Non-ergodic probabilistic seismic hazard analysis and spatial simulation of variation in ground motion

Two problems in the spatial statistics of ground motions are addressed. For the first problem, a method is developed for probabilistic seismic hazard analysis (PSHA) without the ergodic assumption accounting for the impacts on both the median and aleatory standard deviation of the ground-motion model. Impacts of the removal of the ergodic assumption on both the intra-event and inter-event residuals are addressed. A strong motion data set from Taiwan with multiple recordings at each site and multiple earthquakes within small regions are used to quantify the separation of the aleatory variability from the systematic source, path, and site effects. Systematic site effects are accommodated by scale factors at each site. Systematic source and path effects are more complicated because they are spatially correlated. Models of the spatial covariance functions of the systematic source and path effects of the Taiwan data set are developed to capture the spatial correlation of the systematic effects and are then used to generate stochastic spatial simulations of the spatial correlations of the path and source effects for applications to other regions. Example hazard calculations show that there can be up to a factor of four increase in epistemic uncertainty of the hazard when the ergodic assumption is removed if there is no site-specific data. The method developed here to remove the ergodic assumption provides a framework that shows the benefits of installing instrumentation to record site-specific data and using analytical models of the path-specific wave propagation and site-specific site response effects to estimate source-, path-, and site-specific ground motions models to reduce the epistemic uncertainty in the systematic effects.;For the second problem, synthetic seismograms computed from simulated earthquakes using Lawrence Livermore National Laboratory 2D/3D elastic finite-difference wave propagation code, E3D, (Larsen and Shulz, 1994) were used to evaluate if the observed spatial variation of the very high frequency (> 10 Hz) ground motion over short distances (< 50 meters) can be explained by scattering and multi-pathing of elastic waves in two-dimensional and three-dimensional random media. The effects of the autocorrelation function and correlation length of the velocity media, media mean and standard deviation in velocity, source location, half-space velocity model versus layered velocity model, multiple sources, and two-dimensional versus three-dimensional random media are addressed. These simulated wave forms are used to compare the spatial variation of the simulated ground motions from stations with spacings of 10 meters to 50 meters and frequencies less than 30 Hz to the spatial variation from an empirical coherency function. For station spacings less than 50 meters, the simulated ground-motions, on average, significantly over-estimate the spatial coherence in the ground motion. These results suggest that spatial variation in ground motion at short separations, which are important for structures with large rigid foundations, such as nuclear power plants, cannot be adequately explained through the use of simulations computed in a scattering media using a 3D finite-difference wave propagation code. The approach of using numerical simulations in place of empirical coherency functions is not ready for engineering applications.