## 1 Introduction  
Western China has been prone to earthquakes in recent decades; specifically, the Wenchuan earthquake in 2008 was the largest and most widely distributed earthquake disaster in China [1, 2]. Earthquake disasters mainly involve damage directly caused by fault dislocation and damage caused by strong earthquakes [3, 4, 5]. The former is generally in the blind area of the earthquake, which is difficult to prevent, while the latter is mainly affected by geological conditions, as has been verified by the Wenchuan earthquake [6, 7]. By contrast, the approximately 30 m-thick sand and pebble layer below China's Chengdu area effectively consumes the energy transmitted by seismic waves and reduces the impact of ground motion on the tall buildings above [8]. The geological conditions of sites, in short, have a great influence on their seismic response [9, 10, 11, 12, 13]. In Southwest China, many important buildings are built on different types of sites with complex geological structures; in particular, layered sites are a common type of building site. Due to the complex geological materials and structures in layered sites, the seismic response of the sites has been complicated [14, 15, 16, 17]. Therefore, the seismic response of layered sites has become an important research topic in geotechnical engineering. The seismic response of sites has an important effect on the stability of the overlying buildings [18], making it essential to study their dynamic response characteristics. Since [PERSON] realised the influence of site conditions on the seismic dynamic response from the 1928 San Francisco earthquake, researchers have been investigating the seismic response characteristics of stratified sites using quantitative methods due to the lack of measured data on field seismic responses [19; 20]. With the collection and accumulation of seismic damage data from previous earthquakes, the seismic response of sites has attracted increasing attention. Many scholars have obtained meaningful conclusions through studies using the empirical method of strong vibration observation, analytical analysis and numerical simulation [21; 22; 23]. [PERSON] studied the intensity anomalies in the Chile and Mexico earthquakes in 1985 and California earthquakes in 1987 by using the traditional spectral ratio method based on the main and aftershock acceleration histories of earthquakes and thereby obtained the topography and soil layer amplification effect [24]. Based on the aftershock records of the Northridge Earthquake in 1994, [PERSON] et al. used the traditional spectral ratio method, generalised linear inversion method and H/V method to study the field amplification effect in the intensity anomaly area of the San Fernando Valley in California [25]. [PERSON] et al. analysed the Kanto Basin by the generalised linear inversion method and found that the intensity anomaly area was caused by soil layer amplification [26]. In addition, horizontally stratified sites are common geological bodies in southwest China. At present, the main method for obtaining the dynamic response of the layered soil layer is the one-dimensional equivalent linearised wave method [27]. Based on the soil dynamic constitutive model, [PERSON] et al. proposed an explicit finite element method (FEM) for the seismic response of horizontally stratified sites under the condition of transmitting artificial boundaries [28]. According to the propagation principle of seismic waves in layered elastic media, [PERSON] et al. proposed a fast time-history algorithm for calculating the seismic response of layered soil sites by using the method of elastic wave superposition [29]. [PERSON] et al. studied the seismic response of horizontally stratified sites under seismic conditions by using a shaking table test in the time-frequency domain [20].