## 5 Discussion  
In this paper, analytical models of the Stoneley and Knot equations are derived from the non-uniform incidence of P-SV waves in the \(xoz\) coordinate plane. Meanwhile, both analytical models and numerical models are based on P-SV waves. Therefore, the non-uniform spatio-temporal dynamic response and the amplification factor of SRA are considered in this coordinate plane. The ratio of the slopes length and the focal depth \((L/h)\) is the foundation for determining whether the slope model is consistent with BAP or the plane-wave hypothesis, and the parameter that affects the degree of non-uniformity.  
Indeed, the slopes are also influenced by SH waves, which cause polarization of the medium in the \(xoy\) plane. The dynamic response of SH waves to slopes has also been studied based on a variety of methods. The analytical formulation in the framework of classical elastodynamics has been derived for the scattering of oblique incident plane SH waves by a semi-cylindrical canyon [26]. Based on a two-dimensional nonlinear seismic response analysis program, the impact of the incident angle of the SH wave on PGA and the response spectrum of ground motion has been studied [27]. Based on the indirect boundary integral equation method (IBIEM), trapezoidal valley surface ground motion characteristics and distribution laws under SH wave incidence have been analyzed [25; 28]. Based on the indirect boundary element method, the response characteristics of different slopes under  
Figure 13: Contours of amplification factor of SRA with different slope scales under non-uniform seismic incidence. (**a**) \(L=2000\) m, \(L/h=4:20\); (**b**) \(L=1500\) m, \(L/h=3:20\); (**c**) \(L=1000\) m, \(L/h=2:20\); (**d**) \(L=500\) m, \(L/h=1:20\); \(h\) denotes the focal depth; \(L\) denotes the length of the slope.  
SH wave loading with various incident angles have been analyzed [29]. However, further study is required to gain a deeper understanding of the non-uniform spatio-temporal dynamic response and amplification effect caused by the slope scale. The coupling and superposition of SH and P-SV waves gives rise to a more complex dynamic response. Accordingly, the width of the slopes is also a significant variable in the following study.  
Furthermore, large-scale slopes comprise a multitude of intricate stratigraphic sequences and geological formations, including fault lines and fissures. The scattering of seismic waves at discontinuous interfaces can also have an impact on the stability of slopes. For the jointed rock mass, the jointed material model can be employed to simulate its behavior as a continuum [30]. On the other hand, the discretization technique can be applied to study the failure mechanism for non-uniform soil slopes with varying soil strength parameters, which cannot be readily solved in conventional limit analysis [31,32]. The continuous-discontinuous method, combining the finite element method and discrete element method (FDEM), has been adopted to simulate the dynamic response and failure mechanism of the slope due to its entire process of seismic loads [33]. Although the FDM framework used in this study captures essential features of wave propagation and slope deformation, more granular approaches like the Dynamic Lattice Element Method (DLEM) could offer enhanced insight into localized failure mechanisms and cementation effects, particularly in heterogeneous rock slopes [34]. In future studies, the continuum-discontinuity numerical model can be used to explore the integration of multi-physics approaches--particularly those involving thermal-hydraulic-mechanical (THM) coupling to more accurately simulate the complex interactions within geomaterials under seismic loading. For instance, studies investigating cyclic thermal behavior in soils [35, 36, 37] highlight the significance of such interactions in transient response modeling.