Geostatistical and network analysis of non-stationary spatial variation in ground motion amplitudes

When an earthquake causes shaking in a region, the amplitude of shaking varies spatially. Ground motion models have been developed to predict the median and standard deviation of ground motion intensity measures. However, the remaining variation in ground motion prediction "residuals'' is significant, and shows spatial correlations at scales of tens of kilometers in separation distance. These correlations are important when assessing the risk to spatially distributed infrastructure or portfolios of properties. State of the art today is to assume that these spatial correlations depend mainly on separation distance (stationarity assumption). This dissertation aims to advance spatial correlation models of ground motions, by conducting a comprehensive correlation study on various data sets, evaluating key assumptions of current models, and proposing a novel framework for modeling spatial correlations. First, this dissertation proposes a method of site-specific correlation estimation and techniques for quantifying non-stationary spatial variations. Applying these methods to various data sets, factors related to non-stationary spatial correlations are investigated. Using physics-based ground motion simulations, it studies the dependency of non-stationary spatial correlations on source effects, path effects, and relative location to rupture. Using data from recent well-recorded earthquakes in New Zealand, it analyzes site-specific and region-specific correlations in ground motion amplitude for Wellington and Christchurch, and observed strong non-stationarity in spatial correlations. Results suggest that heterogeneous geologic conditions appear to be associated with the non-stationary spatial correlation. Second, this dissertation formulates a framework for detecting and modeling non-stationary correlations. By utilizing network analysis techniques, it proposes a community detection algorithm to find regions in spatial data with higher correlations. Applying this algorithm to physics-based ground motion simulations, it detects communities of earthquake stations with high correlation to uncover underlying reasons for non-stationarity in spatial correlations. Factors associated with the communities of high correlation are identified. Results suggest that communities of high correlation in ground shaking tend to be associated with common geological conditions and relative location along the rupture strike direction. In addition, it applies the algorithm to a mixed-source data set from the simulations, and compares correlation characteristics of simulations and instrumental data. Results suggest that the mixed-source data tend to average out the non-stationary influence of source and path effects from a single rupture. Finally, this dissertation presents a framework for quantifying uncertainty in the estimation of correlations, and true variability in correlations from earthquake to earthquake. A procedure for evaluating estimation uncertainty is proposed and used to evaluate several methods that have been used in past studies to estimate correlations. The proposed procedure is also used to distinguish between estimation uncertainty and the true variability in model parameters that exist in a given data set. Results suggest that a Weighted Least Squares fitting method is most effective for correlation model estimation. Fitted correlation model parameters are shown to have substantial estimation uncertainty even for well-recorded earthquakes, and underlying true variability is relatively stable among well-recorded and poorly recorded earthquakes

Advisor: Baker Jack W. 
Bradley Brendon A. (Brendon Archie) 
Miranda Eduardo (Miranda Mijares)