List of the earthqaukes studied. Origin time (UT), latitude, longitude, and depth are taken from PDE catalog. GCMT parameters are from the GCMT catalog. W Phase results indicate frequency band, number of stations, and channels used for the final solutions. The solutions are the scenario of using PDE location and grid searching For
Ocean-wide tsunamis are almost always triggered by mega-earthquakes, rupturing substantial segments on the zones of interplate boundarybetween subducting slab and overriding plate. Whether, or specifically when, a mega-earthquake will occur on a subduction zone is crucial for preparedness of tsunami hazard mitigations. However, conditions controlling occurrences of mega-earthquakes are not well understood, as the 2004 Mw9.3 Sumatra earthquake contradicted the previous paradigm that the maximum-size earthquake in a given subduction zone can be predicted from its simple tectonic parameters such as slab age and convergence rates (Ruff & Kanamori, 1980). On top of that, the 100 years or so sampling periods of earthquake catalogue since instrumental era are not long enough to reveal the repeating periods, if any, of mega-earthquakes. Consequently, the fault dimensions necessary for a mega-earthquake to rupture in general become the most reliable constraint on its potential - for any subduction zone with length greater than 1,000 km, one cannot rule out the possibility that it is currently accumulating the strain energy of a mega-earthquake, which will release eventually to trigger ocean-wide tsunamis.
In the South China Sea (SCS) region, the Manila subduction zone, stretching over 1,000 km northward from Mindoro, Philippines to offshore SW Taiwan, poses a potential zone for the occurrence of a mega-earthquake and subsequently, thethreat of widespread SCS tsunami hazards. Indeed, it is a reasonable doubt that the historical tsunami hazards on coasts of SW Taiwan in 1661 and 1782(Soloviev & Go, 1984) might be caused by SCS tsunamis, amplified by SCS shelf when approaching Taiwan straits. Although it remains an open question as to when (or even whether) a mega-earthquake will occur in the Manila subduction zone, we endeavor to establish a warning system in Taiwan for SCS tsunamis.
Being able to predict the arrival times and amplitudes of the approaching tsunamis promptly after the occurrence of a tsunamigenic earthquake is key to the success of a tsunami warning system, which in turn hinges on modeling the evolution of earthquake-generated tsunami waves. There are three distinctive stages involved: generation, propagation, and run-up (Titov, 1997). For the generation stage, rapid determination of reliable earthquake source parameters (lon., lat., depth, moment, and focal mechanism) is crucial to infer the seafloor vertical displacements as initial conditions for tsunami wave propagations. Here, we adopt the source inversion using seismic
Given seismic source parameters, the vertical static seafloor displacements, as initial conditions of tsunami wave propagations, can be determined immediately by solving the surface deformations of an inclined fault in a half-space elastic medium, such as those described by Mansinha & Smylie (1971) and Okada (1985). However, the propagation stage that followed is the most time consuming stage and for the warning purposes of a regional scale, it is hardly practical for real-time calculations. Here, we employ the unit tsunami methods (Lee et al., 2005) to solve the dilemma. The methods divide all potential source regions into pixels and calculate the propagations of an initial unit amplitude uniformly assigned on the pixel. The resulting waves to a target station are stored in database and referred to unit tsunamis of that station-source pair. In the case of a real event, the predicted tsunamis of one station are synthesized by linear combinations of those unit tsunamis that are paired the station with all source pixels. The weightings of unit tsunamis in linear combination are determined by the vertical seafloor displacements averaged over the region of the corresponding pixel. We will elaborate the methods further in next section when building the database. Unit tsunamis are conceptually analogous to Green’s functions in Seismology and are applicable solely for linear systems. Therefore, in our warning system, we strategically focus on predicting the offshore arrival times and amplitudes of approaching tsunamis that is prior to the run-up stage and subsequently, the non-linear effects are minor and can be ignored.
2. Data and methods
2.1. Wphase inversion
We refer readers to Kanamori & Rivera (2008) regarding theory, modeling, and source inversion of
We sorted out earthquakes from the GCMT catalog (Dziewonski
2.2. Unit tsunami methods
The unit tsunami methods divide all potential source regions into pixels and assign an initial unit amplitude uniformly on each pixel, called unit source (Figure 4). The propagations of unit sources are pre-calculated with the resulting tsunamis at observing stations recorded as unit tsunamis to be stored in database. Each and every unit source has his unique unit tsunamis to a specific station stored and is pulled out to synthesize the composite tsunamis of that station in the case of a real event. The synthetics are done by linear combinationwith weighting factors determined by vertical seafloor displacements averaged over the region of corresponding unit source. In this way, the time consuming propagation stage is performed in advance, which makes prompt issuing of tsunami warnings more efficient. The principle of unit tsunami methods is conceptually analogous to Green’s function in Seismology and only works in linear systems. As compliance, we aim at predicting the offshore – prior to the run-up stage - arrival times and amplitudes of approaching tsunami waves. Under the circumstances, tsunami amplitudes are in general at least an order of magnitude less than the ocean depths and the nonlinear effects, such as convections and bottom frictions, are negligible. Furthermore, at open seas, the wavelengths (tens to hundreds of kilometers) of ocean-wide tsunamis are always much greater than ocean depths (a few kilometers). The vertical components of accelerations are thus neglected and horizontal motions of water mass are taken as uniform from top to bottom (Satake, 2002). Finally, we end up with the simplest form of hydrodynamic equations to govern the motions of incompressible fluids, i.e. the linear shallow water wave equations.
