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Simulation of spatially correlated spectral accelerations at multiple periods

Graduate Researcher(s): 
Maryia Markhvida (markhvid@stanford.edu)
Luis Ceferino (ceferino@stanford.edu)
Faculty Advisor/PI: 
Jack Baker
Project Sponsor: 
National Science Foundation
Regional seismic risk assessments and quantification of portfolio losses often require simulation of spatially distributed ground motions at multiple intensity measures. For a given earthquake, distributed ground motions are characterized
by spatial correlation and correlation between different intensity measures, known as cross-correlation. In this research project, a new spatial cross-correlation model for within-event spectral acceleration residuals was developed. The model uses a combination of principal component analysis (PCA) and geostatistics, where PCA is used to determine coefficients that linearly transform cross-correlated residuals to independent principal components. Nested semivariogram models are then fit to empirical semivariograms to quantify the spatial correlation of principal components. The resultant PCA spatial cross-correlation model is shown to be accurate and computationally efficient. A step-by-step procedure for rapid simulation of spatially cross-correlated spectral accelerations at multiple periods is proposed. 
 
A further study investigates the effects of spatially cross-correlated ground motions on regional loss estimation. Five ground motion correlation models, ranging from no correlation to full spatial cross-correlation, were used to assess regional losses for a a Mw = 8.8 earthquake scenario in Lima, Peru. Results from the five models provide insight into how different ground motion correlation models effect the distribution of aggregate regional losses and losses for building classes of varying vulnerability. It was shown that both spatial correlation and cross-correlation of within-event residuals play significant roles in quantification of regional losses. In addition, it was found that the effect of spatial correlation on the aggregate losses of different building classes varies depending on the vulnerability of the buildings. For vulnerable infrastructure, ground motion uncertainty has a large effect on the standard deviation but not the mean of losses. For less vulnerable infrastructure, correlation causes a substantial increase in both the mean and standard deviation of losses and yields loss distributions with heavier right tails.
 
                                    
Publications: 

Markhvida, M., Ceferino, L., & Baker, J. W. (2018). Modeling spatially correlated spectral accelerations at multiple periods using principal component analysis and geostatistics. Earthquake Engineering & Structural Dynamics47(5), 1107-1123

Markhvida, M., Ceferino, L., & Baker, J. (2017). Effect of ground motion correlation on regional seismic loss estimation: application to Lima, Peru using a cross-correlated principal component analysis model. In Proc., 12th Int. Conf. on Structural Safety and Reliability (Vol. 1853).