When seismic waves travel from the bedrock into the soil layers, resonance occurs. Generally, the concept of resonance means that the level of damage to surface structures increases. The closer the characteristics of the soil layers are to each other, the less resonance occurs; conversely, the more different these layers are from one another, the greater the resonance. Therefore, the presence of soft soil over bedrock causes the amplified acceleration to be transferred to the foundation of the structure, increasing the likelihood of damage to the structure. Topographic amplification refers to the phenomenon where seismic waves are enhanced or altered as they interact with the topography of a site, such as hills, valleys, and ridges. This amplification can significantly influence the seismic response of structures, leading to increased ground motion and potentially greater damage during an earthquake. Investigating topographic amplification and its effects on the seismic response of topographic sites is an important issue that has attracted considerable interest from many researchers. Studies in the area of topographical influences have shown that the nature of the terrain is instrumental in influencing the level of damage caused by earthquakes. Local topographical formations can enhance intense ground movements during earthquakes, resulting in significant damage.

Iran is located in a seismically active region, with many areas in the country adjacent to various topographies, especially hills. Given the presence of active faults in the country and a history of significant earthquakes, it is essential that the design and construction of structures are carried out in a way that provides sufficient resistance to these influential factors. Studies and research conducted on the effects of topography and the phenomenon of seismic wave amplification as they pass through surface layers have shown that topography has a considerable impact on the extent of earthquake damage.

In this research, the hill model in the form of a semi-sinusoidal shape is examined in two layers, as well as the effects of this type of site on the amplification of ground response. By modeling several semi-sine hills with different stratifications using FLAC software under Rayleigh wave conditions, the impact of topography is investigated. Before conducting the modeling, the accuracy of the analytical method must be verified. For this purpose, validation studies from Wang (1982) and results from other researchers will be used to authenticate the analysis of two problems. Finally, to ensure the accuracy of the FLAC software, a similar model will be constructed, and by applying a Rayleigh wave, the desired parameters will be determined at various points of the site (semi-sinusoidal hills) and compared with the graphs from the article. This research examines how a frequently found topographical feature, particularly semi-sinusoidal hills, influences the seismic reaction of the Earth's surface when exposed to vertically propagating SV waves.

The main objective of this research is to examine the effects of various layering at a specific type of site, namely semi-sinuous hills. The study aims to model and analyze the seismic response of this type of site, investigating the impact of surface topography on seismic behavior and comparing the results obtained from the analysis under different conditions. In this research, efforts have been made to investigate the seismic behavior of sinuous hills under different layering conditions to determine the effects of soil characteristics in the layers, as well as the thickness and angle of the layers on the results obtained.

This study investigated how layering affects the response of semi-sinusoidal hills by analyzing hills with two layers, each featuring different layering characteristics and thicknesses. The study also examines the impact of soil characteristics, layering thickness and angle and the position of the looser layer. Different features in layering have an impact on the overall trend of amplification on the top of hills and de-amplification near the toes of hills in response to the horizontal components of displacement, velocity, and acceleration. The study revealed that in two-layer hills, the effects of soil characteristics are greater compared to the thickness and angle of layering. Overall, the most significant change in the acceleration component was observed when the upper layer was loosened in two-layer hills. Conversely, the smallest change in all three components occurred when the upper layer was halved.