The potential source region of the Manila subduction zone was divided into 14×10 square pixels, each with 0.5° ×0.5° in size and an initial vertical seafloor displacement of 1 m was assigned to each pixel to constitute the group of unit sources (Figure 4). We employed Cornell Multigrid Coupled Tsunami Model (COMCOT; Liu et al., 1998) to simulate the propagations of each unit source. COMCOT is a finite difference scheme and in our case, we solved for linear shallow water wave equations in spherical coordinates with 1 minute (~1.8 km) and 1 sec in space and time, respectively. The boundary conditions were total reflection for ocean-land interfaces and radiation for map boundaries. We set up 32 virtual stations representing existing tidal stations of the Central Weather Bureau (CWB; Figure 5). The wave fields of one station from one unit source were referred to the unit tsunamiscorresponding to the station-unit source pair. For each unit source, we simulated for four-hour propagations with the resulting wave fields as a function of time at the 32 stations to be stored as 32 unit tsunamis in database. In the end, a total of 14×10×32 unit tsunamis were stored in database for synthetics of tsunami waves in the case of a real event. The stored unit tsunamis were readily available for arrival time predictions even without the occurrence of real events. We applied Short Time Average over Long Time Average (STA/LTA; Allen, 1982), a conventional scheme for picking seismic P and S phases, to automatically pick the arrival times of unit tsunamis with results stored in database for arrival time predictions.
In the case of a real tsunamigenic event, we calculated the vertical seafloor displacements caused by the earthquake (Okada, 1985), using source parameters inverted by fitting seismic
We judge the qualities of solutions based on the discrepancies between those of
3.2. Unit tsunamis
Characteristics of tsunami wave propagations in SCS and around Taiwan depend on bathymetric features and can be learned from simulated propagations of unit sources. Figure 8 shows the propagating waves at different time frames of an exemplary unit source, from which we learned that tsunamis triggered by earthquake offshore north Luzon will hit south Taiwan at about 20 min., that the propagation speeds along east Taiwan coasts are much faster than those along west Taiwan coasts, meaning more warning time for the west coasts, and that almost all coasts around Taiwan will be attacked by SCS tsunamis within three hours after the generation of tsunamis. Figure 9a shows the resulting 32 unit tsunamis of the exemplary unit source, which demonstrate that stations 14 to 26 are the most affected ones with southern tip of Taiwan (stations 20, 21, and 23) being the most vulnerable (Figure 6). The STA/LTA scheme works well in determining the arrival times of unit tsunamis (Figure 9b) and we compile the data to produce one arrival-time map for each unit source (Figure 10), which will also be stored in database and are readily for prompt arrival-time predictions.
The experiences learned by conducting the
4.2. Unit tsunamis
We test with a scenario Mw9.0 earthquake in the Manila subduction zone to assess the applicability of predicting maximum amplitudes of tsunami waves using unit tsunami method. The vertical seafloor displacements caused by the scenario earthquake are calculated using Okada (1985)’s scheme [Figure 11(a)]. We first follow the conventional approach to simulate the propagation of the displacements, which takes time. Secondly, we derive the weighting factors of each unit source by averaging over the vertical displacements within each unit source [Figure 11(b)]. The tsunami waves are then synthesized by a linear combination of unit tsunamis – pulled from database – with corresponding weighting factors, which can be done instantaneously. Figure 12 shows resulting tsunami waves of the two approaches for comparison purpose. A maximum-amplitude map can also be created showing the magnitudes on the corresponding stations (Figure 13). By comparing (a) and (b) of Figures 12 and 13, we conclude that the unit tsunami method can produce waveforms and maximum amplitudes similar to those of conventional simulation method, however, only a much less time is needed.
Liu et al. (2009) have also proposed procedures to establish a tsunami early warning system in the SCS. The procedures also apply unit tsunami methods to pre-calculate tsunami waves of fault segments along the Manila subduction zone. The primary differences between the two systems are the ways in determining the weighting coefficients of unit tsunamis in synthetics - Liu et al. (2009)’s procedures invert the real-time observations of nearby ocean-bottom pressure sensors whereas we calculate from source parameters inverted by the
As a final remark, we point out that the unit tsunami methods are not compromised on regions of land or land-ocean boundaries. For pixels on land exclusively, the calculated unit tsunamis are zero for all stations and thus have no contributions to the synthetic tsunamis despite their non-zero weighting factors. Likewise, for pixels on coast lines, the calculated unit tsunamis only constitute contributions from the ocean parts, thus automaticallyproportional to the ocean-land ratio within the pixel. As a result, they will contribute proportionally to the synthetic tsunamis in the processes of linear combinations. As for regions of complicated bathymetries such as trenches, the vertical seafloor displacements in the regions tend to deviate from those estimated by Okada (1985)’s schemes, which assume a half-space elastic medium. However, both conventional approach and unit tsunami methods will suffer from the same deviations. The unit tsunami methods are equally applicable to warnings of local, regional, and global scales. However, strategies in building database of unit tsunamis should be adjusted accordingly; in global scale with greater potential source regions, we may use greater pixels to reduce the size of database, at the expense of reducing spatial resolutions of seafloor displacements; in local scale, the pixels cannot be too small in order that the conditions of long wave validate.
In this study, we propose to combine
This work was supported by Central Weather Bureau with grant number MOTC-CWB-101-E-09 and National Science Council (NSC) in Taiwan with grant number 99-2116-M-008-040.