Delineation of Seismic Sources in Probabilistic Seismic-Hazard Analysis Using Fuzzy Cluster Analysis and Monte Carlo Simulation by A. Ansari, E. Firuzi, and L. Etemadsaeed Abstract Determination of seismic sources is the first step in probabilistic seismic- hazard analysis (PSHA); however, this step, especially in low seismic regions, is often controversial. In conventional PSHA procedure, determination of seismic sources is merely based on the subjective judgments of experts, and in many cases, there are great differences among proposed seismic models in a specific region. As a result, one important source of uncertainty in PSHA is due to determination of seismic sources. In this article, by combination of fuzzy clustering analysis and Monte Carlo simulation, an objective method for determination and probabilistic modeling of seis- mic sources is presented. By clustering spatial locations of earthquakes, it is possible to specify the extent of each seismic source in an objective way. A cluster quality index is used to identify the optimum number of clusters. The density and spread of events in each cluster determines the geometrical shape of seismic sources. More- over, in this article a method is proposed to construct spatial probability density func- tions (PDFs) of earthquake locations based on the results of fuzzy clustering analysis. The spatial PDF of earthquakes can be used for the generation of synthetic events in Monte Carlo simulation. The Azarbaijan region, with its varied seismotectonics and generally high seismicity, is used as an important area of seismicity in which to de- velop and demonstrate the application and capability of fuzzy clustering analysis in specifying seismic sources. The PSHA is performed for the city of Tabriz, and a com- prehensive comparison is made between the results of conventional PSHA, ordinary Monte Carlo hazard analysis, and the proposed method. The results indicate there is an objective relationship between observed seismicity and seismotectonic evidences in the region. Moreover, the distribution of synthetic events is highly correlated with the observed seismicity, seismotectonic, and geological information of the region. Introduction Probabilistic seismic-hazard assessment (PSHA) is widely considered as seismology’ s most valuable contribu- tion to earthquake hazard assessment (Frankel et al., 1996; Abrahamson and Bommer, 2005). Estimating the chance of strong ground motion at a given level is the most critical input for seismic zoning and building code design. The quantification of the earthquake hazard for a site or an area restricts the preparedness and economic potential of earth- quake protection to realistic levels. It also provides the earth- quake engineers with guidelines of quality requirements for future buildings and other constructions. The goal of PSHA is to estimate the probability of exceeding various ground-motion levels at a site, given all possible earthquakes that might occur. The approach for this estimation was first formalized in the late 1960s by Cornell (1968) and generalized by McGuire (1976). In the first step of PSHA, the seismicity data should be spatially disaggre- gated into discrete seismic sources. These are usually repre- sented as line sources (faults) or area sources. At the second step, the seismicity has to be characterized with respect to time for each seismic source, that is, the annual rate of oc- currence of different magnitude earthquakes. This is most often expressed in terms of different forms of the Gutenberg– Richter power law, in which the seismicity of the source is written as an activity rate, a frequency–magnitude slope (the b value), and a maximum magnitude value at which the curve is truncated. However, it is also possible to use observed seis- micity of each seismic zone to construct a probability distri- bution function of magnitude and to circumvent the need to use the Gutenberg–Richter power law. The third step is as- sociated with the use of ground-motion prediction equations (GMPEs) to evaluate the intensity of different ground-motion parameters due to each seismic source. At the final step, the influence of all sources is aggregated, and the annual fre- quency of exceedance is obtained for different values of ground-motion parameters (hazard curves). BSSA Early Edition / 1 Bulletin of the Seismological Society of America, Vol. 105, No. 4, pp. –, August 2015, doi: 10.1785/0120140256