A simple strategy to examine the sources of errors in attenuation relations

A new method is presented in this article to visualize two different sources in the uncertainty of attenuation regression relations. The method utilizes the residuals from regression equations, defined as the log of the ratio of observed to predicted ground-motion parameters, from stations that have recorded more than one earthquake. The earthquake-to-earthquake variance is first calculated. Then the residuals are corrected with the mean residual of the corresponding earthquake. The corrected residual from one event is plotted versus the corrected residual from another event for every station that has more than one record. If site effects are perfectly represented in the regression, the resulting scatter plot will show statistically uncorrelated points, while extension along the diagonal and a positive correlation coefficient is the result of a contribution from site effects. This simple strategy allows us to visualize the uncertainty caused by the earthquake source and path in regression relations and indicates quantitatively how much we can improve the prediction by adding additional site information. The results obtained from this method are very similar to those that are calculated directly from the method proposed by Joyner (personal comm., 1997). In southern California, we find that source and path effects dominate the uncertainties at high frequency, while at low frequency, the regression can be still improved more significantly by correcting for the site effects.