## 1 Introduction
At present, most of the theoretical calculation methods for the seismic response of horizontally stratified sites are based on the assumption of shear wave incidence at the site base, and most of the calculation methods adopt equivalent linearisation simplification. However, in practice, the seismic response of the site has strong nonlinear characteristics. Therefore, the obtained site dynamic response characteristics based on the shear wave incidence hypothesis and equivalent linearisation simplified calculation need to be further verified. At present, the dynamic response of sites is commonly based on time domain acceleration response analysis [30; 31; 32]. Complex slopes have a significant effect on the dynamic mechanics of the sites and lead to significant changes in the frequency components of waves due to wave refraction and reflection effects near the discontinuities in the rock mass [33; 34]. Time domain analysis using PGA (peak ground acceleration) cannot comprehensively reflect the seismic response of sites; therefore, their seismic response should be studied in the frequency domain. The fast Fourier transform (FFT) algorithm is the preferred method for investigating the dynamic response of sites [35; 36]. In addition, because seismic waves are nonlinear and unsteady signals, there are few studies on the seismic response of sites based on their own characteristic parameters and physical quantities [37; 38]. The Hilbert-Huang transform (HHT) is the preferred method to deal with nonlinear and unsteady signals and has a good time-frequency resolution [39]. However, the previous study of the seismic response of sites paid more attention to the analysis of a single domain, and time-frequency joint domain analysis was ignored. Therefore, to better understand the seismic response of layered sites from all directions and angles, a multidomain analysis method needs to be established. This work takes layered sites in the southwest Sichuan Basin, China as examples (Figure 1). A multidomain analysis method is used to investigate the seismic response of the layered sites under earthquake excitation (Figure 2). Three generalised geological models of the layered site are as follows: homogeneous site (Model 1), horizontally layered site (Model 2) and tilted layered site (Model 3). The layered sites contain hard rock, soft rock and gravelly soil (Figure 3). The seismic response characteristics of the layered sites were studied using FEM dynamic analyses according to the acceleration-time histories, modal analysis, Fourier transform, seismic Hilbert energy and marginal spectrum analysis. The wave propagation characteristics through the layered sites and their influence on the seismic response are studied. A new time domain analysis parameter PGA(IMF) based on the empirical mode decomposition (EMD) method is proposed, and its applicability is verified and compared by using PGA. According to the analyses of the time, frequency and time-frequency domains, the dynamic amplification effects of the layered sites are studied. In particular, the influence of the natural frequency of sites on their seismic response characteristics is discussed, and their dynamic response