## 5 Conclusions  
The seismic response of layered sites was investigated based on multidomain analysis. Some main conclusions are as follows.  
1. According to the multidomain analysis, elevation and stratum properties have a magnification effect on the seismic response of the layered sites. The PGA, PFSA, PHSA and PMSA increase gradually with elevation at the layered sites. The characteristics of wave propagation at layered sites are complex, and a weak gravel soil layer has a great influence on the seismic wave propagation characteristics. The dynamic  
Figure 16: The marginal spectrum of different measuring points (I, H, E, and B) of Model 2.  
Figure 17: Change of PMSA and PHSA with increasing elevation: (**a**) PMSA and (**b**) PHSA.  
amplification effect of the interface between soft rock and hard rock is relatively small, while overlying gravel soil has a greater amplification effect on seismic waves than rock mass. The seismic amplification effect of the models is as follows: Model 3 > Model 2 > Model 1. PGA(IMF) was proposed to analyse the dynamic amplification effect of layered sites, which can better reflect the influence of different strata on their seismic response characteristics.
2. The natural frequencies of the layered sites can be determined using Fourier spectrum and modal analysis. Natural frequencies have a significant influence on the dynamic deformation response of the sites. Frequency domain analysis shows that the interface of soft and hard rock mass strata has little influence on the Fourier spectrum characteristics of the sites, and only the PFSA mainly increases to a certain extent. The overlying gravel soil has an obvious magnification effect on the PFSA and U; in our study, the PFSA of the high-frequency band of seismic waves was greatly amplified, and the PFSA of \(f_{6}\)-\(f_{8}\) (\(\geq\)30 Hz) in the gravel soil layer increased rapidly.
3. The seismic energy in the Hilbert energy spectrum and marginal spectrum of the horizontally layered site is mainly distributed in low-order natural frequencies (7-13 Hz) and high-order natural frequencies (27-34 Hz), respectively. Stratum properties have a significant effect on the Hilbert energy spectrum characteristics in layered sites. When waves pass from hard rock to soft rock, the peak value of the seismic Hilbert energy spectrum changes from single to multiple peaks, and the frequency components near the peak become more abundant. When the seismic wave enters gravelly soil, the Hilbert energy spectral peak and its nearby amplitude are significantly magnified, and the frequency components near the PHSA become more abundant. In our study, the seismic energy of the Hilbert energy spectrum in the high-frequency band (28-36 Hz) was obviously amplified. Moreover, the marginal spectrum characteristics changed with elevation in the layered sites. Compared with hard/soft rock, gravel soil had an obvious amplification effect on seismic energy transmission. The PMSA increased with elevation in the high-frequency band; in particular, the frequency components and spectral amplitude of the marginal spectrum became more abundant and significantly larger in gravelly soil.  
Methodology, D.S.; Writing--original draft, L.D. and G.L.; Writing--review & editing, D.S. and G.L. All authors have read and agreed to the published version of the manuscript.  
The National Natural Science Foundation of China (52090081, 41941019, 52109125), the China Postdoctoral Science Foundation (2020M680583), the National Postdoctoral Program for Innovative Talent of China (BX20200191), the Excellent Sino-foreign Youth Exchange Program of China Association for Science and Technology in 2020 (No. 58), and the Shuimu Tsinghua Scholar Program (2019 SM058).  
Not applicable.  
The data used to support the findings of this study are available from the corresponding author upon request.  
The authors would like to thank the editor and the reviewers for their contributions.  
The authors declare that they have no conflict of interest.