Probabilistic Seismic Hazard Analysis without the Ergodic Assumption

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Abstract
INTRODUCTION An ergodic process is a random process in which the distribution of a random variable in space is the same as the distribution of that same random variable at a single point when sampled as a function of time. An ergodic assumption is commonly made in probabilistic seismic hazard analysis (PSHA). A regression analysis is used to obtain a mean curve to predict ground motion as a function of magnitude and distance (and sometimes other parameters). The standard deviation of this ground-motion regression is determined mainly by the misfit between observations and the corresponding predicted ground motions at multiple stations for a small number of well recorded earthquakes. Thus, the standard deviation of the ground-motion regression is dominantly related to the statistics of the spatial variability of the ground motions. An ergodic assumption is made when PSHA treats that spatial uncertainty of ground motions as an uncertainty over time...

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