### 2.267 Tsai et al. (2006)

• Ground-motion model is:

where PGA is in cms2, θ0 = 0.4063, θ1 = 0.7936, θ2 = -0.02146, θ3 = 0.0004183, θ4 = -1.7056, θ5 = 5.7814, θ6 = -0.05656, σe = 0.17561 (inter-event), σs = 0.17065 (inter-site), σr = 0.19925 (residual) and σT = 0.31569 (total).

• Use data from 204 sites.
• Use regression approach of Chen and Tsai (2002) to separate variance into 3 components: inter-event, inter-site and residual.
• Plot inter-event residuals (event terms) of shallow (focal depth 30km) earthquakes w.r.t. ML and on map. Find residuals are independent of magnitude and not correlated with location.
• Plot inter-site residuals (site terms) on map. Find that these are more coherent in space, which are generally consistent with local geology (e.g. positive terms for alluvium sites.).
• Plot direct travel paths from all shallow earthquakes to associated sites. Expect that variability of path-to-path component of error would be similar to event terms or at least not smaller than site terms. Hence assume σP = 0.17321 (path component) and compute refined σs.
• Show that by specifying a priori the variability of path-to-path component that this can be removed from residual.