A Bayesian framework for prediction of seismic ground motion

Current needs of the site-specific hazard and risk analysis for critical facilities and accumulation of the observed records make the development of site-specific ground-motion attenuation relationship feasible. The use of the site-specific attenuation relationship has two advantages: lack of bias and representation of the specific site. This study develops the site-specific attenuation relationship within the Bayesian updating framework. Rather than developing new attenuation relationships, we develop a correction term to the existing past attenuation equation within the Bayesian framework. The correction term is described as a linear function of source magnitude and distance. New data are those observed at the specific site in recent years. Although the use of a prior distribution is one of the most controversial issues of the Bayes' theorem, both the noninformative prior and the informative prior in terms of the gamma-normal prior are used to develop the posterior distribution for the prediction of ground motion. We feel that the reader should focus on the development of the site-specific attenuation relationship and quantification of the uncertainty of ground-motion prediction. Statistical uncertainty has been ignored in the existing attenuation relationships, while it is not ignorable in the site-specific attenuation relationship due to the limited number of data available at the specific site. This is particularly notable for the ground-motion prediction of large-magnitude-near-source earthquakes where seismic hazard is sensitive. Because the unknown parameters are treated as random variables in the Bayesian approach, the statistical uncertainty associated with them can be quantified in terms of the posterior distribution. The Bayesian methodology will be an effective approach to updating the attenuation relationship on a site basis when new data from observations become available.