Two-stage nonlinear site amplification modeling for Japan with V S 30 and fundamental frequency dependency

We describe a two-stage nonlinear site amplification model that considers both the sediment depth and the fundamental frequency of the soil. Adopting a non-reference site approach, empirical site amplification ratios for 1591 Kyoshin and Kiban Kyoshin network sites are developed. This process involves analyzing 92,025 surface ground motion recordings from 305 earthquakes between 1997 and 2012. The model is developed in two stages: first, we regress the total empirical site effects in terms of V_S30; second, we fit a functional form to the residuals from the first stage using the fundamental period of the site. We validate the model through residual analyses and statistical methods. This study shows that the peak soil period increases with the equivalent shear strain (I_γ), while the peak amplitude decreases with I_γ. The first-stage site term reduces the error at mid-to-long period ranges (>0.1 s) by 0.11 from the error of the initial site term without any constraints. The second-stage site term reduces the error further as 0.06. Finally, we discuss the model limitations and the applicability range of the predictor variables.