The Path Effect in Ground-Motion Variability: An Application of the Variance-Components Technique

Chen and Tsai (2002) proposed a variance-components technique to decompose the prediction error of ground motions into three components: the earthquake-to-earthquake, the site-to-site, and the residual errors, with three corresponding variance components. From a data set of over seven thousand records with various site conditions, Tsai and Chen (2003) found that the relative percentages of the three components of variances are dependent upon the numbers of earthquake events and stations providing the sampled records, and the variances of the earthquake and the site components are in general smaller than that of the residual. Noting that the residual encompasses the path-to-path error in ground motions, in this work we show that if the variability of the path effect can be sensibly specified a priori, the path- to-path component of error can be further differentiated from the residual errors. The prediction error can be reduced dramatically after ground-motion estimates have been corrected for the site as well as the path effects of variability in ground motion. Although the path component of error, unlike the site component, cannot be directly eliminated from the ground-motion estimates for future earthquake events, we propose to account for the path effect by turning it into useful information such as the three-dimensional (3D) velocity structural model obtained by the inversion technique. If a 3D model describing the path effect for each source-to-site pair can be constructed, the ground-motion prediction with both the site and path effects accounted for may be feasibly practical.