Ground-motion prediction (attenuation) models predict the probability distributions of spectral acceleration values for a specified earthquake event. These models provide only marginal distributions, however; they do not specify correlations among spectral accelerations with differing periods or orientations. In this article a large number of strong ground motions are used to empirically estimate these correlations, and nonlinear regression is used to develop approximate analytical equations for their evaluation.
Baker J.W. and Cornell C.A., 2006, Correlation of response spectral values for multi-component ground motions: Bulletin of the Seismological Society of America, v. 96, p. 215-227.
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