# Numerical and Statistical Analyses of Tsunami Heights with the L-Moments Method
## 2 Numerical Simulation  
### Study Area and Earthquake Sources  
In this study, we used virtual earthquake sources in Japan that have a high probability of causing damage in the Republic of Korea. The values given by the Ministry of Land, Infrastructure, Transport and Tourism [3] of Japan were used as the fault parameters. Figure 1 shows the areas in Korea chosen for this study--the Imwon Port and the Sadong Port. The East Sea, surrounded by Korea, Japan, and Russia, is also shown (Figure 1). At the Imwon Port, one person was killed and two others were reported missing in the 1983 Central East Sea tsunami that occurred on 26 May 1983. This is the only human casualty recorded in the Korean Peninsula in the last 100 years.  
Firstly, we had to determine the earthquake sources in order to perform numerical experiments for the target area. To estimate the initial water surface displacement of each source, we used a model based on the fault parameters under the assumption that the initial water surface displacement presented by [PERSON] and [PERSON] (1971) [4] was the same as the vertical component of the submarine displacement.  
Numerical model domains of the East Sea, the Imwon Port, and their bathymetries are presented in Figure 2. The numerical information and boundary conditions for each region are given in Tables 1 and 2, respectively. The grid size was decreased by 1/3 based on the dynamic linking method (Table 1). Region A used the free transmission condition, and the other regions used the dynamic linking method as a boundary condition for the open sea. A fully reflected condition was used for the A, B, C, and D regions. The tsunami heights in this study were predicted at all grid points in Region D of Table 1.  
Figure 1: Study areas in Korea—the Imwon Port and the Sadong Port.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Region**} & **Grid Size** & **Mesh Number** & **Time Step Size** & **Numerical** \\  & **(Ax=\(\Delta y\))** & **Imwon** & **Sadong** & **(Af)** & **Model** \\ \hline A & \(1215.0\) m & \(976\times 1114\) & \(3.00000\) s & Linear \\ B & \(405.0\) m & \(979\times 1117\) & \(1.00000\) s & Linear \\ C & \(135.0\) m & \(979\times 1117\) & \(0.33333\) s & Linear \\ D & \(45.0\) m & \(61\times 73\) & \(64\times 79\) & \(0.11111\) s & Linear \\ \hline \hline \end{tabular}
\end{table}
Table 1: Computational information for each region.  
Figure 2: Domain of numerical simulation of tsunamis and geographical information for the Imwon and Sadong Ports. (Regions A, B, C and D are computational regions.)  
Figure 3 shows the distribution of the virtual earthquake sources. All of the sources are located near the west coast of Japan. Many existing studies have reported tsunami traveling times of about 100-150 min from the west coast of Japan to the east coast of Korea (e.g., [1]). In the numerical simulation, we employed all 44 virtual earthquakes plotted in Figure 3. In the figure, Case 1 is the northmost case, while Case 44 is the southmost one. Fault parameters for the virtual earthquakes displayed in Figure 3 are listed in Table 1 in Appendix A.