Correlation of Spectral Acceleration Values from NGA Ground Motion Models Jack W. Baker, a) M.EERI, and Nirmal Jayaram a) Ground motion models (or “attenuation relationships”) describe the probability distribution of spectral acceleration at an individual period, given a set of predictor variables such as magnitude and distance, but they do not address the correlations between spectral acceleration values at multiple periods or orientations. Those correlations are needed for several calculations related to seismic hazard analysis and ground motion selection. Four NGA models and the NGA ground motion database are used here to measure these correlations, and predictive equations are fit to the results. The equations are valid for periods from 0.01 seconds to 10 seconds, versus similar previous equations that were valid only between 0.05 and 5 seconds and produced unreasonable results if extrapolated. Use of the new NGA ground motion database also facilitates a first study of correlations from intra- and inter-event residuals. Observed correlations are not sensitive to the choice of accompanying ground motion model, and intra-event, inter-event, and total residuals all exhibit similar correlation structure. A single equation is thus applicable for a variety of correlation predictions. A simple example illustrates the use of the proposed equations for one hazard analysis application. DOI: 10.1193/1.2857544 INTRODUCTION The utility of ground motion models (GMMs) can be extended if correlations of re- sponse spectral values at multiple periods or orientations (e.g., fault-normal/fault- parallel) are known. These correlations allow existing ground motion models to be adopted for predicting the joint distribution of spectral acceleration values at multiple periods, which is useful for vector-valued probabilistic seismic hazard analysis and gen- eration of custom ground motion models. Predictions of these correlations have been previously proposed, but the NGA project’s new GMMs and expanded ground motion library facilitate the development of an improved equation that is applicable over a wider range of periods. In this paper, the methodology for measuring and predicting these cor- relations is briefly outlined, a new correlation equation is developed, and the new results are examined and compared to previous comparable equations. To describe precisely the correlations being studied, it is helpful to note that ground motion predictions take the following general form a) Dept. of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305-4020 299 Earthquake Spectra, Volume 24, No. 1, pages 299–317, February 2008; © 2008, Earthquake Engineering Research Institute