## 2 Study Area: The Jiazhaigou Earthquake and the High-Steep Rock Slide
### Processing of the Input Seismic Wave Loadings  
Figure 8 shows the original EW (East-West direction), NS (North-South direction), and UD (Up-Down direction) seismic waves used in the numerical model. These curves represent the acceleration time histories of the seismic waves. They are obtained from the 2017 Jiuzhaigou earthquake, corresponding to the \(X,Z\), and \(Y\) directions of the dynamic load input during the simulation process. The geographic coordinates of the selected seismic wave station are \(32.8^{\circ}\) N \(10.4^{\circ}\) E. The dataset is provided by the China Earthquake Networks Center, National Earthquake Data Center ([[http://data.earthquake.cn](http://data.earthquake.cn)]([http://data.earthquake.cn](http://data.earthquake.cn)) (accessed on 20 March 2020)). The frequency component of the input waveform, and the wave velocity characteristics of the rock mass will affect the numerical accuracy of wave propagation. To describe the wave propagation in the model accurately, the study by [PERSON] and [PERSON] shows that the zone size must be less than 1/8-1/10 of the wavelength, corresponding to the highest frequency of the input waveform [35]. On account of the maximum frequency of seismic waves has a more significant impact on the zone size, filtering seismic waves is required. The higher the maximum frequency is, the smaller the zone size is. The aim of filtering seismic wave is to filter out the high-frequency components of the original waveform and reduce the maximum frequency of small seismic waves, thereby increasing the minimum zone size for less calculation time. As an illustration, Figure 9a shows the seismic wave filtering of the EW seismic wave. The frequency corresponding to peak acceleration is mainly concentrated in the range of 10-15 Hz. Therefore, the part of the waveform greater than 20 Hz can be filtered by Wizard software. The maximum frequency of the filtered waveform is about 20 Hz, as shown in the red line in Figure 9a. The equation for calculating the shear wave velocity is \(C_{\rm s}=\sqrt{G/\rho}\), and the equation for calculating the longitudinal wave velocity is \(C_{\rm p}=\sqrt{\frac{K+4G/3}{\rho}}\), where \(G\), \(K\) and \(\rho\) represent the model shear modulus, bulk modulus, and density, respectively. According to the input model parameters, the shear and longitudinal wave velocities of this model can be estimated to be 2435 m/s and 4551 m/s, respectively. According to the calculation equation of wavelength \(\lambda=C_{\rm s}/f\) (\(\lambda=C_{\rm p}/f\)), where \(C_{\rm s}(C_{\rm p}),f,\) and \(\lambda\) represent the shear (longitudinal) wave velocity, highest waveform frequency, and wavelength, respectively. And the wavelength of this seismic wave can be estimated to be from 121 m to 228 m. Therefore, the zone size is set to 5 m for the perilous rock mass and 15 m for the base rock, satisfying the calculation requirements. Figure 8: Ground acceleration records of Jiuzhaigou earthquake. The velocity-time history within 45-55 s when the acceleration peak appears is intercepted as the input dynamic loading, and the bottom boundary of the model is the seismic application source. In the 3 DEC seismic dynamic analysis, if the final input velocity is not zero, or the final displacement obtained by integrating the input velocity is not zero, the velocity and residual displacement will continue to appear at the end of the dynamic calculation. Baseline correction is usually conducted to eliminate the integration errors for time-domain seismic analysis by adding a low-frequency waveform to the original velocity time history. Figure 9b shows the baseline correction progress for EW seismic waves, and Figure 10 illustrates the final input of seismic waves of EW, NS, UD, and EW_NS_UD in 3 DEC.  
Figure 9: Seismic wave filtering and baseline correction. (**a**) Seismic wave filtering (black line: filtered waveform; red line: original waveform).