## 4 Discussion and Conclusions  
In this paper, based on [PERSON]'s theory and IBEM, the Monte Carlo method is used to generate random sedimentary valley samples. The displacement amplitude response under the SV wave incidence is calculated to explore the influence of the randomness of sedimentary media (porosity and permeability coefficients) and boundary randomness on the site response. The following conclusions are drawn:  
1. The change of porosity has little influence on the seismic response under the certain boundary condition, but it has a greater influence under the random boundary condition, and the coefficient of variation is magnified by 1.5-3 times. The influence cannot be ignored. The coefficient of variation of the surface response is positively correlated with sedimentary porosity and increases continuously with the increase in porosity. Therefore, the change of porosity needs to be considered in the uncertain boundary in practical engineering. 2. Compared with the soil porosity, the boundary permeability coefficient has a greater influence on the ground motion amplification effect of the sedimentary valley. Under the certain boundary condition, compared with the permeable case, the coefficient of variation of the impermeable case is magnified by an average of 2-3 times, and the displacement amplitude data are more discrete. The effect is more significant under uncertain boundary conditions, with an average magnification of 5-6 times. The change of media permeability coefficient in the sedimentary valley also leads to a great change in the width of the confidence interval, so it is more necessary to consider the influence of the permeability coefficient in the sedimentary valley. 3. The influence of boundary shape change is related to many factors, such as incident frequency, incident angle, incident wave position, and so on. The variability of the displacement amplitude of the sedimentary part is significant at low frequency, but on the contrary, at high frequency, the significant variability is at the edge of the sedimentary valley. Compared with the vertical incidence, the average magnification of the coefficient of variation at 30\({}^{\circ}\) is 2-3 times, indicating that the angle also has a great influence. The coefficient of variation of the front wave surface is higher than that of the back wave surface, which proves that the position of the incident wave also has a certain influence on the coefficient of variation. 4. The results show that the spatial variation of ground motion is very large. The amplitude of ground motion at the top of the valley slope is much greater than that at the bottom. The amplitude at the front wave surface is greater than that at the back wave surface. These conclusions are consistent with the monitoring conclusions of the Feitsui Canyon ([PERSON], [PERSON] et al. [45]). More parameter analysis and verification is needed, in combination with the measured ground motion records. To sum up, both the randomness of saturated medium and boundary shape have a certain influence on the response of the ground motion of a sediment valley. Compared with porosity, the displacement amplitude is more affected by the randomness of permeability coefficient. In the actual engineering site, selecting the appropriate medium parameters in the confidence interval can greatly simplify the calculation. The critical parameters, such as the permeability coefficient, should be analyzed in detail. In engineering design, special attention should be paid to the spatial variation effect of ground motion in the sedimentary valley site. The conclusion plays an important guiding role in earthquake disaster