Simulating earthquake ground motion at a site, for given intensity and uncertain source location

Following a companion article, ground motion acceleration time histories du ring earthquakes can be described as realizations of non-stationary stochas tic processes with evolutionary frequency content and instantaneous intensi ty. The parameters characterizing those processes can be handled as uncerta in variables with probabilistic distributions that depend on the magnitude of each seismic event and the corresponding source-to-site distance. Accord ingly, the generation of finite samples of artificial ground motion acceler ation time histories for earthquakes of given intensities is formulated as a two-stage Monte Carlo simulation process. The first stage includes the si mulation of samples of sets of the parameters of the stochastic process mod els of earthquake ground motion. The second stage includes the simulation o f the time histories themselves, given the parameters of the associated sto chastic process model. In order to account for the dependence of the probab ility distribution of the latter parameters on magnitude and source-to-site distance, the joint conditional probability distribution of these variable s must be obtained for a given value of the ground motion intensity. This i s achieved by resorting to Bayes Theorem about the probabilities of alterna te assumptions. Two options for the conditional simulation of ground motion time histories are presented. The more refined option makes use of all the information about the conditional distribution of magnitude and distance f or the purpose of simulating values of the statistical parameters of the gr ound motion stochastic process models. The second option considers all prob abilities concentrated at the most likely combination of magnitude and dist ance for each of the seismic sources that contribute significantly to the s eismic hazard at the site of interest.