Effects of nonlinear soil behavior and regionalization on heteroscedastic variance of ground motion amplitudes

Ground-motion models are developed using global dataset and the main assumption when deriving a ground motion prediction equation (GMPE) is ergodic assumption. In stochastic sense ergodicity defined as the point in the time is uniform over the entire process which means a sample from a process represents the mean behavior of entire process. With the increasing ground motion data, using thousands of records increases aleatory variability (σ) and that forces the recent works focus on non-ergodic GMPEs. Using a global dataset, a series of ground-motion predictive models for acceleration response spectra is proposed. The proposed models include regional adjustments to source, path and site terms with nonlinear soil behavior. The regression coefficients are computed with linear and nonlinear mixed-effect regression algorithms. Furthermore, heteroscedastic variability models for between-event, site-to-site and single-site standard deviations are developed. The between-event sigma model depends solely on magnitude, but the single-site standard deviation model depends on both magnitude and distance. Finally, the site-to-site standard deviation model is given in terms of VS30 and spectral acceleration at rock site condition.