This article evaluates the possibility of improving a particular ground-motion relationship for predicting peak acceleration (PGA) and absolute response spectral accelerations at the periods of 0.3, 1.0, and 3.0 sec in southern California. We use the attenuation model of Abrahamson and Silva (1997), which Lee et al. (2000) found satisfactory for this region. We examine differences between observed and predicted values (residuals) as a function of several site attributes to determine whether corrections can be made to improve the predictions. This study differs from that of Steidl (2000) in that we use an attenuation model that accounts for sediment amplification and nonlinearity (Steidl used only a rock-site relationship). Residuals are significantly correlated with basin depth. Depending on the specific frequencies considered, ground motions at the deepest part of the basin average 30% to 80% higher than at the edge of the basin. Residuals are also significantly correlated with the estimates of the average amplification of peak velocity due to the basin velocity structure (Olsen, 2000). Since the basin depth is correlated with the average basin amplification, there is no need to correct the ground-motion model for both effects. Detailed geology is generally found unhelpful in improving ground-motion predictions. Overall, correcting the ground-motion relation reduces the standard error of ground-motion predictions by about 5%. Whether the ground-motion relation modifications suggested here are significant in terms of the implied seismic hazard is evaluated in Field and Petersen (2000).
The weak correlation of residuals with respect to site parameters motivated us to apply the test proposed by Lee et al. (1998). This involves plotting residuals versus residuals for stations that have recorded more than one earthquake. To the extent that systematic site effects cause the misfit between observations and the ground-motion model, such a plot will show correlation among the residuals. Correlation coefficients are, surprisingly, very low, ranging from 0.16 for PGA residuals to 0.26 for 3-sec response spectra. Thus it seems that it will be very difficult to refine ground-motion prediction equations beyond the very general categories now in use. Improved physical understanding of the site, source, and path contributions must play a major role in any future efforts to reduce the uncertainty in the ground-motion predictions.