lower values lead to rougher slip distributions.
In general, the
The maximum possible earthquake magnitude is
The data are available upon request from the authors.
The supplement related to this article is available online at:
The authors declare that they have no conflict of interest.
The authors are grateful for research support from the Ministry of Science and Technology (ROC) and the Department of Earth Science, National Central University (ROC). This work is supported by “Earthquake-Disaster & Risk Evaluation and Management Center, E-DREaM” from the Featured Areas Research Center program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan. The Taiwan Earthquake Research Center (TEC) contribution number for this article is 00145. We thank Eric L. Geist for discussing the stochastic slip model. The authors very much appreciate the constructive comments received on the manuscript by two anonymous reviewers, as well as the thoughtful insights of the editor, Piero Lionello. Edited by: Piero Lionello Reviewed by: two anonymous referees