## 3 Results
### Warning Time Maximization  
It is the most effective way that the Tsunami Warning Center (TWC) gets maximized warning time to reduce the damage from the unexpected, devastating tsunamis [27]. Offshore tsunami observation instruments located in high probability detection areas are not necessarily enough to maximize warning time. We investigated how to further optimize instrument deployment regions to include maximized warning time. Warning time estimations were adopted from previous studies [21,22]. The appropriate warning time for a coastal community is at least 15 min [28]. Warning time estimates can be calculated using Equation (2) [21,22]:  
\[WT=TTT-(D_{d}+D_{tr}+D_{c}) \tag{2}\]  
where \(WT\) is warning time for a specified coastal line, \(TTT\) is tsunami travel time to the coastal line, and \(D_{d}\), \(D_{tr}\), and \(D_{c}\) are the tsunami instrument detection delay time, data transmission from the instruments to the TWC, and TWC measurement confirmation time, respectively. Previous studies estimated the sum of \(D_{d}\) and \(D_{tr}\) to be 10 min [21,22]. This estimation is based on initial tsunami wave periods generated by underwater earthquakes at about 20-min frequencies, with 6 to 8 min to detect the first tsunami wave peak. It takes approximately 2 min to transmit the data (\(D_{tr}\)) when using the Broadband Global Area Network (Inmarsat satellites). Figure 7: Comparison of maximum tsunami height distributions with the same fault parameters except source location and strike angle: (**a**) Location map of potential tsunami sources. Maximum tsunami height distributions are shown for (**b**) case28, (**c**) case33, and (**d**) case38. This is the preferred data transmission method since it has a robust, independent link to the local telecommunication system rather than a regular internet connection that could break during even an insignificant earthquake event [22]. \(D_{c}\) is calculated by the TWC once it confirms the tsunami using a designated threshold value. Since there is no tsunami warning system or threshold for tsunami detection in the eastern sea of Korea, we use delay time estimation from previous studies [22]. These estimates are acceptable because offshore tsunami observation instruments are typically deployed far from coastal areas, making communications times comparable. To determine maximum warning time, we applied the frequency method described in Section 3.1 to the \(D_{d}\), \(D_{tr}\), and \(D_{c}\) estimates and WT calculation from previous studies [21; 22]. The tsunamis, which occurred on the west coast of Japan in 1983 and 1993, took approximately 2 h to reach the east coast of Korea [29]. In this study, we set the TTT to 2 h based on this historical information. Using Equation (2), we calculated WT as 1 h 45 min. However, when considering both the location of the offshore tsunami observation instruments and that WT should be at least 15 min, offshore tsunami observation instruments should detect tsunami components within 1.5 h after the earthquake. To understand tsunami arrival time clearly, Figure 8 shows a time series of randomly chosen points (131.3640\({}^{\circ}\) E, 37.9726\({}^{\circ}\) N) to indicate tsunami arrival time. All parts of the grid are assumed to be in the higher probability detection area and are in the optimal instrument deployment location. We extracted a time series for tsunami arrival time. Figure 9 shows that the probability of tsunami travel time is less than 1.5 h after the earthquake in each grid of 39 potential tsunami scenarios. Furthermore, by multiplying the probability of Figure 9 and the result of maximum likelihood estimation, the optimal area of the tsunami observation instrumentation in the eastern sea of Korea was identified as shown in Figure 10. Results suggest that the region northeast of Ulleung-do is the optimal offshore region for instrument deployment.