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Interperiod Dependence of Ground-Motion Prediction Equations: A Copula Perspective

Department of Earth Sciences, University of Western Ontario, London, Ontario N6A 5B7 Canada kgoda2{at}uwo.ca Gmatkinson{at}aol.com

The conventional approach for developing empirical prediction equations of multivariate ground-motion parameters (e.g., response spectra at a set of vibration periods) is based on regression analysis of the individual parameters; their dependence is subsequently characterized by evaluating the linear correlation coefficient of the logarithm of the ground-motion parameters that are corrected by using a ground-motion prediction equation. A copula technique, which offers a flexible way of describing nonlinear dependence among multivariate data in isolation from their marginal distribution functions, can be used to validate this two-step approach. This new perspective on the multivariate aspects of the development of ground-motion prediction equations is explored through analysis of the strong ground-motion data associated with the Boore and Atkinson (2008) Pacific Earthquake Engineering Research–Next Generation Attenuation of Ground Motions (PEER-NGA) relation. The analysis results demonstrate that multivariate ground-motion parameters can be marginally modeled as a lognormal variate, and their interperiod dependence can be captured by using the normal copula. This finding validates the conventional two-step approach.

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