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

Maryia Markhvida, Luis Ceferino, Jack W. Baker

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1107-1123
Number of pages17
JournalEarthquake Engineering and Structural Dynamics
Issue number5
StatePublished - Apr 25 2018


  • cross-correlation
  • principal component analysis
  • seismic risk
  • spatial correlation
  • spectral accelerations

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Earth and Planetary Sciences (miscellaneous)
  • Civil and Structural Engineering


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