Application of bayesian theory in seismology, case study: the north and north-west of Iran

In probability theory and statistics, Bayes' theorem , describes the probability of an event, based on prior knowledge of conditions that might be related to the event. One of the many applications of the theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesian statistics. The purpose of this study is a modeling method based on hierarchical structure in prioritizing and providing appropriate solutions to reduce seismic hazards in the Alborz-Azerbaijan province. The basis of the work is based on using natural data and Bayesian statistics which is a powerful tool in modeling both uncertainty and randomness. The method can correctly show the values of peak ground acceleration (PGA) along with the quantities of its distribution function in the region. The input information for the method is seismic catalog from 1900 to 2020 and proper ground motion attenuation law. It should be noted that Iran strong motion network had limited data so that there was a gap of large earthquakes of data. This modeling contains a set of processes and rules for using and specifying variables and relationships between them. Based on the results of this study, conducted in the northern and north-western parts of Iran, using Iranian Seismological Center data (http://irsc.ut.ac.ir) that includes 11 stations in the study area, hazard maps were drawn for PGA over a period of next 50 and 475 years, with the highest acceleration in the Alborz region including Tehran and Zanjan and in the Azerbaijan region including Tabriz and Rasht. The correlation between estimated acceleration values by Bayesian method and the values observed by the accelerometer network of Iran Road, Housing and Urban Development Research Center was α=0.95. This indicates that the estimated maximum acceleration is in a good agreement with the observed maximum acceleration. According to the results, the southern part of Alborz (Tehran) and the north-western part of Iran (Tabriz) had the highest PGA. Then, the Bayesian method will give favorable results for probability seismic hazard analysis.The results confirm the uncertainty of different parameters of seismic acceleration. Therefore, all of these parameters calculated, indicate that in the west of the Caspian Sea (Rasht city) the lowest value was allocated. Then, Bayesian method with advantages such as considering the relationship between variables, conditions of uncertainty and high flexibility, has the necessary ability to analyze seismic risk in other parts of Iran. This method can also be used in construction projects. In carrying out such renovations, it is necessary to provide step-by-step protocols and rules guidance for application and specification of variables and relationships between them in designing and correcting the model.