## 3 Results and Discussion
### Slope Erosion Versus Seismic Signals and Acoustic Signals (Baseline Case)
Parametric Study of Influence of Significant Wave Height H\({}_{\rm s}\) and Wave Frequency on the Erosion Ratio, Retreat, and Arias Intensity I\({}_{\rm A}\)  
This section discusses the influence of significant wave height H\({}_{\rm s}\) and wave frequency on the erosion ratio, retreat, and I\({}_{\rm A}\) by comparing the test results from the Baseline Case and Cases 1-11. The significant wave height H\({}_{\rm s}\) is discussed instead of the wave height because the wave height during Stage 3 in the Baseline Case, Case 1, and Case 2 varied too much. Table 2 lists the outcomes of the erosion ratio, retreat, and I\({}_{\rm A}\). These outcomes are  
Figure 15: Profile deformation of the slope model during 4176 s–438 s. (The white dashed rectangle shows the enlarged inset photo of the top portion of the slope model.) evaluated based on the state of the equilibrium profile and a duration of 900 s since the wave maker started. The results are plotted in Figures 16 and 17 with trend lines. According to Figure 16a, there is a noticeable correlation between the erosion ratio and H\({}_{\text{s}}\) (significant wave height); even under the same wave frequency conditions, a higher H\({}_{\text{s}}\) typically indicates a higher erosion ratio. However, under the wave action of 0.33 and 0.416 Hz, the erosion ratio is relatively smaller due to the lower H\({}_{\text{s}}\). This underscores the significant impact of H\({}_{\text{s}}\) on the erosion ratio. Figure 16b illustrates the relationship between retreat and H\({}_{\text{s}}\). Under the same wave frequency conditions, a higher H\({}_{\text{s}}\) results in  
Figure 16: Duration 0–900 s: (**a**) erosion ratio vs. significant wave height, H\({}_{\text{s}}\); (**b**) retreat vs. H\({}_{\text{s}}\); (**c**) erosion ratio vs. wave frequency; (**d**) retreat vs. wave frequency (the dotted lines represent the trend lines). Figure 17: Relationship between Arias Intensity (I\({}_{\text{A}}\)) and erosion ratio (duration 0–900 s). a longer retreat distance. With 0.33 Hz wave action, the retreat is almost negligible, as the lower H\({}_{\rm s}\) restricts erosion primarily to the slope surface. In contrast, under the influence of 0.416 Hz waves, due to the higher H\({}_{\rm s}\), the retreat is notably longer than that at 0.33 Hz. The trend lines derived from linear regression analysis in Figure 16a,b, with an R\({}^{2}\) value of approximately 0.8, demonstrate the strength of these correlations. Figure 16c shows that as wave frequency increases, regardless of whether the H\({}_{\rm s}\) is the same or not, the slope's erosion ratio exhibits an upward trend. Additionally, Figure 16c also reveals that a higher H\({}_{\rm s}\) is associated with a relatively higher erosion ratio. Figure 16d indicates that higher wave frequencies lead to an increase in the retreat distance of slopes, a trend that is consistent across different H\({}_{\rm s}\) values. The linear regression analysis for Figure 16c,d shows trend lines with an R\({}^{2}\) value of about 0.6. These data suggest that the impact of H\({}_{\rm s}\) on the erosion ratio and retreat is greater than that of wave frequency. Figure 17 reveals a significant trend; the higher the erosion ratio, the greater the resulting I\({}_{\rm A}\) and seismic energy. This finding can be an important future application for seismic monitoring and early warning of slope erosion or collapse and sliding under wave actions. For example, if a seismic sensor detects a higher amount of seismic energy, it may indicate that the slope is experiencing more severe erosion. There are various methods to mitigate erosion effects, including hardware engineering measures (such as breakwaters and sea walls), \"software\" measures (like beach nourishment and vegetation planting), and methods to reduce wave energy (such as underwater dissipaters and artificial reefs). The results of this study could be used to help assess the erosion conditions of coastal slopes, aiding in the formulation of strategies to mitigate wave erosion effects.