We propose a model for the effect of sedimentary basin depth on long-period response spectra. The model is based on the analysis of 3-D numerical simulations (finite element and finite difference) of long-period (2–10 s) ground motions for a suite of sixty scenario earthquakes (Mw 6.3 to Mw 7.1) within the Los Angeles basin region. We find depth to the 1.5 km/s S-wave velocity isosurface to be a suitable predictor variable, and also present alternative versions of the model based on depths to the 1.0 and 2.5 km/s isosurfaces. The resulting mean basin-depth effect is period dependent, and both smoother (as a function of period and depth) and higher in amplitude than predictions from local 1-D models. The main requirement for the use of the results in construction of attenuation relationships is determining the extent to which the basin effect, as defined and quantified in this study, is already accounted for implicitly in existing attenuation relationships, through (1) departures of the average “rock” site from our idealized reference model, and (2) correlation of basin depth with other predictor variables (such as Vs30).

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