## 2 Materials and Methods
### Stochastic Finite-Fault Modeling Methods  
To evaluate the ground motion parameters generated by a maximum credible earthquake at a near-field site, we employed stochastic finite-fault modeling based on dynamic corner frequency, which has been confirmed to be suitable for engineering applications [60] (EXSIM12). In the stochastic finite-fault modeling of ground motions, a rupture fault is divided into N subfaults with a length of \(\Delta\)l and a width of \(\Delta\)w, where each subfault is considered a small point source. The ground motion contributed by each subfault can be calculated using the stochastic point-source method and then summed at the observation point with an appropriate time delay to obtain the acceleration time series, a(t), caused by the entire ruptured fault, as follows:  
\[a(t)=\sum_{i=1}^{nl}\sum_{j=1}^{n\text{up}}a_{ij}\left(t+\Delta t_{ij}\right) \tag{16}\]  
where \(nl\) is the number of subfaults along the strike of the entire ruptured fault and \(nw\) is the number of subfaults along the dip. \(\Delta t_{ij}\) denotes the relative delay time for the radiated wave from the \(ij\)th subfault to the site. \(a_{ij}(t)\) represents the acceleration time series of the \(ij\)th subfault at the site simulated using the stochastic point-source method [30]. [PERSON] and [PERSON] [60] reported the dynamic corner frequency and acceleration spectrum of the shear wave of the \(ij\)th subfault \(Aij(f)\) as follows:  
\[A_{ij}(f)=\left\{CM_{0 ij}\left(2\pi f\right)^{2}/\left[1+\left(f_{0 ij}\right)^ {2}\right]\right\}\left\{G\left(R_{ij}\right)\exp\left(-\pi fR_{ij}/Q\beta \right)\right\}\left\{A(f)\exp\left(-\pi f\kappa_{0}\right)\right\} \tag{17}\]  
where \(M_{0 ij}\), \(f_{0 ij}\), and \(R_{ij}\) represent the seismic moment of the subfault, the dynamic corner frequency, and the distance from the \(ij\)th subfault to the site, respectively. For the constant \(C=\frac{R^{\phi}\epsilon_{F}}{4\pi\rho\beta^{3}}\), \(R^{\theta\phi}\) denotes the radiation pattern (average value of 0.55 for shear waves); \(F\) denotes the free surface amplification, which is usually taken as 2.0; the partition of the two horizontal components of \(V\) is 0.71; \(\rho\) denotes the density near the source; and \(\beta\) denotes the average crustal shear wave velocity [61; 62]. The term \(\exp(-\pi f\kappa_{0})\) is a high-cut filter that considers the near-surface attenuation effects, and \(\kappa_{0}\) denotes the spectral decay at high frequencies [51; 63]. The quality factor \(Q(f)\) is related to the anelastic attenuation caused by the propagation path. \(G\left(R_{ij}\right)\) is the geometrical spreading, which is given by a trilinear piecewise model, and \(A(f)\) is the local site amplification, as mentioned in [PERSON]'s work [62]. The source corner frequency of the \(ij\)th subfault is expressed as follows:  
\[f_{0 ij}=4.9\times 10^{+6}\cdot\beta\left(\Delta\sigma/M_{0 ij}\right)^{1/3} \tag{18}\]  
where \(\Delta\sigma\) is the stress drop and \(M_{0 ij}\) represents the seismic moment of the \(ij\)th subfault, which can be expressed as follows:  
\[M_{0 ij}=\frac{M_{0}}{N}\frac{S_{ij}}{\sum_{l=1}^{nl}\left(\sum_{k=1}^{nw}S_{ kl}\right)/N}=\frac{M_{0}S_{ij}}{\sum_{l=1}^{nl}\sum_{k=1}^{nw}S_{kl}} \tag{19}\]  
Here, \(S_{ij}\) is the relative slip weight of the \(ij\)th subfault. The dynamic corner frequency of the \(ij\)th subfault, \(f_{0 ij}(t)\), can be defined as a function of \(N_{R}(t)\) and the cumulative number of ruptured subfaults at time \(t\) as follows:  
\[f_{0 ij}(t)=4.9E^{+6}\cdot N_{R}(t)^{-1/3}\cdot\beta\left(\Delta\sigma/M_{0 \text{ave}}\right)^{1/3} \tag{20}\]where \(M_{\rm{0 ave}}=\frac{M_{\rm{0}}}{N}\) represents the average seismic moment of all subfaults.