## 3 Results  
### Higher Probability Area for Tsunami Detection  
Tsunami observation instruments should be placed in regions where energetic tsunami-related dynamics occur [3]. Previous studies used maximum tsunami wave height distribution to determine tsunami energy location since wave energy is proportional to squared wave height [3; 19]. This study also uses maximum tsunami wave height distribution as calculated using the COMCOT numerical model. The previous studies were conducted using tsunami amplitude Empirical Orthogonal Function (EOF) spatial modes, which helped determine where the tsunami's energy is mainly distributed [3]. The results showed the areas where the modal activity was highest. These areas match locations where tsunami energy is mainly distributed. These EOF analyses have been used to determine wind observation instrument locations for oceanographic and atmospheric research. These studies, however, including [PERSON] et al. (2017), have only examined a small number of potential tsunami scenarios. Tsunamis, generated off the west coast of Japan and propagating to the eastern sea of Korea, mainly damage the eastern coastal cities of Korea due to an underwater mountain ridge called the Yamato Rise [20]. Thus, this study defines a higher tsunami detection probability in areas where tsunami energy is primarily due to topology. Figure 4: Flow chart (blue box) and considerations (white box) used for determining an optical deployment region for offshore tsunami observation instruments. Although we do not consider the accuracy of the tsunami inversion source, distorted tsunami records due to the wave transformation the shallow water region are inadequate for processing tsunami inversion sources and impact our ability to forecast tsunami hazards [25]. Therefore, the minimum water depth limit for higher probability areas was set to 300 m to avoid distorting coastal tsunami records [3] (Figure 5). To confine the higher probability areas, we used the Maximum Likelihood Estimation (MLE hereinafter) instead of EOF spatial analysis because MLE is more cost-effective. MLE is the value that maximizes probability (\(\hat{\theta}\)) of the unknown parameter (\(\theta\)) from observing the given data (\(x\)) from a joint probability distribution. It can be estimated by maximizing the likelihood function (L(\(\theta\))) following formula (1):  
\[\hat{\theta}=\underset{\theta}{\text{argmaxL}}(\theta)\quad\text{ \ \ where L}(\theta)=\prod_{i=1}^{n}f(x_{i};\theta) \tag{1}\]  
The standard MLE approach is called the frequentist method. This method has been widely used for optimizing parameters that best fit the joint probability of the given data (\(x\)) [26]. In this study, MLE was applied using various parameters to determine a location in the eastern sea of Korea with a higher likelihood of tsunami propagation. The Korea Meteorological Administration issues tsunami warnings when there is an earthquake greater than Mw 7.0 and tsunami height reaches 0.5 m or higher at the Korean coast. Considering the effect of coastal morphology, this study estimates that the probability of a 0.1, 0.2, or 0.3m higher maximum tsunami height passing through each grid with the maximum tsunami height distribution as results of the numerical modeling. It was assumed that the occurrences of 39 tsunami scenarios were all independent. The probabilities of tsunami propagation above each standard wave heights in all grids of numerical modeling were calculated. And then, MLE results of each standard wave heights were obtained by the sum of the log probabilities. The location where has higher MLE matches the higher tsunami detection probability area because tsunamis propagate with different parameters more frequently in this region. Figure 5: Colored map of areas where water depth is greater than 300 m in the eastern year of Korea and Japan. This method helps determine the higher probability in the tsunami detection region where far-field tsunami energy is mainly distributed under the various fault parameters.