Bayesian Model Updating Approach for Ground-Motion Attenuation Relations

Abstract

The Bayesian model updating procedure is a powerful and general approach to update the uncertainties in a model response by using the information from available data. It is based on the well-known theorem of Bayes, which states that a posterior (updated) probability distribution for the model parameters conditioned on the data available is proportional to the product between the prior probability distribution and the likelihood function. Herein, the problem of establishing empirical earthquake groundmotion attenuation laws is addressed; in particular, two kinds of regression models are considered. The model parameters are represented by the coefficients of the regression models, and the data consist of a database of strong-motion records from actual earthquakes, where the magnitudes and epicentral distances are known. The computational aspects related to Bayesian updating and predictions are discussed. Two Markov Chain Monte Carlo (MCMC) simulation techniques are used to sample from the posterior distribution. They are based on some modifications of the Metropolis-Hastings procedure. The first one is a resampling adaptive scheme, whereas the second one is a Hybrid Monte Carlo algorithm with Simulated Annealing. The problem of the identifiability of two ground-motion relations is discussed as well. A Bayesian model comparison for the two attenuation relationships is carried out by evaluating the evidence of the two model classes based on the strong-motion data.