Probabilistic prediction of earthquake by bivariate distribution

Abstract

The bivariate lognormal distribution (BLD) is proposed, as a model probabilistic, for joint distribution of earthquake prediction. In the recent decades, the probabilistic earthquake prediction using statistical analysis has become the cornerstone of research works in earthquake engineering field. In the case of earthquake prediction, all probability models have been established by distribution functions other than bivariate distribution functions. There is no denial of the fact that earthquake is absolutely considered as a multivariate phenomenon. Hence, comprehensive analysis of these variables needs joint probabilistic investigations. In this paper, the probability model of earthquake prediction has been studied by bivariate lognormal distribution function. For this aim, the parameters of BLD were estimated by maximum likelihood method. Then, the distribution function is established based upon two variables including earthquake magnitude and recurrence time. In this research, Tehran city, as one of the world’s most populous cities, was considered for the case study due to the fact that severe earthquakes have occurred in the past decades. The capability of using the probabilistic model for Tehran was obtained by Kolmogrov–Smirnov (KS) test. Overall, it was found that the most likely earthquake of Tehran may occur between 10 and 15 years from the last earthquake with magnitude between 6.6 and 6.8.