# MCPSHA: A New Tool for Probabilistic Seismic Hazard Analysis Based on Monte Carlo Simulation
## 5 Discussion  
To verify the accuracy of the results generated by our program, 300 points are randomly chosen in the Baoji area, and the hazard (return period T = 476 years) for each site is computed using both the traditional CPSHA method and the MCPSHA program (shown in Figure 14). Although the results from both methods exhibit similarities, some differences persist (Figure 14). The correlation between the two intensity results is high, at 0.98 (Figure 15a). To further assess the disparity between the CPSHA and MCPSHA results, we calculate the difference by subtracting the two outcomes (Figure 15b). The average difference is 0.16, with a minimum of 0.08, a maximum of 0.2, and a standard deviation of 0.03. The observed difference may stem from the excessive discretization employed by the CPSHA program, specifically in variables such as earthquake magnitude and epicenter distance, intended for simplified integration. In MCPSHA, the utilization of the Monte Carlo method based on [PERSON]'s large number theorem ensures that, with an ample number of random simulations, the frequency of events precisely reflects the probability of their occurrence. Additionally, a comprehensive series of repeated experiments assures the occurrence of all possible conditions. Consequently, as the number of simulations increases, even events with low probability are taken into account. The most appropriate and scientifically sound approach for validating the results of the PSHA method is to rely on historical data specific to the region. The seismic activity history spanning approximately 3000 years in the studied area serves as a valuable validation tool. We have presented the expected occurrence probability for a mean return period of 476 years, a period that repeats more than six times within the historical information of the region. However, due to a lack of data, we were unable to locate several or a few sites with recorded macroseismic intensities. In future research, we intend to compare the modeling of observed intensity occurrences with those estimated by MCPSHA. Such a comparison is sufficient to either substantiate or negate the robustness of the proposed methodology. Figure 14: Seismic hazard maps for 10% probability of exceedance in 50 years calculated by MCPSHA (T = 476 years return period). The current seismic hazard analysis method is generally utilized for engineering seismic fortification; thus, only the extreme intensity of the site is taken into consideration. This method is not applicable to earthquake damage estimation [46, 47]. The seismic loss of a site is not only caused by an earthquake, which corresponds to its extreme intensity. Although the original extreme value (only considering one maximum case) correctly handles the randomness of future earthquake occurrences, if the duration is long and the site is located in a region with frequently occurring strong earthquakes, the loss caused by multiple earthquakes with the same intensity and that associated with one earthquake may obviously differ [48]. Therefore, when calculating the expected earthquake-induced loss, both the occurrence probability and the occurrence frequency of the seismic intensity should be considered. For example, the site may suffer multiple VI-intensity ground motions within a given number of years, and the loss produced in this situation is twice that generated by an earthquake with an intensity of VI. The estimation method based on extreme intensity ignores the above effects. Therefore, the seismic hazard analysis method of the engineering site cannot be directly used. Both the probability of occurrence and exceedance are important indicators of seismic hazards for a given site, but the meaning of the two indicators is distinctly different. Furthermore, the exceedance probability itself contains the meaning of extreme intensity.