## 3 Validation of Effectiveness
### Ground Motion Simulation of the 1994 Northridge Earthquake
The simulation results in the NS, EW, and UD directions are shown from left to right. The black line represents the observed record, the red line represents the GMPE, the yellow line represents the simulation result with the constant rise time when the subfault division number is 9 \(\times\) 10, the green line represents the simulation result with the modified rise time expression when the subfault division number is 9 \(\times\) 10, the brown line represents the simulation result with the constant rise time when the subfault division number is 36 \(\times\) 40, and the blue line represents the simulation result with the modified rise time expression when the subfault division number is 36 \(\times\) 40). and the blue line represents the simulation result with the modified rise time expression when the subfault division number is \(36\times 40\). Comparing the simulation results with the observed records at the stations, it can be seen that if the rise time is constant, the amplitude of the simulated response spectra and amplitude spectra will decrease in the intermediate frequency range. The amplitude decrease becomes more significant as the subfault division number increases. After using the modified rise time expression, the sag phenomenon that appeared in the intermediate frequency range is alleviated, and the simulation results are more consistent with the observed records. As the subfault division number increases, the decrease in amplitude is not as significant as the decrease when the rise time is constant. The simulation results of the horizontal components are compared with the results of the GMPE, and the results show that the response spectra simulated by the improved stochastic Green's function method are generally close to the results predicted by the GMPE, further verifying the rationality of the simulation results. From a sensitivity perspective, for the L4B station, the sensitivity of the simulation results to the subfault division number and the rise time expression is roughly similar in the period range of approximately 0.05 s to 0.5 s, while the simulation results show stronger  
Figure 5: Simulation results of the L09 station. (The comparisons of acceleration time histories are shown in the top row, the comparisons of acceleration response spectra are shown in the middle row, and the comparisons of displacement amplitude spectra are shown in the bottom row. The simulation results in the NS, EW, and UD directions are shown from left to right. The black line represents the observed record, the red line represents the GMPE, the yellow line represents the simulation result with the constant rise time when the subfault division number is \(9\times 10\), the green line represents the simulation result with the modified rise time expression when the subfault division number is \(9\times 10\), the brown line represents the simulation result with the constant rise time when the subfault division number is \(36\times 40\), and the blue line represents the simulation result with the modified rise time expression when the subfault division number is \(36\times 40\)). sensitivity to the rise time expression than the subfault division number in the period range shorter than 0.05 s and longer than 0.5 s. For the L09 station, the simulation results show stronger sensitivity to the rise time expression than the subfault division number in almost the whole period range. For ATB, CHL, and LV1 stations, the simulation results show stronger sensitivity to the subfault division number than the rise time expression in the short period range, while the simulation results show stronger sensitivity to the rise time expression in the long period range, and the boundary is approximately 0.5 s, 2 s, and 0.8 s, respectively. For the HOW station, the sensitivity of simulation results to the subfault division number is stronger than the rise time expression in almost the whole period range. The change in sensitivity may be related to the azimuth and site effects of the station.