# MCPSHA: A New Tool for Probabilistic Seismic Hazard Analysis Based on Monte Carlo Simulation
## 1 Introduction  
China, as one of the world's most seismically active countries [1], faces significant earthquake risks, with over half of its cities situated in zones prone to earthquakes of intensity VII or higher [2, 3]. Recognizing the pivotal role of seismic risk analysis in disaster prevention and reduction, the fundamental aim is to calculate and analyze ground motion characteristics over time, forming an integral part of engineering seismic fortification [4]. Given the escalating global trend in earthquake disasters, conducting medium- and long-term seismic risk assessments becomes crucial. Simultaneously, these assessments providea scientific foundation for disaster prevention and reduction planning [5; 6; 7], as well as informing decisions related to disaster reconstruction and site selection [8; 9]. The probabilistic seismic hazard analysis (PSHA) result is generally expressed by ground-motion with a varying probability of exceedance at a site [10]. Initially introduced by [PERSON] in 1968 [4], this methodology has been extensively applied for seismic risk assessment in numerous regions [11; 12; 13]. However, the Cornell-McGuire method, a prominent approach in PSHA, is often perceived as non-transparent by end-users due to its lack of clarity regarding the relative contributions of different sources and magnitudes to seismic hazards. Many scholars have made notable contributions and enhancements to the program. For instance, [PERSON] et al. [14] applied a logic tree approach to calculate robust seismic hazard estimates for the northeastern regions of Italy. Their methodology involves various seismotectonic knowledge levels, seismicity rate computation methods, maximum magnitude estimation approaches, and PGA attenuation relations. The resulting hazard maps, processed through a GIS system, highlight elevated hazard areas in central Friuli and around Vittorio Veneto. Additionally, [PERSON] and [PERSON] [15] introduced a method specifically designed for estimating seismic hazards through a probabilistic analysis of macroseismic data. This method, available freely upon request, facilitates the computation of hazard curves, intensity, or PGA values with fixed exceedance probabilities. It leverages locally available seismic effects information, integrating both actual and \"virtual\" intensity values from neighboring sites while considering uncertainties and reliability factors. The method also incorporates adaptable, region-dependent coefficients suitable for international applications. In earthquake loss estimation, the extreme probability of intensities is commonly used to replace the probability of occurrence at a certain intensity, which is then combined with the vulnerability matrix to obtain seismic risk results [16; 17]. Although the assessment results are expressed as a percentage, the PSHA results give the probability of exceeding a certain ground motion intensity, and the seismic vulnerability analysis is the expected degree of losses within a defined area under earthquakes with various seismic intensities, often expressed in matrix form [18]. In recent years, only a few studies about the occurrence probability of intensity have been carried out [19]. [PERSON] et al. [20] use the Bernoulli repeated test to simulate and calculate the probability of ground motion occurrence. Attempts have been made to improve the seismic intensity integral interval of the Poisson model, and the complex integral formula is simplified using the Taylor formula by [PERSON] [19]. Based on the actual ground motion, [PERSON] et al. [19] define a reasonable and reliable design earthquake, and the deterministic method is used. However, only by increasing the constraints and simplifying the seismic activity model or mathematical expression can the algorithm be implemented.