## 5 Conclusions  
Based on the fluid artificial boundary, this paper established a 2D finite element model of the reef-island-seawater system and further analyzed the site seismic response under the action of ground motions with different spectral characteristics. The study focuses on the influence of factors such as the slope angle (\(\theta\)) of the bottom layer of the reef island, the reef platform width (\(L\)), and the lagoon topography on the peak ground motion distribution of the reef-island site. The conclusions and findings are as follows:  
1. The influence of the bottom layer slope angle (\(\theta\)) of the reef island on the peak ground motion distribution is mainly reflected in the position of the reef island slope surface. For the distribution of the horizontal ground motion peak, the influence is mainly reflected in the slope surface of the reef. For the vertical ground motion peak distribution, with the increase of the bottom slope of the island, the vertical ground motion peak distribution of the island slope is closer to the vertical ground  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{ \begin{tabular}{c} **Input** \\ **Motion** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} \(L\) \\ **(m)** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **\(\theta\)** \\ **(\(\text{\text{\text{\text{\text@underline{0}}}}}\))** \\ \end{tabular}  } & \multirow{2}{*}{
\begin{tabular}{c} **\(\text{\text{\text@underline{\text{\text@underline{\text{\text@underline{\text{\text@underline{\text{\text@underline{\text{\text@underline{\text{\text@underline{ \text{ \text{ \text@underline{ \text{ \text{   \texttext@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@  
motion distribution of the free-field. The larger the bottom slope angle and the more high-frequency components of ground motion input, the larger the amplification coefficient corresponding to the peak of ground motion on the reef platform surface will be. 2. The influence of the reef platform width (\(L\)) on the peak acceleration distribution is reflected in the peak distribution and peak size on the island slope surface and the reef platform surface. The extent of this influence will decrease as the slope angle (\(\theta\)) increases. For high-frequency input, a smaller reef platform width will induce a larger peak acceleration response on the reef platform surface. For vertical peak ground motion distribution, it is usually shown that high-frequency input motion will cause a large peak ground motion response within a small platform width. 3. Seawater has a significant suppressive effect on vertical ground motion. The more high-frequency components of the input ground motion, the more obvious this suppression effect will be. The influence of the seawater layer is mainly reflected in the seismic peak distribution on the slope of the reef and the surrounding seabed. Due to the suppression effect of seawater layer on vertical ground motion, the maximum horizontal acceleration of the island-seawater model is obviously greater than that of the slope-platform model, while the maximum vertical acceleration is smaller than that of the slope-platform model. 4. The existence of the lagoon will amplify the maximum peak acceleration on the reef platform, and the degree of this amplification is closely related to the slope angle (\(\theta\)), the reef platform width (\(L\)), and the spectral components of the input ground motion. According to the results of different working conditions, the lagoon can amplify the maximum horizontal and vertical peak accelerations on the reef platform by about 19 and 6 times relative to the corresponding free-field results, respectively. It is worth noting that the study in this article assumes that the medium of the reef site is a linear elastic medium. However, under the action of large earthquakes, the medium of the reef will enter a nonlinear stress-strain state.