Modeling spatially correlated spectral accelerations at multiple periods using principal component analysis and geostatistics

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. This study proposes a new spatial cross-correlation model for within-event spectral acceleration residuals that uses a combination of principal component analysis (PCA) and geostatistics. Records from 45 earthquakes are used to investigate earthquake-to-earthquake trends in application of PCA to spectral acceleration residuals. Based on the findings, 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 and an example are presented to illustrate the use of the predictive model for rapid simulation of spatially cross-correlated spectral accelerations at multiple periods.